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```GRADE
3
Building Conceptual Understanding
and Fluency Through Games
F O R T H E C O M M O N C O R E STAT E STA N DA R D S I N M AT H E M AT I C S
PUBLIC SCHOOLS OF NORTH CAROLINA
State Board of Education | Department of Public Instruction
K-12 MATHEMATICS
http://www.ncpublicschools.org/curriculum/mathematics/
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Building Conceptual Understanding and Fluency Through Games
Developing fluency requires a balance and connection between conceptual understanding and computational proficiency. Computational
methods that are over-practiced without understanding are forgotten or remembered incorrectly. Conceptual understanding without
fluency can inhibit the problem solving process. – NCTM, Principles and Standards for School Mathematics, pg. 35
WHY PLAY GAMES?
People of all ages love to play games. They are fun and motivating. Games provide students with
opportunities to explore fundamental number concepts, such as the counting sequence, one-to-one
correspondence, and computation strategies. Engaging mathematical games can also encourage students
to explore number combinations, place value, patterns, and other important mathematical concepts.
Further, they provide opportunities for students to deepen their mathematical understanding and reasoning.
Teachers should provide repeated opportunities for students to play games, and let the mathematical ideas
emerge as they notice new patterns, relationships, and strategies. Games are an important tool for learning.
Here are some advantages for integrating games into elementary mathematics classrooms:
•Playing games encourages strategic mathematical thinking as students find different strategies for
solving problems and it deepens their understanding of numbers.
•Games, when played repeatedly, support students’ development of computational fluency.
•Games provide opportunities for practice, often without the need for teachers to provide the problems.
Teachers can then observe or assess students, or work with individual or small groups of students.
•Games have the potential to develop familiarity with the number system and with “benchmark
numbers” – such as 10s, 100s, and 1000s and provide engaging opportunities to practice
computation, building a deeper understanding of operations.
•Games provide a school to home connection. Parents can learn about their children’s mathematical
thinking by playing games with them at home.
For students to become fluent
BUILDING FLUENCY
Developing computational fluency is an expectation of the Common Core State Standards. Games
provide opportunity for meaningful practice. The research about how students develop fact mastery
indicates that drill techniques and timed tests do not have the power that mathematical games and
other experiences have. Appropriate mathematical activities are essential building blocks to develop
mathematically proficient students who demonstrate computational fluency (Van de Walle & Lovin,
Teaching Student-Centered Mathematics Grades K-3, pg. 94). Remember, computational fluency includes
efficiency, accuracy, and flexibility with strategies (Russell, 2000).
ability to do mathematics.
The kinds of experiences teachers provide to their students clearly play a major role in determining
the extent and quality of students’ learning. Students’ understanding can be built by actively engaging
in tasks and experiences designed to deepen and connect their knowledge. Procedural fluency and
conceptual understanding can be developed through problem solving, reasoning, and argumentation
(NCTM, Principles and Standards for School Mathematics, pg. 21). Meaningful practice is necessary
to develop fluency with basic number combinations and strategies with multi-digit numbers. Practice
should be purposeful and should focus on developing thinking strategies and a knowledge of number
relationships rather than drill isolated facts (NCTM, Principles and Standards for School Mathematics,
pg. 87). Do not subject any student to computation drills unless the student has developed an efficient
strategy for the facts included in the drill (Van de Walle & Lovin, Teaching Student-Centered Mathematics
Grades K-3, pg. 117). Drill can strengthen strategies with which students feel comfortable – ones they
“own” – and will help to make these strategies increasingly automatic. Therefore, drill of strategies will
allow students to use them with increased efficiency, even to the point of recalling the fact without being
conscious of using a strategy. Drill without an efficient strategy present offers no assistance (Van de
Walle & Lovin, Teaching Student-Centered Mathematics Grades K-3, pg. 117).
CAUTIONS
Sometimes teachers use games solely to practice number facts. These games usually do not engage
children for long because they are based on students’ recall or memorization of facts. Some students are
quick to memorize, while others need a few moments to use a related fact to compute. When students
are placed in situations in which recall speed determines success, they may infer that being “smart”
in mathematics means getting the correct answer quickly instead of valuing the process of thinking.
Consequently, students may feel incompetent when they use number patterns or related facts to arrive at
a solution and may begin to dislike mathematics because they are not fast enough.
in arithmetic computation, they
must have efficient and accurate
methods that are supported by
an understanding of numbers and
operations. “Standard” algorithms
for arithmetic computation are one
means of achieving this fluency.
– N
CTM, Principles and Standards
for School Mathematics, pg. 35
Overemphasizing fast fact recall
at the expense of problem solving
and conceptual experiences gives
students a distorted idea of the
nature of mathematics and of their
– S
eeley, Faster Isn’t Smarter:
Teaching, and Learning in the
21st Century, pg. 95
Computational fluency refers to
having efficient and accurate
methods for computing. Students
exhibit computational fluency
when they demonstrate flexibility
in the computational methods they
choose, understand and can explain
these methods, and produce
– NCTM, Principles and Standards
for School Mathematics, pg. 152
Fluency refers to having efficient,
accurate, and generalizable methods
(algorithms) for computing that are
based on well-understood properties
and number relationships.
– N
CTM, Principles and Standards
for School Mathematics, pg. 144
i
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
INTRODUCE A GAME
A good way to introduce a game to the class is for the teacher to play the game against the class. After briefly explaining the rules,
ask students to make the class’s next move. Teachers may also want to model their strategy by talking aloud for students to hear
his/her thinking. “I placed my game marker on 6 because that would give me the largest number.”
Games are fun and can create a context for developing students’ mathematical reasoning. Through playing and analyzing games,
students also develop their computational fluency by examining more efficient strategies and discussing relationships among
numbers. Teachers can create opportunities for students to explore mathematical ideas by planning questions that prompt
students to reflect about their reasoning and make predictions. Remember to always vary or modify the game to meet the needs of
your leaners. Encourage the use of the Standards for Mathematical Practice.
HOLDING STUDENTS ACCOUNTABLE
While playing games, have students record mathematical equations or representations of the mathematical tasks. This provides
data for students and teachers to revisit to examine their mathematical understanding.
After playing a game, have students reflect on the game by asking them to discuss questions orally or write about them in a
mathematics notebook or journal:
1. What skill did you review and practice?
2.What strategies did you use while playing the game?
3.I f you were to play the game a second time, what different strategies would you use to be more successful?
4.How could you tweak or modify the game to make it more challenging?
A Special Thank-You
The development of the NC Department of Public Instruction Document, Building Conceptual Understanding and Fluency Through
Games was a collaborative effort with a diverse group of dynamic teachers, coaches, administrators, and NCDPI staff. We are
very appreciative of all of the time, support, ideas, and suggestions made in an effort to provide North Carolina with quality support
materials for elementary level students and teachers. The North Carolina Department of Public Instruction appreciates any
suggestions and feedback, which will help improve upon this resource. Please send all correspondence to Kitty Rutherford
([email protected]) or Denise Schulz ([email protected])
GAME DESIGN TEAM
The Game Design Team led the work of creating this support document. With support of their school and district, they volunteered
their time and effort to develop Building Conceptual Understanding and Fluency Through Games.
Erin Balga, Math Coach, Charlotte-Mecklenburg Schools
Kitty Rutherford, NCDPI Elementary Consultant
Robin Beaman, First Grade Teacher, Lenoir County
Denise Schulz, NCDPI Elementary Consultant
Emily Brown, Math Coach, Thomasville City Schools
Allison Eargle, NCDPI Graphic Designer
Leanne Barefoot Daughtry, District Office, Johnston County
Renée E. McHugh, NCDPI Graphic Designer
Ryan Dougherty, District Office, Union County
Paula Gambill, First Grade Teacher, Hickory City Schools
Tami Harsh, Fifth Grade teacher, Currituck County
Patty Jordan, Instructional Resource Teacher, Wake County
Tania Rollins, Math Coach, Ashe County
Natasha Rubin, Fifth Grade Teacher, Vance County
Dorothie Willson, Kindergarten Teacher, Jackson County
ii
1. Developing understanding of multiplication and division and strategies for
multiplication and division within 100 – Students develop an understanding
of the meanings of multiplication and division of whole numbers through
activities and problems involving equal-sized groups, arrays, and area
models; multiplication is finding an unknown product, and division is finding
an unknown factor in these situations. For equal-sized group situations,
division can require finding the unknown number of groups or the unknown
group size. Students use properties of operations to calculate products of
whole numbers, using increasingly sophisticated strategies based on these
properties to solve multiplication and division problems involving single-digit
factors. By comparing a variety of solution strategies, students learn the
relationship between multiplication and division.
2. Developing understanding of fractions, especially unit fractions (fractions
with numerator 1) – Students develop an understanding of fractions,
beginning with unit fractions. Students view fractions in general as being built
out of unit fractions, and they use fractions along with visual fraction models
to represent parts of a whole. Students understand that the size of a fractional
part is relative to the size of the whole. For example, 1/2 of the paint in a small
bucket could be less paint than 1/3 of the paint in a larger bucket; but 1/3 of
a ribbon is longer than 1/5 of the same ribbon because when the ribbon is
divided into 3 equal parts, the parts are longer than when the ribbon is divided
into 5 equal parts. Students are able to use fractions to represent numbers
equal to, less than, and greater than one. They solve problems that involve
comparing fractions by using visual fraction models and strategies based on
noticing equal numerators or denominators.
OPERATIONS AND ALGEBRAIC THINKING
Represent and solve problems involving multiplication and division.
3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total
number of objects in 5 groups of 7 objects each. For example, describe
a context in which a total number of objects can be expressed as 5 × 7.
3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret
56 ÷ 8 as the number of objects in each share when 56 objects are
partitioned equally into 8 shares, or as a number of shares when
56 objects are partitioned into equal shares of 8 objects each. For
example, describe a context in which a number of shares or a
number of groups can be expressed as 56 ÷ 8.
3.OA.3 Use multiplication and division within 100 to solve word problems in
situations involving equal groups, arrays, and measurement quantities,
e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem. (Note: See Glossary, Table 2.)
3.OA.4 Determine the unknown whole number in a multiplication or division
equation relating three whole numbers. For example, determine
the unknown number that makes the equation true in each of the
equations 8 × ? = 48, 5 = o ÷ 3, 6 × 6 = ?.
Understand properties of multiplication and the relationship between
multiplication and division.
3.OA.5 Apply properties of operations as strategies to multiply and divide. (Note:
Students need not use formal terms for these properties.) Examples: If
6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property
of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30,
or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)
Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) =
(8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
3.OA.6 Understand division as an unknown-factor problem. For example,
find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Multiply and divide within 100.
3.OA.7 F luently multiply and divide within 100, using strategies such as the
relationship between multiplication and division (e.g., knowing that 8
× 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end
3. Developing understanding of the structure of rectangular arrays and
of area – Students recognize area as an attribute of two-dimensional
regions. They measure the area of a shape by finding the total number
of same-size units of area required to cover the shape without gaps
or overlaps, a square with sides of unit length being the standard
unit for measuring area. Students understand that rectangular arrays
can be decomposed into identical rows or into identical columns. By
decomposing rectangles into rectangular arrays of squares, students
connect area to multiplication, and justify using multiplication to determine
the area of a rectangle.
4. Describing and analyzing two-dimensional shapes – Students describe,
analyze, and compare properties of two-dimensional shapes. They compare
and classify shapes by their sides and angles, and connect these with
definitions of shapes. Students also relate their fraction work to geometry by
expressing the area of part of a shape as a unit fraction of the whole.
MATHEMATICAL PRACTICES
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Solve problems involving the four operations, and identify and explain
patterns in arithmetic.
3.OA.8 Solve two-step word problems using the four operations. Represent
these problems using equations with a letter standing for the
unknown quantity. Assess the reasonableness of answers using
mental computation and estimation strategies including rounding.
(Note: This standard is limited to problems posed with whole
numbers and having whole-number answers; students should know
how to perform operations in the conventional order when there are
no parentheses to specify a particular order – Order of Operations.)
3.OA.9 Identify arithmetic patterns (including patterns in the addition
table or multiplication table), and explain them using properties of
operations. For example, observe that 4 times a number is always
even, and explain why 4 times a number can be decomposed into
NUMBER AND OPERATIONS IN BASE TEN
Use place value understanding and properties of operations to perform
multi-digit arithmetic. (Note: A range of algorithms may be used.)
3.NBT.1 Use place value understanding to round whole numbers to the
nearest 10 or 100.
3.NBT.2 Fluently add and subtract within 1000 using strategies and
algorithms based on place value, properties of operations, and/or
the relationship between addition and subtraction.
3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range
10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and
properties of operations.
NUMBER AND OPERATIONS - FRACTIONS
Note: Grade 3 expectations in this domain are limited to fractions with
denominators 2, 3, 4, 6, and 8.
Develop understanding of fractions as numbers.
3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a
whole is partitioned into b equal parts; understand a fraction a/b as
the quantity formed by a parts of size 1/b.
3.NF.2 U
nderstand a fraction as a number on the number line; represent
fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by defining the
interval from 0 to 1 as the whole and partitioning it into b equal
parts. Recognize that each part has size 1/b and that the endpoint
of the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a
lengths 1/b from 0. Recognize that the resulting interval has size a/b
and that its endpoint locates the number a/b on the number line.
3.NF.3 Explain equivalence of fractions in special cases, and compare
fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same
size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4,
4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a
visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that
are equivalent to whole numbers. Examples: Express 3 in the form 3
= 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a
number line diagram.
d. Compare two fractions with the same numerator or the same
denominator by reasoning about their size. Recognize that
comparisons are valid only when the two fractions refer to the same
whole. Record the results of comparisons with the symbols >, =, or <,
and justify the conclusions, e.g., by using a visual fraction model.
MEASUREMENT AND DATA
Solve problems involving measurement and estimation of intervals of
time, liquid volumes, and masses of objects.
3.MD.1 Tell and write time to the nearest minute and measure time intervals
in minutes. Solve word problems involving addition and subtraction
of time intervals in minutes, e.g., by representing the problem on a
number line diagram.
3.MD.2 Measure and estimate liquid volumes and masses of objects using
standard units of grams (g), kilograms (kg), and liters (l). (Note:
Excludes compound units such as cm3 and finding the geometric
volume of a container.) Add, subtract, multiply, or divide to solve
one-step word problems involving masses or volumes that are given
in the same units, e.g., by using drawings (such as a beaker with
a measurement scale) to represent the problem. (Note: Excludes
multiplicative comparison problems – problems involving notions of
“times as much”; see Glossary, Table 2.)
Represent and interpret data.
3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent
a data set with several categories. Solve one- and two-step “how
many more” and “how many less” problems using information
presented in scaled bar graphs. For example, draw a bar graph in
which each square in the bar graph might represent 5 pets.
3.MD.4 Generate measurement data by measuring lengths using rulers
marked with halves and fourths of an inch. Show the data by making
a line plot, where the horizontal scale is marked off in appropriate
units – whole numbers, halves, or quarters.
Geometric measurement: understand concepts of area and relate area to
3.MD.5 Recognize area as an attribute of plane figures and understand
concepts of area measurement.
a. A square with side length 1 unit, called “a unit square,” is said to
have “one square unit” of area, and can be used to measure area.
b. A plane figure which can be covered without gaps or overlaps by
n unit squares is said to have an area of n square units.
3.MD.6 Measure areas by counting unit squares (square cm, square m,
square in, square ft, and improvised units).
3.MD.7 Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by
tiling it, and show that the area is the same as would be found by
multiplying the side lengths.
b. Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world and
mathematical problems, and represent whole-number products as
rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle
with whole-number side lengths a and b + c is the sum of a × b
and a × c. Use area models to represent the distributive property
in mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear figures by
decomposing them into non-overlapping rectangles and adding
the areas of the non-overlapping parts, applying this technique to
solve real world problems.
Geometric measurement: recognize perimeter as an attribute of plane
figures and distinguish between linear and area measures.
3.MD.8 Solve real world and mathematical problems involving perimeters
of polygons, including finding the perimeter given the side lengths,
finding an unknown side length, and exhibiting rectangles with
the same perimeter and different areas or with the same area and
different perimeters.
GEOMETRY
Reason with shapes and their attributes.
3.G.1 Understand that shapes in different categories (e.g., rhombuses,
rectangles, and others) may share attributes (e.g., having four sides),
and that the shared attributes can define a larger category
(e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares
that do not belong to any of these subcategories.
3.G.2 Partition shapes into parts with equal areas. Express the area of each
part as a unit fraction of the whole. For example, partition a shape into
4 parts with equal area, and describe the area of each part as 1/4 of
the area of the shape.
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Operations and Algebraic Thinking
Double Up! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tic-Tac-Toe Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Snakes Alive, Go for Fives!!. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Raging Rectangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiple Madness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiple Madness II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
No Leftovers Wanted! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Whose Winning Products?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Murphy to Manteo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Operation Match-Up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Find the Unknown Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Charlotte Speedway Race. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Division Duel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Four Quotients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Race to the Resort. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.OA.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.OA.1 and 3.OA.7. . . . . . . . . . . . . . . . . . . . . . 4
3.OA.1 and 3.OA.7. . . . . . . . . . . . . . . . . . . . . . 7
3.OA.1, 3.OA.7 and 3.MD.7. . . . . . . . . . . . . . . 8
3.OA.1 and 3.OA.7. . . . . . . . . . . . . . . . . . . . . . 9
3.OA.1 and 3.OA.7. . . . . . . . . . . . . . . . . . . . . 10
3.OA.1 and 3.OA.7. . . . . . . . . . . . . . . . . . . . . 11
3.OA.1 and 3.OA.7. . . . . . . . . . . . . . . . . . . . . 12
3.OA.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.OA.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.OA.4 and 3.OA.6. . . . . . . . . . . . . . . . . . . . . 24
3. OA.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3. OA.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3. OA.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3. OA.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Number and Operations in Base Ten
The Big “Z”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Corn Shucks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rounding to the Tens/Hundreds Showdown. . . . . . . . . . . . . . . . . . . . . . . . . . .
Take Your Places! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Close Enough. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Money Wheel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Race to 300. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.NBT.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.NBT.2 and 3.NBT.3. . . . . . . . . . . . . . . . . . . 49
3.NBT.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Number and Operations – Fractions
Fraction Match-Up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fraction Roll’Em. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figuring Fourths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Three in a Row Gameboard. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figure Eighths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
“I Have” Fraction Cards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Number Line Madness! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Capturing Hexagons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Snail Nim. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.NF.1 and 3.NF.2. . . . . . . . . . . . . . . . . . . . . . 53
3.NF.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.NF.1 and 3.NF.3. . . . . . . . . . . . . . . . . . . . . . 58
3.NF.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.NF.1 and 3.NF.3. . . . . . . . . . . . . . . . . . . . . . 62
3.NF.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.NF.2 and 3.NF.3. . . . . . . . . . . . . . . . . . . . . . 65
3.NF.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.NF.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Measurement and Data
Race to Midnight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Metric Measure Up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Raging Rectangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cut a Rug. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.MD.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.MD.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.OA.1, 3.OA.7 and 3.MD.7. . . . . . . . . . . . . . . 8
3.MD.7 and 3.MD.8. . . . . . . . . . . . . . . . . . . . 77
1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Geometry
Geo-Matchup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.G.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
REVIEW
Spin and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Online Games for Each Category
Math Basketball. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Estimate Whole Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Helipad Hops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rounding to the Nearest 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rounding to the Nearest 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Match Up Defense Basic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Match Up Defense Advanced. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fractions Shoot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Find Grampy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fraction Track. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fraction Track 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tony’s Fraction Pizza Shop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Willy the Watch Dog. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hickory Clock. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Elapsed Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Line Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.OA.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.NBT.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.NF.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.NF.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.NF.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.NF.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.NF.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.MD.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.MD.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.MD.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.MD.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2
3.OA.1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Double Up!
Building Fluency: multiply within 100
Materials: gameboard, spinner (paper clip and pencil),
8 game markers - different color for each player
7
4
9
•
8
Operations and Algebraic Thinking
6
12
Variation/Extension: Students create their own spinner game
with products, an example might be having players spin two
factors and multiply and cover the products on the board.
25
Directions:
1.Spin and double the number (multiply by 2)
2.Cover the product on the gameboard.
3.If the spinner lands on a line, spin again.
4.The first player to cover three products in a row wins.
11
Number of Players: 2
3
8
18
12
14
16
16
50
8
50
18
22
14
22
12
24
8
24
12
18
16
50
18
14
24
22
DOUBLE UP! CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
4
Operations and Algebraic Thinking • 3.OA.1 and 3.OA.7 & Measurement and Data • 3.MD.7
GRADE 3 • BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Tic-Tac-Toe Array
Building Fluency: products of whole numbers and their relationship to rectangular arrays
Materials: gameboard, pile of centimeter cubes (at least 20), 5 game markers - different color for each player, a spinner (your choice)
Number of Players: 2
Directions:
1.Players take turns spinning the spinner. The player takes the number of cubes shown on the spinner.
2.The player uses the cubes to build one of the rectangles shown on the gameboard & says the equation used to build the rectangle.
3.The player puts the cubes back in the pile and places a marker on the rectangle.
4.The winner is the first player to have three markers in a row.
Variation/Extension: Player may win by being the first to cover four adjacent rectangles to form a box. Use the second spinner.
Player will multiply and use those dimensions to make the rectangle.
5
TIC-TAC-TOE ARRAY CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
20
16
9
4
15
12
8
18
10
4
4
x5
x
4
2 3 x4
3x5 3x3
2x
2x
Variation #2
Spinner
6
4
3x 6
2
x
5
Operations and Algebraic Thinking
•
3.OA.1 and 3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Sakes Alive, Go For Fives!!
Building Fluency: multiply within 100
Materials: gameboard, pair of dice, 20 game markers - different color for each player
Number of Players: 2 or 3
Directions:
1.Players take turns rolling dice. Player covers the product or the two factors with game markers.
2.If the player is not able to cover a number, the turn is lost.
3.The first player to cover five squares in a row, vertically, horizontally, or diagonally wins the game.
Variation/Extension: Play a “doubles” variation. When a player cannot play the factors or the product, they may play a double of
the product. Example: Player rolls 2 and 5. 10 is not available. Player calls “double” and covers the 20.
24
5
16
3
18
2
20 12
4
4
8
6
12
4
3
25
5
8
18
1
36
4
30
5
24
3
2
12
18
2
5
16
6
1
9
4
25
3
2
20
4
5
3
8
25
5
9
1
15
5
18
6
12
1
8
3
5
4
24
3
2
24
6
2
30 25
6
2
8
4
9
3
15
1
9
18
3
6
24 36
20
7
Operations and Algebraic Thinking • 3.OA.1 & 3.OA.7 and Measurement and Data • 3.MD.7
GRADE 3 • BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
8
Raging Rectangles
Building Fluency: products of whole numbers and their relationship to rectangular arrays; relate area to operations of multiplication
Materials: gameboard, pair of dice, 1 crayon - different color per player
Number of Players: 2
Directions:
1.Each player takes a turn rolling the dice to get two factors.
2.The player outlines and colors a rectangle on the gameboard to match the pair of factors. Example: a roll of 6 and 3 is colored as a 6 x 3 rectangle or a 3 x 6 rectangle.
3.The player writes the equation (area) inside the rectangle.
4.A player loses a turn when the rectangle cannot be drawn on the gameboard.
5.The winner is the player with the most area colored.
Variation/Extension: Students can add the two numbers on the dice for the first factor and then use 2, 5 or 10 as the second factor.
Operations and Algebraic Thinking
•
3.OA.1 and 3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Building Fluency: multiply within 100
Materials: gameboard, 8 game markers – different color for each player, 2 paperclips
Number of Players: 2
Directions:
1.The first player places the two paperclips on any factors at the bottom of the page. Both paperclips may be on the same factor.
2.The player covers the product of the two factors with a game marker.
3.The second player moves one of the paperclips then places a game marker on the new product.
4.Players alternate moving a paperclip and marking a product.
5.The winner is the first to cover four products in a row.
Variation/Extension: Multiple Madness II is a variation
1
2
3
4
5
6
8
9
10
12
15
16
20
25
1
2
3
4
5
6
8
9
10
12
15
16
20
25
1
2
3
4
5
6
8
1 2 3 4 5
10
FACTORS:
9
Operations and Algebraic Thinking
•
3.OA.1 and 3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
10
Building Fluency: products of whole numbers
Materials: gameboard, 8 game markers – different color for each player, 2 paperclips
Number of Players: 2
Directions:
1.The first player places the two paperclips on any factors at the bottom of the page. Both paperclips may be on the same factor.
2.The player covers the product of the two factors with a game marker.
3.The second player moves one of the paperclips and places a game marker on the new product.
4.Players alternate moving a paperclip and marking a product.
5.The winner is the first to cover four products in a row.
Variation/Extension: Multiple Madness is a variation
1
2
3
4
5
6
7
8
9
10
12
14
15
16
18
20
21
24
25
27
28
30
32
35
36
40
42
45
48
49
54
FACTORS:
56 63 64 72 81
1 2 3 4 5 6 7 8 9
Operations and Algebraic Thinking
•
3.OA.1 and 3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
No Leftovers Wanted!
20
9
8
12
Materials: gameboard, a die, spinner (pencil and paperclip),
21 color tiles, cubes, or counters
10
21
Building Fluency: products of whole numbers and their relationship
to rectangular arrays
18
6
Variation/Extension: Use the area or number of blocks used in
the array to be the score. Use the area or number of blocks used
in the array minus the leftovers to be the score.
15
Directions:
1.Player spins the spinner and takes that number
of counters.
2.Player rolls the die to see how many equal rows
will be in the array. Then the player builds the array.
3.The number of counters in one row is the player’s score.
The player’s score is doubled if there are no leftovers.
4.Players record their score after each turn.
5.The winner has the highest score after six rounds.
14
Number of Players: 2
PLAYER 1
Turn # of Counters
# of Equal Rows
# in Each Row
# of Leftovers
Score
# of Equal Rows
# in Each Row
# of Leftovers
Score
1
2
3
4
5
6
PLAYER 2
Turn # of Counters
1
2
3
4
5
6
11
Operations and Algebraic Thinking
•
3.OA.1 and 3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
12
Whose Winning Products?
Building Fluency: multiply within 100
Materials: gameboard for each player, spinners (pencil and paper clip), 25 game markers for each player
Number of Players: any number
Directions:
1.Each player completes their gameboard with possible products.
2.Player 1 spins the spinners to find two factors.
3.Find the product and place game marker on the square on the gameboard.
4.In turn, each player spins and multiplies.
5.All players cover the product if it appears on their gameboards.
6.First player to cover 5 in any direction wins.
Variation/Extension: This could be played with a larger group using a document camera. Place the spinner under the document camera
and let players take turns spinning and multiplying.
6
1
5
0
2
4
5
3
9
3
8
10
6
7
7
4
WHOSE WINNING PRODUCTS? CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
13
Operations and Algebraic Thinking
•
3.OA.2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Murphy to Manteo
Building Fluency: fluently divide within 100
Materials: gameboard, a die, game marker
Number of Players: 2
Directions:
1.Players take turns rolling the die to determine how many spaces to move.
2.Player must give the correct answer in each block before moving forward. If an error is made, the player returns to the starting place for that turn.
3.The first player who crosses the state and gets to Manteo wins.
Variation/Extension: If a player misses a question, the other player may answer it correctly and receive a pass for the next
penalty space (go back or lose a turn). For some students, teachers may want to provide a division chart or a calculator to
14
START AT
MURPHY
Lose a
Turn
54÷6
90÷9
6÷1
9÷3
42÷6
12÷3
18÷6
8÷1
16÷8
56÷7
Go Back
5 Spaces
4÷4
Lose a
Turn
63÷7
42÷7
28÷4
48÷8
21÷7
Go Back
6 Spaces
15÷3
27÷9
16÷4
24÷3
5÷5
32÷4
40÷8
36÷6
27÷3
•
54÷9
8÷2
45÷9
36÷4
48÷6
42÷7
MANTEO
YOU WIN!!
30÷6
40÷5
81÷9
64÷8
72÷8
49÷7
56÷8
Go Back
3 Spaces
Murphy to Manteo
MURPHY TO MANTEO CONTINUED, PAGE 2
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
15
Operations and Algebraic Thinking
•
3.OA.4, 3.OA.6 and 3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Out of this World Operations!
Building Fluency: addition, subtraction, multiplication and division
Materials: an operation card per player, and a set of game cards
Number of Players: 4
Directions:
1.Each of the 4 players chooses an operation card.
2.Each player takes turn selecting and reading the game cards.
3.The player with the correct operation to solve the equation takes the card and records it on their recording sheet.
4.The first player to record and collect 10 cards wins.
Variation/Extension: Once students understand the game then they can record they work in their math notebook. This could be
played with 1 or 2 players as a sorting game.
Equation
OPERATION CARD SUBTRACTION (-)
Equation
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
OPERATION CARD MULTIPLICATION (x)
Equation
OPERATION CARD DIVISION (÷)
Equation
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
16
OUT OF THIS WORLD OPERATIONS! CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
x
+
–
48 ? 6 = 8
8 ? 4 = 32
÷
6 ? 8 = 48
8?6=2
3 ? 8 = 24
8 ? 4 = 12
7?7=0
8?4=4
7 ? 7 = 14
7 ? 7 = 49
8?1=8
16 ? 2 = 8
8 ? 2 = 16
8?1=9
17
OUT OF THIS WORLD OPERATIONS! CONTINUED, PAGE 3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
5 ? 4 = 20
6 ? 2 = 12
6 ? 8 = 14
6?2=8
6?2 =4
32 ? 4 = 8
36 ? 6 = 6
6 ? 6 = 12
8?8=0
6?6=0
24 ? 6 = 4
8?8=1
21 ? 3 = 7
5?4=9
5?4=1
8?7=1
6 ? 2 = 12
20 ? 5 = 4
18
OUT OF THIS WORLD OPERATIONS! CONTINUED, PAGE 4
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
7 ? 3 = 21
8 ? 7 = 15
56 ? 8 = 7
7?4=3
7 ? 3 = 10
8 ? 7 = 15
9?8=1
8 ? 9 = 17
9?2=7
2 ? 9 = 18
9?4 =5
8 ? 9 = 72
8 ? 7 = 56
6?6=1
4?6=2
18 ? 2 = 9
6 ? 4 = 10
6?4=2
19
OUT OF THIS WORLD OPERATIONS! CONTINUED, PAGE 5
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
12 ? 2 = 6
6 ? 6 = 36
9 ? 5 = 14
9?7=2
45 ? 9 = 5
7?2=9
7?2 =5
6 ? 5 = 30
6?5=1
6 ? 5 = 11
30 ? 6 = 5
6?3=3
5?5=0
5 ? 5 = 25
5 ? 3 = 15
25 ? 5 = 5
5 ? 5 = 10
18 ? 3 = 6
20
OUT OF THIS WORLD OPERATIONS! CONTINUED, PAGE 6
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
2 ? 9 = 11
9 ? 4 = 13
72 ? 9 = 8
9 ? 7 = 16
5 ? 9 = 45
9?5=4
63 ? 7 = 9
5?3=8
9 ? 7 = 63
7 ? 2 = 14
6?3=9
49 ? 7 = 7
14 ? 2 = 7
6 ? 7 = 42
6 ? 7 = 13
15 ? 3 = 5
42 ? 6 = 7
7?6=1
21
OUT OF THIS WORLD OPERATIONS! CONTINUED, PAGE 7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
8?5=3
7 ? 5 = 12
42 ? 6 = 7
40 ? 8 = 5
8?3=5
3 ? 8 = 11
8?2=6
8 ? 2 = 10
5 ? 8 = 13
5 ? 8 = 40
24 ? 3 = 8
9?6=3
8 ? 8 = 16
6 ? 9 = 15
36 ? 9 = 4
54 ? 9 = 6
8?8=0
4 ? 9 = 36
22
OUT OF THIS WORLD OPERATIONS! CONTINUED, PAGE 8
6 ? 9 = 54
8?8=1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
7?7 =1
7 ? 5 = 35
23
Operations and Algebraic Thinking
•
3.OA.4 and 3.OA.6
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
24
Find the Unknown Number
Building Fluency: understand division as an unknown factor problem
Materials: a recording sheet for each player, unknown number game cards
Number of Players: 2
Directions:
1.Spread out the missing number game cards.
2.Players take turns picking a card and telling the unknown number.
3.The player keeps all cards correctly answered & writes the equation as both a multiplication & division equation on their recording sheet.
Example: 4 x 7 = 28; 28 ÷ 4 = 7
4.If the player answers incorrectly, the card is placed back in the pile.
5.Play until all cards are picked and the player with the most cards wins.
Variation/Extension: When a player misses a question, the other player may answer correctly and keep the card. This game could be
played by an individual just picking and recording equations. A multiplication chart may be needed to solve any disagreements.
PLAYER 1
Multiplication
PLAYER 2
Division
Multiplication
Division
1.
1.
1.
1.
2.
2.
2.
2.
3.
3.
3.
3.
4.
4.
4.
4.
5.
5.
5.
5.
6.
6.
6.
6.
7.
7.
7.
7.
8.
8.
8.
8.
9.
9.
9.
9.
10.
10.
10.
10.
1 x ___ = 2
2 x ____ = 4
3 x ___ = 6
4 x ___ = 8
1 x __ = 3
2 x ____ = 6
3 x ___ = 9
4 x ___ = 12
1 x ___ = 4
2 x ____ = 8
3 x ___ = 12
4 x ___ = 16
1 x ___ = 5
2 x ____ = 10
3 x ___ = 15
4 x ___ = 20
FIND THE MISSING NUMBER CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
25
5 x ___ = 10
1 x ____ = 6
2 x___ = 12
3 x ___ = 18
5 x ___ = 15
1 x ____ = 7
2 x ___ = 14
3 x ___ = 21
5 x ___ = 20
1 x ____ = 8
2 x ___ = 16
3 x ___= 24
5 x ___ = 25
1 x ____ = 9
2 x ___ = 18
3 x ___= 27
FIND THE MISSING NUMBER CONTINUED, PAGE 3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
26
6 x ___ = 12
7x ___ = 14
4 x ___ = 24
5 x ___ = 30
6 x ___ = 18
5 x ___= 50
4 x ___ = 28
5 x ___ = 35
3 x ___= 30
4 x ___= 40
4 x ___= 32
5 x ___= 40
1 x ____ = 10
2 x ____ = 20
4 x ___= 36
5 x ___= 45
FIND THE MISSING NUMBER CONTINUED, PAGE 4
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
27
7 x ___ = 49
8 x ___ = 56
9 x ___ = 63
10x ___ = 70
7 x ___= 56
8 x ___= 64
9 x ___= 72
10x ___= 80
7 x ___= 63
8 x ___= 72
9 x ___= 81
10 x ___= 90
7 x ___= 70
8 x ___= 80
9 x ___= 90
10 x ___= 100
FIND THE MISSING NUMBER CONTINUED, PAGE 5
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
28
7 x ___ = 21
8 x ___ = 24
9 x ___ = 27
10x ___ = 30
7 x ___ = 28
8 x ___ = 32
9 x ___ = 36
10 x ___ = 40
7 x ___ = 35
8 x ___ = 40
9 x ___ = 45
10x ___ = 50
7 x ___ = 42
8 x ___ = 48
9 x ___ = 54
10 x ___ = 60
FIND THE MISSING NUMBER CONTINUED, PAGE 6
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
29
6 x ___ = 42
6 x ___ = 24
8x ___ = 16
9x ___ = 18
6 x ___= 48
6 x ___ = 30
10x ___ = 20
6 x ___= 60
6 x ___= 54
6 x ___ = 36
FIND THE MISSING NUMBER CONTINUED, PAGE 7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
30
Operations and Algebraic Thinking
•
3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Charlotte Speedway Race
1
3
Building Fluency: fluently multiply within 100
Materials: gameboard, spinner (paperclip and pencil), game markers
Number of Players: 2
3 1
Variation/Extension: A player may tell a second factor pair to
make that product and move an extra space.
FINISH
24 25 15 30 18 20
60 6
Trouble on
the Curve –
Go Back
2 Spaces
35
10 15 20 16
Stop for
Gas – Lose
a Turn
START
0
55
14
2
PIT
STOP
2
2
Directions:
1.Each player takes a turn and spins the spinner.
2.Move the number of spaces shown on the spinner.
3.Player must give a multiplication fact for the product
in the space using 2 or 5 as one of the factors.
4.If an incorrect answer is given, the player loses the
turn and returns to the previous position.
5.The winner is the first to cross the finish line.
31
45 12 4
30
Car Stalls –
Lose a Turn
Blows Out –
Lose a Turn
50
35 40 8 18
Operations and Algebraic Thinking
•
3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Division Duel
Building Fluency: division within 100
Materials: gameboard, division cards, game markers (small cube)
Number of Players: 2
Directions:
1.Place the cards face down in the center of the gameboard.
2.Each player takes a card from the stack and answers the problem.
3.The winner of the round is the player whose answer is the larger number.
4.The winner places the marker on the number grid at the bottom of the gameboard and moves the marker each time a point is scored.
5.The champion is the first player to win 14 rounds.
Variation/Extension: Students could make card sets with the division facts they most need to work on.
Place Division
Cards Face
Down Here
PLAYER 1
PLAYER 2
1
2
3
4
5
6
7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
8
9
10
11
12
13
14
32
DIVISION DUEL CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
____
8 ) 48
____
8 ) 24
____
6 ) 36
____
4 ) 32
____
6 ) 42
____
9 ) 63
____
3 ) 24
____
7 ) 35
____
9 ) 81
____
9 ) 36
____
8 ) 72
____
5 ) 30
____
9 ) 54
____
8 ) 56
____
5 ) 40
____
9 ) 27
____
8 ) 40
____
6 ) 48
33
DIVISION DUEL CONTINUED, PAGE 3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
____
6 ) 54
____
6 ) 24
____
9 ) 45
____
6 ) 30
____
7 ) 56
____
7 ) 28
____
4 ) 24
____
8 ) 64
____
8 ) 32
____
7 ) 49
____
5 ) 35
____
7 ) 42
____
4 ) 28
____
9 ) 72
____
4 ) 36
____
7 ) 63
____
3 ) 27
____
5 ) 45
34
Operations and Algebraic Thinking
•
3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Four Quotients
Building Fluency: division within 100
Materials: gameboard, pair of dice, division grid, 15 game markers - different color for each player,
Number of Players: 2
Directions:
1.Player rolls the pair of dice and locates the spaces on the grid named by them.
Example: A roll of a 3 and a 5 could be space (3,5) or space (5,3).
2.The player answers the division problem and places a game marker on that number on the gameboard.
3.The first player to get 4 spaces in a row is the winner.
Variation/Extension: Players could pick a space on the gameboard and give a division fact to match it in order to place a marker on
the board. Example: I pick 7. 42÷6 = 7. The winner could fill an entire row.
1
2
3
4
5
6
1
____
8 ) 48
____
8 ) 24
____
6 ) 36
____
6 ) 54
____
6 ) 24
____
9 ) 45
2
____
4 ) 32
____
6 ) 42
____
9 ) 63
____
6 ) 30
____
7 ) 56
____
7 ) 28
3
____
3 ) 24
____
7 ) 35
____
9 ) 81
____
4 ) 24
____
8 ) 64
____
8 ) 32
4
____
9 ) 36
____
8 ) 72
____
5 ) 30
____
7 ) 49
____
5 ) 35
____
7 ) 42
5
____
9 ) 54
____
8 ) 56
____
5 ) 40
____
4 ) 28
____
9 ) 72
____
4 ) 36
6
____
9 ) 27
____
8 ) 40
____
6 ) 48
____
7 ) 63
____
3 ) 27
____
5 ) 45
35
FOUR QUOTIENTS ONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Four Quotients
9
3
6
5
9
4
4
9
5
5
6
7
7
8
7
9
3
6
6
9
6
4
5
3
3
8
5
7
9
4
8
9
4
5
3
7
36
Operations and Algebraic Thinking
•
3.OA.7
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Race to the Resort
37
START
____
6 ) 42
Building Fluency: division within 100
Materials: a die, gameboard, a game marker – different color for each player
Number of Players: 2
Directions:
1.Players take turns rolling a die and move that many spaces answering all of the facts
along the way. If the player misses a fact, the player returns to the previous position.
2.If a player lands on the same space as the other player, the other player goes back
to the beginning. The winner is the first to finish the game.
Variation/Extension: If a player misses an equation, the other player may answer it correctly
and receive a pass for the next time they land on a penalty space.
____
3 ) 36
____
7 ) 49
64 ÷ 8
48 ÷ 6
49 ÷ 7
64 ÷ 4
No Wind:
Move Back
3 Spaces
54 ÷ 9
____
5 ) 35
____
6 ) 30
36 ÷ 9
20 ÷ 5
Bonus:
1 Space
56 ÷ 8
____
5 ) 25
____
4 ) 36
Stormy Seas:
Move Back
2 Spaces
____
6 ) 42
24 ÷ 4
48 ÷ 8
____
3 ) 15
24 ÷ 8
____
9 ) 81
____
6 ) 18
_____
10 ) 100
____
4 ) 32
Out of Gas:
Lose a Turn
____
4 ) 28
YOU WIN!!
Low on Fuel:
Lose a Turn
____
9 ) 72
____
8 ) 72
Ship Ran
Aground:
Move Back
3 Spaces
Flat Tire:
Lose a Turn
16 ÷ 4
Number and Operations in Base Ten
•
3.NBT.1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
38
The Big “Z”
Building Fluency: place value and rounding to nearest 10 and 100
Materials: gameboard, a die, game marker, scrap paper and pencil
Number of Players: 2-4
Directions:
1.A player rolls the die and moves one space vertically, horizontally, or diagonally to any space that contains the number on the die.
2.Points are determined by the value of the number and records on scrap paper. Example: Player is on 542 and rolls a 6. If the player moves to 461, the score is 60. If the player moves to 625, the score is 600.
3.Players total their scores on paper and at the end of the game, player with the highest score wins.
Variation/Extension: Players roll the die and travel that many spaces. If the number of the die is even (2, 4, 6) the player rounds the number
in the space landed on to the nearest 10. If the number on the die is odd (1, 3, 5), the player rounds the number to the nearest hundred.
342
423
364
132
453
361
534
234
536
425
241
421
613
362
625
461
653
423
362
425
241
542
124
315
532
641
253
364
453
265
154
635
126
241
643
435
514
243
532
356
643
351
436
324
413
534
165
513
234
652
143
365
413
243
351
146
425
651
543
564
136
562
251
536
425
264
132
653
351
413
624
Number and Operations in Base Ten
•
REVIEW
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
39
Corn Shucks
Building Fluency: review place value - compare multi-digit numbers
Materials: recording sheet, digit cards (or 0-9 die)
Number of Players: 2-4
Directions:
1.The first player selects 4 digit cards and makes the largest possible four-digit number with those digits.
Example: cards show these digits: 6, 4, 3, 3, this order makes the largest possible number for those digits.
2.The player writes that number on line 1.
3.The second player selects 4 digit cards and makes the smallest possible number for those digits.
4.The player writes that number on line 10.
5.T he next player selects 4 digit cards and must make a number that falls between the other two. They can choose any line
to place that number on.
6.T he next player selects 4 digit cards and makes a number using those digits that could be placed on an empty line
between any two existing numbers.
7.Game continues until a number is correctly placed on each line. (All 10 lines contain a number and they are in the correct
order), OR players cannot place a number correctly on any of the empty lines.
Variation/Extension: Once students understand the game they can create their own recording sheet in their math notebook.
Teacher can modify this game by changing the number of digits or number of lines.
1 _______________________________________
2 _______________________________________
3 _______________________________________
4 _______________________________________
5 _______________________________________
6 _______________________________________
7 _______________________________________
8 _______________________________________
9 _______________________________________
10 _______________________________________
CORN SHUCKS CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
40
Number and Operations in Base Ten
•
3.NBT.1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
41
Rounding to the Tens/Hundreds Showdown
Building Fluency: rounding to nearest ten and nearest hundred
Materials: recording sheet, deck of standard playing cards (remove 10’s and face cards) or digit cards
Number of Players: 2
Directions:
1.Each player takes two cards from the deck and places them on the table in the order drawn. Each player rounds their number
to the nearest ten. Players may use a number line to help in rounding. Players should record their cards drawn and the rounded
number on the recording sheet.
2.The player with the largest rounded number takes all 4 cards. In the event of a tie, draw new cards and the winner gets all 8 cards.
3.Continue until all cards are drawn.
4.The player with the most cards at the end wins.
Example: Player 1 wins the round!
PLAYER 1
PLAYER 2
Cards Drawn
Rounded Number
Cards Drawn
Rounded Number
90
70
86
74
0
10
20
30
40
50
60
70
80
90
100
Variation/Extension: Each player takes 3 cards from the deck and places them in the order drawn. Players round the numbers to the
nearest HUNDRED. The player with the largest number takes all 6 cards.
Example: Player 2 wins the round!
PLAYER 1
PLAYER 2
Cards Drawn
Rounded Number
Cards Drawn
Rounded Number
600
700
738
564
0
100
200
300
400
500
600
700
800
900
1000
ROUNDING TO THE TENS/HUNDREDS SHOWDOWN CONTINUED, PAGE 2
Cards Drawn
0
GRADE 3 • BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Rounded Number
10
20
30
40
Cards Drawn
50
60
Rounded Number
70
80
90
100
42
ROUNDING TO THE TENS/HUNDREDS SHOWDOWN CONTINUED, PAGE 3
Cards Drawn
0
GRADE 3 • BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Rounded Number
100
200
300
400
Cards Drawn
500
600
Rounded Number
700
800
900
1000
43
Number and Operations in Base Ten
•
3.NBT.1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
44
Building Fluency: use place value to understand rounding to the nearest 10 or 100
Materials: spinner 0-9 (pencil and paperclip), recording sheet
Number of Players: 2-4
Directions:
1.First player spins, tells the number and says, “Take your places.”
2.Each player writes the number on their recording sheet in any place in the first round. A number cannot be moved after it is written. If you choose not to use the number then it can be placed in the “Trash” column, only 1 number per round.
3.Players in turn spin and announce numbers for all players to place on their sheets.
4.After 4 spins, each player rounds to the nearest hundred.
5.The player with the highest number earns 2 points. If the numbers are the same, each player earns a point.
6.The player with the highest score after 6 rounds wins.
Variation/Extension: Round to the nearest 10. Once students understand the game they can create their own recording sheet in their
math notebook.
HUNDREDS
TENS
ONES
TRASH
ROUNDED
NUMBER
POINTS EARNED
HUNDREDS
TENS
ONES
TRASH
ROUNDED
NUMBER
POINTS EARNED
PLAYER 1
1.
2.
3.
4.
5.
6.
PLAYER 2
1.
2.
3.
4.
5.
6.
TAKE YOU PLACES CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
45
HUNDREDS
TENS
ONES
TRASH
ROUNDED
NUMBER
POINTS EARNED
HUNDREDS
TENS
ONES
TRASH
ROUNDED
NUMBER
POINTS EARNED
PLAYER 3
1.
2.
3.
4.
5.
6.
PLAYER 4
1.
2.
3.
4.
5.
6.
TAKE YOU PLACES CONTINUED, PAGE 3
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
6
3
9
7
0
2
5
1
•
46
8
4
Number and Operations in Base Ten
•
3.NBT.2
1,000
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Close Enough
1,000
Building Fluency: Add and subtract within 1000.
Materials: Spinner (pencil and paper clip), base ten blocks (ones, tens, and hundreds), recording sheet
Number of Players: 2-4
Directions:
1.A player spins and takes either that number of ones, tens, or hundreds blocks
2.The player records the number on their recording sheet. Example: a spin of 4 may be recorded as 4, 40, or 400.
3.Players take turns spinning, collecting blocks, and recording their numbers.
4.After six spins, the player with the total closest to 1000, but not more than 1000, wins the game.
Variation/Extension: Once students understand how to play the game, they can record their work in their math notebook
students could vary the game by changing the desired final number.
2 3
4
0 1
9
47
5
6
7 8
CLOSE ENOUGH CONTINUED, PAGE 2
PLAYER 1
SPIN
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
PLAYER 2
NUMBER
SPIN
1
1
2
2
3
3
4
4
5
5
6
6
TOTAL
TOTAL
PLAYER 3
SPIN
NUMBER
PLAYER 4
NUMBER
SPIN
1
1
2
2
3
3
4
4
5
5
6
6
TOTAL
TOTAL
NUMBER
48
Number and Operations in Base Ten
•
3.NBT.2 and 3.NBT.3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Money Wheel
Building Fluency: multiply one-digit whole numbers by multiples of 10
Materials: spinners (pencil and paperclip), paper, money (optional)
Number of Players: 2-4
Directions:
1.Players take turns spinning the “How Many?” spinner and the “How Much?” spinner.
2.Record the product and describe the strategy to the other players.
Example: I spun 8 and 50 cents. I know that 8 times 5 is 40 so 8 times 50 is 400 cents.
(Student could use play money to represent the amount spun.)
3.After each player has had 5 turns, total the value. The player with the most money wins.
Variation/Extension: Change the amounts on the spinners; spinner could be changed to have 80 cents and 90 cents instead of
10 cents and 20 cents.
PLAYER 1
How Many?
PLAYER 2
How Much?
Amount of Money
How Many?
1
1
2
2
3
3
4
4
5
5
TOTAL
Amount of Money
TOTAL
PLAYER 3
How Many?
How Much?
PLAYER 4
How Much?
Amount of Money
How Many?
1
1
2
2
3
3
4
4
5
5
TOTAL
How Much?
TOTAL
Amount of Money
49
MONEY WHEEL CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
1
50
7
How Many?
2
6
8
3
4
5
¢
0
7
10¢
60¢
20¢
¢
0
5
3
0
¢
40¢
How Much?
Number and Operations in Base Ten
•
3.NBT.3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Race to 300
Building Fluency: multiply one-digit whole numbers by multiples of ten
Materials: a die, recording sheet
Number of Players: 1-4
Directions:
1.Each player rolls a die in turn. The player multiplies that number by 10 and records the answer.
2.Add the numbers after each turn.
3.The first player to reach or pass 300 wins.
Variation/Extension: Once students understand how to play the game they can record their work in their math notebook. Students
could play 10 rounds and see who has the lowest score. Students change the goal number and make it a higher or lower.
Example:
NUMBER
ROLLED
NUMBER X 10
3
3 x 10= 30
30
6
6 x 10= 60
30 + 60=90
4
4 x 10= 40
90 + 40= 130
5
5 x 10= 50
130 + 50= 180
2
2 x 10 = 20
180 + 20=200
6
6 x 10= 60
200 + 60= 260
5
5 x 10= 50
260 + 50= 310 – GOAL REACHED
NUMBER
ROLLED
NUMBER
X 10
TOTAL SUM
TOTAL SUM
NUMBER
ROLLED
NUMBER
X 10
TOTAL SUM
51
RACE TO 300 CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
NUMBER
ROLLED
NUMBER
X 10
TOTAL SUM
NUMBER
ROLLED
NUMBER
X 10
TOTAL SUM
NUMBER
ROLLED
NUMBER
X 10
TOTAL SUM
NUMBER
ROLLED
NUMBER
X 10
TOTAL SUM
NUMBER
ROLLED
NUMBER
X 10
TOTAL SUM
NUMBER
ROLLED
NUMBER
X 10
TOTAL SUM
52
Number and Operations - Fractions
•
3.NF.1 and 3.NF.2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Fraction Match-Up
Building Fluency: understand fractions and how they are represented on the number line
Materials: fraction bar cards and number lines cards
Number of Players: 2
Directions:
1.Mix up the fraction bar cards and place them face down on one side of the game area. Mix up the number line cards and put
them face down on the other side.
2.Players take turns turning up one card from each area. If the cards represent the same fraction, the player takes the cards.
If they do not match, the player turns the cards back over.
3.The player with the most matches wins.
Variation/Extension: Have students make different representations of fractions (shaded circles or rectangles) and play the game
matching those to number lines.
53
FRACTION MATCH-UP CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
54
FRACTION MATCH-UP CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
55
Number and Operations - Fractions
•
3.NF.1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Fraction Roll’Em
Building Fluency: understand fractions as parts of a whole
Materials: gameboard, pair of dice, game markers - different color for each player
Number of Players: 2
Directions:
1.Each player takes turns rolling dice to create a fraction.
2.The smaller number is the numerator and the larger number is the denominator.
3.The player finds the fraction on the gameboard and covers it with a marker.
4.If the fraction is already covered the player loses that turn.
5.The player with the most markers on the board wins.
Variation/Extension: Have students create other fraction gameboards with different representations such as circles or number lines.
56
FRACTION ROLL’EM CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
57
Number and Operations - Fractions
•
3.NF.1 and 3.NF.3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
58
Figuring Fourths
Building Fluency: understand fractions
Materials: gameboard, four two-color counters, one small cup, game markers
Number of Players: 2
Directions:
1.Each player choose one of the colors from the two color counters.
2.Player 1 shakes and spills the two-colored counters.
3.Player determines the fraction that the chosen color represents.
Example: Player’s color is yellow. The markers are 1 yellow and
3 red. The yellow represents ¼. The player moves to the first
space that represents ¼.
4.Player 2 shakes and spills the counters and moves
according to the appropriate space.
5.Players take turns. Player loses their turn if there is
no move. First player to land on FINISH exactly wins.
Variation/Extension: Instead of players choosing a
color for the two-sided counters, they could choose
the fraction on each move that works the best for
them. Example: Three red counters and one
yellow counter could be moved as ¼ or as ¾.
3 out
of 4
4
4
2
2
1
4
1 out
of 4
2 out
of 4
1
2
1
2
1 out
of 4
3
4
1
2
4 out
of 4
1
4
START
FINISH
1 out
of 4
3
4
Number and Operations - Fractions
•
3.NF.1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Three in a Row Gameboard
Building Fluency: understand fractions
Materials: gameboard, game cards, nine game markers per player.
Number of Players: 2-6
Directions:
1.Choose an answer board for each round.
2.Shuffle the Three-In-A-Row game cards and place them face down.
3. Turn over the top card.
4.All players cover the fraction with a game marker if it appears on their board.
5.Three in a row is a winner, horizontally, vertically or diagonally.
Variation/Extension: Players play using the same gameboard but take turns turning cards with only one player marking the play
for each turn. Players could cover the entire board.
1
6
3
4
5
6
1
2
3
3
3
8
3
5
7
8
1
4
59
THREE IN A ROW GAMEBOARD CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
1
6
3
4
5
6
5
8
2
3
1
4
1
2
3
3
3
8
3
4
2
5
2
8
3
5
7
8
1
4
3
3
1
2
5
6
5
8
1
2
3
6
4
8
5
6
1
2
2
3
3
8
4
4
1
6
3
5
2
8
7
8
2
5
1
3
2
3
6
6
1
4
2
8
1
3
5
6
1
2
3
5
6
6
2
5
4
4
2
3
2
3
1
8
3
4
1
2
7
8
1
4
4
6
1
3
4
8
60
THREE IN A ROW GAMEBOARD CONTINUED, PAGE 3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
61
Number and Operations - Fractions
•
3.NF.1 and 3.NF.3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Figure Eighths
Building Fluency: understand fractions
Materials: gameboard, eight two-color counters, one small cup, game markers
Number of Players: 2
Directions:
1.Each player chooses one color of the two-colored counters and chooses a game marker.
2.Player 1 shakes and spills the two-colored counters. Player determines the fraction that the chosen color represents. Each player moves on every spill. Example: Player’s color is yellow. The markers are 2 yellow and 6 red. The yellow represents ¼. The player moves to the first space that represents ¼. Player 2 has red. The red represents ¾. Player 2 moves to the first space that represents ¾.
3.Player 2 shakes and spills the counters and each player moves to the appropriate space. Players move in a continuous pattern to form a figure eight. Player loses a turn if there is no move.
4.First player to land on FINISH exactly wins.
Variation/Extension: Players take turns spilling and moving and choose the fraction that works best for that turn.
1
2
1
4
RT H
A
ST NIS
one
FI
fourth
1
8
7 out
of 8
3
8
3
4
one
eighth
1
2
5
8
8
8
1 out
of 8
three
fourths
1
4
3
8
one half
7
8
3 out
of 8
62
Number and Operations - Fractions
•
3.NF.2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
“I Have” Fraction Cards
Building Fluency: Understand a fraction as a number on the number line.
Materials: 2 sets of “I Have” cards
Number of Players: 2
Directions:
1.Shuffle cards. Each player has one set of the cards below.
2.First player draws a card saying, “Who has ___?” or the fraction on the card that is drawn by the first player. The second player finds the card that shows ___ and explains how the number line shows ___. If correct, the second player says, “Who has ___?”
3.Player #1 finds the card with a number line that shows ___. Player one explains how the number line represents the fraction. Once card is used they place the card face up on the table. Continue until all cards have been played by both players.
Variation/Extension: Students might work with partners to create more cards. Teacher and class may create more cards together.
I have
I have
I have
I have
Who has 3 ?
4
Who has 1 ?
4
Who has 6 ?
8
Who has 1 ?
8
I have
I have
I have
I have
Who has 2 ?
8
Who has 2 ?
2
Who has 3 ?
6
Who has 1 ?
2
I have
I have
I have
I have
Who has 3 ?
4
Who has 1 ?
4
Who has 6 ?
8
Who has 1 ?
8
I have
I have
I have
I have
Who has 2 ?
8
Who has 2 ?
2
Who has 3 ?
6
Who has 1 ?
2
63
“I HAVE” FRACTION CARDS CONTINUED, PAGE 2
I have
1
?
1
?
1
?
1
Who has
I have
1
?
1
Who has
I have
1
?
1
Who has
?
0
1
Who has
?
?
I have
0
1
Who has
?
I have
I have
0
1
Who has
1
Who has
I have
0
0
?
0
?
?
I have
I have
0
1
Who has
1
Who has
I have
0
0
?
0
?
?
I have
1
Who has
1
Who has
I have
0
?
0
?
0
I have
0
Who has
Who has
1
Who has
1
I have
0
I have
Who has
?
64
I have
0
I have
0
Who has
1
Who has
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
I have
0
I have
Who has
•
I have
0
Who has
?
0
1
Who has
?
1
1
•
0
PLAYER 2
3.NF.2 and 3.NF.3
0
Variation/Extension: Play with the plus fraction cards only. Have each player draw
a card. Compare fractions. Player with the larger fraction plays. Continue to draw
with only one player moving each turn.
Directions:
1.Each player in turn draws a card to see where to jump on the number line.
2.The player places the marker in the correct location.
3.Some cards move forward and others move backward. If the card requires a
player to move lower than 0, the player loses the turn.
4.The player who lands exactly on 1 is the winner.
•
PLAYER 1
Number of Players: 2
Materials: gameboard, game cards, and game marker
Building Fluency: understand fractions on the number line
Number of Players: 1-2
Number and Operations - Fractions
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
65
NUMBER LINE MADNESS! CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
+1
8
-1
8
+ 2
8
-2
8
3
8
4
+
8
4
8
5
+
8
6
+
8
6
8
7
+
8
7
8
1
2
1
+
4
1
4
3
+
4
3
+
8
5
8
1
+
2
3
4
66
Number and Operations - Fractions
•
3.NF.3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Capturing Hexagons
Building Fluency: understanding fractions
Materials: gameboard per player, spinner (pencil and paperclip), and pattern blocks (hexagons, triangles, trapezoids, and rhombuses)
Number of Players: 2-4
Directions:
1.Players take turns spinning the spinner and placing the pattern blocks on the gameboard. Players should be encouraged to trade up whenever possible.
2.When a player captures an entire hexagon, the shape is covered with a hexagon.
3.The winner is the first player to capture all of the hexagons on the gameboard.
Variation/Extension: The spinner contains two 1/3 opportunities. Label one of these as “take away”.
67
CAPTURING HEXAGONS CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
68
2 3
1
3
1
3
1
2 3
1
1
1
6
3 6
5
3 6
1
6
1
3
2
5
1
2 3
2
5
1
3
1
69
1
6
1
6
1
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
2
2 3
1
•
2
1
3 6
CAPTURING HEXAGONS CONTINUED, PAGE 3
3 6
5
Number of Players: 2
Variation/Extension: The winner places the last piece or players
may not cover adjoining hexagons in the same way. Example:
If a player covers one hexagon with 2 trapezoids, the adjoining
hexagons must have at least two different shapes.
Materials: gameboard and pattern blocks (triangles, parallelograms, trapezoids, hexagons)
Directions:
1.Players take turns placing pattern blocks on the snail. The player announces the fraction
being placed. Example: Player places a triangle on the board and says “This is 1/6 of the
hexagon.” Player places a trapezoid on the board and says “This is ½ of the hexagon.”
2.The person who places the last block on the gameboard loses the game.
Building Fluency: equivalent fractions
Snail Nim
Number and Operations - Fractions
•
3.NF.3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
70
Measurement and Data
•
3.MD.1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Race to Midnight
Building Fluency: telling time
Materials: gameboard, spinner (pencil and paperclip),
number line for each player
Number of Players: 2 or 3
Directions:
1.Each player will have a number line and begin at 8:00.
2.In turn, players spin and add or subtract the time indicated
on the spinner and record on the number line.
3.The winner is the first player to reach 12:00 midnight.
Variation/Extension: Students can create their own number lines using
different begin and end times.
+ 20
u te
n
i
m
s -5m
inut
es
+ 10
s
ute + 45 mi
n
min
u
t
es
s - 30
e
t
min
inu
u t es
m
+5
71
+ 15
u te
min
s - 10
min
u
t
e
s
8:30
8:30
8:30
8:00
8:00
8:00
9:00
9:30
10:00
10:00
10:00
10:30
10:30
10:30
11:00
11:00
11:00
11:30
11:30
11:30
12:00
12:00
12:00
•
9:30
9:30
9:00
9:00
RACE TO MIDNIGHT CONTINUED, PAGE 2
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
72
Measurement and Data
•
3.MD.2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
73
Metric Measure Up
Building Fluency: understand metric measurement
Materials: gameboard, a die, game marker, metric unit cards
Number of Players: 2-4
Directions:
1.Each player places game markers on “Start”.
2.Player 1 draws the top card from the deck and reads it. Then player 2 fills in the correct unit of measure.
3.If the player answers correctly, the player rolls the die and moves that many spaces. If the player answers incorrectly, the turn is over.
4.Play continues to the right with one player reading and the next player answering and moving.
5.The winner is the first player to reach “Finish”.
Variation/Extension: Cards can be dealt out to each player. In turn a player can turn over a card, read it and answer it. Teacher may
START
Move Back
2 Spaces
Lose
a Turn
FINISH
Lose
a Turn
1 Space
Roll Again
METRIC MEASURE UP CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
5 ________ of water.
350 _______ of juice.
100 _______ of soup.
(liters)
(milliliters)
(milliliters)
2 _______ of water.
Eyeglasses can weigh
A watermelon is
(liters)
(grams)
(kilograms)
A milk jug contains
An eye dropper contains
(liters)
(milliliters)
A washing machine
6 _____ of water.
115 _____ of water.
A drinking glass holds
A tennis ball weighs
(liters)
(milliliters)
(grams)
(liters)
74
METRIC MEASURE UP CONTINUED, PAGE 3
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
122 ______ long.
3,000_____ long.
A dictionary weighs
(centimeters)
(centimeters)
(kilogram)
A necktie weighs
25 ______ long.
A Blue Whale weighs
(grams)
(centimeters)
(kilograms)
A large bottle of soda
137______ long.
An airplane weighs
(liters)
(centimeters)
(kilograms)
69 ______ long.
20 ______ long.
1,000______.
(meters)
(centimeters)
(grams)
75
METRIC MEASURE UP CONTINUED, PAGE 4
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
15 ______ long .
A hotdog weighs
(centimeters)
(kilograms)
(grams)
A roll of 50 pennies
120______.
A motorcycle weighs
two ______ long.
(kilograms)
(meters)
A medium sized dog
A roll of 50 pennies in
A motorcycle is
kilograms
(centimeters)
(centimeters)
A piano weighs
A medium sized dog is
(kilograms)
(centimeters)
The keyboard on
two _____ long.
(grams)
(meters)
76
Measurement and Data
•
3.MD.7 and 3.MD.8
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Cut a Rug
Building Fluency: understand area and perimeter
Materials: pair of dice, recording sheet, centimeter grid paper
Number of Players: 2
Directions:
1.Player tosses the dice, finds the sum and puts the total in the length box. The player tosses the dice again to find the width.
2.Using the length and width, the player creates a rectangle on the grid paper and records the perimeter and area on the recording sheet. Then Player 2 does the same.
3.After each round the players look at their numbers together. Which player has the greater area? Which player has the greater perimeter? Is the perimeter always bigger? Always smaller? Can they be the same?
4.After 4 rounds, players total their perimeters and their areas. The winner has the highest total area.
Variation/Extension: Once students understand how to play this game they can create their own table in their math notebook.
“I Get Around” is a variation of this game.
PLAYER 1
Round
Length
Width
Perimeter
Area
1
2
3
4
Total Score
PLAYER 2
Round
Length
Width
Perimeter
1
2
3
4
Total Score
Area
77
CUT A RUG CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
78
Geometry
•
3.G.1
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Geo-Matchup
Building Fluency: reason with shapes and their attributes
Materials: a set of Geo-Matchup cards per player
Number of Players: 2-4
Directions:
1.Each player has a set of cards.
2.Players match up their cards.
3.Players compare their answers and agree or disagree.
4.Players defend and prove their answers until all players agree.
Variation/Extension: Play as a memory game. First player turns over two cards. If they match, the player takes the cards and
plays again. If not, the player turns the cards back over and play passes to the next player. Players can create additional cards.
A polygon with 8 sides
and 8 angles
2 pairs of parallel sides,
all right angles, and
all sides equal
4 sides equal and
2 pairs of parallel sides,
no right angles
A polygon with 5 sides
and 5 angles
2 pairs of parallel sides
and all right angles. All
sides are not congruent
one pair of parallel sides
A polygon with 3 sides
and 3 angles
sides. The four sides do not
all have the same length.
A polygon with 4 sides
and 4 angles
A polygon with 6 sides
and 6 angles
pairs of parallel sides
79
GEO-MATCHUP CONTINUED, PAGE 2
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
80
REVIEW
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Spin and Review
Building Fluency: review of multiple concepts
Materials: spinner (pencil and paper clip), game cards, approximately 50 counters
Number of Players: 3-4
Directions:
1.Cards are shuffled and placed face down. Then the first player draws a card and reads it to player 2.
2.If the player answers correctly, the player spins the spinner and takes that number of counters. The game card is placed in a discard pile.
3.If the player answers incorrectly the card is placed at the bottom of the pile and no spin is taken.
4.Player 2 reads a card for Player 3 and play continues around.
5.When all of the cards have been answered, the player with the most counters wins.
Variation/Extension: Students can write more questions for this game.
0
2
3
7
1
81
4
5
6
REVIEW CONTINUED, PAGE 2
Ellen has 5 groups of bracelets.
There are 6 bracelets in each group.
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
What is the missing factor?
John cut a brownie into two parts.
He ate one part. What fraction
of the brownie did he eat?
(A. 6)
(A. ½)
Alan began jogging at 9:15.
He jogged until 10:00. How
long did he jog?
Mary has 7 packs of gum, each pack
has 10 pieces. How many total
pieces of gum does Mary have?
John has 3 bags of candy. Each bag
contains 4 pieces. Caroline has
4 bags of candy. Each bag contains
2 pieces. Who has more candy?
(A. 45 minutes)
(A. 70 pieces)
Which digit is in the tens place in 843?
Would two quarters, one dime and
five pennies be the same amount of
money as six dimes and one nickel?
What equation expresses this?
(A. 5 x 6)
(A. 4)
Name a polygon with four congruent
sides and four congruent angles.
(A. Square)
8 x ___ = 48
(A. yes, 65¢)
Jake drew the numbers 3, 5 and 2
out of a bag of number tiles. What is
the largest number he can make using
all three numbers only once?
(A. 532)
Suckers are 15¢ each. Mary bought six.
How much did she spend?
What operation would you use
to solve this problem?
John measured the distance around
the entire outside of his desk.
What do we call this measurement
around an entire object?
(A. Perimeter)
Tina collects dimes. She had 198 dimes
and gave her brother 36. How many
did she then have? What operation
would you use to solve this problem?
Susie works in a flower shop.
She received a shipment of tulips
and roses. She received 38 tulips.
She received 50 more roses than tulips.
How many roses did she receive?
What operation should you use?
(A. Subtraction)
(A. John)
If you were skip counting by 3’s,
would you say the number 15?
(A. yes)
Marcus traced his hand on a piece of
paper. What do we call the measurment
of space on the inside of his drawing?
(A. Area)
Lamont was building a cube.
He used six of the same polygon.
What polygon did he use?
(A. Square)
There were eight clowns at the circus.
Each clown was juggling four
bowling pins. How many bowling pins
were there? What operation would
you use to solve this problem?
82
REVIEW CONTINUED, PAGE 3
Tyler drew a closed figure with
six sides. What was the name
of this figure?
(A. Hexagon)
Round 432 to the tens place.
(A. 430)
What is x?
3 x 2 = 2x
(A. 3)
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
200 + 40 + 3 is an example of...?
(A. Expanded Notation)
(A. One Whole Pizza)
(A. Polygon)
Does a 3 cm x 6 cm rectangle and
a 2 cm x 9 cm rectangle cover
the same amount of space?
What unit of measure would yo
use to give the weight of a paper clip?
Grams or Liters?
(A. Yes)
(A. Grams)
Katie buys a shirt for \$7.99 and a belt
for \$5.49. She paid with a \$20.00 bill.
How much change will she receive?
How many operational steps will
it take to solve this problem?
Would three dimes, two nickels and
ten pennies be the same amount of
money as two quarters?
(A. 2)
Blake ordered a medium pizza and
ate one half and Ernest ordered a
medium pizza and ate one half. How much
pizza did they have left all together?
A closed figure with three or more
straight sides is called a ____?
Judy arrived at school at 8:15. LuAnn
arrived 20 minutes later. What time
did LuAnn arrive at school?
(A. 8:35)
(A. yes)
83
Online Game Options
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Online Games Available
Operations and Algebraic Thinking
3.OA.5 – please add a description here... a few lines about how this game will help or how is works.
Number and Operations in Base Ten
Estimate Whole Numbers
http://studyjams.scholastic.com/studyjams/jams/math/numbers/nestimate-whole-numbers.htm
3.NBT.1 – please add a description here... a few lines about how this game will help or how is works.
3.NBT.1 – S tudents need to land the helicopter in the correct rounded number pad.
Rounding to the Nearest 10
http://www.aaamath.com/est32_x2.htm
3.NBT.1 – Basic rounding to nearest ten, gives student feedback.
Rounding to the Nearest 100
http://www.aaamath.com/est32_x3.htm
3.NBT.1 – Basic rounding to nearest hundred, gives student feedback
Match Up Defense Basic
http://www.mathnook.com/math/mathpup-defense-basic.html
3.NBT.1 – Defense Pup Basic: Students need to use their rounding skills to the nearest ten to defend
their house. They “shoot” the attacker with the correct rounded answer. Allows students to level up if
they do well.
3.NBT.1 – Students need to use their rounding skills to the nearest hundred to defend their house. They
“shoot” the attacker with the correct rounded answer. Allows students to level up if they do well.
84
Online Game Options
•
BUILDING CONCEPTUAL UNDERSTANDING & FLUENCY THROUGH GAMES
Number and Operations – Fractions
Fractions Shoot
http://www.sheppardsoftware.com/mathgames/earlymath/fractions_shoot.htm
3.NF. 1 – A great introduction game to fractions. Students need to touch the fraction identified by
the game. Students can pick relaxed mode, timed mode, and which fractions they can play with.
Find Grampy
http://www.visualfractions.com/FindGrampy/findgrampy.html
3. NF. 2 – Students need to identify the location of “Grampy” when he goes behind some bushes.
Set up in a fraction bar/number line. It gives students clues where to go if they do not respond
correctly the first time:
Fraction Track -- WEBSITE DID NOT WORK
http://illuminations.nctm.org/ActivityDetail.aspx?ID=18
3.NF.2 and 3.NF.3 – Students need to get their pieces to the end of the track with the least amount
of moves. The game corrects the students if they are incorrect. Equivalent fractions are also
allowed to be used on the track. Denominators go up to 12ths.
Fraction Track 2
http://www.curriculumsupport.education.nsw.gov.au/countmein/children_fraction_track.html
3.NF.2 and 3.NF.3 – Students need to get their pieces to the end of the track with the least amount
of moves. The game corrects the students if they are incorrect. Equivalent fractions are also
allowed to be used on the track. Denominators go up to 10ths.
Tony’s Fraction Pizza Shop
http://mrnussbaum.com/pizza_game/
3.NF.1 and 3.NF.3 – The computer gives a pizza order, listing the size of pizza and what toppings.
Students need to select the correct toppings with the correct fractional amount. Students
receive earnings for each pizza done correctly. Some pizzas are listed with equivalent fractions.
Measurement and Data
Willy The Watch Dog -- Can you take a screen capture for me?
http://www.harcourtschool.com/activity/willy/willy.html
3.MD.1 – An online board game for 1-2 players. Students need to move the clock to the time identified.
Hickory Clock
http://www.ictgames.com/hickory4.html
3.MD.1 – Students need to identify the correct time so the mouse can get the cheese.
If they are incorrect, a cat comes in.
Elapsed Time
http://www.shodor.org/interactivate/activities/ElapsedTime/
3.MD.1 – Students need to advance the time to see how much time as passed.
Multiple levels available.
Line Plots
http://studyjams.scholastic.com/studyjams/jams/math/data-analysis/line-plots.htm
3.MD.4 – please add a description here... a few lines about how this game will help or how is works.
85
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