Bridges in Mathematics Grade 4 Teachers Guide

Bridges in Mathematics Grade 4 Teachers Guide
Teachers Guide
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GRADE 4 – UNIT 3 – MODULE 2
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Module 2
Comparing, Composing & Decomposing
Fractions & Mixed Numbers
Session 1 Exploring Fractions on the Geoboard������������������������������������������������������������������������������������������� 3
Session 2 Last Equation Wins���������������������������������������������������������������������������������������������������������������������������������� 9
Session 3 Comparing, Adding & Subtracting Fractions��������������������������������������������������������������������������� 17
Session 4 Dozens of Eggs����������������������������������������������������������������������������������������������������������������������������������������21
Session 5 How Many Candy Bars?�����������������������������������������������������������������������������������������������������������������������27
Session 6 Racing Fractions��������������������������������������������������������������������������������������������������������������������������������������33
Student Book Pages
Pages renumber with each module.
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Teacher Masters
Page numbers correspond to those in the consumable books.
Equivalent Fractions Checkpoint������������������������������������������ T1
Last Equation Wins��������������������������������������������������������������������98
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Geoboard Area of One�������������������������������������������������������������T2
Pizza Party Planning������������������������������������������������������������������97
What’s the Share?���������������������������������������������������������������������100
Egg Carton Diagram������������������������������������������������������������������ T4
Comparing, Adding & Subtracting Fractions�����������������101
Unit 3 Work Place Log��������������������������������������������������������������� T5
Adding & Subtracting Fractions������������������������������������������103
Work Place Guide 3A Dozens of Eggs��������������������������������� T6
Introducing Dozens of Eggs�������������������������������������������������104
3A Dozens of Eggs Record Sheet������������������������������������������T7
Work Place Instructions 3A Dozens of Eggs�������������������105
How Many Candy Bars Forum Planner�������������������������������T8
Egg Carton Fractions���������������������������������������������������������������107
Work Place Guide 3B Racing Fractions�������������������������������T9
How Many Candy Bars?����������������������������������������������������������108
3B Racing Fractions Record Sheet��������������������������������������T10
Fractions & Mixed Numbers�������������������������������������������������109
3B Racing Fractions Game Board���������������������������������������� T11
Work Place Instructions 3B Racing Fractions������������������ 110
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Geoboards������������������������������������������������������������������������������������T3
Understanding Fractions & Mixed Numbers������������������ 111
Home Connections Pages
Page numbers correspond to those in the consumable books.
Brownie Dessert������������������������������������������������������������������������� 55
Planning a Garden���������������������������������������������������������������������57
Fractions & More Fractions����������������������������������������������������� 59
Bridges in Mathematics Grade 4 Teachers Guide
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Unit 3
Unit 3
Module 2
Module 2
Comparing, Composing & Decomposing
Fractions & Mixed Numbers
Overview
In this module, the geoboard is assigned a value of 1. Students name fractional parts of the geoboard and describe the parts’
relationships to one another. Their observations are then extended into comparing fractions with unlike numerators and
denominators, and adding fractions with like denominators. The last three sessions in the module feature an extended problem-solving opportunity followed by a math forum, as well as two new Work Places that provide practice with composing and
decomposing fractions.
Planner
Session & Work Places Introduced
PI
PS
MF
WP
A
HC
DP
Session 1 Exploring Fractions on the Geoboard
This session begins with a quick checkpoint on equivalent fractions. Then students learn how
to represent fractions on the geoboard. Students name fractional parts of the geoboard and
describe the parts’ relationships to one another.
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Session 2 Last Equation Wins
Students play, first as a class and then in pairs, a game that provides practice with decomposing
fractions represented on a geoboard and recording those decompositions with equations. Toward
the end of the session, students solve addition problems involving fractions with like denominators.
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Session 3 Comparing, Adding & Subtracting Fractions
Students work together as a class to create a chart of equivalent fractions for 1/4, 1/2, and 3/4. Students
make observations about the chart and the equivalent fractions, and then they use those fractions
as benchmarks with which to make comparisons among fractions with like and unlike denominators. Finally, they practice adding and subtracting fractions with like denominators.
Session 4 Dozens of Eggs
Today, students add fractions using the egg carton model. The teacher then introduces a related
Work Place game by playing it with the class. Students spend any time remaining in the session
visiting Work Places, including the new one.
Work Place 3A Dozens of Eggs
Players take turns drawing from a deck of fraction cards, modeling the designated fraction on an
Egg Carton Diagram with colored tiles and string, and recording their results. Players take turns until
one person has filled all four egg cartons on his or her record sheet and written a matching addition
equation that equals 1 whole for each carton. The first player to fill all four egg cartons wins.
Session 5 How Many Candy Bars?
Mrs. Wiggens is bringing the dessert treats for the annual class picnic, and needs help figuring
out how many candy bars she’ll have to buy if she gives each student 3/4 of a bar. The trouble is,
she’s not quite sure how many of her fourth graders will be attending the picnic. Students add
fractions on an open number line and track their results on a ratio table, working together to help
Mrs. Wiggens initially, and then complete the work on their own or in pairs.
Session 6 Racing Fractions
Students discuss solutions and strategies for the candy bar problem from the previous session
in a math forum. During the discussion, the class talks about adding fractions to mixed numbers
and multiplying a fraction by a whole number. Then the teacher introduces the equivalent fraction game, Racing Fractions, which will become a Work Place in later sessions.
Work Place 3B Racing Fractions
Players draw from the Racing Fractions Cards deck and move game markers along the Racing
Fractions Game Board, which shows fraction number lines for halves, thirds, fourths, fifths, sixths,
eighths, and tenths. Each player has a game marker on each line and may move one or more
markers in a single turn to equal the fraction on the card drawn. Players may also move backward
on a turn. The first player to move her markers to 1 on all of the number lines is the winner.
PI – Problems & Investigations, PS – Problem String, MF – Math Forum, WP – Work Place, A – Assessment, HC – Home Connection, DP – Daily Practice
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Introduction
Unit 3 Module 2
Materials Preparation
Each session includes a complete list of the materials you’ll need to conduct the session, as well
as notes about any preparation you’ll need to do in advance. If you would like to prepare materials ahead of time for the entire module, you can use this to-do list.
Task
Done
Copies
Run copies of Teacher Masters T1–T11 according to the instructions at the top of
each master.
Run a single display copy of Student Book pages 98–99, 101–102, 104, and 108.
Additional
Resources
Please see this module’s
Resources section of the
Bridges Educator site for
a collection of resources
you can use with students
to supplement your
instruction.
If students do not have their own Student Books, run a class set of Student Book
pages 97–111.
If students do not have their own Home Connections books, run a class set of the
assignments for this module using pages 55–60.
Work Place
Preparation
Prepare the materials for Work Places 3A & 3B using the lists of materials on the
Work Place Guides (Teacher Masters T6 & T9).
Charts
Before Session 1, on a piece of chart paper titled “Geoboard Regions,” outline five
columns titled Region A, Region B, Region C, Region D, and Region E.
Before Session 4, prepare student Work Place folders with the Unit 3 Work Place Log.
Before Session 3, using a copy of the Geoboards Teacher Master, draw 1/2, 1/4, and
3/4, each on a separate geoboard; then cut them out. Divide a piece of chart paper
into 4 columns and 4 rows and label them as shown below.
Fourths
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Halves
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Before Session 4, cut 10” pieces of heavy string or yarn, 6 per student. (You will
also need to cut 6 pieces per student pair for Work Place 3A, introduced in that
session. See the Work Place Guide 3A materials list.)
Eighths
Sixteenths
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Special Items
1
4
1
2
3
4
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Unit 3 Module 2
Unit 3
Module 2
Session 1
Session 1
Exploring Fractions
on the Geoboard
Summary
This session begins with a quick checkpoint on equivalent fractions. Then students learn how
to represent fractions on the geoboard. Students name fractional parts of the geoboard and
describe the parts’ relationships to one another.
Skills & Concepts
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•
•
•
•
•
Use a visual model to explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) (4.NF.1)
Use a visual model to generate and recognize equivalent fractions (4.NF.1)
Write an equation showing a fraction a�b as the sum of a number of the unit fraction 1�b (4.NF.3)
Express a fraction as the sum of other fractions with the same denominator in more than
one way and write equations to show those decompositions (4.NF.3b)
Add fractions with like denominators (supports 4.NF)
Write an equation showing that a fraction a�b is the product of a × 1�b (4.NF.4a)
Multiply a fraction by a whole number (4.NF.4b)
Reason abstractly and quantitatively (4.MP.2)
Model with mathematics (4.MP.4)
Materials
Copies
Kit Materials
Classroom Materials
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Assessment Equivalent Fractions
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•
•
•
•
TM T1
Equivalent Fractions Checkpoint
• student-made fraction kits
• egg carton fraction materials
Problems & Investigations Exploring Fractions on the Geoboard
TM T2
Geoboard Area of One
Daily Practice
SB 97
Pizza Party Planning
• geoboards with geobands (class
set, plus 1 for display)
• student math journals
• chart paper
Vocabulary
An asterisk [*] identifies
those terms for which Word
Resource Cards are available.
area*
region
unit*
HC – Home Connection, SB – Student Book, TM – Teacher Master
Copy instructions are located at the top of each teacher master.
Preparation
On a piece of chart paper titled “Geoboard Regions,” outline five columns titled “Region A,
Region B, Region C, Region D, Region E.” See step 9 in the lesson for an example.
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Unit 3 Module 2
Session 1
Assessment
Equivalent Fractions Checkpoint
1
Introduce today’s activities.
• Let students know that they will take a quick assessment to show what they’ve learned
about equivalent fractions.
• After that, they will investigate fractions using a new model—the geoboard.
2
Display the Equivalent Fraction Checkpoint and give students a minute to
look it over and ask any questions. Then have them start work.
• Let students know that they can use the egg carton fraction materials and/or the fraction kits they made a few days ago during the assessment, and tell them how to access
these materials.
• Encourage students to read each question carefully and remind them they can ask you
for help reading any of the questions.
• While students work, walk around the room to make observations and answer questions.
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• Give students 10–15 minutes to do the checkpoint. As this is not a timed test, if you
have students who do not finish the checkpoint in the time allotted, give them a chance
to finish later on.
Collect students’ checkpoints.
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• See the Grade 4 Assessment Guide for scoring and intervention suggestions.
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Problems & Investigations
Exploring Fractions on the Geoboard
4
Explain that today students will investigate fractions with the geoboard.
5
Display the Geoboard Area of One Teacher Master and invite students to
think quietly about, then share in pairs their observations about the six
regions shown. After pairs have had a minute to discuss, ask volunteers to
share with the class.
Tell students that for today’s session the largest square on the geoboard has an area of 1 unit.
Students The parts are all different sizes.
The parts go from bigger at the top to smaller at the bottom.
You could fit some of the smaller ones into the bigger ones.
A is the biggest and E is the smallest.
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Unit 3 Module 2
Session 1
Unit 3 Module 2
Sess ons 1 , 2 and 4 1 copy for d sp ay
Geoboard Area of One
Area = 1 sq. unit
A
B
6
D E
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C
Give each student a geoboard and bag of geobands. Have students use the
geobands to divide their geoboards into the six regions shown on the display.
Ask students to think quietly, then talk in pairs, about the area of region A.
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Students will use the letter names when referring to regions, but they will not write the
names on their geoboards.
Listen for evidence that students relate the part (the region) to the whole (the large square).
Teacher Let’s take a look at the region labeled with the letter A.
What is the area of region A?
Freddie Region A has an area of 8.
Teacher What makes you say that?
Freddie Because there are 8 little squares inside it, and each square is
worth one … oh, wait … you said the whole thing has an area of 1! Let
me think. That means A is worth 1/2.
Teacher I like the way you corrected your own thinking. What makes
you think it’s now worth 1/2?
Freddie Because two A’s will cover the whole thing. And there are
16 little squares inside of the whole big square and A covers 8, or
half of them.
Teacher What other fraction name is that, besides 1/2?
Monica Oh—8/16. That’s why Freddie said 8 earlier. It’s 8 out of 16
little squares.
Teacher I am going to add what you two said to a chart up here on the
board. I am also going to record how A relates to the whole large square.
8
Record students’ thinking about region A on the chart you prepared earlier.
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Unit 3 Module 2
9
Session 1
Ask students to consider the area of region B. Give them a few moments to
think privately, and then invite students to share their thoughts while you
record them on the chart.
Dario B is smaller than A. You can fit four of them on the large
square, so that’s 1/4.
Lola I’m not sure how you got that. I’m pretty sure it’s 4 out of 16.
Teacher Can anyone help make things clearer?
Ethan I think they’re both right. It’s 1/4 and 4 out of 16. B is 1/4 of the
big square because you can fit 4 of them inside it. But if you look at
the 16 little squares, 4 of them are inside the B part, so that’s 4 out of
16. One is 1/16, so B has 1/16, 2/16, 3/16, 4/16.
Dario We’re both right, because 1/4 and 4/16 are just different ways of
looking at it!
Teacher On our chart, I am going to write both 1/4 and 4/16. I am also
going to write 1/16 + 1/16 + 1/16 + 1/16 and 4 × 1/16 to model what Ethan said
while he was counting them for us.
8 out of 16 little
squares, or 168
8
16
+ 168 = 16
16 = 1
2 × 168 = 16
16 = 1
1
4
of a large square
4 out of 16 little
squares, or 164
Region D
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of a large square
Region C
Region E
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1
2
Region B
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Region A
1
16
+ 161 + 161 + 161 = 164
4 × 161 = 164
10 Repeat step 9 for regions C, D, and E.
11 Then, tell students they are going to examine the regions’ relationships to
one another. Model for students by thinking aloud about the relationship
between regions A and B.
Teacher We’ve listed fractional names for each region in relation
to the whole geoboard, but now we’re going to shift our thinking a
bit. Let’s consider instead how the regions relate to each other. For
instance, when I look at regions A and B, I could say that B is half of
A. Who thinks they can explain what I mean?
Chin B is worth 4 little square and A is worth 8 little squares, and 4
is half of 8.
Teacher So, how could I describe that in an equation?
Pilar You could write that 1/4 + 1/4 = 1/2. That would mean that 2 of the
B pieces are worth the A piece.
Teacher I’ll add that to the chart along with a sentence that says “B is
half of A.” I’m going to also add 2 × 1/4 = 1 /2.
12 Give students about 10 minutes to turn and talk with a partner about other
relationships they can find between regions and record them in their journals.
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Unit 3 Module 2
Session 1
Have students record the relationships in their journals with both words and equations.
Pair students with a classmate who can describe the relationships between
regions. Suggest that students build models of the regions on geoboards to compare them.
Use sentence frames for example, “The area of this region is ___”.
SUPPORT/ELL
13 Gather the class together to share students’ discoveries.
• Record the relationships on the chart with both words and equations.
• Encourage students to refer to the whole when describing fraction names.
SUPPORT/ELL As students share, model the relationships on a geoboard and clarify that
when we talk about regions, we are talking about the area of each region as a fraction of
the whole geoboard.
8 out of 16 little
squares, or 168
8
16
of a large square
+ 168 = 16
16 = 1
2 × 168 = 16
16 = 1
1
4
4 out of 16 little
squares, or 164
1
16
of a large square
+ 161 + 161 + 161 = 164
4 × 161 = 164
Region C
1
8
2 out of 16 little
squares, or 162
1
16
of a large square
+ 161 = 162
2 × 161 = 162
Region D
1
16
of a large square
1 out of 16 little
squares
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1
2
Region B
region B equals 4 Ds
+ 161 + 161 +161 = 164 = 14
1
16
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Region A
region C equals 2 Ds
1
1
2
1
region A equals 4 Cs region B equals 8 Es region C is half of B 16 + 16 = 16 = 8
1
1
2
1
1
1
1
1
1
4
1
1
8 + 8 = 8 = 4
2 = 8 + 8 + 8 + 8 = 8
4 = 8 × 32
1
16 × 16 = 1
region C is twice D
1
1
4 = 2 × 8
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If a relationship is stated that students cannot agree upon after brief discussion, record it
on a sticky note and place it on the chart to revisit later in the module.
Ask students to find ways to prove or disprove the statements on sticky notes.
Have them model the relationships with labeled sketches, words, or numbers.
CHALLENGE
14 Close the session by inviting students to tell one observation shared today
that was particularly interesting or confusing.
• Note confusing statements to inform your work with students during the next session.
• Save the Geoboard Area of One Teacher Master and chart for use in future sessions in
this module.
Bridges in Mathematics Grade 4 Teachers Guide
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Region E
1
32
of a large square
1
of one of the
little squares
2
1
32
4 Es makes 1 C
+ 321 + 321 + 321 = 324 = 18
32 × 321 =1
Extension
The class will probably
not have time during the
session to explore all the
possible relationships
shown on the geoboard.
Leave the chart hanging
so students can continue
to consider it, and place
stacks of sticky notes
nearby. When students
have time, they can
record their thoughts on
sticky notes and attach
them to the poster.
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 1
Daily Practice
The optional Pizza Party Planning Student Book page provides additional opportunities
to apply the following skills:
• Use a visual model to explain why a fraction a�b is equivalent to a fraction n × a�n × b (4.NF.1)
• Use a visual model to generate and recognize equivalent fractions (4.NF.1)
• Add fractions with like denominators (supports 4.NF)
• Solve story problems involving addition of fractions referring to the same whole and
with like denominators (4.NF.3d)
• Express a measurement in a larger unit in terms of a smaller unit within the same
system of measurement (e.g., convert from liters to milliliters) (4.MD.1)
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• Multiply a 2-digit whole number by 10 and by 100 (supports 4.NBT)
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Unit 3 Module 2
Unit 3
Module 2
Session 2
Session 2
Last Equation Wins
Summary
Students play, first as a class and then in pairs, a game that provides practice with decomposing fractions represented on a geoboard and recording those decompositions with equations.
Toward the end of the session, the teacher invites students to solve addition problems involving fractions with like denominators. Finally, the teacher introduces and assigns the Brownie
Dessert Home Connection.
Skills & Concepts
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• Write an equation showing a fraction a⁄b as the sum of a number of the unit fraction 1⁄b (4.NF.3)
• Express a fraction as the sum of other fractions with the same denominator in more than
one way and write equations to show those decompositions (4.NF.3b)
• Add fractions with like denominators (supports 4.NF)
• Demonstrate an understanding that a fraction a⁄b is the product of a × 1⁄b (4.NF.4a)
• Solve problems involving the addition of fractions with like denominators (4.NF.3d)
• Make sense of problems and persevere in solving them (4.MP.1)
• Look for and express regularity in repeated reasoning (4.MP.8)
Copies
Kit Materials
Problems & Investigations Last Equation Wins
Home Connection
HC 55–56
Brownie Dessert
Daily Practice
SB 100
What’s the Share?
• spinner overlays (1 per student
pair, plus 1 for display)
• geoboards and bands (1 per
student, plus 1 for display)
• Geoboard Area of One (from
Session 1)
• Geoboard Regions chart (from
Session 1)
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TM T3
Geoboards
SB 98–99*
Last Equation Wins
Classroom Materials
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Materials
HC – Home Connection, SB – Student Book, TM – Teacher Master
Copy instructions are located at the top of each teacher master.
Vocabulary
An asterisk [*] identifies
those terms for which Word
Resource Cards are available.
denominator*
equivalent fractions*
numerator*
product*
sum or total*
* Run 1 copy of these pages for display.
Preparation
When it comes time for students to play Last Equation Wins in pairs, you’ll want partners to
be working at roughly the same level of comfort with fractions. Spend some time before this
session deciding how you will pair students.
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Unit 3 Module 2
Session 2
Problems & Investigations
Last Equation Wins
1
Review the Geoboard Area of One Teacher Master and the Geoboard
Regions chart from the previous session.
• Ask students to review what fraction of the geoboard is represented by each region and
Se s on 1 , 2 an
1 copy or d
n
odule 2
label the
teacher master
if you haven’t
already.
• Invite them to refer to the Geoboard Regions chart they created in the previous session.
Geoboard Area o One
• Briefly review some of the addition and multiplication equations they wrote to represent each region as the sum or product of other numbers.
4
8 out of 16 little
squares, or 168
8
16
1
of a large square
+ 168 = 16
16 = 1
4 out of 16 little
squares, or 164
1
16
2 × 168 = 16
16 = 1
of a large square
+ 161 + 161 + 161 = 164
4 × 161 = 164
Region C
1
8
Region D
1
of a large square
16
2 out of 16 little
squares, or 162
1
16
+ 161 = 162
2 × 161 = 162
region A equals 4 Cs
= 18 + 18 + 18 + 18 = 48
region B equals 8 Es
= 8 × 321
region C is half of B
+ 18 = 28 = 14
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1
2
1
4
1
8
1
4
Region E
1
32
of one of the
little squares
2
region B equals 4 Ds
+ 161 + 161 +161 = 164 = 14
1
16
region C equals 2 Ds
+ 161 = 162 = 18
16 × 161 = 1
of a large square
1
1 out of 16 little
squares
1
16
of a large square
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1
2
Region B
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Region A
1
32
4 Es makes 1 C
+ 321 + 321 + 321 = 324 = 18
32 × 321 =1
region C is twice D
= 2 × 18
1
C
A
1
2
B
1
4
D E
1
8
1
32
1
16
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Unit 3 Module 2
Session 2
2
Display your copy of the Last Equation Wins Student Book page, and explain
that today students are going to play a game that will give them more practice
thinking about different ways to write equations for fractions.
3
Briefly explain how the game is played.
• Players take turns spinning the spinner to see who goes first.
• The first player spins the spinner two times and records the number from each spin.
Players work together to record a fraction in which the smaller number is the numerator and the larger number is the denominator.
• The first player records the fraction below the geoboard for Round 1 and then draws
the fraction on the geoboard, confirming with the other player that this is indeed a
representation of the fraction.
• Players take turns writing unique equations for the fraction.
»» Each equation must show the fraction as either the sum of other fractions with
the same denominator or as the product of a whole number and a fraction with
the same denominator.
»» Equations with the same numbers, but in a different order, are considered the same
because of the commutative property of addition and multiplication.
• The partner who is able to write the last unique equation wins.
Give each student a geoboard and a set of geobands. Begin the game
by spinning for a fraction and then recording and modeling it on the
geoboard, with input from students.
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»» If both partners have written five equations, players can choose to call it a draw and spin
for a new fraction, or they can continue writing equations as long as it interests them.
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There are a variety of ways to model each fraction on the geoboard, with the exception of
those fractions that are equal to 1. Invite students to work in pairs to find a few ways to
model the fraction on their geoboards, and settle on the model that seems like it will be
most helpful as students decompose the fraction. Remind students that they can look at the
Geoboard Area of One Teacher Master from the previous session for ideas, but that they are
not confined to those representations.
Teacher How did you show 4/16? Jayden, can you bring your geoboard
up and show us what you did?
Jayden I looked at the picture from yesterday and I remembered that
the part D is 1/16 of the whole. There are 16 of those little squares on
the geoboard, so each one is 1/16 of the whole. So I outlined 4 squares
on my board like this.
Teacher Did someone do it differently?
Mei I looked at the chart we made yesterday and I saw that we talked
about how region B was 4/16 because it’s 4 of the little squares, so I
made a picture of region B on my geoboard.
Bridges in Mathematics Grade 4 Teachers Guide
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Unit 3 Module 2
Session 2
Rosa Wait, I’m confused. We just said today that region B was 1/4.
Mei Well, it’s both, remember?
Rosa I don’t get how it can be both. It’s just one fraction.
Teacher Let’s pause a moment. I’d like everyone to use their
geoboards and talk in pairs. Can this part of the geoboard be both 1/4
and 4/16? How can you tell? You might divide one partner’s geoboard
into fourths and the other’s into sixteenths and put one on top of the
other and talk about what you see. … Who can come tell us what you
figured out?
Dominick We just made region B on our boards, and we counted
that there were 4 of the little squares inside it. So we were sure that it
can be 1/4 and 4/16 at the same time. There are 4/16 inside 1/4.
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Rosa We did what you said. I divided my board up into the 16 small
squares and my partner divided her board up into 4 rectangles that
look like region B.
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Mei Then we put mine on hers, and look … If you look at one of the
fourths, you can see it’s the same as 4 of the sixteenths.
Rosa Wow, so it’s the same part of the whole, but you can call it
different things.
Teacher We call 4/16 and 1/4 equivalent fractions. That means that
they name the same fraction of the whole. 4/16 of the geoboard is equal
to 1/4 of the geoboard.
Bridges in Mathematics Grade 4 Teachers Guide
12
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
5
Session 2
Write the first equation, and ask students to use their geoboards to prove
to each other that the equation is true. Remember that the fractions in the
equation must have the same denominator as the original fraction.
Session 2
Unit 3 Module 2
NAME
| DATE
Last Equation Wins page 1 of 2
Teacher
Player 1 ___________________________
Students
Player 2 ___________________________
8 2
32
16
4 8
Round 1
1
+ 16
6
+
1
16
+
1
16
=
4
16
4
16
Our fraction is:
When it is the students’ turn, give them time to think silently and then talk
in pairs about some equations they could write for this fraction. Ask them
to use their geoboards to prove their thinking to each other.
7
Call on a student to write an equation on the students’ side.
8
Then ask pairs of students to use their geoboards to make certain that the
equation makes sense.
9
Continue taking turns until either you or the students cannot write another
equation, or you have written five equations each.
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6
Unit 3 Module 2
Math Practices
in Action 4.MP.1
Session 2
NAME
| DATE
Games give students a
wonderful opportunity to
make sense of problems
and persevere in solving
them. As they persevere to write as many
equations as possible,
students are deepening
their understanding and
developing skills that
will help them compute
fluently with fractions.
Last Equation Wins page 1 of 2
Teacher
Player 1 ___________________________
Students
Player 2 ___________________________
8 2
16
32
4 8
Round 1
1
1
+ 16 + 16
6
1
+ 36 = 46
6
2
4
2 x 16
= 16
+
1
16
=
2
16
4
16
Our fraction is:
10
+
4x
2
= 46
6
1
4
=
6
6
4
16
Teacher Can you think of any other addition or multiplication equations to write for this
fraction that use only sixteenths?
Ramona No way. We got all the addition and all the multiplication.
Holly What about 3/16 + 1/16?
André That’s the same as 1/16 + 3/16. I think we lost this round!
11 At this point, you can either continue to play as a class or have students
play in pairs. You might also have most students work in pairs while you
play as a small group with students who seem to need more support.
Bridges in Mathematics Grade 4 Teachers Guide
13
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 2
• Have students locate the Last Equation Wins Student Book page in their books.
• Point out that there is a second page, allowing them to play 6 rounds if they have
enough time.
• Explain that in this game, the players share a record sheet, as you have just done with
the class, so one of the students in each pair can put their book away for now.
• Let students know that if they would prefer to draw rather than build on the geoboards
they can use the Geoboards Teacher Master. Place the copies in a central location
where students can get them if they like.
Work in a small group with students who seem to need extra support. Instead of
spinning for each fraction, present an accessible fraction (e.g. 4/8) to the group and focus on
adding and multiplying with the unit fraction (in this example, the unit fraction would be 1/8).
SUPPORT
CHALLENGE You can make this game more challenging by modifying the rules in the following ways. An example is provided with each suggested modification.
»» Try to be the first partner to write four equations, each of which uses a different
basic operation. (1/16 + 3/16 = 4/16, 8/16–4/16 = 4/16, 4 × 1/16 = 4/16, 8/16 ÷ 2 = 4/16)
»» Write equations that use fractions with different denominators. (1/8 + 2/16 = 4/16)
»» Write equations that show equivalent fractions. (4/16 = 1/4)
»» Write equations without referring to the geoboard model.
You can provide more of a challenge to students by asking them to generate a
list of all of the possible fractions they could get using two spins on this spinner and then
considering the following the questions. (You might suggest that students create a table
with spin 1 represented along the side, spin 2 represented along the top, and all the resulting fractions on the grid, as shown.)
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CHALLENGE
2
4
8
8
16
32
equal to 1
2
2/2
2/4
2/8
2/8
2/16
2/32
4
2/4
4/4
4/8
4/8
4/16
4/32
8
2/8
4/8
8/8
8/8
8/16
8/32
8
2/8
4/8
8/8
8/8
8/16
8/32
16
2/16
4/16
8/16
8/16
16/16
16/32
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Spin 1
Spin 2
equal to 1/2
equal to 1/4
equal to 1/8
32
2/32
4/32
8/32
8/32
16/32
32/32
equal to 1/16
»» What fractions come up most frequently?
»» What fractions come up least frequently?
»» Which of those fractions are equal to 1? (to 1/2, 1/4, 1/8, 1/16, 1/32)
»» What do you notice about each collection of equivalent fractions? Do you notice
any patterns?
»» Can you add to each collection of equivalent fractions, using fractions with other
denominators? How did you know what fractions to write?
»» If we had two 4s on the spinner instead of two 8s, how would the results be different?
12 As students play, clarify the following points as needed.
• All fractions in the equations should have the same denominator as the original fraction.
• Students can use addition or multiplication in their equations.
Bridges in Mathematics Grade 4 Teachers Guide
14
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 2
• If students get a fraction that is identical or equivalent to one they have already worked
with, they can spin for a new fraction. (If students don’t recognize the fraction as
equivalent to one they have worked with previously, it is probably a good use of their
time to continue working with that fraction.)
• If each partner has written 5 equations, they can continue writing equations for the fraction if they’re interested, or they can call the round a draw and move on to a new round.
• Students should prove their thinking to each other using either the geoboard itself or
copies of the Geoboards Teacher Master.
13 When there are about 10 minutes left in your math period, ask students
to finish writing the equations they are working on and put away their
Student Books, while you pass out a copy of the Geoboards Teacher Master
for each student.
14 Spend the rest of the session exploring addition of fractions with like
denominators.
• Explain that you saw someone write the following expression while playing the game:
1/8 + 1/8 + 1/8 + 1/8
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• Ask students to write the expression on a copy of the Geoboards Teacher Master and
determine what fraction the student was playing for.
• Ask them to use the geoboards on the teacher master as needed and to write their final
answer as an equation.
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15 Repeat this exercise as time allows, inviting students to work in pairs first
and then share as a group. Select from the following examples, or make up
your own, based on students’ needs and comfort level.
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1/16 + 1/16 + 1/16 + 1/16
3/16 + 1/16
4 × 1/16
4 × 1/8
1/8 + 1/8 + 1/8 + 1/8
Invite students who complete each problem quickly to write additional equations
for the fraction, using fractions with different denominators and any of the four basic operations. For example, for 4/8, students might write the following kinds of equations:
CHALLENGE
1/2 = 4/8
1/4 + 1/4 = 4/8
(2 × 1/8) + (2 × 1/8) = 4/8
4 ÷ 8 = 4/8
8/8 ÷ 2 = 4/8
7/8 – 3/8 = 4/8
16 Close the session by letting students know that tomorrow they will work
more with adding, as well as subtracting, fractions. Collect students’ papers
if you want to review them prior to Session 3.
Bridges in Mathematics Grade 4 Teachers Guide
15
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 2
Home Connection
17 Introduce and assign the Brownie Dessert Home Connection, which
provides more practice with the following skills:
• Use a visual model to explain why a fraction a�b is equivalent to a fraction n × a�n × b (4.NF.1)
• Use a visual model to generate and recognize equivalent fractions (4.NF.1)Add fractions with like denominators (supports 4.NF)
• Solve story problems involving addition of fractions referring to the same whole and
with like denominators (4.NF.3d)
Daily Practice
The optional What’s the Share? Student Book page provides additional opportunities to
apply the following skills:
• Find all factor pairs for a whole number between 1 and 100 (4.OA.4)
• Determine whether a whole number between 1 and 100 is prime or composite (4.OA.4)
• Recognize equivalent fractions (4.NF.1)
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• Use a visual model to explain why a fraction a�b is equivalent to a fraction n × a�n × b (4.NF.1)
• Use the symbols >, =, and < to record comparisons of two fractions with different
numerators and different denominators (4.NF.2)
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• Write an equation to show a fraction as the sum of other fractions with the same
denominator (4.NF.3b)
Bridges in Mathematics Grade 4 Teachers Guide
16
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Unit 3
Module 2
Session 3
Session 3
Comparing, Adding &
Subtracting Fractions
Summary
Students work together as a class to create a chart of equivalent fractions for 1/4, 1/2, and 3/4. Students
make observations about the chart and the equivalent fractions, and then they use those fractions
as benchmarks with which to make comparisons among fractions with like and unlike denominators. Finally, they practice adding and subtracting fractions with like denominators.
Skills & Concepts
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• Use a visual model to explain why a fraction a�b is equivalent to a fraction n × a�n × b (4.NF.1)
• Recognize equivalent fractions (4.NF.1)
• Compare two fractions with different numerators and different denominators and explain
why one must be greater than or less than the other (4.NF.2)
• Explain subtraction of fractions as separating parts referring to the same whole (4.NF.3a)
• Add and subtract fractions and mixed numbers with like denominators (4.NF.3c)
• Model with mathematics (4.MP.4)
• Look for and express regularity in repeated reasoning (4.MP.8)
Copies
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Materials
Kit Materials
Classroom Materials
Problems & Investigations Comparing, Adding & Subtracting Fractions
• geoboards and bands
(class set, plus 1 for
display)
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TM T3
Geoboards
SB 101–102*
Comparing, Adding & Subtracting Fractions
Daily Practice
• chart paper
(see Preparation)
• glue or tape
• scissors
Vocabulary
An asterisk [*] identifies
those terms for which Word
Resource Cards are available.
denominator*
equivalent fractions*
numerator*
SB 103
Adding & Subtracting Fractions
HC – Home Connection, SB – Student Book, TM – Teacher Master
Copy instructions are located at the top of each teacher master.
* Run 1 copy of these pages for display.
Preparation
Using a copy of the Geoboards Teacher Master, draw 1/2, 1/4, and 3/4, each on a separate
geoboard and cut them out. Divide a piece of chart paper into 4 columns and 4 rows, and
label them as shown.
Halves
Fourths
Eighths
Sixteenths
1
4
1
2
3
4
Bridges in Mathematics Grade 4 Teachers Guide
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© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 3
Problems & Investigations
Comparing, Adding & Subtracting Fractions
1
Begin the session by calling students’ attention to the chart you prepared.
Give them some time to think quietly about what they notice, and then
have them share observations and ideas, first in pairs and then as a group.
2
Explain that today they will think of different names for each of these fractions and then use that information to compare other fractions.
3
Begin by generating two equivalent fractions for 1/4, one in eighths and
another in sixteenths, together as a class. For each equivalent fraction,
draw a new geoboard model together with the class and then have a student
volunteer cut out the model and glue or tape it to the chart in the column
where it belongs (see graphic).
Teacher Let’s start by thinking of some fractions that are equal
to 1/4. Does anyone have another fraction name for this part of the
geoboard?
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Darnell You could also call it 2/8.
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Teacher Can you come on up and draw 2/8 on a geoboard to prove
that 2/8 is equal to 1/4? I’d like you to first show the whole divided into
eighths, and then color in 2/8.
Darnell OK, here are 8 equal parts. Each of these little rectangles is
an eighth. So I’ll just color in 2 of them.
Halves
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Teacher Thanks. Could you please label that 2/8 and cut it out and
put it in the eighths column of the 1/4 row?
Fourths
1
4
Eighths
Sixteenths
2
8
1
2
3
4
4
Complete the chart by drawing and labeling the missing fractions for each row.
• Give students time to work in pairs with copies of the Geoboards Teacher Master to
draw and label equivalent fractions for 1/2 and 3/4 (and 1/4 if you did not complete the row
together as a class).
Bridges in Mathematics Grade 4 Teachers Guide
18
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 3
• As you circulate around the room, you might find it useful and even necessary to invite
pairs to focus on specific fractions. For example, you might say to a pair of students, “I
haven’t seen anyone show 3/4 using sixteenths. Can you find a way to do it?”
• Reconvene and ask students to volunteer their equivalent fractions, working in one row
at a time and placing the fractions in each row in order by denominator.
5
When the chart is complete, ask students to think silently about what they
notice about the fractions in each row and column. Do they see any patterns?
Students might notice the following patterns:
• For all equivalent fractions, the numerators and denominators double as you move
from left to right across each row.
• In each column, the denominators stay the same, but the numerators change. The
numerators change by a constant amount.
Eighths
1
4
2
8
2
4
Sixteenths
3
4
Asking students to
describe patterns they
notice on the chart
invites them to look for
and express regularity in
repeated reasoning. In
their search for regularity,
students will make
observations related to
equivalent fractions and
adding fractions with like
denominators.
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4
16
4
8
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1
2
Fourths
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Halves
Math Practices
in Action 4.MP.8
6
8
8
16
12
16
Shawn I noticed that the numbers get bigger as you go across the row.
Teacher Hmm, I thought that all the fractions in each row were
equal. Can you point to what you’re seeing and tell us about it?
Shawn Well, yeah, the fractions are the same size. But look. The
numerators and denominators get bigger and bigger. So you start here
with 1 over 4. And then 2 over 8, and 4 over 16.
Veronica Hey! They’re doubling.
Shawn What do you mean?
Veronica Here. So 1 over 4 and then 2 over 8. You double the 1 to get
2 and then the 4 to get 8.
Shawn Oh yeah, it does that to get to 4 over 8 too. So 2 doubled is 4
and 8 doubled is 16.
Teacher Let’s pause for a moment. Turn to your partner and see
if you can explain to each other what’s going on. Take a look at the
other rows on our chart as well, and see if you notice anything else.
What if you skip over a column, like to go from 1/4 to 4/16? What’s
happening there?
6
After spending some time discussing the patterns students notice on the
chart, ask them to turn to the Comparing, Adding & Subtracting Fractions
Student Book pages.
Bridges in Mathematics Grade 4 Teachers Guide
19
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
7
Session 3
Review the problems on the page, do one or two of the comparison problems together as a class, and then give students about 20 minutes to work
independently or in pairs on the pages.
• While students work, circulate around the room and make note of which problems are
most interesting and challenging for your students. Plan to revisit them as a group at
the end of this session.
• Encourage students to refer to the chart you created at the beginning of the session as
needed to make comparisons.
• Encourage students to use copies of the Geoboards Teacher Master to solve the addition and subtraction problems.
SUPPORT
Gather a small group of students who are struggling to work with you.
Invite students to work on their own and solve as many of the challenge
problems on the second page as they’re able to in the time available.
CHALLENGE
8
Reconvene the entire class when you have about 15 minutes left in the
period. Spend the time talking about some of the more challenging problems together as a group.
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• When discussing comparison problems, be sure to have students share strategies that
involve using comparisons to the landmarks 1/4, 1/2, and 3/4, as well as strategies that involve
thinking in terms of a common denominator. For example, a student might conclude
that 1/4 is less than 5/8 because 5/8 is clearly more than 1/2 (4/8), and 1/4 is less than 1/2. Another
student, however, might see that 1/4 is equal to 2/8 and must, therefore, be less than 5/8.
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• When discussing comparisons, be sure students understand that they are not comparing numerators with numerators and denominators with denominators, but two entire
fractions that both refer to the same whole. For example, 3/4 is greater than 5/8, even
though 5 is greater than 3 and 8 is greater than 4. Note with students that the comparisons they’re making are valid only when each fraction refers to the same whole.
• Be sure to have students explore an addition problem and a subtraction problem that
involve mixed numbers.
• Be sure to have students model the addition and subtraction problems on geoboards
or the Geoboards Teacher Master to demonstrate why, when the two fractions share a
common denominator, students can simply find the sum or difference of the numerators and keep the denominator the same to find the sum or difference of the two
fractions (e.g., 2/8 + 5/8 = 7/8 and 6/8 –2/8 = 4/8).
Daily Practice
The optional Adding & Subtracting Fractions Student Book page provides additional
opportunities to apply the following skill:
• Solve story problems involving addition and subtraction of fractions referring to the
same whole and with like denominators (4.NF.3d)
Bridges in Mathematics Grade 4 Teachers Guide
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© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Unit 3
Module 2
Session 4
Session 4
Dozens of Eggs
Summary
Today, students add fractions using the egg carton model. The teacher then introduces a
related Work Place game by playing it with the class. Students spend any time remaining in
the session visiting Work Places, including the new one. At the end of the session, the teacher
introduces and assigns the Planning a Garden Home Connection.
Skills & Concepts
Use a visual model to explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) (4.NF.1)
Use a visual model to generate and recognize equivalent fractions (4.NF.1)
Explain addition of fractions as joining parts referring to the same whole (4.NF.3a)
Express a fraction as the sum of other fractions with the same denominator in more than
one way (4.NF.3b)
• Write an equation to show a fraction as the sum of other fractions with the same denominator (4.NF.3b)
• Model with mathematics (4.MP.4)
• Look for and make use of structure (4.MP.7)
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•
•
•
•
Materials
Kit Materials
Classroom Materials
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Copies
Problems & Investigations Combining Egg Carton Fractions
• colored tiles (12 per
student)
• heavy string or yarn, 10"
lengths, 6 pieces per student
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TM T4
Egg Carton Diagram
Work Places Introducing Work Place 3A Dozens of Eggs
TM T5
Unit 3 Work Place Log
TM T6
Work Place Guide 3A Dozens of Eggs
TM T7
3A Dozens of Eggs Record Sheet
SB 104*
Introducing Dozens of Eggs
SB 105–106**
Work Place Instructions 3A Dozens of Eggs
• Dozens of Eggs Fraction
Cards (1 deck)
• 12 colored tiles
• 6 base ten linear pieces
• game markers
• students’ Work Place folders
(see Preparation)
• colored pencils in several
different colors (class set)
Vocabulary
An asterisk [*] identifies
those terms for which Word
Resource Cards are available.
denominator*
equal*
equation*
equivalent fractions*
numerator*
sum or total*
twelfths
Work Places in Use
2A What’s Missing? Bingo (introduced in Unit 2, Module 1, Session 4)
2B Division Capture (introduced in Unit 2, Module 2, Session 1)
2C Moolah on My Mind (introduced in Unit 2, Module 3, Session 4)
2D Remainders Win (introduced in Unit 2, Module 4, Session 3)
2E More or Less Multiplication (introduced in Unit 2, Module 4, Session 4)
3A Dozens of Eggs (introduced in this session)
Home Connection
HC 57–58
Planning a Garden
Daily Practice
SB 107
Egg Carton Fractions
HC – Home Connection, SB – Student Book, TM – Teacher Master
Copy instructions are located at the top of each teacher master.
* Run 1 copy of the page for display.
** Run 1 copy of this page and store it for use by the teacher and other adult helpers during Work Place time.
Bridges in Mathematics Grade 4 Teachers Guide
21
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 4
Preparation
• Remove the Unit 1 Work Place Log from the front of each student’s Work Place folder, and
replace it with a copy of the Unit 3 Work Place Log, stapled at all four corners. Leave the
Unit 2 Work Place Log stapled to the back of each folder. This will allow students to keep
track of the number of times they have visited the Unit 2 Work Places that will remain in
use during Unit 3, and also track their progress through the new Work Places as they’re
introduced, starting today.
• In today’s session, you’ll introduce Work Place 3A Dozens of Eggs. Before this session, you
should review the Work Place Guide, as well as the Work Place Instructions. Run a class set of
the Dozens of Eggs Record Sheet and store the copies in the Work Place 3A Dozens of Eggs
tray, along with the 4 decks of Dozens of Eggs Fraction Cards you’ll find in your Bridges Kit.
This activity replaces Work Place 1F, to keep the total number of Work Places steady at six.
• Write a list of Work Places from which students can choose today. You can just write the
numbers (2A–3A) or write out the full names if you prefer. (See the Work Places in Use row
of the Materials Chart for the complete list of Work Places in use today.)
Problems & Investigations
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Combining Egg Carton Fractions
Open the session by letting students know they are going do some more
thinking about adding fractions, learn a new Work Place game, and then
visit Work Places in pairs.
2
Distribute the materials students will need for the first part of the session
and have them pair up.
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1
• Give each student a copy of the Egg Carton Diagram Teacher Master, 12 colored tiles,
and 6 pieces of heavy string or yarn.
• Have the students pair up so they have 2 copies of the Egg Carton Diagram with which
to work.
3
Pose the first problem and have students work with their partners to solve it.
1
1
• Write 3 and 4 on the board, and ask each pair to show 1/3 on one of the egg cartons and
1/4 on the other.
• Then ask pairs to combine the tiles from both sheets onto one.
• Ask them to share observations about the results and suggest ways to name this fraction.
1
3
1
4
1
1
7
+
=
3
4
12
Students It’s like half a carton and one more.
We got an odd number of eggs. It’s a hard one.
It’s 7 out of 12, so it must be seven-twelfths.
4
Ask students to share observations or questions about what happened when
they added 1/3 and 1/4.
If students do not mention that the problem began with thirds and fourths and ended up
with twelfths, make a comment to invite further discourse and reflection.
Bridges in Mathematics Grade 4 Teachers Guide
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© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 4
Teacher How did we start with a third here and a fourth here and
end up with twelfths over here? Does that seem right? Talk with the
person next to you about why we ended up with twelfths.
Ebony We got 7 eggs in all. The only way you can even say a fraction
for 7 eggs is 7/12 because you can’t make that number into thirds, or
fourths, or even sixths.
Armando I think we got twelfths because we added a fourth and a
third together. If we just added a fourth plus a fourth, or a third plus a
third, it would be easy.
Bobbie I think it’s funny because 3 and 4 both go into 12.
5
After some discussion have student pairs combine the fractional amounts
shown below, one combination at a time.
Work Places
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1/6 and 3/4 [11/12]
3/12 and 3/6 [9/12 or 3/4]
1/3 and 1/2 [10/12 or 5/6]
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Each time, ask students to talk first in pairs and then as a group about the methods for building and combining the two fractions, as well as their observations about the results. Have them
express their totals in twelfths and any other fraction names that make sense to them.
6
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Introducing Work Place 3A Dozens of Eggs
Introduce the game Dozens of Eggs.
• Display your copy of Introducing Dozens of Eggs Student Book page, and show
students a few of the Dozens of Eggs Fraction Cards.
• Explain that the game will help them practice combining fractions.
• Have students find the Introducing Dozens of Eggs Student Book page in their books,
and get out their colored pencils in preparation for learning this new game.
• Let the students know that they will record the results for both teams—you and the
class—during today’s demonstration game.
7
Briefly summarize the game before playing it with the class.
Ongoing
Assessment
The Assessment Guide
includes a Work Places
Differentiation Chart for
each unit. If you like, you
can use these charts to
make notes about which
students need support or
challenge with the skills
featured in each Work
Place. Suggestions for
differentiating a particular
Work Place activity are
included on the Work
Place Guide.
Players take turns drawing from the deck of fraction cards, modeling the designated fraction
on an Egg Carton Diagram with colored tiles and string, and recording the results. Players
take turns until one person has filled all four egg cartons on his or her record sheet and
written a matching addition equation that equals 1 whole for each carton. The first player to
fill all four egg cartons wins.
8
Shuffle the deck of fraction cards, place them in a stack face-down near
your display area, and begin the game by taking the first turn.
• Draw a card from the deck and read it aloud. Then use the plastic game markers and
base ten linear pieces to build a model of the fraction in the large egg carton diagram
at the top of the sheet.
Bridges in Mathematics Grade 4 Teachers Guide
23
© The Math Learning Center | mathlearningcenter.org
Session 4
Unit 3 Module 2
Unit 3 Module 2
2
3
Session 4
| DATE
NAME
Introducing Dozens of Eggs
Dozens of Egg
s Fraction Card
QCB6001
• Have students talk with their partners to see if they agree that you have modeled the
fraction accurately, and invite two or three volunteers to explain how they know.
• When there is general agreement, use a single color to sketch the eggs (but not the
subdivision lines) in one of your smaller egg carton diagrams on the lower part of the
sheet, and have the students do the same on their sheets.
• Work with student input to record the results of your first turn in twelfths.
w
Teacher In this game, we’re going to use a different color to record the
eggs we get on each turn. We’re also going to write all the fractions we
get as twelfths so we can add them more easily. Talk with the person
next to you about this. How would we write 2/3 as a fraction that has
12 in the denominator?
Monica I think it’s 8/12 because each egg is like a twelfth.
ie
Abe If you use more of the divider line things, you can put the carton
into twelfths. Can I show?
9
Pr
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Carlos Another thing I noticed is that if you double both of the
numbers on 2/3, it’s 4/6, and then double that, and you get 8/12.
Now clear away the game markers and linear pieces and have students take
their turn.
• Call up a volunteer to draw a card for the class and build the designated fraction at the
top of the sheet.
• When the rest of the students agree that the fraction has been built accurately, have
them sketch the eggs in one of the cartons on their side of the sheet and record their
results in twelfths.
Un t 3 Module 2
Session 4
| DATE
NAME
Introducing Dozens of Eggs
1
4
Dozens of Eggs Fraction Card
Students
Teacher
Equation:
8
12
QCB6001
Equation:
Bridges in Mathematics Grade 4 Teachers Guide
3
12
24
© The Math Learning Center | mathlearningcenter.org
Session 4
Unit 3 Module 2
10 Continue to take turns with the students until one team has filled in all
four egg cartons.
Refer to the Work Place Instructions 3A Dozens of Eggs Student Book page as needed.
• Sketch the results of each turn within a single egg carton diagram using a different
color and have students do the same on their sheets. Work with the class to write each
fraction as a number of twelfths.
• Make sure students understand that the fraction on the card they draw must be
Sess on
4
Unit in
Mo one
ule 2 egg
recorded
carton
and cannot be split into two cartons. For example, if you
AME
| DA E
have a carton with 4 empty spaces and you draw a card that
says 2/4, you cannot use 4 of
the eggs inI one
carton
and
2
in
another.
You
can,
however,
start
a new carton.
trod ng D zens of ggs
• If one team or the other draws a card for a fraction that cannot be placed in one of
their 4 egg cartons, they lose that turn.
11 Pose questions like the following to promote discussion of fraction skills
and concepts while you play.
»» Can you tell how many twelfths there will be in the fraction on the card your
classmate just drew for your team?
»» How many more twelfths do you need to fill this egg carton? Is there a single fraction
card you could draw that would give you that many twelfths? How do you know?
w
»» Which team is ahead, and by how much?
8
12
+ 122 + 121
Equation:
5
12
Equation:
3
12
+ 129 = 12
12
Pr
ev
Equation:
Students
ie
Teacher
Equation:
4
12
Teacher Who’s ahead?
Students We are, because we’ve already filled one whole egg carton.
We got really lucky on our second turn, when we got 3/4. That was
worth 9 twelfths!
Actually, I think we’re tied because both teams have 8/12 left until they
fill up 2 whole cartons. You still have 1/12 to fill on your first carton,
and then 7/12 more to go on your second carton.
But it’s our turn next, so I think we can get ahead.
Teacher Is there one fraction card you could draw that would make it
possible for you to finish filling your second egg carton?
Willie Yeah! If we get 8/12!
Teacher I can tell you that there’s no card in the deck for 8/12, but there
are a couple of other cards with fractions that are equivalent to 8/12.
Ann What are they?
Teacher I’ll give you a hint. One of them has a 6 in the denominator.
Roberta It’s sixths … .oh, I know! It must be 4/6 because that’s the
same as 8/12. I hope we get that card!
12 When the game is finished, ask students to turn to a partner and summarize the directions for Dozens of Eggs. Then let them know this game will
be available during Work Places for the next several weeks.
Bridges in Mathematics Grade 4 Teachers Guide
25
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 4
Work Places
13 If time allows, have students find a partner, get their Work Place folders
and pencils, and choose one of the available Work Place games or activities.
Note with students that you have removed the Unit 1 Work Place Log from the front of
their folders, and replaced it with a Work Place Log for Unit 3. Point out that the Unit 2
Work Place Log is still stapled to the back of their folders, and all the Work Places from
the previous unit are available, along with the new game you introduced today.
14 Close the session.
Have students clean up and put away materials.
Home Connection
15 Introduce and assign the Planning a Garden Home Connection, which
provides more practice with the following skill:
ie
Daily Practice
w
• Solve story problems involving addition and subtraction of fractions referring to the
same whole and with like denominators (4.NF.3d)
The optional Egg Carton Fractions Student Book page provides additional opportunities
to apply the following skills:
Pr
ev
• Use a visual model to demonstrate why a fraction a/b is equivalent to a fraction (n × a)/
(n × b) (4.NF.1)
• Use a visual model to generate equivalent fractions (4.NF.1)
• Use the symbols >, =, and < to record comparisons of two fractions with different
numerators and different denominators (4.NF.2)
Bridges in Mathematics Grade 4 Teachers Guide
26
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Unit 3
Module 2
Session 5
Session 5
How Many Candy Bars?
Summary
Mrs. Wiggens is bringing the dessert treats for the annual class picnic and needs help figuring out how many candy bars she’ll have to buy if she gives each student 3/4 of a bar. The
trouble is, she’s not quite sure how many of her fourth graders will be attending the picnic.
Students add fractions on an open number line and track their results on a ratio table, working together to help Mrs. Wiggens initially, and then complete the work on their own or in
pairs. As they finish the assignment, which will be revisited during a math forum next session,
students go to Work Places.
Skills & Concepts
Convert a fraction to a mixed number (supports 4.NF)
Explain addition of fractions as joining parts referring to the same whole (4.NF.3a)
Add fractions and mixed numbers with like denominators (4.NF.3c)
Solve story problems involving addition of fractions referring to the same whole and with
like denominators (4.NF.3d)
• Make sense of problems and persevere in solving them (4.MP.1)
• Look for and express regularity in repeated reasoning (4.MP.8)
w
•
•
•
•
Copies
Kit Materials
Problems & Investigations How Many Candy Bars?
Work Places in Use
Classroom Materials
• student math journals
• space on the whiteboard or
chart paper
Pr
ev
SB 108*
How Many Candy Bars?
TM T8
How Many Candy Bars Forum Planner
ie
Materials
2A What’s Missing? Bingo (introduced in Unit 2, Module 1, Session 4)
2B Division Capture (introduced in Unit 2, Module 2, Session 1)
2C Moolah on My Mind (introduced in Unit 2, Module 3, Session 4)
2D Remainders Win (introduced in Unit 2, Module 4, Session 3)
2E More or Less Multiplication (introduced in Unit 2, Module 4, Session 4)
3A Dozens of Eggs (introduced Unit 2, Module 2, Session 4)
Daily Practice
SB 110
Fractions & Mixed Numbers
HC – Home Connection, SB – Student Book, TM – Teacher Master
Copy instructions are located at the top of each teacher master.
* Run 1 copy of this page for display.
Preparation
• Write a list of Work Places from which students can choose today. You can just write the
numbers (2A–3A) or write out the full names if you prefer. See the Work Places in Use row
of the chart above for the complete list of Work Places in use today.
• Read Session 6 to see how students might share their work from today’s session. Before
tomorrow’s forum, use the How Many Candy Bars Forum Planner to help select students to
share their work.
Bridges in Mathematics Grade 4 Teachers Guide
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© The Math Learning Center | mathlearningcenter.org
Session 5
Unit 3 Module 2
Problems & Investigations
How Many Candy Bars?
1
Set the stage for today’s session.
• Let students know that they are going to tackle a problem that involves adding fractions today. They will work together at first and then complete the work on their own
or with a partner.
• As they finish, they will go to Work Places.
• Have students get out their math journals and Student Books. Ask them to find the
next available page in their journal, label it with the date, and title it “How Many
Candy Bars?”
2
Introduce today’s problem by explaining that Mrs. Wiggens, a fourth grade
teacher, hosts a class picnic every year. She usually brings the dessert, and
has decided to give each student 3/4 of a candy bar this year.
ie
w
Teacher Mrs. Wiggens wants to bring dessert treats for the class
picnic. She has decided to buy candy bars and give each student 3/4
of a bar. Her students are checking with their parents to see if they
can come. Meanwhile, since she isn’t sure yet how many students
are coming, Mrs. Wiggens wants to figure out the different amounts
of candy bars she might have to buy depending how many students
attend. She needs our help.
Ask students to turn and talk to a partner about how Mrs. Wiggens could
find and keep track of the candy bar information.
Math Practices
in Action 4.MP.1
4
Display the How Many Candy Bars? Student Book page, and ask students
to find the page in their own books.
By working together first,
you provide scaffolding
to help students begin
to make sense of the
problem and persevere
in solving it. Students
can continue to use the
number line model if
they like when they begin
working independently.
They can also choose to
use models and strategies
of their own.
Pr
ev
3
• Introduce the chart on the page.
• Note with the class that the chart includes space to enter information about the
number of candy bars and the number of students.
• Work on the first few entries together. Use an open number line to model the addition
of each 3/4 of a candy bar, and ask students to work along with you in their journals.
Teacher I’m going to draw an open number line to use in modeling
this situation and I’d like you to do the same in your math journals.
Let’s start by marking and labeling 0, 1/2, and 1 on the line.
0
1
2
1
Teacher Where should we mark the line to show 3/4 of a whole candy
bar for 1 student?
Quinlan It’s exactly halfway between 1/2 and 1, because one-half is
the same as two-fourths, and then you need to add another fourth on.
Bridges in Mathematics Grade 4 Teachers Guide
28
© The Math Learning Center | mathlearningcenter.org
Session 5
Unit 3 Module 2
1 student
3
4
0
1
2
3
4
Teacher So, how do we figure out how many candy bars Mrs.
Wiggens would need for 2 students?
Students Add 3/4 to that 3/4.
Just take another hop of 3/4 on the line.
Teacher All of you, please use your lines to model and solve 3/4 + 3/4.
(Waits for students to mark and label their number lines.) What did
you get? How many candy bars for 2 students?
Students It’s 1 1/2.
I already knew the answer in my head, but I found a good way to do it
on the line. Can I show? You can add 1/4 first, and that takes you to 1.
Then, if you add another 1/2 to make 3/4, it’s 1 1/2.
0
1
4
1
2
1
2
1
3
4
ie
3
4
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1 student 1 student
1 12
Pr
ev
Teacher Did anyone figure this a different way?
Lin I just took 2 hops of 3/4. That made 6/4 in all, and I know that’s 1 1/2
because 4/4 make 1, and then 2/4 more makes another half.
1 student 1 student
3
4
0
1
4
1
2
1
2
1
3
4
6
4
1
2
(1 )
Teacher Now how about for 3 students? How do we add another 3/4?
Everyone, please try that on your line, and share your strategy with
the person sitting next to you.
Trevor So, I was at 1 1/2. Then I jumped another half, and that got me
to 2, and then I just added the last fourth to get up to 2 1/4.
Donna I got the same thing.
1 student 1 student
3
4
0
1
4
1
2
3
4
1 student
1
2
1
1
2
1 12
Bridges in Mathematics Grade 4 Teachers Guide
1
4
2 2 14
29
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Session 5
Unit 3 Module 2
Teacher Let’s talk about 4 students now. How many candy bars?
Take a few moments to figure it out, and then let’s hear some ideas.
Extension
Have students develop
a chart for Mrs. Wiggens
to use that shows the
number of candy bars
needed if each student
gets 2/3 of a candy bar
instead of 3/4.
Eduardo We were at 2 1/4, right? So I just added on another 3/4, and
that’s 3 in all. It’s 3 candy bars for 4 kids.
1 student 1 student
3
4
0
1
4
1
2
3
4
1 student 1 student
1
2
1
1
2
1 12
1
4
3
4
2 2 14
3
Cora I got 3, but I did it a different way. I knew that for 2 students
it was 1 1/2 candy bars, so I just doubled that to get 3 candy bars for 4
students, like this.
0
1 12
3
Have students record the first four answers on the chart in their Student
Books if they haven’t already, and then fill in the rest of the chart on their
own or with a partner.
ie
5
2 students
w
2 students
Pr
ev
• Explain that you’ll revisit Mrs. Wiggens’s situation as a class next session during
math forum, but for now students need to complete the assignment on their own or
with a partner.
• Let students know that they can model the fraction addition on an open number line, but
they don’t have to if they have alternative strategies. In either case, they should continue
to use the journal page they’ve labeled to do their figuring. (Note with them that they
need to describe their strategies on the worksheet when they’ve completed the chart.)
• Encourage students to search for patterns as they work.
6
Circulate to provide support and look for students to share their thinking
in a math forum in the next session. As you circulate, use your copy of
the How Many Candy Bars Forum Planner Teacher Master to make notes
about the strategies students are using.
SUPPORT If students struggle to repeatedly add 3/4, help them use a number line to model
the addition.
CHALLENGE Encourage students to come up with a general rule for determining the
number of candy bars needed for any number of fourth graders.
7
As students finish the assignment, have them meet with other classmates to
share and compare their answers.
Encourage them to take responsibility for resolving any differences by re-examining the
problem together.
Bridges in Mathematics Grade 4 Teachers Guide
30
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 5
Work Places
8
When students have shared their work with at least one classmate, have
them get their Work Place folders and choose a Work Place to use quietly.
SUPPORT
Suggest specific Work Places for struggling students to work on critical skills.
Encourage students to think about the strategies they use and share their
thinking. Encourage students to generalize what happens in certain Work Places.
CHALLENGE
9
Close the session by reminding students that tomorrow you will discuss
their solutions and strategies during a math forum.
Daily Practice
The optional Fractions & Mixed Numbers Student Book page provides additional opportunities to apply the following skills:
• Convert a mixed number to a fraction and vice versa (supports 4.NF)
Pr
ev
ie
w
• Use a visual model to generate equivalent fractions (4.NF.1)
Bridges in Mathematics Grade 4 Teachers Guide
31
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w
ie
Pr
ev
Bridges in Mathematics Grade 4 Teachers Guide
32
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Unit 3
Module 2
Session 6
Session 6
Racing Fractions
Summary
Students discuss solutions and strategies for the candy bar problem from the previous session in a math forum. During the discussion, the class talks about adding fractions to mixed
numbers and multiplying a fraction by a whole number. Then the teacher introduces the
equivalent fraction game, Racing Fractions, which will become a Work Place in later sessions.
At the end of the session, the teacher introduces and assigns the Fractions & More Fractions
Home Connection.
Skills & Concepts
Copies
Pr
ev
Materials
ie
w
• Use a visual model to generate and recognize equivalent fractions (4.NF.1)
• Explain addition of fractions as joining parts referring to the same whole (4.NF.3a)
• Express a fraction as the sum of other fractions with the same denominator in more than
one way (4.NF.3b)
• Add and subtract fractions and mixed numbers with like denominators (4.NF.3c)
• Demonstrate an understanding that a fraction a/b is a multiple of the unit fraction 1/b (4.NF.4a)
• Write an equation showing that a fraction a/b is the product of a × 1/b (4.NF.4a)
• Multiply a fraction by a whole number (4.NF.3b)
• Demonstrate an understanding that any multiple of a/b is also a multiple of the unit fraction 1/b (4.NF.3b)
• Make sense of problems and persevere in solving them (4.MP.1)
• Construct viable arguments and critique the reasoning of others (4.MP.3)
Kit Materials
Classroom Materials
Math Forum How Many Candy Bars?
SB 108*
How Many Candy Bars?
• student math journals
An asterisk [*] identifies
those terms for which Word
Resource Cards are available.
denominator*
equivalent fraction*
improper fraction*
mixed number*
numerator*
pattern*
ratio table*
whole
Work Places Introducing Work Place 3B Racing Fractions
TM T9
Work Place Guide 3B Racing Fractions
TM T10
3B Racing Fractions Record Sheet
TM T11
3B Racing Fractions Game Board
SB 110**
Work Place Instructions 3B Racing Fractions
Vocabulary
• game markers
(7 red and 7 blue)
• Racing Fractions Cards
(1 deck)
Home Connection
HC 59–60
Fractions & More Fractions
Daily Practice
SB 111
Understanding Fractions & Mixed Numbers
HC – Home Connection, SB – Student Book, TM – Teacher Master
Copy instructions are located at the top of each teacher master.
* Run 1 copy of this page for display.
** Run 1 copy of this page and store it for use by the teacher and other adult helpers during Work Place time.
Bridges in Mathematics Grade 4 Teachers Guide
33
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 6
Preparation
In today’s session, you’ll introduce Work Place 3B Racing Fractions, which takes the place of Work
Place 2A What’s Missing? Bingo. Before this session, you should review the Work Place Guide, as
well as the Work Place Instructions. Make copies of the 3B Racing Fractions Record Sheet and
the 3B Racing Fractions Game Board Teacher Master as directed at the top of each master. Pull
out one copy of each for use during this session and store the rest in the Work Place 3B Racing
Fractions tray, along with the 4 decks of Racing Fraction Cards from your Bridges kit.
Math Forum
How Many Candy Bars?
Let students know that you’re going to hold a math forum to discuss the
problem they worked on yesterday, and then you’re going to teach them a
new Work Place game.
2
Display your copy of the How Many Candy Bars? Student Book page from
the previous session and have students take out their completed pages, as
well as their math journals.
w
1
• Review the problem with the class.
Unit 3 Module 2
ie
• Work with input to fill in the first two rows of the chart.
Session 5
NAME
| DATE
How Many Candy Bars?
Mrs. Wiggens is hosting her annual class picnic. She wants to give each student 3/4 of
a candy bar for a dessert treat.
Pr
ev
1
a
b
c
11
3
How many candy bars will she need for four students? _______
2
How many candy bars will she need for two students? _______
In order to make things easier for Mrs. Wiggens, fill in the chart below so she
will know how many candy bars she might need.
Number of
Candy Bars
3
4
Number of
Students
1
Number of
Candy Bars
Number of
Students
3
6
9
1 12 2 14
2
3
4
7
1
2
10
3
8
1
4
11
3 3 34 4 12 5 14
6
4
8
5
9 9
12
3
4
13
6
7
1
2
10 11
14
1
4
15
12
16
Ask students to discuss, first in pairs and then as a whole class, any patterns
they can find in the numbers on the chart so far.
Patterns students might comment on include, but are not limited to the following:
• The number of students increases by 1 each time, while the number of candy bars
increases by 3/4.
• Although most of the answers involve mixed numbers, there is a repeating pattern in
the fractions that accompany the whole numbers: 3/4, 1/2, 1/4, and no fraction at all; 3/4, 1/2,
1/4, and no fraction at all.
• Every fourth box in the row for the number of candy bars features a whole number.
• In looking at every fourth entry on the chart, the number of candy bars increases by 3,
while the number of students increases by 4 (e.g., 3 bars, 4 students; 6 bars, 8 students;
9 bars, 12 students; 12 bars, 16 students).
You might quickly sketch a ratio table on the board and enter just the ratios that involve
whole numbers to make this pattern visible to all the students. Students may also be invited
to make predictions based on this pattern.
Bridges in Mathematics Grade 4 Teachers Guide
34
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 6
Number of Candy Bars
3
6
9
12
Number of Students
4
8
12
16
Students Oh my gosh! I never noticed that yesterday!
The candy bars go by 3s and the students go by 4s.
You know what’s really weird? If those were fractions, they’d all be the
same as 3/4. Look—6/8, 9/12, and 12/16 are all the same as 3/4!
Teacher Can you extend this pattern? What numbers will we see the
next time there’s a whole number of candy bars?
Students It would be 15 on the top and 20 on the bottom—15 bars for
20 kids.
And the one after that would be 18 and 24—18 bars for 24 kids.
Explain that as you were watching students work last session, you noticed
that they used different strategies to figure out the numbers of candy bars.
Now you’re going to invite several pairs of students to share their strategies
in a math forum.
5
After students share, work with the class to come up with a general rule for
determining the number of candy bars needed for any number of students.
w
4
ie
During this part of the discussion, emphasize the connections between unit fractions,
common fractions and multiplying a fraction times a whole number. For example:
• 1/4 + 1/4 + 1/4 = 3 × 1/4 = 3/4 (3 one-fourths is three fourths)
• 5 × 3/4 = 5 × (3 × 1/4) = 15 × 1/4 = 15/4 (5 times 3/4 is just like 5 times (3 groups of 1/4))
Pr
ev
Teacher So, if you were Mrs. Wiggens, how would you find the
number of candy bars you need for any number of students? Is there a
general rule that you could use?
Carlos No matter how many students, each one of them will always
need 3/4 of a candy bar. So, if you had 5 students, then you need 5 of
those 3/4s.
Teacher Five 3/4s? How many one-fourths is that?
Georgia It’s like 5 groups of 3/4s. And each 3/4 is 3 one-fourths. So 5
groups of 3 groups of 1/4.
Helen And 5 groups of 3 groups is 15. So, you have 15 one-fourths.
Teacher I am going to write what you just said: 5 × 3/4 = 5 × 3 × 1/4 =
15 × 1/4. […] How do we write 15 × 1/4?
Carlos 15 fourths.
Teacher OK, let’s add that to our equation: 5 × 3/4 = 5 × 3 × 1/4 =
15 × 1/4 = 15/4. If we had 15 one-fourth candy bars, how many whole
bars would that be?
Georgia Since 12/4 is 3 candy bars, it’s 3 and 3/4 candy bars. Almost 4.
Helen I thought about 16/4 because that’s 4 candy bars. This is just 1/4
short, so it’s 3 3/4.
Bridges in Mathematics Grade 4 Teachers Guide
35
© The Math Learning Center | mathlearningcenter.org
Session 6
Unit 3 Module 2
Work Places
Introducing Work Place 3B Racing Fractions
6
Let students know that you are going to teach them how to play a new
Work Place game that will help them think flexibly about fractions, find
equivalent fractions, and add fractions. First, however, you want them to
take a close look at the game board.
The game board itself is a powerful visual; virtually a guide to equivalent fractions, so don’t
skip this step.
• Display a copy of the Racing Fractions Game Board Teacher Master, and give students
a few moments to examine it quietly.
1
2
3
1
4
0
2
4
3
4
1
8
0
1
10
2
6
3
5
3
6
4
5
4
6
5
6
Pr
ev
© The Math Learning Center | mathlearningcenter�org
1
6
0
0
2
5
2
8
2
10
3
8
3
10
4
8
4
10
5
10
1
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T11
1
5
0
1
w
1
3
0
5
8
6
10
6
8
7
10
7
8
8
10
Session 6 4 copies stored in the Work Place tray
1
2
0
Unit 3 Module 2
Bridges in Mathematics Grade 4 Teacher Masters
3B Racing Fractions Game Board
1
1
1
9
10
1
• Ask students to share, first in pairs and then as a whole group, any observations they
can make about the board. Observations may include but are certainly not limited to
the following:
»» There are 7 number lines on the game board, and they all go from 0 to 1.
»» Each number line is divided into smaller and smaller parts.
»» The parts keep getting smaller, but the denominators of the fractions keep getting
larger. (Here, you might want to ask students to explain why this is the case.)
»» If you look down all the lines, you can see some equivalent fractions. For example,
1/2, 2/4, 3/6, 4/8, and 5/10 all land exactly halfway along their lines. (If you lay a ruler
perpendicular to the set of 7 lines along a set of equivalent fractions such as those
just listed, it will help all the students see and understand.)
»» You can see that fifths and tenths relate to one another because 1/5 and 2/10 land on
the same place along their lines. Same with 2/5 and 4/10, 3/5 and 6/10, and so on.
»» There are equivalent fractions on the lines for thirds and sixths; also halves, fourths,
and eighths.
Bridges in Mathematics Grade 4 Teachers Guide
36
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
7
Session 6
Briefly summarize the game before playing against the class.
Players draw from a deck of Racing Fractions Cards and move game markers along the
Racing Fractions Game Board, which shows fraction number lines for halves, thirds, fourths,
fifths, sixths, eighths, and tenths. Each player has a game marker on each line and may
move one or more markers in a single turn to equal the fraction on the card drawn. Players
may also move backward on a turn. The first player to move his or her markers to 1 on all of
the number lines is the winner.
8
Play a game of Racing Fractions against the class. Use your copy of the
Work Place Instructions 3B Racing Fractions Student Book page as needed.
Pose questions like the following to promote flexible thinking and strategy development
while you play:
• What are some possible moves for this card?
• Which move will help you the most?
• How can you check to see if the moves you made add up to the fraction on the card
you chose?
• When would you want to move backward? Why?
Ask students to turn to a partner to summarize the directions for the
Racing Fractions Work Place.
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10 Close the session.
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Home Connection
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• Let students know this game will be available during Work Places for several more weeks.
11 Introduce and assign the Fractions & More Fractions Home Connection,
which provides more practice with the following skills:
• Order fractions (including mixed numbers) on number lines (supports 4.NF)
• Use visual models to generate equivalent fractions (4.NF.1)
• Express a fraction as the sum of other fractions with the same denominator in more
than one way (4.NF.3b)
• Write an equation to show a fraction as the sum of other fractions with the same
denominator (4.NF.3b)
• Solve story problems involving addition of fractions referring to the same whole and
with like denominators (4.NF.3d)
• Multiply a fraction by a whole number (4.NF.4b)
Daily Practice
The optional Understanding Fractions & Mixed Numbers Student Book page provides
additional opportunities to apply the following skills:
• Convert a mixed number to a fraction (supports 4.NF)
• Convert a fraction to a mixed number (supports 4.NF)
• Create a visual representation of a mixed number or improper fraction (supports 4.NF)
Bridges in Mathematics Grade 4 Teachers Guide
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© The Math Learning Center | mathlearningcenter.org
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Bridges in Mathematics Grade 4 Teachers Guide
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© The Math Learning Center | mathlearningcenter.org
Teacher Masters
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GRADE 4 – UNIT 3 – MODULE 2
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Unit 3 Module 2
Session 1 class set, plus 1 copy for display
NAME
| DATE
Equivalent Fractions Checkpoint
1
Write three equivalent fractions to show what part of the egg cartons in each row
is filled. Draw lines on the egg cartons in each row to show how you divided them
into equal parts.
a
c
2
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b
1
2
LaTonya says that 2 , 4 , and
3
6
can all be worth the same amount.
a
Do you agree with her? _______
b
Use labeled sketches to explain your thinking.
Bridges in Mathematics Grade 4 Teacher Masters
T1
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Sessions 1 , 2 and 4 1 copy for display
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Geoboard Area of One
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Area = 1 sq. unit
A
B
D E
C
Bridges in Mathematics Grade 4 Teacher Masters
T2
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Sessions 2 and 3 3 class sets, double-sided
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Geoboards
Bridges in Mathematics Grade 4 Teacher Masters
T3
© The Math Learning Center | mathlearningcenter.org
Sessions 4 class set, plus 4–6 extra copies for the Work Place 3A tray
NAME
Egg Carton Diagram
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| DATE
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Unit 3 Module 2
Bridges in Mathematics Grade 4 Teacher Masters
T4
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 4 class set, plus 1 copy for display
NAME
| DATE
Unit 3 Work Place Log
3B Racing Fractions
3D Decimal More or Less
3E Fractions & Decimals
3C Decimal Four Spins to Win
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= 1.00
Personal Practice
Bridges in Mathematics Grade 4 Teacher Masters
Computer Activity
T5
Work with the Teacher
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 4 1 copy stored for use by the teacher and other adult helpers during Work Place time
Work Place Guide 3A Dozens of Eggs
Summary
Players take turns drawing from a deck of fraction cards, modeling the designated fraction on an Egg Carton Diagram with colored
tiles and string, and recording their results. Players take turns until one person has filled all four egg cartons on his or her record
sheet and written a matching addition equation that equals 1 whole for each carton. The first player to fill all four egg cartons wins.
Skills & Concepts
•
•
•
•
Use visual models to recognize equivalent fractions (4.NF.1)
Explain addition of fractions as joining parts referring to the same whole (4.NF.3a)
Express a fraction as the sum of other fractions with the same denominator in more than one way (4.NF.3b)
Write an equation to show a fraction as the sum of other fractions with the same denominator (4.NF.3b)
Materials
Kit Materials
Classroom Materials
TM T6
Work Place Guide 3A Dozens of Eggs
TM T7
3A Dozens of Eggs Record Sheet
TM T4
Egg Carton Diagram
SB 107-108
Work Place Instructions 3A Dozens of Eggs
• 3 decks Dozens of Eggs Fraction Cards
• 36 colored tiles
• 18 pieces of heavy string or yarn, 10” long
• crayons
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Assessment & Differentiation
Differentiate
Example
A student struggles to build a model of the
fraction drawn.
SUPPORT Use strings to model cutting the
egg carton into pieces and have the student
name the fractional parts.
"I see your card is 3/4. How many equal parts do
we need? Lets use the pieces of string to split
the egg carton into that many equal pieces.
Show me how you could split the 12 egg
compartments into 4 equal groups."
Students are unable to determine whether
the fraction drawn can fit into one of their
cartons.
SUPPORT Have partners work together to name
the fraction that is left in each diagram and
any equivalent fractions they can determine
before they try to fill the carton with the
fraction drawn.
One or more students struggles to play the
game due to a lack of comfort with fractions,
the egg carton model, or the process of
building and recording each time.
SUPPORT Have students play game variation
A with classmates who are more comfortable
with the game.
One or more students easily build the
designated fractions, fill the egg diagrams, and
record equations to match without difficulty.
CHALLENGE Have students play using game
variation B.
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If you see that … SUPPORT Gather a small group of these
students during Work Places and have them
play as a team against you.
English-Language Learners Use the following adaptations to support the ELL students in your classroom.
• Have ELL students observe other students playing the game before playing it themselves.
• Pair each ELL student with a supportive partner (an English-speaking student or another ELL student with more command of English) who can
offer support and explain the instructions while they play.
• Play the game with the ELL students yourself. Model how to play and put emphasis on how to model the fraction on the egg carton.
• Once students understand the game, help them demonstrate their strategies and verbalize them.
Bridges in Mathematics Grade 4 Teacher Masters
T6
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 4 class set, plus more as needed, stored in the Work Place tray
NAME
| DATE
3A Dozens of Eggs Record Sheet
Game 1
Game 2
Equation:
Equation:
Equation:
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Equation:
Equation:
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Equation:
Equation:
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Equation:
Game 3
Equation:
Game 4
Equation:
Equation:
Equation:
Equation:
Equation:
Equation:
Equation:
Bridges in Mathematics Grade 4 Teacher Masters
T7
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Sessions 5 & 6 1 copy for teacher use
How Many Candy Bars Forum Planner
Use this planner to make a record of the strategies you see students using to solve problems during Session 5. Prior to
Session 6, use the third column to indicate the order in which you plan to have students share during the forum.
How many candy bars if each student gets 3/4?
Strategy
Student Names and Notes
Order of Sharing in Forum
Adding 3/4
Add 3/4 to get each new figure,
breaking it apart into 1/2 + 1/4 when it
is advantageous to do so.
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Using a ratio
Use known information to find
more answers by keeping the ratio
the same. For example, students
know that three students get 2 1/4
bars and four students get 3 bars, so
they add 2 1/4 + 3 = 5 1/4 to find the
number of bars for seven students.
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Doubling or multiplying
Double 3/4 to make 1 1/2 candy bars
for two students, double again
to make three candy bars for four
students, and so on.
Bridges in Mathematics Grade 4 Teacher Masters
T8
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 5 1 copy stored for use by the teacher and other adult helpers during Work Place time
Work Place Guide 3B Racing Fractions
Summary
Players draw from the Racing Fractions Cards deck and move game markers along the Racing Fractions Game Board, which
shows fraction number lines for halves, thirds, fourths, fifths, sixths, eighths, and tenths. Each player has a game marker on
each line and may move one or more markers in a single turn to equal the fraction on the card drawn. Players may also move
backward on a turn. The first player to move her markers to 1 on all of the number lines is the winner.
Skills & Concepts
•
•
•
•
•
Recognize equivalent fractions (4.NF.1)
Explain addition of fractions as joining parts referring to the same whole (4.NF.3a)
Express a fraction as the sum of other fractions with the same denominator in more than one way (4.NF.3b)
Add and subtract fractions with like denominators (supports 4.NF)
Add and subtract fractions with unlike denominators, including mixed numbers (5.NF.1)
Materials
Kit Materials
TM T9
Work Place Guide 3B Racing Fractions
TM T10
3B Racing Fractions Record Sheet
TM T11
3B Racing Fractions Game Board
SB 112
Work Place Instructions 3B Racing Fractions
• 21 red and 21 blue game markers
(7 of each per student pair)
• 3 decks of Racing Fractions Cards
If you see that … ie
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Assessment & Differentiation
Classroom Materials
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Copies
One or more students are uncertain
when moving game markers.
Differentiate
Example
SUPPORT Gather a small group to work together as
a team against you. Each time you take a turn, share
your thinking, and ask students to do the same.
SUPPORT Have these students play cooperatively
rather than competitively with classmates who
are working more easily with fractions.
A student always tries to move only
one game marker exactly the value
of the card.
SUPPORT Ask the student to find two or three
possible moves for each card. Then ask the
student which possibility is the best move.
"You have the 5/8 card. What are some different ways
you could move 5/8? What fractions add up to 5/8?"
One or more students are readily
making correct moves for any card.
CHALLENGE Ask students questions that prompt
them to make generalizations and extend their
thinking about the game.
"Which cards are the most helpful to draw at the
beginning of the game?"
"Since the cards have all of the fractions with
denominators 2, 3, 4, 5, 6, 8, 10, what are the fewest
possible moves you could make to win?"
"When would you want to move backward? Why?"
One or more students are
developing strategies for playing
the game.
Partway through a game, ask students
which cards would or would not work at this
point. Challenge them to communicate their
reasoning clearly.
CHALLENGE
English-Language Learners Use the following adaptations to support the ELL students in your classroom.
• Post Word Resource Cards for important vocabulary such as equivalent fractions, numerator, and denominator.
• Pair ELL students with supportive partners who can explain the game, including others who speak the same language.
• Play a demonstration game, focusing on different possibilities for each fraction card selected. Emphasize developing game strategies.
Bridges in Mathematics Grade 4 Teacher Masters
T9
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 6 half-class set, plus more as needed, stored in the Work Place tray
NAME
| DATE
3B Racing Fractions Record Sheet
Player 1____________________________ Player 2____________________________
Use the chart below to record your work with Racing Fractions. Write the fraction on
the fraction card in the first column. Write an equation that represents your moves in
the second column. The first one has been filled in for you as an example.
Player 1
Fraction
Equation
1
2
+
1
4
=
Fraction
3
4
4
5
Equation
1
2
+
1
5
+
1
10
=
4
5
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3
4
Player 2
Bridges in Mathematics Grade 4 Teacher Masters
T10
© The Math Learning Center | mathlearningcenter.org
1
4
10
4
8
5
10
6
10
5
8
4
6
3
6
Bridges in Mathematics Grade 4 Teacher Masters
T11
0
0
0
0
0
0
0
1
10
1
8
1
6
1
5
2
10
2
8
1
4
3
10
2
6
3
8
2
5
2
4
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3
3B Racing Fractions Game Board
1
2
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3
5
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2
3
7
10
6
8
3
4
4
5
8
10
5
6
7
8
9
10
1
1
1
1
1
Session 6 4 copies stored in the Work Place tray
1
Unit 3 Module 2
© The Math Learning Center | mathlearningcenter.org
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Student Book
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GRADE 4 – UNIT 3 – MODULE 2
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Unit 3 Module 2
Session 1
NAME
| DATE
Pizza Party Planning
A fourth grade class won a pizza party for collecting the most paper for recycling in their
school contest. Medium pizzas were cut into 8 slices, and large pizzas were cut into 12 slices.
1
Mariah ate 2 slices of a large pizza. What fraction of the pizza did she eat? Draw a
sketch to show your thinking.
2
Carlos said that Mariah ate of
3
Mariah’s table seats 4 students. Each student ate 2 slices of a large pizza. Write an
equation that shows what fraction of a pizza was eaten at Mariah’s table.
4
Tony ate 3 slices of a medium pizza. His friend, Connor, ate 4 slices of the same pizza.
a pizza. Tell why you agree or disagree.
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1
6
a
Write two different fractions to describe how much pizza Connor ate.
b
What fraction of the pizza did the boys eat together? _______
5
Lionel’s table group drank 1 1 liters of juice with their pizza. How many milliliters
2
did they drink? Show your work.
6
Complete the problems.
100
× 45
79
× 10
100
×
8,500
Bridges in Mathematics Grade 4 Student Book
20
×
1,400
97
35
× 40
240
×
7,000
60
× 60
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 2
NAME
| DATE
Last Equation Wins page 1 of 2
Player 1____________________________ Player 2____________________________
8 2
32
16
4 8
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Round 1
Our fraction is: ________________
Round 2
Our fraction is: ________________
Round 3
Our fraction is: ________________
Bridges in Mathematics Grade 4 Student Book
98
(continued on next page)
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 2
NAME
| DATE
Last Equation Wins page 2 of 2
Player 1____________________________ Player 2____________________________
8 2
32
16
4 8
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Round 1
Our fraction is: ________________
Round 2
Our fraction is: ________________
Round 3
Our fraction is: ________________
Bridges in Mathematics Grade 4 Student Book
99
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 2
NAME
| DATE
What’s the Share?
1
If the area of the largest square on the geoboard is 1, what is the area of each region?
A
B
E
C
D
A
C
D
E
Write four statements and matching fraction equations that compare two regions.
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2
B
is half of E
Equations
2×
1
4
=
1
2
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Statements
3
Fill in the blank with the correct relational symbol: <, >, or =.
1
2
1
6
3
4
3
8
4
9
4
List all the factor pairs for the number 32.
5
List three prime numbers greater than 20.
Bridges in Mathematics Grade 4 Student Book
100
6
9
4
8
5
10
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 3
NAME
| DATE
Comparing, Adding & Subtracting Fractions page 1 of 2
Use the symbols >, =, or < to compare each pair of fractions.
3
8
1
4
3
8
4
16
3
8
4
16
7
16
5
8
1
4
5
8
7
16
3
4
Find each sum.
1
3
4 + 4 =
2
1
4 + 4 =
1
2
5
+
8
8 =
1
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14 + 4 =
3
1
4
2
16
2
3
4 + 4 =
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2
2
8
3
4
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1
5
6
+
8
8 =
Find each difference.
3 1
4 – 4 =
14 – 4 =
6 2
8 – 8 =
18 – 8 =
Bridges in Mathematics Grade 4 Student Book
1
1
3
2
101
1
3
3
4
14 – 4 =
18 – 8 =
© The Math Learning Center | mathlearningcenter.org
Session 3
Unit 3 Module 2
NAME
| DATE
Comparing, Adding & Subtracting Fractions page 2 of 2
CHALLENGE
b
c
d
5
1
8
1
4
2
3
Describe how you can write equivalent fractions for any fraction.
CHALLENGE
Find each sum.
1
1
2
3
8 + 4 =
12 1
16 + 8 =
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a
Write as many equivalent fractions as you can for each fraction shown below.
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4
6
CHALLENGE
Find each difference.
1
1
14 – 2 =
Bridges in Mathematics Grade 4 Student Book
3 3
4 – 8 =
102
1
5
16 – 4 =
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 3
NAME
| DATE
Adding & Subtracting Fractions
Ariel got a new box of 8 crayons and a set of 10 markers for her birthday. Use this
information as you solve each problem below. Use numbers, labeled sketches, or words
to show your thinking.
Ariel used 5 crayons to make a thank-you card. What fraction of the box did she use?
2
Ariel gave her brother 4 crayons. What fraction does she have left out of her box of 8?
3
After she gave some crayons to her brother, Ariel’s dog ate 2 of her crayons.
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1
Now what fraction does Ariel have left of her original box of 8 crayons?
b
What fraction of the crayons went to Ariel’s brother and her dog?
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a
4
Ariel took 6 markers out of her marker set. What fraction of the markers are left in the set?
5
Two of Ariel’s markers are green, 2 are red, and 3 are blue. What fraction of the
markers are
green? ________
red? ________
blue? ________
Bridges in Mathematics Grade 4 Student Book
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© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 4
NAME
| DATE
Equation:
Students
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Introducing Dozens of Eggs
Equation:
Equation:
Equation:
Equation:
Equation:
Equation:
Equation:
Bridges in Mathematics Grade 4 Student Book
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© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 4
NAME
| DATE
Work Place Instructions 3A Dozens of Eggs page 1 of 2
Each pair of players needs:
•
•
•
•
•
•
2 Dozens of Eggs Record Sheets
1 deck of Dozens of Eggs Fraction Cards
1 Egg Carton Diagram
6 pieces of string or yarn
12 colored tiles
colored pencils or crayons
1 Players shuffle the fraction cards and lay them face-down in a stack. Each player draws one card. The
player with the larger fraction goes first. The cards just drawn go at the bottom of the stack.
Players may build fractions on the Egg Carton Diagram if needed to determine which fraction is larger.
2 Player 1 draws a card from the top of the deck, reads the fraction out loud, and uses string and colored
Dozens of Egg
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tiles to build a model of the fraction on the Egg Carton Diagram. Player 2 checks Player 1’s work.
s Fraction Card
QCB6001
Jasmine Wow! I got a really big fraction on my first turn. So I’m going to divide the egg carton
into 3 equal parts, and fill 2 of them, like this.
Sara I agree that
of a carton.
2
3
of the egg carton is 8 eggs, because I know that there are 4 eggs in one-third
3 Player 1 draws circles to represent that number of eggs in one of the diagrams on her record sheet and
records that number of twelfths as a fraction on the sheet.
2
3
Dozens
of Eggs
Fraction
Card
Jasmine
8
12
1
QCB600
Jasmine I have to change 23 into twelfths, but that’s easy, because each egg is one-twelfth of the
8
carton, so I got 12
on my first turn. I only need 4 more twelfths to fill this carton.
(continued on next page)
Bridges in Mathematics Grade 4 Student Book
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© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 4
NAME
| DATE
Work Place Instructions 3A Dozens of Eggs page 2 of 2
4 Player 1 empties the egg carton diagram and puts the card in a discard stack. Then Player 2 takes a turn.
5 Players continue to take turns until one person has filled in all four cartons on the record sheet.
Players should use a different color to record each new turn.
When all the cards in the deck have been used, shuffle the deck and use it again.
6 On each turn, players must put all of the eggs in one carton. However, players may begin to fill
another carton before the first is completely filled.
7 If the fraction drawn does not fit into one of the cartons, the player misses that turn.
8 When a carton is filled, the player writes an equation by inserting plus signs between the fractions for
that carton and showing them equal to 1 whole.
+ 122 + 122 =1
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12
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Jasmine
9 The winner is the first player to fill all four cartons on his record sheet. If Player 1 is the first to fill all
four cartons, Player 2 may take one last turn.
Game Variations
A Players work together to fill all four cartons on a single record sheet rather than playing against each other.
B Players begin with all four cartons filled, by drawing 12 circles in each of the cartons and writing 12
12 at
the start of each equation line. Then each player subtracts the fractions that are written on the cards
they get, crossing out that many eggs and subtracting that many twelfths. Players must subtract the
entire fraction from one carton rather than splitting the fraction between two or more cartons. The
winner is the first player to get rid of all the eggs from all four cartons.
Bridges in Mathematics Grade 4 Student Book
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© The Math Learning Center | mathlearningcenter.org
Session 4
Unit 3 Module 2
NAME
| DATE
Egg Carton Fractions
1
2
Solve the following multiplication and division problems. They might help you
think about the egg cartons in problem 2.
12 ÷ 2 = ______
12 ÷ 3 = ______
12 ÷ 4 = ______
12 ÷ 6 = ______
6 × 3 = ______
4 × 2 = ______
3 × 3 = ______
2 × 5 = ______
Write a fraction to show the amount of each egg carton that is filled with eggs. (The
cartons are divided into equal parts for you.) Then write an equivalent fraction with
12 in the denominator.
a
Equation:
4
= 12
c
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1
3
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Equation:
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Equation:
d
Equation:
e
Equation:
3
Equation:
Use the symbols >, =, or < to compare each pair of fractions.
ex
1
4
1
2
ex
1
2
b
1
3
1
4
c
e
1
2
2
4
f
<
Bridges in Mathematics Grade 4 Student Book
1
3
a
4
6
2
3
3
4
5
6
d
1
3
3
4
2
3
3
4
g
2
6
1
3
>
107
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 5
NAME
| DATE
How Many Candy Bars?
1
Mrs. Wiggens is hosting her annual class picnic. She wants to give each student 3/4 of
a candy bar for a dessert treat.
a
How many candy bars will she need for two students? _______
b
How many candy bars will she need for four students? _______
c
In order to make things easier for Mrs. Wiggens, fill in the chart below so she
will know how many candy bars she might need.
Number of
Candy Bars
1
2
3
9
10
11
Number of
Students
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Number of
Candy Bars
Number of
Students
5
6
7
8
12
13
14
15
16
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Number of
Candy Bars
4
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Number of
Students
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Number of
Candy Bars
Number of
Students
2
3
How did you get your answers on the chart above? Use numbers, words, or labeled
sketches to describe your strategy.
What kind of general rule could you give Mrs. Wiggens to know how
many candy bars to get no matter how many students she has?
CHALLENGE
Bridges in Mathematics Grade 4 Student Book
108
© The Math Learning Center | mathlearningcenter.org
Unit 3 Module 2
Session 5
NAME
| DATE
Fractions & Mixed Numbers
1
The circles below are divided into equal parts. Write two fractions to show what
part of each circle is filled in.
ex
2
4
b
d
e
2
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c
1
2
a
The circles below are divided into equal parts. Write a fraction and a mixed number
to show how many circles are filled in.
Fraction
ex
3
2
Mixed
Number
1
1
2
b
3
Fraction
a
Mixed
Number
c
Fill in the missing fractions or mixed numbers.
Challenge
Fractions
5
2
Mixed
Numbers
2 12
9
2
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14
4
62
3
1
32
109
3
24
1
30 3
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Unit 3 Module 2
Session 6
Work Place Instructions 3B Racing Fractions
Each pair of players needs:
•
•
•
•
•
1 Racing Fractions Record Sheet to share
1 Racing Fractions Game Board
7 red game markers
7 blue game markers
1 deck of Racing Fraction Cards
1 Players decide who will play with the red game markers, and who will play with the blue markers. Then
both players place one of their game markers at the beginning of each number line on the game board.
2 Players shuffle the fraction cards and lay them face-down in a stack. Each player draws one card. The
player with the larger fraction goes first. Players put the cards just drawn at the bottom of the stack.
3 Player 1 draws a new card and moves one or more game markers the distance shown on the card.
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Player 1 I got 36 . That’s the same as 12 , so I could go 12 , 24 , 36 , 48 , or 10
. Hmm...or I could do 13 and
1
1
6 . I remember those make 2 from when we looked at egg carton fractions. I think I’ll do that.
4 Player 1 records the fraction in his Fraction column on the record sheet and writes the fraction or
equation that describes how the game markers were moved in his Equation column.
(If the player selected 12 and moved 12 , he would write
another marker to 16 , he would write 13 + 16 = 12 .)
1
2.
If the player selected
1
2
and moved one marker to
1
3
and
5 Player 2 checks first player’s work on the record sheet. Player 1 tries again if an error was made.
6 Then Player 2 draws a fractions card and takes a turn. Player 1 checks the second player’s work.
7 Players continue to take turns, record moves, and check each other’s work until one player’s game
markers are all on 1. If Player 1 is the first to land on 1, Player 2 may take one last turn.
If a player cannot find a possible move for a card he has drawn, the player loses the turn.
Players may also move game markers backward. For example, if a player selects 13 , she can move one marker up
and another back 16 . The sum or the difference of the moves still needs to equal the value on the fraction card.
1
2
Game Variations
A Play cooperatively. Players can work together and help each other finish the track in a certain time period.
B Double the length of each track by taping 2 copies of the Racing Fractions Game Board Teacher
Master together, writing a 1 in front of every fraction on the second sheet, and changing the 1 at the
end of each track on the second sheet to a 2.
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Unit 3 Module 2
Session 6
NAME
| DATE
Understanding Fractions & Mixed Numbers
1
Sketch and label a picture that represents 1 2 .
2
Answer each question below:
4
a
How many halves are in 2 ? _____
b
c
How many thirds are in 3 ? _____
e
What do you notice about problems a–d?
d
6
How many fifths are in 5 ? _____
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8
7
How many fourths are in 4 ? _____
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3
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3
1
Write each fraction as a mixed number. Make a drawing, if needed.
a
5
2
= _____
b
7
6
= _____
c
4
3
= _____
d
12
8
= _____
Write each mixed number as a fraction. Make a drawing, if needed.
a
1 3 = _____
b
1 5 = _____
c
2 4 = _____
d
3 2 = _____
2
3
1
1
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Home Connections
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GRADE 4 – UNIT 3 – MODULE 2
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Unit 3 Module 2
Session 2
NAME
| DATE
Brownie Dessert page 1 of 2
A fourth grade class earned a brownie dessert party for having the highest attendance
in one grading period. Small pans of brownies were cut into 9 pieces, and large pans
were cut into 16 pieces.
Tori ate 2 brownies from a small pan. What fraction of the brownies in that pan did
she eat? Draw a sketch to show your thinking.
2
Holly ate 1 more brownie than Tori from the same small pan. Write two equivalent
fractions that describe how much Holly ate.
3
Henry’s table group seats 5 students. Each student ate 2 brownies from a large pan.
Write an equation that shows what fraction of a large pan of brownies was eaten at
Henry’s table.
4
April ate 1 brownie from a large pan, and her friend, Christina, ate 4 brownies from
the same pan.
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1
a
Write two fractions to tell how much of the large pan of brownies Christina ate.
b
What fraction of a large pan of brownies did the girls eat together?
(continued on next page)
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Unit 3 Module 2
Session 2
NAME
| DATE
Brownie Dessert page 2 of 2
1
1
8
of the
w
2
Freddy had 2 of the brownies from a large pan. His friend said he ate
brownies in that pan. Tell why you agree or disagree.
In an 18-egg carton, 3 equals 6 eggs. Use the grids below to help you
imagine and draw cartons where:
CHALLENGE
1
2
is 9 eggs.
b
3
8
is 18 eggs.
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1
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Unit 3 Module 2
Session 4
NAME
| DATE
Planning a Garden page 1 of 2
The Brown family is trying to decide how to plan their garden for the vegetables they
want to grow. Use the geoboard model to design a garden that fits each description.
Label every area to show where each vegetable will be planted.
1
The Browns could plant
2
They could plant
3
The Brown family might plant 8 tomatoes, 8 cabbage, and
what fraction of their garden will be unplanted?
tomatoes,
1
4
1
4
squash,
squash, and
1
4
1
4
lettuce.
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tomatoes,
lettuce,
1
8
peppers, and
1
8
cabbage.
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1
4
1
2
1
1
1
8
peppers. If they do,
(continued on next page)
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Unit 3 Module 2
Session 4
NAME
| DATE
Planning a Garden page 2 of 2
1
1
4
cabbage, and
2
8
peppers, what fraction of their
Create a plan for a garden that has room for 5 different vegetables. Label
the vegetables in the garden and write a equation to represent the model.
CHALLENGE
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2
If the Browns plant 163 tomatoes,
garden will be unplanted?
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Session 6
Unit 3 Module 2
NAME
| DATE
Fractions & More Fractions page 1 of 2
Ethan used an egg carton model to add fractions. Draw eggs in the cartons to show
and solve the problem. Then fill in the blank to show the answer.
1
2
2
Put the following numbers in order on the number line below.
1
2
1
3
5
12
1
4
3
1
14
7
8
14
1
2
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0
Maria is writing as many different addition and multiplication equations as she can
2
for 2 8 . Her rule is that all the fractions in each equation must have a denominator
of 8.
a
b
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1
6=
+
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1
Here are the equations Maria has written so for. Fill in the bubble beside each
equation that is true.
NN
28 = 1 + 1 +
NN
28 =
NN
5
8
NN
18 ×
2
2
+
8
8
5
8
1
8
+
+
5
8
2
8
10
8
+
4
8
2
= 28
2
= 28
2
Write at least four more addition or multiplication equations for 2 8 in which all
the fractions have a denominator of 8.
(continued on next page)
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Unit 3 Module 2
Session 6
NAME
| DATE
Fractions & More Fractions page 2 of 2
4
Calvin and Leah are playing a game that has them draw fraction cards to add up to
1
numbers that fill a 12-egg carton. Calvin had 3 of his egg carton full when he chose a
8
card with 12 on it. He says he will fill his egg carton. Do you agree or disagree? Why?
Use a labeled sketch in the egg carton diagram below to help explain your answer.
5
Leah had 6 of her egg carton full when she chose the 12 card. Can she fit 12 in this
egg carton? Why or why not? Use a labeled sketch in the egg carton diagram below
to help explain your answer.
5
5
Imagine you are playing the game with egg cartons that hold 18 eggs,
and the fraction cards refer to 18 eggs instead of 12 eggs. (For example, if you draw
1
the 2 card, that means half of 18, not half of 12.)
CHALLENGE
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a
If you have 3 of your first 18-egg carton full, how many more eggs will fit in that
carton? What fraction card will you need to draw to fill the first carton exactly?
b
You have 3 of your second 18-egg carton full when you select the 6 card. Can
you use this card to place more eggs in the second carton, or will you have to
use your third carton instead?
2
1
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