1 / 18

Engage NY Math Module 5

Engage NY Math Module 5. Lesson 5: Connect visual models and the distributive property to partial products of the standard algorithm without renaming. Estimate Products by Rounding. Estimate and then multiply. 29 x 11 ≈ ____ 29 x 21 ≈ ____ 29 x 31 ≈ ____ 23 x 12 ≈ ____

moe
Download Presentation

Engage NY Math Module 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Engage NY Math Module 5 Lesson 5: Connect visual models and the distributive property to partial products of the standard algorithm without renaming.

  2. Estimate Products by Rounding • Estimate and then multiply. • 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 ≈ ____

  3. MULTIPLY MENTALLY • 9 x 10 = ____ • 9 x 10 = 90 • 9 x 9 = 90 - ____ Write the number sentence, filling in the blank. • 9 x 9 = 90 - 9 • 9 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 - 9 • 9 x 99? • 891

  4. MULTIPLY MENTALLY • 15 x 10 = ____ • 15 x 10 = 150 • 15 x 9 = 150 - ____ Write the number sentence, filling in the blank. • 15 x 9 = 150 - 15 • 15 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 - 29 • 29 x 99? • 2,871

  5. MULTIPLY BY MULTIPLES OF 100 • 31 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 = ____

  6. Application Problem: • 30 twelves – 1 twelve = 29 twelves • (30 x 12) – (1 x 12) = 360 – 12 = 348 • 20 twelves + 9 twelve = 29 twelves • (20 x 12) + (9 x 12) = 240 + 108 = 348 Aneisha’s puppy will have 348 square feet of play space. 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.

  7. Concept 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 5’s and 1 more 5. The product is 105. • Represent that thinking with a tape diagram. 5 . . . . 5 5 5 21 fives • So you chose the factor 5 to be the unit. Can you imagine the area in each unit? • Draw the first image.

  8. Concept 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. 1 five 20 fives . . . . • There are so many units in the above drawing. Let’s represent all the boxes using an area model like the type you used in fourth grade. • Draw the image.

  9. Concept Development – Problem 1:Represent units using first the tape diagram, then the area model. • Draw the area model. 5 1 20 • 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 fives • 100 and 5 • 105

  10. Concept Development – Problem 1:Represent units using first the tape diagram, then the area model. 5 1 1 x 5 = 5 • 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. 20 x 5 = 100 20 21 5

  11. Concept 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, let’s connect it to a written method – the standard algorithm. • 23 x 31 • Let’s think about which factor we want to name as our unit. Which do you think is easier to count, 31 twenty-three’s or 23 thirty-ones? Turn and talk to those at your table. • It’s easier to count units of twenty-three because we can find 30 of them and then just add 1 more. • Let’s 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 doesn’t matter. The area will be the same. • What’s the product of 1 and 23? • What’s the product of 30 and 23? • Now add your partial products to find the total area of our rectangle. • 690 + 23 = 713 • What is 23 x 31? • 713 23 1 23 690 30

  12. Concept Development – Problem 2:Products of two-digit and two-digit numbers, the area model and standard algorithm. • Now, let’s 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.

  13. Concept Development – Problem 3:Products of two-digit and three-digit numbers. • 343 x 21 • What should we designate as the unit? • 343 • Let’s label the top with our unit of 343. • Let’s split our 21 into 1 and 20. • What’s the product of 1 and 343? • 343 • What’s the product of 20 and 343? • 6,860 • Now add your partial products to find the total area of our rectangle. • 343 + 6,860 = 7,203 • What is 343 x 21? • 7,203 343 1 343 20 6860

  14. Concept Development – Problem 3:Products of two-digit and three-digit numbers. • Now, let’s 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.

  15. 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?

  16. Exit Ticket

  17. Problem Set Display Problem Set on the board. Allow time for the students to complete the problems with tablemates.

  18. HOMEWORK TASK Assign Lessons 4 and 5 Homework Tasks. Due Date: Tuesday, January 21.

More Related