Multiply Greater Factors

Transcription

1 Boost lesson 2c Students apply the Distributive Property and write equations to multiply two 2-digit factors. MATHEMATICAL BACKGROUND The Distributive Property is the basis for the standard algorithm. Learning how to apply the Distributive Property prepares students for simplifying and solving algebraic expressions. MATHEMATICAL PRACTICE Reason Abstractly Using properties of operations helps students to make sense of quantities and their relationships. Multiply Greater Factors set Up Review the Anchor Video Paint the Town. Replay the Anchor Video Paint the Town. The video shows how artists use multiplication and measurement to create a giant mural. Anchor Video: Paint the Town Ask targeted questions to help students connect area and measurement to multiplication. How did the artists approach the job of painting the buildings? (They made a drawing on a grid to show each of the parts.) In what other ways did they use grids? (They used grids to find the dimensions of the walls.) How did the grids help the artists to find the dimensions of the walls? (They used the grids to show length and width so they could find the areas of the walls.) We use multiplication to find area. EngagE Multiply a 2-digit by a 2-digit number. Display the first problem on RDI Practice, page 42. Read the directions aloud. Now, let s multiply two 2-digit numbers. First, let s estimate the answer. How can we estimate 13 17? (10 20 = 200) MATHEMATICAL PRACTICE Reason Abstractly Guide students in renaming the factors and applying the Distributive Property. First we use place value to split each factor. How do we rewrite as the product of two expressions? (Write 13 as and 17 as ) How do we find the product? (Multiply the parts to find the partial products, and then add the products.) Have students complete the problem as shown and check the reasonableness of their solutions Estimate: ( ) 3 ( ) ( ) 1 ( ) 1 ( ) 1 ( ) 10 Π10 = Π7 = 70 3 Π10 = 30 3 Π7 = Is your estimate reasonable? yes 40 MATH 10 Block 2 BOOST

2 BOOST STRATEGY BANK Model this problem-solving strategy with your students. Draw a Model Look for Patterns Make a List Work Backwards Simplify the Problem EXploRE Apply the Distributive Property to solve a contexualized problem. Ramón paints a mural on the side of his school. The mural is 24 feet long and 1 feet high. How many square feet does Ramón paint? Estimate: ( ) 3 ( 10 1 ) ( ) 1 ( 20 3 ) 1 ( ) 1 ( 4 3 ) 20 Œ 10 = Œ = Œ 10 = 40 4 Œ = sq. ft. Display the second problem on RDI Practice, page 42. Read the directions aloud. We can write an equation to help us understand and solve the problem. What expression do we need to multiply to solve the problem? (24 1) How can we estimate 24 1? (20 20 = 400) How can we write an equation to represent the problem? (24 1 = (20 + 4) (10 + )) Display the equation. What is ? (34) Have a student complete the equation on the screen. Understanding Point out to students that they applied the Distributive Property to solve the problem. Point to the equation and expression. MODEL REASONING The problem asked how many square feet Ramó n paints, so we multiplied the length and the width of the mural to find the area. We used an expression to represent the problem. What expression did we use? (24 1) Then we estimated the answer. Point to the estimate. What was our estimate? (400) MODEL REASONING Next, we split the factors and wrote an equation to find the partial products. Why did we split both factors? (Both factors had more than one place value. ) How many square feet does Ramon paint? (34) Is 34 is close to the estimate of 400? (yes) Is our answer reasonable? (yes) Ramó n paints 34 square feet. Understanding the Distributive Property helps us to write equations to solve multiplication problems. EXtEnD Have student pairs consolidate their skills as you circulate. 43 PRACTICE Students apply the Distributive Property to multiply 2-digit by 2-digit numbers. How did you split the factors? How did you find the partial products? CHALLENGE Students apply the Distributive Property to solve another real-world problem. How does writing an equation help you solve the problem? Do you think the area is double the area of Ramon s mural? REFLECT Students complete the refl ection on how to apply the Distributive Property. How is this process different than the process of multiplying a 1-digit number by a 2-digit number? Multiply Greater Factors 41

3 Your Name Boost lesson 2C EngagE Use the Distributive Property to Multiply estimate the product. split both factors and use the Distributive Property to multiply. Compare your answer to the estimate to determine if your answer is reasonable. Partner s Name Multiply Greater Factors Estimate: 3 5 page 1 of ( 1 ) 3 ( 1 ) ( 3 ) 1 ( 3 ) ( 3 ) 1 ( 3 ) EXploRE STRATEGY BANK Draw a Model Look for Patterns Solve a Problem Use the Distributive Property to solve the problem. Ramó n paints a mural on the side of his school. The mural is 24 feet long and 1 feet high. How many square feet does Ramón paint? Is your answer reasonable? Make a List Work Backwards Simplify the Problem TM & Scholastic Inc. All Rights Reserved. 3 5 Estimate: 3 5 Ramón paints square feet. My answer is reasonable because. 42 MATH 10 Block 2 BOOST Resource Links Math 10 RDI: page 42 SAM Keyword: Distributive Property

4 Your Name Partner s Name Page 2 of 2 Boost lesson 2C practice Apply the Distributive Property Multiply Greater Factors (continued) Estimate the product. Split the factors and use the Distributive Property to multiply. that your answer is reasonable Estimate: 5 Estimate: ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( ) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) TM & Scholastic Inc. All Rights Reserved. challenge Is your answer reasonable? Solve Another Problem equation to solve this problem using the Distributive Property. Vicki paints a mural that has double the length and height of Ramón s mural. Vicki s mural is 4 feet long by 32 feet high. How many square feet does Vicki paint? REflect Is your answer reasonable? Wrap Up Using an example, explain how to multiply two 2-digit factors using the Distributive Property.. Resource Links Math 10 RDI: page 43 SAM Keyword: Distributive Property Multiply Greater Factors 43

5 StREtch lesson 2a Students apply their critical thinking skills to solve complex number puzzles with factors and multiples. MATHEMATICAL BACKGROUND Arithmogons are rich problem-solving puzzles that help students make connections and identify relationships between numbers. Like crossword puzzles, arithmogons are self-corrective. MATHEMATICAL PRACTICE Make Use of Structure Students should analyze the multiplication patterns in the structure of the arithmogons to find the correct missing factors. Solve Arithmogons With Multiplication SEt Up Analyze an arithmogon. Display the first problem on RDI Practice, page 14. Read the directions aloud. In this puzzle, the number in each square is the product of 2 missing factors in the circles on either side. This means that the missing numbers on either side of 10 must be factors of 10. Allow students to complete the arithmogon on their own Have students complete RDI Practice, pages in pairs. OR Guide students through the Practice pages using the following instruction. EngagE Identify the rule and discuss student reasoning. MATHEMATICAL PRACTICE Make use of structure Guide students to analyze the problem structure as you complete the arithmogon on screen. Point to the factors and products as you think aloud. 2 MODEL REASONING I see that each pair of products has a common factor, which means that they share a factor. 10 and have a common factor of 2. How can you tell this is true from the other numbers in the arithmogon? (10 and 15 have a common factor of 5; and 15 have a common factor of 3.) Ask students targeted questions. Does the structure of the arithmogon remind you of any other puzzles? (Sudoku; Crossword puzzles) How did you solve those puzzles? Now, let s solve another arithmogon using multiple strategies. 144 MATH 10 Block 2 STRETCH

6 STRETCH STRATEGY BANK Model this problem-solving strategy with your students. Draw a Model Look for Patterns Make a List Work Backwards Simplify the Problem EXploRE Compare multiple strategies to solve a similar problem Make a List Factors of V 1, 2, 3, Factors of V 1, 2, 4, Factors of 12 V 1, 2, 3, 4,, 12 2 x 3 = 2 x 4 = 3 x 4 = 12 2 x 3 = 2 x 4 = 3 x 4 = 12 Have students list the factors for each product. This is an organized method of finding the missing numbers. To solve this problem, we can make a list of the factors of. (1, 2, 3, and ) Guide students to use the list to identify the 2 factors in the circles adjacent to. Then, have a student complete the arithmogon on screen. MODEL REASONING If one of the factors of is 2, the other factor must be = 12. The missing factors are 2, 3, and 4. Have students check their work by writing the 3 equations in the arithmogon. Ask students to guess the missing factors. You can also use the guess-and-check strategy to find the missing factors in the circles. Encourage students to justify their reasoning. Did anyone guess a wrong factor, like 5 or 7? How did you know it was wrong? Is this strategy a faster way to solve the problem? Remind students that the process of guessing still relies on mathematical sense. Even though you are making a guess, knowing your multiplication facts helps to choose the right numbers in the circles. EXtEnD Have student pairs consolidate their skills as you circulate. 147 PRACTICE Students apply their skills to complete two additional arithmogons. How did you begin solving the arithmogons? How do you know your answers are correct? CHALLENGE Students create their own arithmogons. Then, have students trade problems with their partners to solve. How did you make sure that each pair of products shared a common factor? REFLECT Students complete the refl ection to explain how they solved the arithmogons. Is it easier to find the missing factors of a lesser product, like, or a product with less factors, like 7? Solve Arithmogons With Multiplication 145

7 Your Name StREtch lesson 2A EngagE Analyze an Arithmogon Partner s Name Solve Arithmogons With Multiplication page 1 of 2 An arithmogon (uh-rith-muh-gon) is a puzzle made up of connected number patterns. Find the missing factors. In this puzzle, each square represents the product of 2 factors in the circles on either side EXploRE Make a List STRATEGY BANK Draw a Model Solve an Arithmogon Using Multiple Strategies list the factors for each product. Then, identify the factors that belong in the circles. Look for Patterns Make a List Work Backwards Simplify the Problem Guess the missing factors in the circles. Then, use multiplication to check if your answer makes sense TM & Scholastic Inc. All Rights Reserved Factors of 1, 2, 3, Factors of 1, 2, 4, Factors of 12 1, 2, 3, 4,, MATH 10 Block 2 STRETCH Resource Links Math 10 RDI: page 14 SAM Keywords: Factors, Multiples

8 Your Name STRETCH lesson 2A practice Partner s Name Solve Arithmogons With Multiplication (continued) Apply Your Skills to Solve More Problems Complete the missing factors in the circles. Page 2 of TM & Scholastic Inc. All Rights Reserved. challenge 32 Create Your Own Arithmogon y 1- or 2-digit numbers in the circles, and multiply to find the factors. Then, trade problems with your partner to solve. REflect 10 Wrap Up Which strategy did you use to solve the arithmogons? The strategy I chose to solve the arithmogons was. This strategy was more effective because. Resource Links Math 10 RDI: page 147 SAM Keywords: Factors, Multiples Solve Arithmogons With Multiplication 147