Lesson 2.5 Name Multiply Using The Distributive Property .

NameMultiply Using the Distributive PropertyEssential Question How can you use the Distributive Property to multiply a2-digit number by a 1-digit number?InvestigateInvestigateLesson 2.5Number and Operations in BaseTen—4.NBT.B.5MATHEMATICAL PRACTICESMP1, MP7HandsOnMaterials color pencils, grid paperYou can use the Distributive Property to break apartnumbers to make them easier to multiply.The Distributive Property states that multiplying a sum by anumber is the same as multiplying each addend by the numberand then adding the products.A. Outline a rectangle on the grid to model 6 13.B. Think of 13 as 5 8. Break apart the model to show6 (5 8). Label and shade the smaller rectangles. Usetwo different colors.Use the Distributive Property. Find the product eachsmaller rectangle represents. Then find the sum of theproducts. Record your answers. C. Model 6 13 again. Think of 13 as a different sum. Break Houghton Mifflin Harcourt Publishing Companyapart the model to show 6 ( ). Find theproduct each smaller rectangle represents. Then find thesum of the products. Record your answers. Chapter 287

Draw Conclusions1. Explain how you found the total number of squares in eachmodel in Steps B and C.2. Compare the sums of the products in Steps B and C with those ofyour classmates. What can you conclude?3.To find 7 23, is it easier to break apart the factor,23, as 20 3 or 15 8? Explain.SMARTERHandsOnMakeMake ConnectionsConnectionsSTEP 1STEP 2STEP 3Use base-ten blocks tomodel 6 13.Break the model into tensand ones.Add the tens and the onesto find the product.6 rows of 1 ten 3 ones(6 1 ten)(6 3 ones)(6 10)(6 3)So, 6 13 78.In Step 2, the model is broken into two parts. Each partshows a partial product. The partial products are 60 and 18.88(6 10) (6 3)60 18MathTalkMATHEMATICAL PRACTICES 4Model Mathematics Whyis this a good model forthe problem? Houghton Mifflin Harcourt Publishing CompanyAnother way to model the problem is to use base-tenblocks to show tens and ones.

NameSharehhowShare andand ShowShMATHMBOARDBModel the product on the grid. Record the product.1. 3 13 2. 5 14 Find the product.3. 6 14 4. 5 18 5. 4 16 Use grid paper or base-ten blocks to model the product.Then record the product.6. 7 12 7. 5 16 8. 9 13 Oqnakdl Rnkuhmf @ookhb shnmrOqnakdl Rnkuhmf @ookhb shnmr Houghton Mifflin Harcourt Publishing Company9.10.MATHEMATICALPRACTICE6Explain how modeling partial products can be usedto find the products of greater numbers.SMARTERUse the Distributive Property tomodel the product on the grid. Record the product.4 14 Chapter 2 Lesson 5 89

MATHEMATICAL PRACTICES11.COMMUNICA5& t 1&34E7&3& t CONSTRUCT ARGUMENTSSMARTERKyle wentto a fruit market. The marketsells a wide variety of fruits andvegetables. The picture at theright shows a display of oranges.Write a problem that can besolved using the picture.Pose a problem.DEEPERDescribe how you could change the problem bychanging the number of rows of oranges and the number ofempty spaces in the picture. Then solve the problem. Houghton Mifflin Harcourt Publishing Company Solve your problem.90

Practice and HomeworkLesson 2.5NameMultiply Using the Distributive PropertyCOMMON CORE STANDARD—4.NBT.B.5Use place value understanding and properties ofoperations to perform multi-digit arithmetic.Model the product on the grid. Record the product.761. 4 19 102. 5 13 944 10 40 and 4 9 3640 36 76Find the product.3. 4 14 4. 3 17 5. 6 15 ProblemProblem SolvingSolving6. Michael arranged his pennies in the Houghton Mifflin Harcourt Publishing Companyfollowing display.7.Math Explain how you can use amodel to find 6 17.WRITEHow many pennies does Michaelhave in all?Chapter 291

Lesson Check (4.NBT.B.5)1. The model shows how Maya planted5 18.flowers in her garden.102. The model below represents the expression53How many flowers did Maya plant?How many tens will there be in thefinal product?Spiral Review (4.OA.A.2, 4.NBT.A.2, 4.NBT.B.4, 4.NBT.B.5)one thousand, seventy people. Write thepopulation in standard form.5. Allison has 5 times as many baseball cardsas football cards. In all, she has 120 baseballand football cards. How many baseballcards does Allison have?4. Central School collected 12,516 poundsof newspaper to recycle. Eastland Schoolcollected 12,615 pounds of newspapers.How many more pounds of newspaperdid Eastland School collect than CentralSchool?6. A ruby-throated hummingbird beats itswings about 53 times each second. Abouthow many times does a ruby-throatedhummingbird beat its wings in5 seconds?FOR MORE PRACTICEGO TO THE92Personal Math Trainer Houghton Mifflin Harcourt Publishing Company3. Center City has a population of twenty

Michael arranged his pennies in the following display. How many pennies does Michael have in all? 7. WRITE Math Explain how you can use a model to find 6 17. 3. 4 14 _ 4. 3 17 _ 5. 6 15 _ Find the product. 76 Practice and Homework Lesson 2.5 COMMON CORE STANDARD—