FAMILY MATH ACTIVITIES

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1 Toronto Catholic District School Board from the Mathematics Department FAMILY MATH ACTIVITIES for Kindergarten to Grade 8 using Math Learning Tools cards/dice 2 colour counters interlocking cubes pattern blocks square tiles tangrams Version 2 - November 2015

2 Superintendents of Education Cristina Fernandes, Early Learning Patrick Keyes, Student Success Dan Koenig, Curriculum & Accountability Mathematics Department Kathy Kubota-Zarivnij (program coordinator) Luciano Lopez Grace Mlodianowski Stefana Penelea Adrian Pope Wilma Simmons 2014 Toronto Catholic District School Board 80 Sheppard Avenue East, Toronto, Ontario M2N 6E8 TCDSB Family Math Activities, K to 8 2

3 Helping Your Child LEARN and LOVE Mathematics! Learning Mathematics Successfully What does it mean to learn mathematics successfully? Learning mathematics successfully or with mathematical proficiency includes the five components or strands of competencies: Conceptual Understanding understanding of mathematical concepts, operations, and relations; integrated and functional grasp of mathematical ideas that enables students to learn new ideas by connecting to ideas they already know through reasoning, proving and communication; supports retention and prevents common errors Procedural Fluency - carrying out procedures flexibly, accurately, efficiently, and appropriately. Strategic Competence - formulate, represent, and solve mathematical problems. Adaptive Reasoning - capacity for logical thought, reflection, explanation, and justification Productive Disposition - is habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy. (National Research Council, 2001) Also, when students analyse other students solutions to problems, they are compelled to reflect on their own mathematical thinking and the thinking of others and how their mathematical ideas strategies are connected. What Can Parents/Guardians Do At Home? Parents/guardians, school and the local community have the shared task of nurturing our students confidence in loving and learning mathematics and in applying their mathematical knowledge to solve real-life problems. The disposition of appreciating and enjoying mathematics is necessary for our students to persevere in learning mathematics with depth and precision and to continuously improve the clarity of their mathematical communication. It is common knowledge that parent's and/or guardian's attitudes toward mathematics has an impact on children's attitudes towards mathematics. In fact, students whose parents/ guardians show an interest in and enthusiasm for mathematics around the home will be more likely to develop that enthusiasm themselves and persevere to learn and succeed in mathematics. About Student's Mathematical Learning Students learn math best through experiences that allow them to explore new ideas, solve problems using information they have gathered themselves, reflect on what they have discovered, as well as through their own thinking, and explain their solutions through reasoning. Students learn more easily when they connect mathematical concepts and procedures with their own experience. The seven mathematical processes (i.e., Problem Solving, Reasoning and Proving, Reflecting, Selecting Tools and Computational Strategies, Connecting, Representing, Communicating) support students acquisition and application of mathematic knowledge and skills. By solving problems in different ways, using reasoning skills, and making connections between mathematical concepts and strategies, students develop a deeper understanding of mathematics. 3 Ways to participate in your child's mathematics learning are as follows: show a positive attitude towards learning mathematics by talking positively about it expect your child to complete mathematical activities and solve problems encourage your child to persevere when the mathematical work becomes difficult appreciate different ways to make calculations and solve math problems listen carefully to your child's explanation of a solution to a lesson problem estimate and count anything in different ways (forwards, backwards, by 2s, 5s, 10s, 100s) play board and card games solve jigsaw, number and logic puzzles build models with different materials (e.g., lego TM, stacking blocks, rolled newspaper tubes) involve your child in household activities that involve math. (e.g. measuring in the kitchen, setting the table, pairing socks) look for and describe mathematics in the books you read with your child. (e.g., find patterns, count objects, find shapes, identify probability) support homework completion by being a colearner and encourage perseverance to think TCDSB Family Math Activities, K to 8

4 About the Family Math Activities Educational Goals Parents/guardians will: experience different strategies for engaging their children in mathematics learning (e.g., solving math problems, playing math games, using mental math challenges) develop an awareness of the range of mathematical concepts across kindergarten to grade 8 using different mathematics learning tools use and develop their mathematical communication strategies Family Math Activities Parents/guardians and students will preview and collaboratively engage in math takehome activities using math learning tools, such as: solving math problems playing math games solving mental math challenges Table of Contents Cards and Number Cubes (Dice). 5 2 Colour Counters 13 Interlocking Cubes 21 Pattern Blocks 29 Square Tiles.. 37 Tangrams 45 TCDSB Family Math Activities, K to 8 4

5 WHICH NUMBER COMES UP THE MOST? Kindergarten Describe probability using informal language 1 deck of cards 1 dice Problem to Solve Take out the jacks, queens and kings; aces are worth 1 Problem Which number comes up the most with rolling 1 dice or drawing from a deck of playing cards? Solving the Problem Look at the numbers in 1 deck of cards or 1 dice. Predict which number (1 to 10) will come up most often when drawing a card from 1 deck of playing cards and when rolling 1 dice. Roll the dice 10 times. Record the number that came up from each dice roll. Draw 10 cards. Record the number that came up after each card drawn. Compare your prediction with the numbers you recorded. What did you find out? Roll the dice 20 times again. Record the numbers that came up from each dice roll. Draw 20 cards. Record the number that came up after each card drawn. Compare your prediction with the numbers you recorded. What did you find out? Why do some numbers come up more often than others? Do the same numbers come up more than when rolling 1 dice or when drawing playing cards? Roll 2 die at the same time. Use half of the deck of playing cards. ADDITION GO FISH Kindergarten Composing whole numbers to 7 1 deck of playing cards Math Game Instructions Players 2 to 4 Remove all cards higher than 7; aces are worth 1 Goal highest number of pairs at end of game (all cards matched) Playing the Game Deal out 5 cards to each player and keep remaining cards in a draw pile. All players lay down pairs of cards that sum (add) to 7 (i.e., 6+1; 5+2; 4+3). Player to right of the dealer asks other players, one at a time for a card that he/she needs to make a sum of 7. Player can keep asking for cars until no further matches When no other matches can be made, player is told to Go Fish and draw a card from the pile. The next player takes a turn trying to make pairs of cards that sum to 7. When a player runs out of cards, he chooses 5 cards from the draw pile. Game ends when all cards have been matched into pairs. How did you know when a pair of playing cards made (summed to) 7? Is possible that not all of the laying cards will pair up to make 7? Change to sum to a higher number, like 8, 9 or 10 (then remove cards higher than 8, 9 or 10). 5 TCDSB Family Math Activities, K to 8

6 MORE THAN, LESS THAN, OR SAME? Kindergarten Comparing whole numbers as more than, less than and 1 deck of cards the same or 2 die Mental Math Activity People 2 people Use 1 deck of playing cards, aces to 10 only; divide cards into black and red card piles Using Mental Math Each person shuffles their set of cards (black or red set) Each person faces up one card. Compare the numbers on the cards. If red card number is greater than the black card number, put both cards in one pile (called red pile). If black card number is greater than the red card number, put both cards in second pile, called the black pile Tf the same number comes up for black and red, the cards are put in a separate pile. Mental math practice ends when 1 player has no more cards. How do you know when 1 number is more than another number? How do you know when 1 number is less than another number? Which pile (red or black) had the greatest number of pairs? Why? Roll 2 die rather than face up cards from 2 piles or roll 1 die and face up 1 card from 1 deck. When compare numbers on cards, focus on number less than the other number. MAKING TENS Grades 1 and 2 Add 1 digit whole numbers to make ten 1 deck of playing cards Problem to Solve Jane and Kyle are playing a game with 1 deck of playing cards. The jacks, queens and kings are removed. The player who makes the greatest number of pairs of cards that sum to 10 wins the game. For example, Kyle faces up 2 cards to show an ace and 9 to make 10. Jane faces up 2 cards to show a 2 and 5, so she returns them to her pile and shuffles her cards. What are the greatest number of pairs of cards that sum 10 that Jane and Kyle can make? How do you know? What are the possible pairs of cards that make 10? Is it possible that some cards will not be paired to make a ten? Why? Pairs of cards make odd numbers or even numbers. Use 2 decks of cards. TCDSB Family Math Activities, K to 8 6

7 ADDITION CONCENTRATION Grades 1 and 2 Add 2 digit whole numbers using mental strategies cards, number cubes (dice) Math Game Instructions Players 2 to 4 1 deck for 2 players; jacks, queens and kings are worth 10; aces are worth 1 Goal Highest sum at the end of the game (no cards left) Playing the Game Face down 1 deck of playing cards in an array (4 rows x13 columns cards = 52 playing cards) Take turns facing up 2 cards at a time. If the cards have 4 different number, player can make 2 sets of numbers and add them together (e.g., 4, 6 -> 4+6=10; 10, 5 -> 10+5=15 Any cards that are the same number are returned face down. Keep track of points by totaling the scare after each turn. Game ends when there are no cards left to face up. What addition strategy did you use? How did you decide how you made numbers from the cards to add together? Subtract the 2 cards to get the difference; difference is the number of points gained. Each player faces up a card at the same time, smaller card gets the sum of the 2 cards for points WHAT S THE DIFFERENCE? Grades 1 and 2 Subtract 1 digit whole numbers using mental strategies 1 deck of cards or 2 die Mental Math Activity Persons deck of cards or 2 die for 2 players; aces are worth 1; remove jacks, queens and kings Mental Math Challenge Divide the cards equally among the people. Each person faces up 1 card at the same time. The person with the larger number identifies the difference between the 2 numbers. When the 2 cards have the same number, they are placed in a pile. When a person has no cards left, the cards in the pile are shuffled and divided equally between the 2 people. Mental math practice ends when there are no more cards to compare. What strategies did you use to figure out the difference between two cards? What does difference mean? How does difference relate to subtraction? Person with the smaller number identifies the difference between the 2 numbers. Add 1 ten to one of the whole numbers. 7 TCDSB Family Math Activities, K to 8

8 WHAT S THE NEXT CARD? Grades 3 and 4 Predicting the frequency of an outcome cards, numbered 1 to 10 Problem to Solve Kathy has ten cards, numbered 1 to 10. She mixes them up and faces them down in a row. She shows the first four cards 8, 3, 2, 5. What is the chance that the next number (5 th card) will be lower than 5? How do you know? If the 5 th card is 1, what is the probability that the 6 th card will be lower than 5? Explain. If the 6 th card is 4, what is the probability that the 7 th card will be lower than 5? Explain. Is it possible for another 8 to come up by the 7 th card? How do you know? Carry out the problem with 10 cards, number 1 to 10. How does your experiment compare with your prediction? MULTIPLICATION CONCENTRATION Grades 3 and 4 Multiplying pairs of numbers and add 1 digit and 2- digit whole numbers. 1 to 2 decks of playing cards Math Game Instructions Players 2 to 4 1 deck for 2 players; 2 decks for 4 players; remove 8s and up; aces are worth 1 Goal Highest sum at end of the game (no cards left) Playing the Game Face down 1 deck of playing cards in an array. Take turns facing up 2 cards. If the cards have the same number, player can multiply the numbers to get points (e.g., 2x2 = 4 points). If cards are not the same number, the 2 cards are returned face down. Keep track of points by totaling the scare after each turn. Game ends when there are no cards left. How did you know which cards to choose to make points? What did you think about to multiply 2 same numbers, like 3x3 or 5 x 5? What strategies did you use to add 1 and 2 digit whole numbers? Gain points if turn up pairs of same numbers (e.g., 2 x 2=4 points) and lose points if turn up pairs of different numbers (2x3=6 lose 6 points). Name and description of variation 2. TCDSB Family Math Activities, K to 8 8

9 WHO S CLOSER TO 100 Grades 3 and 4 Add and subtract 2 digit whole numbers using mental strategies 1 deck of cards Mental Math Activity Persons 2 or 2 groups of 2 students face up 5 cards Mental Math Challenge Shuffle a deck of cards. Face up 5 cards. Use numbers on those cards to create any 1 and 2 digit whole numbers to add up and subtract as close to 100 as possible. Mental math practice ends where there are less than 5 cards left. Describe the addition and subtraction strategies that you used. How did you decide which numbers to make using the cards? Use 4 cards to make 50. Include multiplication of 1 digit whole numbers. IS THIS A FAIR GAME? Grades 5 and 6 Comparing theoretical and experimental probability 2 die Problem to Solve Stefana and Grace are playing the Multiplying Dice Game. Here are the rules: Roll 2 die and multiply the two numbers. If the product is even, Stefana wins 1 point. If the product is odd, Grace wins 1 point. Is this a fair game? Does Stefana and Grace both have an equal chance of winning? How do you know? What does a fair game mean within the context of this game, Multiplying Dice? What does a unfair game mean within the context of this game, Multiplying Dice? Scoring if product is equal to and greater than 24, half the score. Scoring if the product is equal to and greater than 12 triple the score> 9 TCDSB Family Math Activities, K to 8

10 AIM TO BE LAST Grades 5 and 6 Multiply and add 1 and 2 digit whole numbers using mental strategies 1 deck of cards or 2 die Math Game Instructions Players - 2 Goal highest score at the end of the game Playing the Game Shuffle the deck and place 13 cards face down in a circle. Players take turns picking up 1 or 2 cards at a time (their choice) to make 1 or 2 digit number with 1 or 2 cards. (e.g., pick up 9, make 9; pick up 3 and 6, make 63 or 36) Players record the cards they picked up, the number they made and the score for the turn and the cumulative score by the end of that turn. Player who picks up the last card scores 50 additional points Deal another 13 cards for additional rounds (3 more). Game ends when there are no cards left. Is it best to be the last player? Why or why not? How do you decide whether to make a 1 digit or 2 digit number? If an odd 1 digit or 2 digit whole number is made from 1 or 2 cards (, player has the option to have the other player deduct that amount from their total score. If 2 cards are drawn with the same number, player makes double the 2 digit number (e.g., 3, 3 are drawn, so points is 33x2=66). WHAT S THE FINAL NUMBER? Grades 5 and 6 Add, subtract, multiply and divide 1 digit numbers using mental strategies 1 deck of cards or 5 die Mental Math Activity Persons 2 to 4 Mental Math Challenge Start with <card 1 or dice 1>. Double it. Add <card 2 or dice 2>. Subtract <card 3 or dice 3>. Multiply by <card 4 or dice 4>. Divide by <card 5 or dice 5>. What s the final number? Describe the strategies you used to add, subtract, multiply and/or divide? Why are some final numbers estimates rather than actual results? Use only addition and subtraction. Make a number cube with operations and roll it to randomly determine the operation for each card or dice roll. TCDSB Family Math Activities, K to 8 10

11 IS THIS A FAIR GAME? Grades 7and 8 Compare the theoretical and experimental probability of a compound event 3 dice Problem to Solve Have you played Rock, Paper and Scissors? Players A, B and C simultaneously display the rock, paper or scissors sign of their choice. Here s a different way to score: Player A gets 1 point all the signs are the same (e.g., rock, rock, rock) Player B gets 1 point 2 signs match (e.g., rock, rock, paper) Player C gets 1 point no signs match (e.g., rock, paper, scissors) (a) Wilma predicted that this game is not fair. How did she figure that out? (b) Play the game and see if your prediction is true. Roll dice to play the game. Rock (1 or 3), Paper (2 or 4) and Scissors (3 or 6). Roll 3 dice at the same time and keep track of the outcomes. What did you find out? (c) Do all 3 players have an equal chance of winning? Explain. What are the total possible outcomes when playing rock, paper, scissors with 3 people? How could this 3 player game be made fair? 2 players with points for either same or different signs. 3 players with player A and C getting 3 points and player B getting 1 point CLOSEST TO +1 Grades 7 and 8 Adding positive and negative 1-digit integers cards Math Game Instructions Players 2 to 4 players red card is negative and black card is positive; jacks are 11, queens are 12 and kings are 13 Goal player with the most cards wins Playing the Game Shuffle and deal 6 cards per player. Remaining cards are in the pick-up pile. Players take turn laying down a card until a positive 1 is made. (e.g., Player who makes positive 1wins all the cards. When a player runs out of cards, pick up 6 cards from the pick-up pile. Game ends when one player has no more cards and there are no more cards to pick up. Question 1 (Sample Response Question 2 (Sample Response - player with no cards left wins players lay down 2 cards at a time to make 2 digit integers 11 TCDSB Family Math Activities, K to 8

12 MAKE THE TARGET Grades 7 and 8 Use order of operations with integers 1 deck of cards Mental Math Activity Persons 2 to 4 ace is 1, jack is 11, queen is 12 and king is worth 13; red card is negative, black card is positive Mental Math Challenge Shuffle cards and deal 4 cards to each player. People select order of operations for the 4 numbers (from the cards) to make a result closest to 24). Discuss and compare choice of operations and order of operations from other people. Mental math practice ends when 4 cards cannot be dealt to each person. What mental math strategies did you use to select operations? What strategies did you use to determine the order of operations? 3 or 5 cards are dealt to each player. Change the target to a different integer, such as -24 or 13. TCDSB Family Math Activities, K to 8 12

13 SPILL THE NUMBERS Describe number relationships to 10 Problem to Solve What different ways can you show 10 with red and yellow counters? How many times Grab 10 counters and spill them on a surface. How many red counters? How many yellow counters? Record the number of red and yellow counters in a chart. Repeat again until you have all different ways to make ten using red and yellow counters. Kindergarten 2 colour counters How do you know that you have all different ways to make ten? How many times did you have to spill the counters to get all the combinations for 10? Show 5 in different ways. How is 5 related to 10? Show 4 in different ways. Show 8 in different ways. How is 4 related to 8? COUNTER - OH - OH! Counting forwards and backwards Kindergarten 2 colour counters 1 dice Math Game Instructions Players 2 or more Goal player with the most counters wins. Playing the Game Start with a pile of 10 counters, the first player rolls the dice and removes the number of counters indicated by the number cube roll. Each player takes a turn. The game ends when there are no more counters in the pile. Players count their counters; the winner is the player with the most counters. Players can use paper and pencil to keep track of the number of turns. What strategy did you use to count the counters that you took from the pile? What happens to the number of counters in the pile as the counters are removed? Change the starting pile to 5. Did the game end faster or slower than the first game? Why 13 TCDSB Family Math Activities, K to 8

14 QUICK! GUESS MY NUMBER! Kindergarten Recognizing without counting quantities (subitizing) 2 colour counters Mental Math Activity People 2 Mental Math Challenge One person arranges up to 7 counters on a surface (e.g., far apart and/or close together, in an array) while the other players cover their eyes. One person challenges the other person, Quick, Guess my number! Other person guesses the number of counters in the arrangement as quickly as they can. Players then count the number of counters to see if they are right. Repeat with different number of counters. Change roles of arranging the counters and guessing the counters. How did you know the number of the counters that were covered? What did you see? What other ways could you see the counters in order to count them differently? Use 5 counters. Use 10 counters. SHARING COUNTERS Grades 1 and 2 Dividing by sharing equally 2 colour counters Problem to Solve How can you equally share counters? Place 20 counters in a bag. With a partner, take one turn each to pull out one handful of counters. Count out the number of counters each partner has. How many do you have altogether? Who has more?.. Equally share the counters. Show more than one way to equally share the counters. What action did you use to share your counters? How is knowing ways to share 20 counters equally help you to know different ways to share 40 counters equally? Share 30 counters equally. How does knowing about sharing 30 counters equaly help you now different ways to share 60 counters equally? TCDSB Family Math Activities, K to 8 14

15 COUNTER - OH - OH! Grades 1 and 2 Counting forwards and backwards 2 colour counters 1 dice Math Game Instructions Players 2 or more Gaol player with the most counters wins. Playing the Game Start with a pile of 50 counters, the first player rolls the dice and removes the number of counters indicated by the number cube roll. Each player takes a turn. The game ends when there are no more counters in the pile. The players count their counters; the winner is the player with the most counters. Players can use paper and pencil to keep track of the number of turns. What strategy did you use to count the counters that you took from the pile? What happens to the number of counters in the pile as the counters are removed? Increase the starting pile to 20 QUICK IMAGES Grades 1 and 2 Estimate the number of objects in a set and check by counting 2 colour counters blank 8-1/2 x 11 paper Mental Math Activity Persons - 2 Mental Math Challenge Grab a large handful of counters and drop them on the table and cover them with paper. Uncover the counters for 5 sec then cover again. How many counters did you see? How do you know? Uncover the counters to check. Return the counters and repeat the activity. Compare the number of counters you grabbed, the number of counters you saw, and then the number of counters you counted. How close was your estimate. How could you improve the accuracy of your count? How many counters are there, if you imagine double its amount. How many counters are there, if you imagine half its amount. 15 TCDSB Family Math Activities, K to 8

16 SKIP COUNTING PATTERNS Grades 3 and 4 : Count by 2s and 5s Problem to Solve How many numbers do you have to count to get to 100? Use a 100 chart and the counters to represent the 2 patterns Start at 0 and add 2 each time until I get to 100. Start at 0 and add 5 each time until I get to 100. What numbers are counted in both number patterns? 2 colour counters BLM3 Hundreds Chart What are the numbers when you start at 0 and add 3 each time? What are the numbers when you started at 0 and added 4 each time? Start a 1 and add 2 each time to get to 100. Start at 1 and add 5 each time to get to 100. What numbers are counted in both number patterns? Start at 3 and add 3 each time to get to 100. Start at 3 and add 5 each tie to get to 100. What numbers are counted in both number patterns? WHERE IS IT? Grades 3 and 4 Locating objects on a coordinate grid (area) map 2 colour counters BLM4 Interlocking Cube Paper Math Game Instructions Players 2 or more Use the BLM Interlocking Cube Paper to make an area grid map Goal guess the coordinates of the hidden counter Playing the Game Each player gets one coordinate grid and 3 counters spaced out on the grid. Set up a divider so that players cannot see each other s grid. Players place 3 counters on the grid. Take turns guessing the coordinates of each other s counters and give feedback like, found ( if correct guess), keep looking (if far) or very close (It s 1 space away) Keep playing until one player guesses all of the other players coordinates Explain how to use the coordinate grid map to identify location of an object on it. What location or positional words did you use to give feedback about the guesses. Place the 3 counters close together rather than spaced out. Use only 1 counter. TCDSB Family Math Activities, K to 8 16

17 SEING FRACTIONS AS A SET Grades 3 and 4 Represent and compare fractions in a set 2 colour counters paper and pencil Mental Math Activity Take 5 counters, shake them and spill them Record how many red and yellow counters in the set of 5 counters. What fractions do you see? Record the fractions Shake and spill 5 counters again, until you have represented all possible fractions using 5 counters Repeat the entire activity with 10 counters Compare the fractions you see with 5 counters and with 10 counters. How are the fractions similar and how are they different? Explain 2 different fractions with 5 counters and with 10 counters. What is the relationship between the fractions you see with 5 counters and the fractions you see with 10 counters? Use 4 counters sand then 8 counters Use 3 counters then 6 counters and then 12 counters. HOW MANY COUNTERS TO START? Grades 5 and 6 Represent fractions in a set Problem to Solve Ben, Jack and Emma were playing a game with a box of 40 counters they were not using all of them. They each had a small pile of counters. Ben passed a third of his counters to Jack. Jack passed a fourth of his counters to Emma. Emma passed a fifth of her counters to Ben. Then, they all passed on more than one counter. After passing on 1 counter, Ben, Jack and Emma all had the same number of counters. How many counters could Ben, Jack and Emma each have at the start? Show your work. 2 colour counters What does a third of his counters mean? Fourth of his counters? Fifth of her counters mean? Is it true that you need 36 counters were needed to solve this problem? What strategy did you use to solve this problem? Is it true that this problem could be solved with 12 total counters? Explain. Is it true that this problem could not be solved with 40 total counters? Explain. 17 TCDSB Family Math Activities, K to 8

18 THE SUM OF TWO DICE Grades 5 and 6 Add decimal amounts to hundredths 11 2 colour counters 2 die BLM 1 Game board Math Game Instructions Players 2 or more 11 counters and 1 game board per player Goal fewest rolls wins Playing the Game Each numeral represents hundredths (e.g., 2 means 2 hundredths or 0.02). Each number on the dice represents hundredths Each player arranges 11 counters on the game strip and records their arrangement. Players can place more than one counter on a number if they choose. Once the counters are arranged, players take turns rolling the dice. For each roll, a player can remove one counter, if it is on the sum rolled. Players keep track of the number of rolls of the dice it takes to clear their game board. Fewest rolls wins. How did your arrangement change from one game to the next? Why where some sums harder to roll than others? Players can choose to remove a counter (subtract hundredths) from their board or add (hundredths) a counter to their opponents board that matches the sum rolled. WHAT S THE PATTERN RULE? Grades 5 and 6 Describing pattern rules in words 2 colour counters Mental Math Activity What is staying the same? What is changing? What s the pattern rule? What s the term value for the 10 th figure (at term number, 10)? What would the table of values be for this growing pattern? What is the changing variable in this growing pattern? Change the term number where the original figure 1 (term number is 1) and now figure 0 or term number is 0. What if there are 2 yellow counters at every term number. How does that change the patterning rule? TCDSB Family Math Activities, K to 8 18

19 DIVIDING FRACTIONS Grades 7 and 8 Divide a whole number by a fraction Problem to Solve Why is 6 4 not the same as 6 ¼? Use colour counters to show your solution 2 colour counters What does 6 4 mean, in terms of the size of one group and the number of groups? What does 6 ¼ mean, in terms of the size of one group and the number of groups? Why is 60 4 not the same as 60 ¼? How does the quotient of 60 4 and 60 ¼ relate to the quote of 6 4 and 6 ¼? FRACTION BINGO Grades 7 and 8 Add and subtract fractions with simple like and unlike denominators 2 colour counters 2 dice Math Game Instructions Players 2 Goal to have a score closest to 0 Playing the Game Make a plying card by recording on a 3x3 grid, 9 fractions that are close to 0, using denominators 1, 2 3, 4, 5 or 6. Roll a pair of dice two times. Use 1 dice roll as the numerator and the other dice roll as the denominator of one proper fraction. Roll a second time to determine the 2 nd proper fraction. Choose the sum or difference of the two fractions is on a card, put a counter on the number on your 3x3 grid. Take turns rolling and calculating. Check each other s work. The winner is the first player with three counters in a row horizontally, vertically, or diagonally. How do you know when two fractions are equivalent? How do you know which fraction that is the result of a sum or difference is closest to 0? Math Activity Variation Use numbers on the dice roll as improper fractions. Multiply fractions to get a result closest to TCDSB Family Math Activities, K to 8

20 INTEGER OPERATIONS Grades 7 and 8 Represent integer operations Mental Math Activity Visualize this integer equation using colour counters. [(-6) + (+3) x (+8)] (6) - (-3) = (6) 2 colour counters What is the order of integer operations for this equation? If the brackets are removed, is the final result (6) changed to a different result? Why? If the (-6) is changed to (-4) and (6) is changed to (4) how, is the final result changed? Explain. If the (-6) is changed to (-2) and (6) is changed to (2), how is the final result changed? Explain. TCDSB Family Math Activities, K to 8 20

21 MAKING A PATTERN Create repeating and growing patterns Kindergarten interlocking cubes Problem to Solve What different repeating patterns can be made with only 10 yellow and 10 green cubes? Show 2 different repeating patterns, with at least 3 repetitions. What is repeating in your pattern? How many repeats are in your pattern? Use 5 yellow, 5 green and 5 red cubes. Use only 10 yellow cubes. RACE TO FIVE OR TEN Adding and subtracting numbers to 5 or 10 Kindergarten interlocking cubes, 2 die BLM2 Race to 5 or 10 Math Game Instructions Players - 2 or more cover one dice with paper and write + or - on 3 sides of the dice each, one 5-frame Goal fill exactly one 5-frame with 5 cubes Playing the Game Take turns rolling the number dice and +/- dice. If the + comes up on the dice, then place the number of cube (as on the number dice) on the 5- frame. If - then remove the number of cubes (as on the number dice) on the 5-frame The goal is to get exactly 5 cubes on in the frame. If a player goes over 5, then they have to start a 10-frame and aim to get exactly 10 cues on the 10-frame How could you keep track of the number of cubes put on and taken off the 5-frame or 10-frame? Do some numbers come up more often than other numbers when rolling the number dice? If score goes over 5, add another 5 frame; if score goes over 10, add another 5 frame. 21 TCDSB Family Math Activities, K to 8

22 MEASURING LENGTHS USING CUBES Measure lengths using non-standard units Kindergarten interlocking cubes Mental Math Activity People 2 Mental Math Challenge Look at objects around you whose length can be measured. Think about the length of paper, a shoe, the width of a door Estimate (visualize) the number of cubes that match the length of an object. Check the estimate by lining up and counting the number of cubes (end to end) that it takes for match the length of an object. How close is your estimate to the actual length of the object, using the cubes? How could the estimate and actual measurement be closer when using the cubes? What could you do differently to estimate the length of another object using cubes? Choose objects to measure that you estimate are less than 5 cubes long? Choose objects to measure that you estimate are about 10 cubes long? MAKING PREDICTIONS USING PATTERNS Grades 1 and 2 Skip counting to solve patterning problems interlocking cubes 6 blue, 6 orange, 6 yellow Problem to Solve How can you make a pattern with interlocking cubes to show skip counting by two s? Discuss your ideas. Predict what colour the eleventh cube will be. Create your pattern. Record your colour pattern and number the cubes. Was your prediction of the colour for the eleventh cube correct? Why or Why not. Use your interlocking cubes to make a skip counting pattern of three s. What colour is the eleventh cube? Record your pattern. Explain how it shows a skip counting pattern for threes. Repeat this pattern using skip counting with 5 interlocking cubes. Explain your pattern using colours, using numbers. How can you change your pattern of two s (or three s) to show skip counting by three s (or five s) Create a pattern of twos so that the 7 th cube will be (choose a colour) Name and description of variation 2 TCDSB Family Math Activities, K to 8 22

23 GUESS AND CHECK TEN Grades 1 and 2 Predicting the outcome of an event 20 interlocking cubes 1 brown paper bag paper, pencil, crayons Math Game Instructions Players 2 or more Goal first to reach 10 points First player reveals and then places 2 orange and 8 green interlocking cubes in a bag. Second player reveals and then places 2 yellow, 2 red, 2 orange, 2 blue, 2 green interlocking cubes in a bag. Each player takes turns predicting and then drawing one colour cube from bag. A correct prediction is worth 1 point. Player who reaches 10 points to win. How did you decide which colour to predict? Which player had a better chance of drawing a green cube? Why? Use 5 orange and 5 green interlocking cubes. Use 8 orange and 2 green interlocking cubes. WHAT DOES A 25 PATTERN LOOK LIKE? Grades 1 and 2 Making combinations of 25 using different values of cubes interlocking cubes blue, 6 yellow, 6 green Mental Math Activity If blue cubes are 1, yellow cubes are 2 and green cubes are 5, then what would a pattern worth 25 look like? What does the least number of cubes in a pattern worth 25 look like? Which kind of pattern did you use: repeating or growing? Use 9 blue and 9 yellow cubes. Use 6 blue and 12 yellow cubes. 23 TCDSB Family Math Activities, K to 8

24 THE STAIRCASE Grades 3 and 4 Describing and extending a pattern. Problem to Solve How can you figure out the number of cubes you need to build a staircase without counting every cube? Build staircases with steps (see diagram) that are 3 cubes wide using cubes. Look for a pattern - predict the number of cubes you would need to make a 6-step staircase. Describe the pattern rule for the staircase. Is the pattern repeating or growing? How do you know? Make steps that are 5 cubes wide. Predict the number of cubes to make a 10 step staircase. interlocking cubes LOOSE CABOOSE Grades 3 and 4 Making equal size groups interlocking cubes Math Game: Players 2 Goal greatest number of points wins Playing the Game Start with a pile of 27 snap cubes Pick a number between 1 10 to decide how many cubes to take from the pile. (e.g., if you choose 6, then take away 6 cubes at a time, meaning the group size of cubes is 6) Take turns removing a specific number of cubes from the pile of 27 cubes, until there are no more cubes of that group size to take from the pile (e.g., group size of 6, mean that on the 5 th turn, there will be 3 cubes left) For every group of cubes removed, 1 point is gained. Start with another pile of cubes, like 24. Pick another number between 1-10, to determine group size of cubes. Take turns removing the same group size of cubes until there are no more cubes of that group size to take away from the pile. What numbers could you make into 2 trains with no leftover cubes? What happened when you chose the number 1? Start with a pile of 37 cubes. Start with a pile of 54 cubes. TCDSB Family Math Activities, K to 8 24

25 NUMBER TOWERS Grades 3 and 4 Adding and subtracting 2 digit whole numbers using mental strategies. interlocking cubes Mental Math Activity People 2 yellow cubes represent tens and blue cubes represent ones; 1 tower is a set of cubes attached (e.g., 2 yellow, 4 blue makes a tower of 6 cubes) Mental Math Challenge Make seven different towers of 2 digit numbers using yellow (tens) and blue (ones) cubes (e.g., 2 yellow, 4 blue represent 2 tens and 4 ones or 24). Take turns challenging each other to add three or more addends of 2 digit numbers (e.g., How many altogether? 2 yellow,4 blue; 4 yellow, 2 blue; 3 yellow, 3 blue à = 9 tens + 9 ones = 99 What strategy did you use to add three addends of 2 digit numbers? Which combinations of 2 digit numbers are easier and more difficult to add? Determine the difference between 2 towers; that is, subtract two 2 digit whole numbers. Increase the number of addends to four and five 2 digit whole numbers. INVESTIGATING PATTERNS Grades 5 and 6 Extending growing patterns interlocking cubes Problem to Solve What does the 10 th figure look like? Build the three cube models as shown in the diagram. What will the 4th figure look like? Build it. Without building the 5th figure, build the 6th figure. How many cubes would be in the 10th figure? How did you decide the number of cubes for the 4 th, 5 th and 6 th cube figure? How do you know that the 10 th cube figure you built is accurate? Build the first three models of a different growing pattern. Challenge a friend to determine the 10th figure. 25 TCDSB Family Math Activities, K to 8

26 END OF THE LINE Grades 5 and 6 Analysing game playing strategies to improve the likelihood of winning the game. interlocking cubes Math Game Instructions Players 2 Goal to avoid taking the last cube - start the game with a line of 21 connected cubes. Playing the Game Players take turns removing 1, 2, or 3 linked cube from the line of cubes. The player that holds the last cube in at the end of the line and loses the game Does it matter which player goes first? Why did you decide to take 1, 2, or 3 cubes on one turn? Player taking the last cube wins Each player can only take 2 or 3 cubes; the player who takes the last cube loses Each player can only take 1 or 3 cubes; the player who takes the last cube loses WHAT IS THE SMALLEST SURFACE AREA? Grades 5 and 6 Estimating the surface area of a cube structure interlocking cubes Mental Math Activity People 2 Mental Math Challenge Create as many different cube structures from as you can that have 12 linking cubes. Determine the number of square faces without viewing all faces. Check by examining all faces. Sort cube structures that have the same number of square faces What do you notice about the structure that has the least number of square faces visible? What visualization strategies did you use to determine the number of faces on the structure that you couldn t see? Use 16, 24, or 36 cubes. Make only tower (straight line) structures. TCDSB Family Math Activities, K to 8 26

27 BUILDING TOWERS Grades 7 and 8 Determining the relationship between the height, the area of the base, and the volume of prisms Problem to Solve Each tower pictured here is a prism. Build each prism and determine the volume of each building by counting cubes. Complete the table of measures for each tower Tower A B C Area of Base Height of Tower Volume counting cubes interlocking cubes pencils, markers BLM4 Interlocking Cubes Paper What relationship do you notice between volume, area of the base, and height? Make a generalization (i.e., formula) for calculating volume of a prism when you know the area of the base and the height of the prism. Test your formula for accuracy by building two other prism towers and determining the volume. Sketch your towers and show calculations on this table. Describe the accuracy of your formula and explain any adjustments that you made. What do you notice about the structure that has the least number of linking cube faces visible? Try the same activity with 16 or 24 cubes. CHAIR AND TABLE Grades 7 and 8 Enlarging and reducing 3D figures Tower A Tower B Tower C interlocking cubes Mental Math Activity Make a table using cubes. How many cubes did you use? Visualize the size of the table doubled. How many cubes do you need? Check your estimate by building a table double the original size. Visualize the size of the table halved. How many cubes do you need? Check your estimate by building a table half its original size. What parts of the table did you double? What is the relationship between the number of cubes for the original table and table doubled? Build a different object, like a chair. Build a tower only. (Its easier to see doubling and halving.) 27 TCDSB Family Math Activities, K to 8

28 ROLLING FOR A CATERPILLAR Grades 7 and 8 Analysing the frequency of dice rolls in relation to game playing strategies Math Game Instructions (adapted from Edutopia) Players - 2 to 4 Goal - build the longest caterpillar with blocks by the end of the game. Playing the Game Each player begins the game by placing two blocks on any two mushroom spaces they choose. One turn consists of a player rolling the two dice and recording the sum on a frequency chart. Any player with a block on a mushroom space touching the sum rolled receives an extra block of his or her color. Each turn also includes the opportunity to place accumulated blocks in order to build the longest caterpillar on the board. The game ends when there are no more spaces available on the board. Players then reference their dice rolls on the frequency chart to determine the most frequently rolled number. That number is the "bird," which eats the caterpillars at the end of the game. Players must remove pieces from any space around the number that has been determined to be the bird. The player with the longest caterpillar intact at the end of this explosion is the winner! interlocking cubes BLM5 Caterpillar Game Board, 2 die, frequency chart How do you decide if the first move is a "good" and "bad" move, in terms of where the first two blocks are placed on mushroom spaces? How these spaces on the board correspond to the most and least frequently rolled two dice sums? Changes on first move place. TCDSB Family Math Activities, K to 8 28

29 HOW MANY MORE? Creating the same shape using different combinations of 2D shapes Kindergarten pattern blocks BLM6 Pattern Block paper Problem to Solve What different ways can the same shape be made? Put 1 trapezoid and 1 hexagon together to make a shape. Make this shape using different number and types of pattern blocks. Sketch the different ways that the same shape is made using pattern block paper. How do you know your shape is the same? Why is it possible to make the shape using several same shapes (e.g., using only green triangles)? Create a shape using the pattern blocks. Ask : How can you copy my shape? you cannot use the same blocks I did. ATTRIBUTE CONNECTION Covering a space using 2D shapes Kindergarten pattern blocks BLM6 Pattern Block paper Math Game Instructions Players 2 to 4 Goal be the last player to cover a space with a pattern block Playing the Game Each player selects 8 pattern blocks Players take turns take turns placing a pattern block to cover a space on the game board. When a player has placed 8 blocks, then they take another more pattern blocks. Game ends when there is no more space on the game board to cover by a whole pattern block. Last person to cover space on the game board wins. Which pattern block shape did you use more often? Why? Which pattern block shape did you use less often? Why? Last person to cover the space loses. Use only 1 type or 2 types of pattern blocks. 29 TCDSB Family Math Activities, K to 8

30 MAKING SAME IMAGES Using spatial relationships to compose pictures using 2D shapes Kindergarten pattern blocks Mental Math Activity Persons 2 Mental Math Challenge Put up a visual divider, like a book between the 2 people. 1 person makes and gives spatial directions (e.g., above, below, to the right, to the left) to tell how to make a picture of an object (e.g., dog) using pattern blocks. 2 nd person makes the picture fro the oral directions using pattern blocks Compare the intended picture with the picture made from the oral instructions. Switch roles where the 2 nd person makes and gives spatial directions while the 1 st person makes the picture from the oral instructions. How did you decide which pattern blocks to use to make the picture? How did you decide what to tell your partner so he/she could make your picture using pattern blocks? When you compare your picture with your partner s picture, what parts were the same? What parts were different? How did that happen? Try only using 2 types of pattern blocks. Which ones did you choose to use? UNDER COVER Grades 1 and 2 Compose and decompose shapes using smaller or larger shapes pattern blocks number cube Problem to Solve Is it possible to make the same shape with less number of pattern blocks? Create a shape with the pattern blocks. Trace your shape Cover your shape using the least number of blocks? How many blocks did you use? Now cover your shape using the greatest number of blocks? How many blocks did you use? What strategy did you use to cover the same shape with the least number of pattern blocks? What strategy did you use to cover the same shape with the greatest number of pattern blocks? Double the size of the original shape. How does that change the least number of blocks used? How does that change the greatest number of blocks used? Change the shape. TCDSB Family Math Activities, K to 8 30

31 NAME MY PATTERN Grades 1 and 2 Creating and describe repeating or growing patterns pattern blocks dice Math Game Instructions Players - 2 Goal - first player to reach 10 points wins Playing the Game Players roll dice to determine who goes first; lowest roll goes first Player 1 rolls the number cube to indicate the number of pattern blocks to use to begin a repeating or growing pattern. Player 2 rolls the dice to indicate the number of shapes to use to continue the pattern started by player 1, then describes the pattern rule (1 point if accurate) and/or pattern attributes (1 point if accurate). Repeat the process with player 2 starting. First player to reach 10 points wins. What are the attributes of each pattern? What changes and what stays the same in the patterns? Use 1 pattern block shape only. Use 2 pattern block shapes only. COVER THE BOARD Grades 1 and 2 Making Pictures and Movement pattern blocks Mental Math Activity Persons - 2 Mental Math Challenge Person 1 creates an animal using pattern blocks. Person 2 imagines which pattern blocks to move or change so that the animal looks like it is walking. Person 1 imagines which pattern blocks to move or change so that the animal looks like it is looking up towards the sky. Person 1 builds the shape with the change to check. Person 2 creates a different animal using pattern blocks. Repeat the process. How did you decide which pattern block to move or change to show the movement? Which part of the shape did you use to show movement? Why? Visualize and then discuss how to make a pattern block animal, then take turns adding one pattern block at a time to build the picture, without communicating to one another. Create pictures of objects in the classroom. 31 TCDSB Family Math Activities, K to 8

32 THE TOY FACTORY Grades 3 and 4 Represent money amounts to $10 pattern blocks Problem to Solve: Is it possible to build 2 different toys that are made of the same number and type of pattern blocks and are worth $9.75? The values of the pattern blocks are: green triangle (5 ), blue rhombus, square, trapezoid, parallelogram (10 ), hexagon (25 ) Use any number or combination of pattern blocks. Show the calculations to determine the worth of each toy. Which pattern block did you use most often? Why? What strategy did you use to make 2 different toys with the same number and type of pattern blocks? Change the value of each pattern block. Use only 2 types of pattern blocks. DON T BREAK THE WAGON Grades 3 and 4 Use strategies to cover an area with the least or greatest number of 2D shapes pattern blocks BLM6 Pattern Block Paper Math Game Instructions: Players 2 Make the game board by drawing an outline of a wagon on pattern block paper, using the pattern block paper lines Goal avoid placing the last block to win Playing the Game Take turns placing blocks on the game board. The blocks must fit within the outline. Player who places the last block on the board breaks the wagon! Avoid being the last person to place a block and break the wagon. Play again. Is it better to go first or second? Did your strategy change as the board became more full? How many pattern blocks were used the 1 st time, the 2 nd time? Was the game played in a shorter amount of time the 1 st or 2 nd time? Why? Make a different shape for the wagon as game board outline. Use only 1 or 2 types of pattern blocks. TCDSB Family Math Activities, K to 8 32

33 PATTERN BLOCK WALLS Grades 3 and 4 Create and extend a growing pattern pattern blocks Mental Math Activity Persons 2 Mental Math Challenge Person 1 imagines a growing pattern and explains the pattern rule. Person 2 creates the growing pattern from person 1 s description. Change roles and repeat the process. What stayed the same and what changed in your growing pattern? What information is important to include in a pattern rule? Growing pattern starts at 5, but changes in a way determined by the persons. Growing pattern changes by add 5 again and again, but the person determines the start. HOW MANY WAYS CAN YOU MAKE 360 O? Grades 5 and 6 Creating polygons with rotational symmetry. pattern blocks Problem to Solve How many ways can 360 o be made? Place combination of pattern blocks adjacent to one another to create a design where the pattern blocks meet at one point. Create such a design with 1 type, 2 types, 3 types, 4 types, 5 types or 6 types of pattern blocks. How do you know you ve created a set that is 360 o How does the design change as you increase the type of pattern blocks used? What designs have a line of symmetry? How does the choice and number of pattern blocks used contribute to creating a line or lines of symmetry within the design? What designs have rotational symmetry? How does the choice and number of pattern blocks used contribute to creating a rotational symmetry within the design? Is it possible to create a 360 o design that has 1 line, 2 lines, 3 lines, 4 lines, 5 lines or 6 lines of symmetry? 33 TCDSB Family Math Activities, K to 8

34 TILE IT UP! Grades 5 and 6 Make calculations using proportional relationships pattern blocks, dice BLM6 Pattern Block Paper Math Game Instructions Players 2 to 4 exclude square and the parallelogram Goal cover the greatest area Playing the Game - Every player chooses a different pattern block Roll a die to determine the number of pattern blocks that can place on the Pattern Block Paper game board in one turn. A player skips a turn when they cannot place a pattern block on the grid. Make a chart to keep track of the number of blocks each player places on the game board. Determine value of the area covered by the pattern blocks using proportional reasoning (i.e., If the triangle - $1.25, then 1 blue rhombus is $1.25 x 2 = $2.50 as 2 triangles). When no more pattern blocks can be placed on the game board, calculate the total area covered by your team s blocks. Player(s) that cover(s) the greater area wins. How did you choose which block you should use? How did you decide where to place your blocks? What strategy did you use to determine the value of the pattern blocks placed on the game board? Change the values of the pattern blocks Include the square and parallelogram and assign values for each shape. CREATING FRACTION BLOCK FRACTIONS Grades 5 and 6 Represent equivalent fractions pattern blocks 2 die Mental Math Activity Roll die and use one number as the numerator and the other number as the denominator of a proper fraction. Visualize different pattern blocks models of the fraction (include equivalent fractions). Create different representations of the same fraction using the pattern blocks How are the pattern blocks helpful for creating equivalent fractions? Represent the fraction using pattern blocks as a set of objects, rather than as an area model. Use 3 dice to create a mixed number (greater than one). Make an improper fraction. TCDSB Family Math Activities, K to 8 34

35 DANCING BLOCK PEOPLE Grades 7 and 8 Solve problems that involve determining whole number percents pattern blocks Problem to Solve Is it possible that the 2 dancing people represents different fractional amounts? The "Dancing Block People" are made out of three different pattern blocks. What s the value of the whole? What is the percentage of the design is made up of each shape? Explain your thinking. Change the value of the whole. Now what is the percentage of the design is made up of each shape? Explain your thinking. Is it possible to change the value of the whole again? If so, what s the percentage of the design is made up of each shape? Explain your thinking. How are the pattern block shapes related to each other? How does the value of the whole impact the value of its fractional parts? Number of original figures are increased to three or four. Original shapes can be changed (e.g., house, car). REDUCING PATTERN BLOCKS Grades 7 and 8 Creating composite shapes using combinations of 2D shapes Math Game Instructions Players - 2 Goal greatest number of combinations wins Playing the Game Take turns creating a different combination of pattern blocks to make the same shape. Player that makes the greatest number of combinations of the same shape wins the game. pattern blocks How are the pattern blocks related to one another? How are the areas of the pattern blocks related to one another? What strategies did you use to create combinations of the same shape? Use composite shapes that are made up of 4 or more pattern blocks. Use pictures of objects made from pattern blocks. 1 Trapezoid + 2 Rhombi (3 shapes ) reduces to 1 Hexagon + 1 Triangle (2 shapes) 35 TCDSB Family Math Activities, K to 8

36 SHAPES, SHAPES Grades 7 and 8 Compare the area of 2D shapes Mental Math Activity pattern blocks How are the areas of the shapes related? How many triangles will make other given shapes How do you know? Other pattern block shapes are compared. Compare combinations of pattern blocks shapes, rather than single pattern block shapes. TCDSB Family Math Activities, K to 8 36

37 5 SQUARE TILES Kindergarten Build and sort non-traditional shapes Problem to Solve What different shapes can be made with 5 square tiles? List o directions To make shapes from square tiles, the sides must line up end to end Shapes may be the same, but in a different position by a reflection or a rotation. Trace outlines of your shape on the square tiles paper. square tiles BLM7 Square Tiles Paper yes no no What strategies did you use to make different shapes using 5 square tiles. How did you check to make sure that you did not include same shapes. Use 4 square tiles only. Use 6 square tiles only. One Two Three in a Row Develop and use strategies when playing a game. Math Game Instructions Players 2 Goal create 3 a row of 3 tiles through the centre of the game board Playing the Game The first player places square tile on any one of the nine circles on the game board. The second player then places square tile on one of the empty circles. The players continue to take turns placing one counter at a time on a circle. When all six square tiles are on the board, players take turns moving one square tile at a time along a line to an empty circle. The players can not jump square tiles The winner is the first player to create a row of three square tiles through the centre. The game is a draw if neither player can complete a row of three square tiles How did you decide what direction to move the square tiles? Double the square tiles for every circle. Double square tiles for every other circle. Kindergarten 6 square tiles BLM8 3 in a Row Gameboard 37 TCDSB Family Math Activities, K to 8

38 MORE OR LESS? Estimating and counting a set of objects Kindergarten square tiles Mental Math Activity Person 2 Grab a handful of square tiles and dump them on the table and asks, e.g., Are their more or less red_ than _blue_?, Which has the most?, or Which has the least? How many altogether? Other person makes at estimate based on visual inspection. Check the visual estimates by counting the number of square tiles and compare the number of colour square tiles. Compare the estimate to the actual count. Repeat the process again, switching roles. Which colour has more/less than the other colour? What strategies did you use to estimate the number of colour square tiles. Select only 2 colours. Select only 3 colours. MAKING RECTANGLES Grades 1 and 2 Compare rectangles by area Problem to Solve How many different rectangles can you make, using only 20 rectangles? Create different rectangles using 20 rectangles. Sketch each rectangle that you created on the square tile paper. square tiles BLM7 Square Tile Paper How do you know if you have all possible rectangles? What could the rectangle look like if the 20 tiles used only to build the edges of the rectangle? Use 12 square tiles. Use 40 square tiles. TCDSB Family Math Activities, K to 8 38

39 WHERE S YOUR SQUARE TILE? Grades 1 and 2 Describing location of objects using positional language square tiles BLM7 Square Tiles Paper Math Game Instructions Players 2 Assign colour tile to each player and green colour tiles to be the environment objects, 2 game boards. Goal Locate the other player s object first. Playing the Game Agree to place 3 different size green rectangles on both game boards. Put up a visual divider between the 2 game boards. Each player places their one colour square tile on the game board. Take turns asking each other questions about the location of each other s colour square tile using position language like, Is it above the rectangle made of 3 square tiles? Is it to the right of the rectangle made of 4 square tiles? Game ends when a player locates the other player s colour square tile. Which positional words did you use most often? Which object did you use as the reference for other objects? Each player can place 2 colour tiles to find Increase the number of green colour tiles as environmental objects WHAT S MY SHAPE? Grades 1 and 2 Identify a shape by its geometric properties and attributes square tiles Mental Math Activity People 2 Mental Math Challenge Make a 2D shape using 5 square tiles Describe the 2D shape, one geometric attribute at a time (e.g., My shape has 1 side that is 2 linear units. What s my shape) The other person creates the shape using square tiles from each description. Continue until the person accurately creates the shape. Switch roles and repeat the process. yes no no How did you decide what description to tell first and then tell last? What details best helped you the create the shape? Have person 2 ask questions about the shape, rather than person 1 giving one detail at a time. Brainstorm the possible shapes first, before visualizing the shape chosen. 39 TCDSB Family Math Activities, K to 8

40 BEN S GARDEN Grades 3 and 4 Measure area and perimeter of a rectangle using square and linear units. colour square tiles Problem to Solve Ben is designing a fenced in garden that is 24 square units. Show all the different ways you can design his garden plot. Use square tiles. Which garden plot design will have the longest fence? Will the fence be the same length for every shape of garden? Which garden plot design will have the shortest fence? Use 36 square units. Use 48 square units. AREA LOGIC Grades 3 and 4 Measure the area of rectangles using square units colour square tiles BLM7 Square Tile Paper Math Game Instructions Players 2 each player chooses 2 colours of square tiles (to designate the area they covered) Goal Cover the greatest area on the game board Playing the Game Players take turns rolling 2 dice. Use the product of the 2 numbers from each die to determine the area of a rectangle. Cover the area on the square tile paper using square tiles. Player loses a turn when the die rolls require an area that cannot be with square tiles. Continue taking turns until no player can cover a rectangle on the square tile paper with square tiles. Add up the number of square units. What did you notice about the arrangement of square tiles in a rectangle? What strategy did you use to make it difficult for the other player to cover an area on the game board with square tiles? What strategy did you use to help you to cover an area on the game board with square tiles? Use 1 dice to determine the number of square tiles or area to cover on the game board (easier version) Add the value of 2 dice to determine the number of square tiles or area to cover on the game board. TCDSB Family Math Activities, K to 8 40

41 DOUBLES, DOUBLES, DOUBLES Grades 3 and 4 Measure the area of rectangles using square units Mental Math Activity People 2 Mental Math Challenge Visualize a shape using 6 square units. Double the number of square tiles again. Double the number of square tiles again. How many square tiles do you need to make that shape? What does the rectangle look like after the second doubling? Describe the shape to your partner so he/she can build the shape. Have the partner predict the original rectangle (rows x columns) colour square tiles How does doubling the number of square tiles affect the area of the rectangle made from square tiles? Is it true that doubling 2 times means quadrupuling? Explain using your square tile rectangles. Visualize a shape with 10 square units. Visual a final shape that is 60 square units and work backwards to the original shape. AREA POSSIBILITIES Grades 5 and 6 Measuring the perimeter of a rectangle using linear units. square tiles Problem to Solve Lisa plans to use 48 metres of fencing to enclose her dog s rectangular play area. What dimensions would give the dog the largest possible play area? Use square tiles to model different playing areas to determine which play area will have the largest dimensions. What strategy did you use to find rectangles of 48 meters? Based on the models you made, what can you say about how perimeter affects area? Use 25 metres of fencing. Use 36 metres of fencing. 41 TCDSB Family Math Activities, K to 8

42 WHAT S YOUR PREDICTION? Grades 5 and 6 Comparing predictions to the results of an experiment Square tiles paper bag paper and pencil Math Game Instructions Players - 2 or more One player fills the bag with 8 square tiles The second player(s) take turns taking a sample from the bag, recording what they picked, and replacing the tile in the bag. The second player continues until they are ready to make a prediction about how many of each colour tile is in the bag. Players reveal the contents of the bag to compare to the predictions How did you decide how many of each colour tile was in the bag? How could you change the experiment so that your prediction is closer to the actual experimental results? Increase the number of tiles. Increase the number of draws from the bag FRACTION FLAGS Grades 5 and 6 Describe fractions using an area model square tiles Mental Math Activity People - 2 Use the 3 different colour tiles to visualize a rectangular flag designs for flags. what fraction is represented by each of colours on your flag. Use your visualization to tell your partner how to create your flag. Use only fractional language. What was your strategy for determining the fractions that represent the colours of your flag? Determine the percentage of space taken up by each of the colours of your flag. Use 2, 4, or 5 square tiles. TCDSB Family Math Activities, K to 8 42

43 ON THEIR OWN Grades 7 and 8 Organizing and interpreting data, making predictions square tiles paper bags Problem to Solve: There are 30 colour square tiles in a bag. The tiles are red, blue, green, and yellow. How can you figure out the number of tiles of each color square tile by drawing one colour tile at a time? Take turns sampling the tiles in the bag by drawing 1 tile from the bag without looking inside. Each time you draw a tile, record the color and then return the square tile to the bag. Make only 10 draws. Record your group s predictions, the number of each color picked, and the total number of samples you took. Be ready to explain how you made your predictions. Continue the experiment for 10 more draws from the bag. Draw a conclusion. Can you predict the number of different color tiles after first, second, third drawings? What facts support your predictions? Math Activity Variation Different combinations of tiles colors placed in the bag. Increased number of coloured tiles in a bag. ALGE-SCRABBLE Grades 7 and 8 Model linear relationships using tables of values, graphs, and equations square tiles Math Game Instructions Players 2 to 4 Goal highest score wins Playing the Game Place the tiles with their blank sides facing up. Each of 2-4 players chooses 15 tiles- 5 green, 5 blue and 5 yellow tiles at the beginning of the first turn. The red tiles can be used whenever they are needed. Players take turns placing tiles on the game board to form an equation with a variable, such as 3n+2=20. Players score points equal to the value of the variable that solves their equation. At the end of each turn, players draw new tiles to replace the tiles used. Players can use tiles that are already on the game board to build an equation, but the original value of the variable cannot change. The game is finished after five rounds. The player with the highest score wins. What is the relation between the independent and dependent variables? If the game boards includes double value and triple value squares, the variable tiles can be placed on these squares to score extra points. 43 TCDSB Family Math Activities, K to 8

44 RECTANGLES AND SQUARES Grades 7 and 8 Describe the relationship between the lengths of sides in a rectangle and in a square Mental Math Activity Use the square tiles to make five rectangles with the dimension shown. Length (cm) Width (cm) Area (cm! ) Square? (yes/no) square tiles chart paper, markers Side Length of Square (cm) After constructing the shape, record the area of the shape. Try to rearrange the tiles in each rectangle to make a square. Which rectangles can you make into square? Record the side length of each square in your table. Which rectangles from your chart can you make into square? How is the area of each square related to its side length? Various length and widths can be given for students to investigate areas. TCDSB Family Math Activities, K to 8 44

45 TANGRAM MOVES Compose picturess using 2D shapes Problem to Solve A tangram has a set of 7 shapes. Different pictures cam be made with them. How many tangram pieces need to be moved in the first shape to make the second shape? original shape Kindergarten 2 sets of tangrams new shape How are the 2 shapes similar? How are they different? Describe the movement of the 2 shapes from the original shapes to the new shape? Make a different boat by changing 2 tangram pieces. Make the square using 7 tangram pieces. SHAPE MAKER Kindergarten Compose shapes using 2D shapes 1 set of tangrams, blank paper Math Game Instructions Players - 2 Goal player with the greatest number of points wins Playing the Game Make shapes with 3 sides, 4 sides, 5 sides and 6 sides. Use 1 to 7 tangram pieces. Trace around your shapes on paper. Points 3 points for 3-sided shape, 4 points for 4-sided shape, 5 points for 5-sided shape and so on. Add the points gained for each player. How are the shapes you made with tangrams the same? How are the shapes different? Which shapes did you make the most? 3-sided? 4-sided? 5-sided? Change the shapes to animals, like cats. (Show one example of a cat as a starter.) Change the shapes to objects, like boats. 45 TCDSB Family Math Activities, K to 8

46 SAME? DIFFERENT? Kindergarten Show spatial relationships and movements 2 sets of tangrams Mental Math Activity Which tangram pieces should be moved in the first shape to make the second shape? original shape new shape How are the 2 shapes similar? How are they different? Describe the movement of the 2 shapes from the original shapes to the new shape? Rotate the new shape and pose the mental math challenge again. Rotate the original shape and pose the mental math challenge again FILLING IN SHAPES Grades 1 and 2 Cover an outline puzzle with 2D shapes Problem to Solve Use all 7 tangram pieces to fill in these tangram outline puzzles. Is it possible for a tangram outline puzzle to be filled in more than 1 way? 1 set of tangrams BLM12-15 Outline Puzzles 1-4 Which tangram piece did you use most often to start? Why? Which tangram piece did you use most often as the last piece? Why? Change the orientation of an outline puzzle already solved, then challenge the students to solve the tangram outline puzzle again. TCDSB Family Math Activities, K to 8 46

47 CATS GALORE Grades 1 and 2 Make pictures using 2D shapes Math Game Instructions Here is one example of a tangram cat. Make different cats using all 7 tangrams. tangrams What did you keep the same and what did you change to make different cats? Which tangram pieces better showed details of the cat shape than others? Make different letters of the alphabet using all 7 tangrams. Make different people using all 7 tangrams. CATS ON THE MOVE Grades 1 and 2 Describe the relative locations and movements of objects Mental Math Activity Which tangram pieces should be moved to show that the cat is sitting? Name the pieces by their shape (e.g., triangle, square, parallelogram) and their size (e.g., small triangle, medium triangle, large triangle) Where are the tangram pieces moved to in relation to the original tangram pieces? Use words like above, beside, below, to the right of, to the left of and so on. Which shape is below the small triangle? Which shape is above the large triangle? 2 sets tangrams Which tangram pieces should be moved to show that the cat is laying down? Which tangram pieces should be moved to show that the cat s head is looking downwards? 47 TCDSB Family Math Activities, K to 8

48 THERE S MORE THAN 1 SQUARE Grades 3 and 4 Compose a 2D shape using different number of shapes tangrams Problem to Solve Which squares can and cannot be made with tangram pieces? Predict and try each one. Square using 1 tangram piece. Square using 2 tangram pieces Square using 3 tangram pieces. Square using 4 tangram pieces. Square using 5 tangram pieces. Square using 6 tangram pieces. Square using all 7 tangram pieces. What spatial visualization strategies did you do to make each square with different number and types of tangram pieces? What spatial visualization road blacks did you experience? Why? Is it possible to create a triangle using 1, 2, 3, 4, 5, 6 and 7 tangram pieces? Is it possible to create a trapezoid using tangram pieces? WHERE S THE TAN? Grades 3 and 4 Identify location (by spaces) on a grid system 2 sets of tangrams BLM16 Tangram Battleship Grid (Area) Math Game Instructions Players 2 Goal locate the spaces covered by the tan on the tangram battleship grid Playing the Game Place visual barrier at the centre of the Tangram Battleship grid. Each player places 1 tangram piece (tan) on the tangram battleship game board. Players take turn guessing the location of the area covered by the tan. First player to identify the entire area that the tan covers, wins. How did you use the Tangram Battleship grid to identify the area (in square units) covered by the tan? What strategy did you use to choose the grid areas covered by the tan? Use 2 tans that are joined together to make a larger polygon. Identify the location of 1 tan translated 3 square units to the left of the original position. TCDSB Family Math Activities, K to 8 48

49 HOW TO MAKE A TANGRAM Grades 3 and 4 Divide whole objects into equal parts and identify the parts using fractional names tangrams Mental Math Activity Make the square using all 7 tangram pieces. Examine the tangram pieces as fractions of a whole. Visualize the size of the tangram pieces in relation to each other. Make all 7 tangram pieces by paper folding. Are there different ways to make a square using 7 tangram pieces? Question 2 (Sample Response - Is it possible to make a parallelogram that is not a square with all 7 tangram pieces? Is it possible to make a triangle using all seen tangram pieces? BIRD WATCHING Grades 5 and 6 Sort polygons according to geometric properties and attributes tangrams BLM10 Tangram Birds Problem to Solve Students designed many different birds using all 7 tangram pieces. Here is a small sample of their bird designs. What different ways could these birds be sorted and classified in terms of geometric properties (i.e., angles, sides and symmetry) and geometric attributes.) Use BLM XX Tangram Birds to cut out the birds. What did you look for in the bird designs to sort them by sides, angles and symmetry? What is the difference between geometric properties and geometric attributes? Design other birds using all 7 tangram pieces. Sort them according to geometric properties and geometric attributes. 49 TCDSB Family Math Activities, K to 8

50 WHERE S THE TAN? Grades 5 and 6 Identify location (by lattice points) on a grid system tangrams BLM17 Tangram Battleship Lattice Grid Math Game Instructions Players 2 Goal locate the coordinate points of the vertices of the tan on the tangram battleship grid Playing the Game Place visual barrier at the centre of the Tangram Battleship grid. Each player places 1 tangram piece (tan) on the tangram battleship game board. Players take turn guessing the location of vertices of the tan (points on the grid, A1) Game ends when a player to identify all vertices of the tan, wins. How did you use the grid to identify point location of all the vertices of the tan? What strategy did you use to choose each point/vertex of the tan on the Battleship Grid? Use 2 tans that are joined together to make a larger polygon. Identify the location of 1 tan translated 2 linear units east of its original position FROM SITTING TO STANDING Grades 5 and 6 Create and analyse designs by reflecting, translating and/or rotating a shape or shapes Mental Math Activity Which tangram shape or shapes would you transform to make the bird move from its sitting position to a standing position? Visualize the shape transformation(s) to show the bird standing? Explain the transformation(s). Show the transformation(s) that show the bird sitting to showing the bird standing, using the tangrams. tangrams How do geometric transformations show movement? What tools could be used to verify the transformations you described? Which shape and which transformation(s) would you use to show the bird tilting its beak? Which shape and which transformation(s) would you use to show the bird s tail moving? TCDSB Family Math Activities, K to 8 50

51 TANGRAMS AND FRACTIONS Grades 7and 8 Represent fraction operations in expressions and equations. tangrams Problem to Solve Fraction expressions include addition, subtraction, multiplication and division operations. Write equations that represent 1 tangram and its 7 fractional parts. Use different fraction operations. (a) 1 tangram has the value of 1 (b) 1 tangram has the value of 2 (c) 1 tangram has the value of ½ (d) 1 tangram has the value of 2 ½ How are the fraction equations for (a), (b), (c) and (d) related to each other? How do the fractional parts relate to one another? Is this fraction equation accurate for 1 tangram? 1= (1/7) x 7 Why or why not? Write fraction equations that represent 5 tangrams? Write fraction equations that represent 2 ½ tangrams? TANGRAM COVER-UP Grades 7 and 8 Solve problems involving rates and fraction relationships 2 sets of tangrams BLM XX Tangram Paper Math Game Instructions Players 2 Goal player with the greatest number of points wins Playing the Game Players choose tangram pieces from 2 sets of tangrams. Players take turns covering up the game board with one tangram piece at a time. Tangram pieces must be completely placed on the game board grid. Tangram pieces may not overlap. The largest tangram piece (2 large triangles) is worth 10 points. The other tangrams are worth double or quadruple the points of 1 large triangle. For example the small triangle is ¼ of 1 large triangle, so it is worth quadruple the large triangle points or 10 points x 4 = 40 points. Game ends when all the tangram pieces are placed or if there are no more spaces left for a tangram piece to be placed on the game board. What strategy did you focus on for winning the game: choosing small tangram pieces first to make points or placing more tangram pieces than the other player? How did you determine the number of points for each tangram piece? Change the value of the tans, so that the largest tan has the greatest number of points Use 3 sets of tangrams. 51 TCDSB Family Math Activities, K to 8

52 HOW TO MAKE A TANGRAM Grades 7 and 8 Analyse and describe designs using area and angle relationships of polygons tangrams Mental Math Activity (a) Explain how to make a tangram by visualizing paper folding using the known angle relationships and area relationships between the 7 tangram pieces. (b) Test your explanation on a 4 x 4 square grid paper by paper folding. (c) Keep track of the paper folding steps. (d) Through paper folding, were you able to make the 7 tangram pieces accurately? Which angles did you refer to most often when constructing a tangram? Why? How did the 4 x 4 square grid help you in explaining the construction of a tangram? Could the paper folding steps be done in a different order, yet still make the 7 tangram pieces accurately? Could you construct the tangram pieces using fractional relationships only? TCDSB Family Math Activities, K to 8 52

53 BLM 1 The Sums Decimal Hundredths of Two Dice Game Board 53 TCDSB Family Math Activities, K to 8

54 BLM 2 Race to 5 or 10 Game Board TCDSB Family Math Activities, K to 8 54

55 BLM 3 Hundreds Chart for Interlocking Cubes 55 TCDSB Family Math Activities, K to 8

56 BLM 4 Interlocking Cubes Paper TCDSB Family Math Activities, K to 8 56

57 BLM 5 Caterpillar Game Board (adapted from Edutopia) 57 TCDSB Family Math Activities, K to 8

58 BLM 6 Pattern Block Paper TCDSB Family Math Activities, K to 8 58

59 BLM 7 Square Tiles Paper 59 TCDSB Family Math Activities, K to 8

60 BLM 8 Three in a Row Game Board TCDSB Family Math Activities, K to 8 60

61 BLM 9 - Tangrams Paper 61 TCDSB Family Math Activities, K to 8

62 BLM 10 Tangram Birds TCDSB Family Math Activities, K to 8 62

63 BLM 11 Tangram Squares, Triangles and Other Polygons 63 TCDSB Family Math Activities, K to 8

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