Bemidji State University Number Sense and Operations Activities Summer Math Institute Summer 2006 Grades 1 and 2 Mac Grewe [email protected] Eileen Spilman [email protected] 1 Table of Contents Executive Summary of Friday Fun Activities ............................ 3 Survey of Hair and Eye Colors.................................................... 4 Tug Addition ................................................................................. 6 Step-Down Subtraction ................................................................ 8 Exchange Game: One-Dollar Exchange .................................. 10 Exchange Games: Base-10 Exchange........................................ 13 Jackpot Math .............................................................................. 16 Number Grid Game.................................................................... 19 Remainder of One....................................................................... 21 Yekttis (Yek-tees)........................................................................ 23 Animals in the Neighborhood .................................................... 31 2 Executive Summary of Friday Fun Activities The first lesson that we have chosen is to be used on the first Friday of the school year to enable the students to get to know each other, with the goal of creating a classroom of cooperative learners. We have chosen a ten number of activities to be used on Fridays throughout the school year to reinforce the lessons that have previously been presented to our students. This will enable the students to have additional practice as needed, and give us an additional opportunity to see if the students have mastered the presented objectives. Many of our activities are also games that once introduced to the class, may be placed in the Math center for children to use during center time. This unit addresses 6 of the 20 Minnesota Academic Standards in Mathematics for first grade standards and 4 of the 15 Minnesota Academic Standards in Mathematics for second grade. 3 Survey of Hair and Eye Colors Standards: 1.1.1.7 Use a variety of models and strategies to solve addition and subtraction problems in real world and mathematical contexts. Objective: A beginning of the year activity which will allow all students in the class to get to know each other. Students will learn to collect data, and interpret their results through counting and comparison skills to create and analyze tally charts. Students will be able to predict the probability of outcomes of simple experiments and test the predictions. Materials: Printed activity sheet and class list for each student. Launch: Introduce yourself to your neighbor. Do you have the same name? Do you look the same? How are you different from your neighbor? How are you the same? Explore: Hand out survey to each student, and give instructions. They will begin by placing a tally mark in the appropriate space that describes him. They then interview every other student in the class to complete their worksheet, checking off the name on the class list as they go. After interviewing each student and recording their tally marks they will go back to their desks and complete the worksheet. Share: Students will discuss their results and predictions and turn in their completed assignments. What was the most common hair color? What was the most common eye color? Which is your favorite eye color? Do more girls have blue eyes than boys? Do more boys than girls have brown eyes? Summarize: Students were able to collect data by completing their survey. The students were able to predict the probability of the eye and hair color of the next student to walk into their classroom. The student will also have had the opportunity to get to know everyone else in their class, including putting a name with a student. Citation: http:illuminations.nctm.org/LessonDetail.aspx?ID=L230 4 Survey of Hair and Eye Colors Complete this survey by interviewing all your classmates. Remember to begin with yourself. Hair Color Tally Marks Total Black Brown Blond Red Eye Color Tally Marks Total Brown Blue Green Complete the following: 1. Which hair color is most common?__________ Least common?_________ 2. Which eye color is most common?__________ Least common? 3. On the basis of your survey, predict the eye and hair color of the next student to walk into our classroom. _____________________________________________________________ 4. Explain how you arrived at your prediction. _____________________________________________________________ 5 Tug Addition Standards: 1.1.1.5 Count, compare and represent whole numbers up to 120, with an emphasis on groups of 10 and ones; use a variety of models and strategies to solve addition and subtractions problems in real world and mathematical contexts. Objective: Understanding estimating of two digit sums, as well as actually adding the two digit sums and comparing estimate with answer. Materials: Each group of 2 needs a number cube 1-6 (die), two counters and worksheet Launch: Catch their interest by asking about their experiences (if any) of playing Tug of War. Discuss rules of game – the object of the game is to “pull” all members of the other team across the start line onto your side. Explore: Divide players into teams of two, distribute worksheet, counters and die to each group. Players both put their playing pieces on Start. In the first move of the game, partners each roll the number cube and move that number of spaces in opposite directions from Start. They look at the numbers they each land on and estimate what the sum will be. Have players write their guesses. They then add the two numbers and compare the actual sums with their estimates. The child whose estimate is closer to the sum rolls the number cube first on the next turn. Both children must then move their pieces in that player’s directions on the board. (In case of a tie, the children will both shake the die and the highest number goes first.) Play continues until one player has moved off of the board, winning the tug addition. Share: Discuss how the students estimates related to the actual sums, and did the estimates become more accurate as the game proceeded? Did you enjoy the game? Was it difficult to make an estimate? What strategies did you use to come up with your estimated? Summarize: The main point of this lesson was to further develop their estimating abilities and 2 digit addition skills. It also gave the instructor the opportunity to see which students need additional help in this area. Citations: Creed, Margaret, Grade 2 Brain Boosting Math Activities, p. 18-19. Scholastic Inc., 1997 6 7 Step-Down Subtraction Standards: 1.1.2.1 Use a variety of models and strategies to solve addition and subtraction problems in real-world and mathematical contexts. Objective: To help the child see the relationship between the numbers they are subtracting and the idea of counting back by that number. Materials: Each group of 2 students needs a worksheet, pencil and die. Launch: Have any of you seen the movie with Meg Ryan “You Got Mail”? Where did Meg Ryan and Tom Hanks meet on New Years Eve in N. Y. C.? Where have you seen a staircase with many steps? Explore: Divide the class into pairs and pass out the worksheet. Explain that partners each start at the top of the steps. One should be X and the other O. They take turns rolling the number cube (die) and moving down from 1 to 6 steps. On the step where they land, they should draw an X or an O to record their own move. Then they write a subtraction sentence for the move, beginning with 25 and taking away the number of their first roll. Share: When children are finished, invite them to share the sentences they wrote. Ask them to look back at the X’s and O’s. Did they ever end up on the same step? How did that happen? How many turns did it take for each of them to land at the bottom? If not the same number of turns, why not? Summarize: As the children are working, notice what strategies they use to subtract. Listen as partners talk about the numbers they use. Do they use the steps on the sheet to count back from a number? What patterns do they notice in the equations they write? How do they do the computation when subtracting from 2 digit numbers? Is their subtraction an “automatic” process when they get to basic facts, or do they use a counting technique to determine the answers? Citation: Creed, Margaret, Grade 2 Brain Boosting Math Activities, p. 20-21. Scholastic Inc., 1997 8 9 Exchange Game: One-Dollar Exchange Standards: 1.3.2.3 Use basic concepts of measurement in real-world and mathematical situations involving length, time and money. Objective: Identify pennies and dimes and find the value of a group of these coins, up to one dollar. Materials: A player board (yellow) for each child, 1 bank board for each group, 2 dice, realistic money (1 – 1 dollar bill, 20 dimes and 20 pennies) for each group. Launch: How many of you have gone to the store and purchased a candy bar? What was the cost? Did you have enough money? Did you get change back? Was the amount of change you received the correct amount? How do you know? What are the names of the different coins? Would you rather have one dollar bill or 100 pennies? Which is easier to carry? Explore: Divide group into pairs. The object of the game is to be the first player to make an exchange for a dollar bill. The bank starts with a $1 bill, 20 dimes and 20 pennies. Players take turns. Player one rolls the die. The player takes that number of pennies from the bank and places the pennies on the game-board. Whenever possible a player exchanges 10 pennies for a dime. The player not rolling the dice checks the accuracy of the transactions. The first player to make an exchange for a dollar bill wins the game. Share: Students will discuss their transactions, and how long it took them to get to a dollar. What would change if we added a nickel? What would change if we added a quarter? Would it take longer to get to a dollar using a quarter? Summarize: Students should understand that 10 pennies equals a dime and 10 dimes equal a dollar. Citation: Grades 1-3 “Everyday Mathematics Family Games Kit Guide”, page 15, Wright Group/McGraw-Hill, 2003. 10 11 12 Exchange Games: Base-10 Exchange Standards: 1.1.1.2 Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones. Objective: Reinforce the student’s understanding of our number system – that 10 ones (cubes) is equal to 1 ten (long) and that 10 tens (longs) is equal to 1 hundred (flat). Materials: A player board (yellow) for each child, 1 exchange board for each group, 2 dice, 1 flat, 20 longs and 20 cubes for each group. Launch: Have you ever exchanged trading cards with a friend? Do you always exchange one card for one card? Are some cards worth more than others? If so, how do you make the exchanges? Explore: Divide group into pairs. The object of the game is to be the first player to make an exchange for a hundred (flat). The bank starts with 1 hundred (flat), 20 tens (longs), and 20 ones (cubes). Players take turns. One player rolls the dice. The player takes that number of cubes from the bank and places the cubes on the game-board. Whenever possible, a player exchanges 10 cubes for 1 long. The player not rolling the dice checks on the accuracy of the transactions. The first player to make an exchange for a flat wins the game. Share: Were all exchanges accurate on the first try? If you were the one checking the accuracy and you thought there was a mistake made, were you able to explain the error and help the other person correct the error? How many turns did it take to get a long? 2 longs? 5 longs? The flat? Summarize: Does each student have an understanding that 10 cubes equal 1 long and 10 longs equal a flat? Reinforce the concept of base 10. Citation: Grades 1-3 “Everyday Mathematics Family Games Kit Guide”, page 14, Wright Group/McGraw-Hill, 2003. 13 14 15 Jackpot Math File Folder Game Standards: 2.1.2.1. Demonstrate mastery of addition and subtraction basic facts; add and subtract one and two digit numbers in real world and mathematical problems. Objective: Develop and demonstrate fluency with basic addition and related subtraction facts. Materials: 1 file folder game board per group, 1 die and one set of math cards. You could use any number cards you presently have, or cut 30 - 3 by 5 cards – in half, and write the numbers 1 through 20 on the cards. You will have three cards with each number for the set. Launch: Discussion about playing games at home with the family. Share how often we play games, what types, etc. Have children share about their favorite games. Lead into the introduction of this game. Explore: Divide group into pairs (three in a group at the most). Game board and set of math cards divided into two separate piles are placed in front of the group. Student A draws one card from each pile. He reads the numbers and adds them together, telling student B the answer. Student B also adds them together, and if he determines that the answer is correct, then student A continues his turn by shaking the die. He places his cards on the area of the game board covering the number he shook. If it is determined that the answer is incorrect, the cards go on the bottom of the draw pile, and his turn is finished without shaking the die. It is then the next persons turn to draw a card from each pile. Reversing rolls, student A now decides if the answer student B gives is correct. Again if correct, he shakes the die and covers the number on the board that correlates to the number on the die. If that number is already covered, his cards will be placed in the Jackpot space. The object of the game is to cover the last number 1 through 6 on the game board. If time permits to play a number of games, it is fun to keep track of points for the entire game. The winner (person who covers the last number) receives all the points for that round – one round for every card on the game board. Share: Students will share with the class what was easy about this game, and what was difficult about this game. What was the largest number of points any one person received during a round? Compare answers. Can the game be completed in 6 throws of the die? What do you like about this game? Can you think of any other ways we can use this game other than adding the numbers on the cards together? 16 Summarize: This game could be played using the same cards, and changing the computation to subtraction. It gives the children the opportunity to develop speed and accuracy while having fun playing the game. If several of the children in the class have mastered their addition facts using numbers up to 20, add higher numbers to their set of cards. Also if you have a group of children struggling with addition facts, you could easily let them practice using numbers 1 to 10, gradually increasing the numbers they will use. 17 18 Number Grid Game Standards: 1.1.1.2 Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones. Objective: Read whole numbers up to 100, including using these numbers when adding and/or subtracting. Practice counting by 1’s and 10’s and identifying place-value patterns. Materials: Number chart 1 to 100, 1 die and 2 markers – for each group of two students. Launch: Discussion of running races, the fastest runner gets to the finish line first. Does the same person always win the race? If someone gets ahead right at the beginning of the race is it possible to someone else to catch up and win the race. Introduce the game as a race to the finish. Explore: Divide into pairs. Choose different colored markers and place your marker above the number 1. Players take turns. For each turn, a player will roll the die. If he rolls a 1 he may choose to move 1 space or 10 spaces. If he rolls a 2 he may choose to move 2 spaces or 20 spaces. If he rolls a 3, 4, 5 or 6 you may only move a corresponding number of spaces (3, 4, 5 or 6). The winner is the first player to get to 100 or past 100. Share: Discussion of how one person was able to reach 100 before the other person. What was the final difference between the two scores? Why was one person able to reach 100 before the other person? Summarize: Teacher may move among students and see which students can do this easily and which students need extra practice. A variation would be to begin at 100, and using subtraction, move back to 0. You could also extend the number sheet to 120, 150 or 200. Citation: Grades 1-3 “Everyday Mathematics Family Games Kit Guide”, page 14, Wright Group/McGraw-Hill, 2003. 19 20 Remainder of One Standards: 2.2.1.1. Recognize, create, describe and use patterns and rules to solve real-world and mathematical problems. Objective: Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects. Use patterns to solve problems in various contexts. Materials: Worksheet and scissors Launch: Do you remember what Asian Beetles look like? Did they get into your house? Ask how many Asian Beetles did you have in your house? Read book Remainder of One. Explore: Distribute worksheets and scissors. Cut out 25 insects carefully. Arrange bugs on desk in as many different arrays as possible, including arrangements with a remainder of one. Share: Discussion with students on how many different arrays they found. Model answers on magnetic board. Summarize: Review how many patterns students can make with 25 insects. How many insects were in each row? Practice counting insects by 2’s. What is your remainder? Citation: Pinces, Elinor J. A Remainder of One, Houghton Mifflin Co., 1995 21 22 Yekttis (Yek-tees) Guess My Rule with Yektti Cards Standards: 2.3.1.1. Identify and compare basic shapes according to their geometric attributes. Objective: The students will identify attributes of a data set. They will work on grouping data by similar attributes, recognizing facial features, shapes and grouping of attributes. Materials: Prepared set of large Yektti Picture cards (one set for class). Prepared set of small Yektti picture cards (one set per group). Prepared set of Yektti word cards (1 set per group). Launch: Read “A Strange Discovery”, page 23, to introduce what Yekttis are. Explore: Show students large Yektti cards one at a time. Discuss the attributes of each Yektti shown on the cards and ask what is the same or different about the Yektti. Model some of the descriptions, (this one has a square head and three antennae) etc. Ask students to summarize the attributes they found (no nose, a mouth, no ears, different type of eyes, etc.). Divide class into groups of 3 or 4. Describe the game “Guess my Rule” with Yektti cards. Show word cards. One person picks out one or two Yektti word cards and says “These Yekttis fit my rule: He then places the card(s) face down in front of him. The other group members will take turns guessing an attribute (Does this Yektti with a square head fit your rule?) and if not correct they will place the card face down, and the turn moves to the next group member. When a group member guesses the rule correctly, the person to the right chooses the next mystery rule. Every group member should have a chance to choose a mystery rule. Share: The students should discuss how many classifications of attributes they found. Taking turns and giving positive feed back to each other should be modeled and encouraged. Summarize: The students will collaborate to guess the mystery rule of each Yekttis. Students will identify and group data by similar attributes. Encourage students to notice shapes, eyes and mouths which will be helpful for special needs students, especially students with ASD, to recognize facial expressions. Citation: Russell, Susan Jo. Sorting and Classifying Data, Does It Walk, Crawl or Swim? Grade 2 p. 23-25. Dale Seymour Pub. 1998. 23 square hexagon triangle diamond plain eyes Ringed eyes 1 antenna 2 antennae 3 antennae 4 antennae 24 25 26 27 28 29 30 Animals in the Neighborhood Standards: 2.2.1.1 Recognize, create, describe and use patterns and rules to solve realworld and mathematical problems. Objective: Students will construct categories to describe data. Students will articulate clear definitions of categories. Students will organize categorical data. Materials: Sticky notes or index cards, chart paper, large sheets of paper, crayons or markers and 2 student worksheets. Launch: Read Splash aloud. Make a list of the animals in the backyard and count the animals. Explore: Today we will be collecting data by thinking about what we already know about the animals that live in our neighborhood. Think back to when you have walked around your neighborhood. What animals have you seen that live around you? Some animals are easy to see and some animals are hard to see. What animals do you see in the winter? What animals do you see in the summer? What animals are easy to see? What animals hide or are very tiny and you have to look carefully to find? List all the animals that the children have named. There may be some animals students have seen whose names they don’t know. Find some way to identify them – maybe other students know what they are, or make up a name for them (silver bathtub bug, little yellow bird). After creating list, then talk about how animals move differently. As a class make a list of the different ways animals move (walk, fly, crawl, swim, hop, etc.). Today we are going to divide our list of animals by how they move. Separate students into groups of 4 or 5. Each group will make a chart showing how animals move. They may decide which categories of movement they will use on their chart, utilizing the class list of movements, or changing and adding some of their own ideas. Provide each group with sticky notes or index cards so each animal may be written down separately. Each group also needs a large sheet of paper on which to record their groupings. Let students experiment with different arrangements for their categories. Encourage students to sort the animals in whatever ways make sense to them and to articulate why they are putting certain animals into certain categories. It’s important that students discuss their reasoning with one another. Students may not always agree, but they should be encouraged to resolve differences by clarifying the definitions of their categories. Hand out student sheet 7 and 8. Complete as homework that needs to be returned the following day. 31 Share: Students will present their findings to the class by sharing their large paper showing animal lists, and explaining how and why they did their charts. Summarize: Students were able to organize categorical data as a small group, working cooperatively to describe their data. Students were able to articulate clear definitions of categories during their presentations. Citation: Russell, Susan Jo. Sorting and Classifying Data, Does It Walk, Crawl or Swim? Grade 2 p. 58-65. Dell Seymour Pub. 1998. 32 Name_____________________________________ Animals in the Neighborhood 1. What question did you answer about the animals in your neighborhood? 2. What categories did you use to sort your data? 3. Draw a picture of the representation you made of your data. 4. What are three interesting things you noticed about your data? Write them on the back of this paper. 33 Name_________________________________ Animals near My Home Look carefully in, around, and near your home for any kind of animal. The animal may be the tiniest bug or a large, furry creature! Draw or write about your findings. What category or categories might this animal fit? If you see more than one animal, what different categories might they fit? You may use the back of this sheet. 34 35

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