LEARNING ABOUT MATH FOR K TO 5. Dorset Public School. April 6, :30 pm 8:00 pm. presented by Kathy Kubota-Zarivnij
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1 LEARNING ABOUT MATH FOR K TO 5 Dorset Public School April 6, :30 pm 8:00 pm presented by Kathy Kubota-Zarivnij kathkubo@rogers.com
2 TODAY S MATH TOOLS FOR colour square tiles Hexalink cubes KKZ, 2016 dice bingo chips playing cards tangram
3 NIM (ANCIENT CHINESE) Put 10 bingo chips in an array (2 rows x 5 columns = 10 tiles). Players taken turns taking either 1 or 2 bingo chips at a time from the array. Player left with the last 1 or 2 bingo chips from the array wins! How do you know if you are going to lose? How did you decide if you would take 1 or 2 bingo chips? How many square tiles do you need the other people to leave for you to ensure you will win? Any Age 2 to 4 (pairs) players 10 blue or 10 red square tiles Have the last 1 or 2 square tiles Use problem solving strategies and reasoning skills.
4 COUNTERS GONE Start with a pile of 10 counters. Kindergarten Players take turns taking rolling the die and removes the number of counters indicated by the die. Game ends when there are no more counters in the pile. What strategy did you use to count the counters you took from the pile? What happens to the number of counters in the pile as the counters are removed? 2 to 4 (pairs) players 10 square tiles, 1 die Have the greatest number of counters. Counting forwards and backwards.
5 WHAT S THE DIFFERENCE? Grades 1/2 Divide the cards equally among 2 to 4 people into piles. Players face up 1 card (1-digit) or 2 cards (2-digit) at the same time. Player with the larger number identifies the difference between the 2 numbers and claims all cards if correct. If the cards have the same number, they are placed in a common pile. When a player has no cards left, the cards in the pile are shuffled and divided equally among all the players. What strategies did you use to figure out the difference between the 2 cards? How does difference relate to subtraction? 2 to 4 (pairs) 10 blue or 10 red square tiles Have the greatest number of cards Subtract 1-digit or 2- digit whole numbers using mental strategies.
6 ADDITION CONCENTRATION Grades 2/3 Face down 1 deck of playing cards in an array (4 rows x 13 columns = 52 playing cards) Players take turns facing up 2 cards (two 1-digit numbers) or 4 cards (two 2-digit numbers) at a time. Only add number on cards if they are different -one-digit numbers have two cards 2, 5 -> 2+5=7; -two-digit numbers have four cards 2,3,5,7 -> 73+52=125) If number on cards are the same, are returned face down. Game ends when there are no cards left face down. What strategies did you use to figure out the difference between the 2 cards? How does difference relate to subtraction? 2 to 4 (pairs) 1 deck playing cards where aces (1), face cards (10) Greatest sum Add 1-digit or 2-digit whole numbers using mental strategies.
7 WHAT S THE VALUE OF MATH GAMES FOR LEARNING MATHEMATICS? Mathematics game playing: improves learners awareness of how to use rules and constraints, within a natural and enjoyable way encourages observation, analysis and constant revision of thinking. develops reasoning, decision-making, analysis and development of strategies involves both chance and skill, incorporates estimation, prediction, risk-taking, collaboration and competition. (Oldfield, 1991; Sarama and Clements, 2009)
8 SETTING THE MATHEMATICS CONTEXT MULTIPLICATION FROM GRADES 1 TO 3 -Gr1 - solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of mental strategies (e.g., doubles); -Gr2 - represent and explain, through investigation using concrete materials and drawings, multiplication as the combining of equal groups (e.g., use counters to show that 3 groups of 2 is equal to and to 3 x 2) -Gr3 - relate multiplication of one-digit numbers to real- life situations, using a variety of tools and strategies (e.g., place objects in equal groups, use arrays, write repeated addition; multiply to 7x7, using a variety of mental strategies Doubles 4 Repeated addition Equal Size Groups Array Multiplication expression defined as multiplicand x multiplier 0 size of 1 group multiplicand 2 groups of 4 2 rows x 4 columns 4 x 2 number of groups multiplier
9 LINE UP FOUR Any Age Player 1 (8 blue square tiles) Player 2 (8 red square tiles) Players take turns placing a square tile onto one empty square at a time on a 4x4 square grid game board Game ends when player makes four in a row. Why is it important to pay attention to the other player s moves? What can you do to keep the other player from lining up four tiles in a row? If you begin by placing your square tile in a corner, how many ways are there to line up 4 tiles in a row? 2 to 4 (pairs) players 8 red square tiles and 8 blue squares and 4x4 square grid Make 4 square tiles in a row (horizontal, vertical, diagonal) Use spatial reasoning to make predictions and strategies.
10 EFFECTIVE MATHEMATICS GAMES HAS THESE FEATURES: has solution-centered activity with the game player in charge of the process uses the game player s current mathematical knowledge involves a challenge against an opponent organized by a definite set of rules freely engages players has a definite number of solutions has an ending or finishing point provokes specific mathematics learning goals has the capacity for several game-playing variations
11 SQUARE TILES COVER-UP Grades 3 to 4 Getting Readyto Play What different rectangles are made of 12 square units? 2x6=12 3x4=12 3 rows 5 columns 3x5 3 rows x 5 columns 2 Players 30 red square tiles and 30 blue squares and 10x10 square grid 4 rows 5 columns 4 x 5 4 rows x 5 columns Cover the largest area on 10x10 square grid with rectangles. What is the greatest size of an array made from 2 dice rolls? What is the least size of an array that could be made from 2 dice rolls? Variations Change grid size to 3x3, 5x5, 6x6. Change the shape of the game board (e.g., t-shape, l-shape, c-shape using square grids). Represent multiplication of 1-digit whole numbers using an array. Add 1-and 2-digit whole numbers using mental strategies KKZ, 2016
12 SETTING THE MATHEMATICS CONTEXT MULTIPLICATION FROM GRADES 4 TO 6 Grade 4 multiply to 9x9 using a variety of mental strategies; solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x x 8); multiply whole numbers by 10, 100, and 1000, using mental strategies; multiply two-digit whole numbers by one-digit whole numbers, using a variety of tools (e.g., base ten materials or drawings of them, arrays), studentgenerated algorithms, and standard algorithms; Grade 5 solve problems involving the multiplication of whole numbers, using a variety of mental strategies (e.g., use the commutative property: 5 x 18 x 2 = 5 x 2 x 18, which gives 10 x 18 = 180); multiply decimal numbers by 10, 100, 1000, and , using mental strategies multiply two-digit whole numbers by two-digit whole numbers, using estimation, studentgenerated algorithms, and standard algorithms; Grade 6 use a variety of mental strategies to solve, multiplication, problems involving whole numbers (e.g., use the commutative property: and distributive property multiply whole numbers by 0.1, 0.01, and using mental strategies multiply decimal numbers by 10, 100, 1000, and using mental strategies multiply decimal numbers to tenths by whole numbers, using concrete materials, estimation, algorithms, and calculators (e.g., 4 x 1.4) solve problems involving the multiplication of whole numbers (four- digit by twodigit), using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms);
13 MULTIPLICATION NUMBER BATTLE A Grade 4 Players split a deck of cards into 2 piles (one pile per player) Players simultaneously flip over 2 cards from the top of their piles. Numbers on each card are multiplied. Highest product wins all 4 cards. If the cards have the same value, the cards are returned to the pile. Player with the greatest umber of cards win. What strategies did you use to determine the product of the 2 numbers? Is it possible that some card combinations could have the same product? How could you know that before playing the game? 2 to 4 (pairs) players 1 deck playing cards (aces (1) ; face cards are worth 10 Greatest number of playing cards Multiplying pairs of numbers and add 1- digit and 2-digit whole numbers
14 MULTIPLICATION NUMBER BATTLE B Grades 5 Players split a deck of cards into 2 piles (one pile per player). Aces are worth 11, face cards are worth 10. Players simultaneously flip over 3 cards from the top of their piles. Multiply the number on each card to get a product Highest product wins all 6 cards. If the cards have the same value, the cards are returned to the pile. Player with the greatest umber of cards win. 2 to 4 (pairs) players 1 deck playing cards (aces (11) ; face cards are worth 10 Greatest number of playing cards What strategies did you use to determine the product of the two 2-digit whole numbers? Is it possible that some card combinations could have the same product? How could you know that before playing the game? Multiplying 2-digit whole numbers by 10 using mental strategies.
15 ADDITION OR MULTIPLICATION TARGETS Choose a target number. Decide on the type of numbers the dice rolls represent (e.g., 1 dice -> 1-digit whole number; 2 dice -> 2-digit whole number; 3 dice 3-digit whole number) Roll 4 dice or face up 4 playing cards. Players make a number expression that is equal to the target number. Use any combination of addition, subtraction, multiplication or division operations. Player who makes an accurate number expression to the target number wins the round and either gets points the same quantity as the target number or keeps 4 cards. What strategies did you use to make the target number? Grades 2 to 6 2 to 4 (pairs) 2 to 4 dice or playing cards Have the greatest number of of points or playing cards Use 1-digit and 2- digit whole numbers to carry out number operations
16 TOWERING TOWERS Grades 2 to 6 Make different rectangular prisms. Which rectangular prisms have the greatest volume in cubic units.. Roll 2 dice to identify the volume in cubic units. Make the rectangular prism using the hexalinks. What strategies did you use to make the rectangular prism with the greatest volume? KKZ, to 4 (pairs) 2 to 4 dice and hexalinks Make the tallest rectangular prism Represent the volume of rectangular prisms and multiplication
17 MAKING A TANGRAM BY PAPER FOLDING Grades 4 to 6 Make a tangram by paper folding. Use known angle relationships and area relationships between the 7 tangram pieces. Angles à 90 0 (right angles), 45 0 (half of a right angle) Area of 1 large triangle is ¼ of the large square. 4x4 square grid paper Use spatial reasoning to make 2D shapes Compose shapes using 2D shapes.
18 TANGRAM COVER-UP Players divide up tans from 2 sets of tangrams K to Grade 6 Players take turns covering up the game board with 1 tan at a time. Tangram pieces must be placed completely and not overlap. Scoring each tan is worth specific points. Game ends when all tans are placed or no spaces are left on the board. What strategies did you use to create different bird designs? What different ways could these bids be sorted and classified in terms of geometric attributes (i.e., angles, sides, line of symmetry)? 2 to 4 (pairs) 2 sets of tangrams Achieve the greatest number of different bird designs. Use rotations, translations and reflections to rotate 2D shapes.
19 SHAPE MAKER A Kindergarten, Grade 1 Identify the types of shapes and sizes of shapes of the 7 tans. (e.g., 2 large triangles, 1 medium triangle, 2 small triangle, 1 small square, 1 small parallelogram) Make shapes with 3 sides, 4 sides, 5 sides and 6 sides. Use 1 to 7 tangram pieces. Trace tangram shapes on paper. 1 point for each shape made. Each player adds their points. How are the shapes made with tangrams the same? How are they different? Which shapes were made the most? (3 sided?, 4-sided?) 2 to 4 (pairs) players 2 sets of tangrams Achieve the greatest number of points. Compose shapes using 2D shapes.
20 SHAPE MAKER B Grades 2 and 3 Identify the types of shapes and sizes of shapes of the 7 tans. (e.g., 2 large triangles, 1 medium triangle, 2 small triangle, 1 small square, 1 small parallelogram) Make shapes with 3 sides, 4 sides, 5 sides and 6 sides. Use 1 to 7 tangram pieces. Trace tangram shapes on paper. Scoring: 3 points for 3 sided shape, 4 points for 4-sided shape, 5 points for 5-sided shape. Add total points. How are the shapes made with tangrams the same? How are they different? Which shapes were made the most? (3 sided?, 4-sided?) 2 to 4 (pairs) players 2 sets of tangrams Achieve the greatest number of points. Compose shapes using 2D shapes.
21 TANGRAM SHAPES (POLYGONS)
22 SHAPE MAKER C Create a bird using one set of tangrams Grades 4, 5 and 6 Players create different bird designs using all 7 tangrams. Flip, slide and turn parts or tans on the bird. Player with the greatest number of different bird designs wins. What strategies did you use to create different bird designs? What different ways could these bids be sorted and classified in terms of geometric attributes (i.e., angles, sides, line of symmetry)? 2 to 4 (pairs) 2 sets of tangrams Achieve the greatest number of different bird designs. Use rotations, translations and reflections to rotate 2D shapes.
23 TANGRAM BIRD DESIGNS
24 ROCK, PAPER, SCISSORS Any Age On the count of 3, say Rock, Paper, Scissors reveal either rock (fist), paper (open hand) or scissors (2 extended fingers). Playing the NEW Game Player A wins if all 3 players make the same hand shape Player B wins if exactly if 2 players make the same hand shape. Player C wins if none of the players make the same hand shape. Is the original and new game fair? How is the new version different than the original version? 2 to 3 people Get highest number of points. Make inferences and predictions from data and apply basic concepts of probability.
25 WHAT MATHEMATICS ARE OUR STUDENTS LEARNING? WHY? Conceptual Understanding - understanding of mathematical concepts, operations, and relations; enables the learning of new ideas by making mathematical connections to ideas already known through reasoning, proving and communication; supports retention and prevents common errors Procedural Fluency - carrying out procedures flexibly, accurately, efficiently, and appropriately for different and particular purposes Strategic Competence - formulating, representing and solving mathematical problems in different ways relevant to particular contexts Adaptive Reasoning - capacity for logical thought, reflection, explanation and justification in relation to different problem solving contexts and ways of thinking Productive Disposition - seeing oneself as an effective learner and doer of mathematics through perseverance (i.e., a steady effort in learning mathematics pays off); perceiving mathematics as being useful, worthwhile and accessible.
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