Mathematics Alignment Lesson

Transcription

1 Mathematics Alignment Lesson Materials Needed: Blackline Masters for each pair: o Product Game Rules o The Product Game board Blackline Masters for each student: o Product Game Recording Sheet o Playing the Product Game o Strategies to Win Sentence Frames (from Product Game Rules ) recorded on the board Colored Counters (2 colors per pair) Paper clips (2 per pair) Assessment Informal: Student discussion and written responses on Playing the Product Game Student discussion during Math Talk Vocabulary Factor: One of two or more numbers multiplied to find a product. Multiple: A number that is the product of the given number and an integer. Product: The answer to a multiplication problem. Standards for Mathematical Practice Standard 3 - Construct viable arguments and critique the reasoning of others. Standard 7 - Look for and make use of structure. Alignment Lesson: The Product Game 1. Use a Think-Pair-Share to review the meanings of product and factor. Circulate as students are thinking and pairing to determine potential misconceptions that remain after the previous days lessons introducing this vocabulary. 2. During the Share portion of the Think-Pair-Share, record a few ideas on the board, being careful to include correct definitions as well as those that contain misconceptions. Use Math Talk to address and clear up student misconceptions. Make corrections to the recorded definitions during the discussion. 3. Briefly introduce the term multiple and explain that students will learn more about multiples as they play and discuss the game. 4. Display Blackline Master, Product Game Rules, and read the rules with the class. Reference the sentence frames you have recorded on the board as you read the directions with students. 5. Play a brief game with the class to model correct play of the game using Blackline Master, The Product Game. Use two colors to mark products, one for the class's products and the other for your own. Record the factors you use to make products as you play on Blackline Master, Product Game Recording Sheet, and have one student be the recorder for the class (using the same sheet as you). Reinforce the use of the recording sheet, but do not try to display it until after you have finished the round with the class. Then, display your completed sheet to show what it will look like when pairs have finished their first round. 6. After you have modeled how to play the game with the whole class (without discussing strategies), invite student pairs to play the game. Student pairs will need one copy of Blackline Master, The Product Game, one copy of Blackline Master, Product Game Recording Sheet, and two colors of counters. Have students play more than once so they can explore strategies for winning. After the first round, students should only record new factor pairs on the Product Game Recording Sheet. Teachers should circulate as pairs play the game to facilitate discussion and remind students to use the sentence frames. 7. After students have played multiple times, distribute Blackline Master, Playing the Product Game, for students to discuss and complete with their partners. Each student should have his/her own copy on which to write. 8. Engage the class in Math Talk about the questions posed on Blackline Master, Playing the Product Game. Encourage and reinforce appropriate vocabulary use by students. At the end of the discussion, students should place their Product Game Recording Sheets in their math folder/binder for use with a future lesson. 9. Students should complete Blackline Master, Strategies to Win. Note: An online interactive tool of The Product Game with directions can be found at Source: Adapted from NCTM Illuminations The Product Game

2 Blackline Master Standard 4.OA.4 The Product Game Rules Read the following rules before you begin playing The Product Game. 1. Player 1 places a paper clip on a number in the factor list grid and says to his or her partner, I m placing my clip on the factor. (No square on the product grid is covered with Player 1 s color because only one factor has been marked; it takes two factors to make a product.) 2. Player 2 places the other paper clip on any number in the factor list grid (including the same number marked by Player 1) and says to his or her partner, I m placing my clip on the factor. Player 2 covers the product of the two factors on the product grid with his or her colored chip and says to his or her partner, The product is a multiple of the factors and. Player 2 records the factors used beside the correct product on the Product Game Recording Sheet. 3. Player 1 moves either one of the paper clips to another number and then covers the new product with his or her colored chip, continuing to use the sentences above to talk to his or her partner about what he or she is doing using correct vocabulary. Player 1 records the factors used beside the correct product on the Product Game Recording Sheet. 4. Each player, in turn, moves a paper clip and covers a product. If a product is already covered, the player does not get to cover a product for that turn. The winner is the first player to cover four squares in a row -- up and down, across, or diagonally. Source: Adapted from NCTM Illuminations The Product Game

3 Blackline Master Standard 4.OA.4 Source: NCTM Illuminations The Product Game

4 Blackline Master ONE PER STUDENT Product Game Recording Sheet Name: Date: Product Factors Product Factors Product Factors

5 Blackline Master ONE PER STUDENT Playing the Product Game Name: Date: 1. Look at your Product Game Recording Sheet. For each product, record the factors of that product that are missing from your list in a different color. Hint: There may be factors not listed on the game board! 2. Imagine it is your turn to play the game. Suppose one of the paper clips is on 5. What products can you make by moving the other paper clip? The products you listed are multiples of 5. A multiple of a whole number is the product of that number and another whole number. If a number is a multiple of 5, then 5 is a factor of that number. These four sentences are all ways of expressing 5 3 = 15: 5 is a factor of is a factor of is a multiple of is a multiple of List ten multiples of 5 that are not on the game board. Multiples can also be found as a result of skip counting by a number. For example, to find multiples of 8, skip count by 8s, starting with 8. Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, etc. 4. Write the multiples for each of the factors of 24 below. For each factor, stop listing the multiples when you get to What do you notice about the relationship between multiples and factors based on the lists of multiples you wrote above. Source: Adapted from NCTM Illuminations The Product Game

6 Answer Key Standard 4.OA.4 Playing the Product Game Answer Key 1. Product Factors Product Factors Product Factors , 3, 5, , 2, 3, 4, 6, 9, 12, 18, , , 2, 4, 8, , 2, 4, 5, 8, 10, 20, , , 2, 3, 6, 9, , 2, 3, 6, 7, 14, 21, , 2, , 2, 4, 5, 10, , 3, 5, 9, 15, , , 3, 7, , 2, 3, 4, 6, 8, 12, 16, 24, , 2, 3, , 2, 3, 4, 6, 8, 12, , 7, , , 5, , 2, 3, 6, 9, 18, 27, , 2, 4, , 3, 9, , 2, 4, 7, 8, 14, 28, , 3, , 2, 4, 7, 14, , 3, 7, 9, 21, , 2, 5, , 2, 3, 5, 6, 10, 15, , 2, 4, 8, 16, 32, , 2, 3, 4, 6, , 2, 4, 8, 16, , 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, , 2, 7, , 5, 7, , 3, 9, 27, x 1 = 5 5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 5 x 5 = 25 5 x 6 = 30 5 x 7 = 35 5 x 8 = 40 5 x 9 = Possible Answers: 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, Factors of 24: 1, 2, 3, 4, 6, 8,12, 24 Multiples: 1, 2, 3, 4, , 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 3, 6, 9, 12, 15, 18, 21, 24 4, 8, 12, 16, 20, 24 6, 12, 18, 24 8, 16, 24 12, Any whole number is a multiple of each of its factors. (Question 4 shows that 24 is a multiple of each of its factors, 1, 2, 3, 4, 6, 8, 12, and 24.) Also, the number of multiples listed gives the factors that form that product (i.e. there are eight 3 s in 24 I listed 8 multiples of 3 to get to 24).

7 Blackline Master ONE PER STUDENT Strategies to Win The Product Game Homework Name: Date: Directions: Play The Product Game again with a partner. Then, explain your thinking to the following questions below. Be prepared to share your thinking with the class. What strategies did you observe or use when playing the game? How did you change your strategies as you played multiple times? Is it better to be Player 1 or Player 2? Prove your thinking by providing examples of your strategies that you used.

8 Blackline Master Standard 4.OA.4 Source: NCTM Illuminations The Product Game

9 Answer Key Standard 4.OA.4 Strategies to Win The Product Game Homework Answer Key Directions: Play The Product Game again with a partner. Then, explain your thinking to the following questions below. Be prepared to share your thinking with the class. What strategies did you observe or use when playing the game? How did you change your strategies as you played multiple times? Is it better to be Player 1 or Player 2? Prove your thinking by providing examples of your strategies that you used. Student responses will vary. Responses may include statements like It is better to go second, because if you go first, you do not get to make a move on the board. When you get toward the end of the game, you have to avoid the factors of the numbers your opponent needs. If you have to go first, you should choose the number 1 because it gives your opponent fewer choices about where to go to get four in a row.