Engage NY Math Module 1

Engage NY Math Module 5

Lesson 5: Connect visual models and the distributive property to partial products of the standard algorithm without renaming.29 x 11 ____29 x 21 ____29 x 31 ____23 x 12 ____23 x 22 ____23 x 32 ____23 x 42 ____37 x 13 ____37 x 23 ____36 x 24 ____24 x 36 ____43 x 11 ____43 x 21 ____403 x 21 ____303 x 21 ____203 x 21 ____41 x 11 ____41 x 21 ____41 x 31 ____401 x 31 ____501 x 31 ____601 x 31 ____801 x 31 ____803 x 31 ____703 x 11 ____43 x 34 ____53 x 34 ____53 x 31 ____53 x 51 ____93 x 31 ____913 x 31 ____73 x 31 ____723 x 31 ____78 x 34 ____798 x 34 ____

Estimate Products by RoundingEstimate and then multiply.MULTIPLY MENTALLY9 x 10 = ____ 9 x 10 = 90

9 x 9 = 90 - ____ Write the number sentence, filling in the blank.9 x 9 = 90 - 99 x 9?81

9 x 100 = ____ 9 x 100 = 900

9 x 99 = 900 - ____ Write the number sentence, filling in the blank.9 x 99 = 900 - 99 x 99?891

MULTIPLY MENTALLY15 x 10 = ____ 15 x 10 = 150

15 x 9 = 150 - ____ Write the number sentence, filling in the blank.15 x 9 = 150 - 1515 x 9?135

29 x 100 = ____ 29 x 100 = 2,900

29 x 99 = 2,900 - ____ Write the number sentence, filling in the blank.29 x 99 = 2,900 - 2929 x 99?2,871

MULTIPLY BY MULTIPLES OF 10031 x 100 = ____ 31 x 100 = 3,100

3,100 x 2 = ____3,100 x 2 = 6,200

31 x 200 = ____= 31 x 100 x 2 = 31 x 200 = 6,200

Solve these two problems using the same method.24 x 300 = ____34 x 200 = ____

Aneisha is setting up a play space for her new puppy. She will be building a fence around part of her yard that measures 29 feet by 12 feet. How many square feet of play space will her new puppy have? Try to solve this problem in more than one way.Application Problem:Aneishas puppy will have 348 square feet of play space.30 twelves 1 twelve = 29 twelves(30 x 12) (1 x 12) = 360 12 = 34820 twelves + 9 twelve = 29 twelves(20 x 12) + (9 x 12) = 240 + 108 = 348Concept Development Problem 1:Represent units using first the tape diagram, then the area model.21 x 5 Can you solve this mentally using the unit form strategy? (20 x 5) plus 5 more. This is twenty 5s and 1 more 5. The product is 105.

Represent that thinking with a tape diagram.So you chose the factor 5 to be the unit. Can you imagine the area in each unit?Draw the first image.5. . . . 55521 fivesConcept Development Problem 1:Represent units using first the tape diagram, then the area model.Imagine that all 21 boxes are stacked vertically. Draw the second image.There are so many units in the above drawing. Lets represent all the boxes using an area model like the type you used in fourth grade.Draw the image.. . . . 1 five20 fivesConcept Development Problem 1:Represent units using first the tape diagram, then the area model.Draw the area model.What values could you put in the area model? How many units are in each part of the rectangle?1 x 5 = 5 and 20 x 5. 1 five and 20 fives100 and 51051205Concept Development Problem 1:Represent units using first the tape diagram, then the area model.How are the area model and the tape diagram similar? How are they different?They both show the same number of units. The tape diagram helped us think 21 x 5 as (20 x 5) plus 5 more.The area model helped us show all the boxes in the tape diagram without having to draw every single one. It made it easier to see (20 x 5) + (1 x 5).

Can we turn this area model so that we count 5 groups of 21? What effect will turning the rectangle have on our area (product)? Draw it.12051 x 5 = 520 x 5 = 100215Concept Development Problem 2:Products of two-digit and two-digit numbers, the area model and standard algorithm.Now that we have discussed how the area model can show multiplication, lets connect it to a written method the standard algorithm.23 x 31Lets think about which factor we want to name as our unit. Which do you think is easier to count, 31 twenty-threes or 23 thirty-ones? Turn and talk to those at your table.Its easier to count units of twenty-three because we can find 30 of them and then just add 1 more.

Lets label the top with our unit of 23. We showed units of five before. How can we show units of twenty-three now?Does it matter how we split the rectangle? Does it change the area (product)?No it doesnt matter. The area will be the same.Whats the product of 1 and 23?Whats the product of 30 and 23?Now add your partial products to find the total area of our rectangle.690 + 23 = 713What is 23 x 31?7131306902323Concept Development Problem 2:Products of two-digit and two-digit numbers, the area model and standard algorithm.Now, lets solve 23 x 31 using the standard algorithm. Show your neighbor how to set up this problem using the standard algorithm.Work with your neighbor to solve using the standard algorithm.

2 3 x 3 1

Take a look at the area model and the standard algorithm. Compare them. What do you notice?We added 1 unit of 23 to 30 units of 23.In the area model we added two parts just like in the algorithm.First we wrote the value of 1 twenty-three. Then we wrote the value of 30 twenty-threes.Explain the connections between (30 x 23) + (1 x 23), the area model and the algorithm.Concept Development Problem 3:Products of two-digit and three-digit numbers.343 x 21What should we designate as the unit?343

Lets label the top with our unit of 343. Lets split our 21 into 1 and 20.Whats the product of 1 and 343?343Whats the product of 20 and 343?6,860Now add your partial products to find the total area of our rectangle.343 + 6,860 = 7,203What is 343 x 21?7,2031206860343343Concept Development Problem 3:Products of two-digit and three-digit numbers.Now, lets solve 343 x 21 using the standard algorithm. Show your neighbor how to set up this problem using the standard algorithm.Work with your neighbor to solve using the standard algorithm.

3 4 3 x 2 1

Did your area model match your standard algorithm? Explain the connections between (20 x 343) + (1 x 343), the area model and the algorithm.Concept Development Problem 4:Products of two-digit and three-digit numbers.In your math journal, solve the following problem using an area model and the standard algorithm.

2 3 1 x 3 2

Did your area model match your standard algorithm? Exit Ticket

Display Problem Set on the board. Allow time for the students to complete the problems with tablemates.Problem SetAssign Lessons 4 and 5 Homework Tasks. Due Date: Tuesday, January 21.HOMEWORK TASK