1 of 17

Eureka Math

5th Grade

Module 2

Lesson 8

At the request of elementary teachers, a team of Bethel & Sumner educators met as a committee to create Eureka slideshow presentations. These presentations are not meant as a script, nor are they required to be used. Please customize as needed. Thank you to the many educators who contributed to this project!

Directions for customizing presentations are available on the next slide.

2 of 17

Customize this Slideshow

Reflecting your Teaching Style and Learning Needs of Your Students

When the Google Slides presentation is opened, it will look like Screen A.
Click on the “pop-out” button in the upper right hand corner to change the view.
The view now looks like Screen B.
Within Google Slides (not Chrome), choose FILE.
Choose MAKE A COPY and rename your presentation.
Google Slides will open your renamed presentation.
It is now editable & housed in MY DRIVE.

Screen A

“pop-out”

Screen B

3 of 17

Icons

Read, Draw, Write

Learning Target

Think Pair Share

Individual

Partner

Whole Class

Small Group Time

Small Group

Personal White Board

Problem Set

Manipulatives Needed

Fluency

4 of 17

5 of 17

I can fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

6 of 17

State in Exponential Form (3 min)

10² =

Say the base…

10

Say the exponent …

2

Say 10 squared as a multiplication sentence starting with 10 …

10 x 10 = 100

More Practice:

10³

10⁴

10⁵

10⁷

7 of 17

Multiply using the Area Model with a Zero in One Factor (4 min)

Solve these problems using the area model:

342 × 201

804 x 135

8 of 17

Application Problem

Erin and Frannie entered a rug design contest. The rules stated that the rug’s dimensions must be 32 inches × 45 inches and that they must be rectangular. They drew the following for their entries. Show at least three other designs they could have entered in the contest. Calculate the area of each section, and the total area of the rugs.

9 of 17

Application Problem

10 of 17

Concept Development Problem 1

314 x 236 = (round each factor to estimate the product)

Multiply your rounded factors to estimate the product, what is 300 x 200?

Express 60,000 as a multiplication expression with an exponent.

6 x 10⁴

Since we rounded both of our factors down to the nearest hundred, will our actual product be more than or less than our estimated product? Why? Tell a neighbor.

Now solve using the standard algorithm.

Think about your estimated product, is our answer reasonable? Turn and talk.

T: (Write 314 × 236 on the board.) Round each factor to estimate the product. Turn and talk.

S: 314 is closer to 3 hundreds than 4 hundreds on the number line. 236 is closer to 2 hundreds than 3 hundreds on the number line.

T: Multiply your rounded factors to estimate the product. What is 300 times 200?

S: Hundreds times hundreds makes ten thousands. 3 × 2 is 6. So, we’ll get 6 ten thousands, or 60,000.

T: Express 60,000 as a multiplication expression with an exponent.

S: 6 × 10⁴ .

T: I noticed that we rounded both of our factors down to the nearest hundred. Will our actual product be more than or less than our estimated product? Why? Tell a neighbor.

S: The answer should be more than 60,000. Our actual factors are greater, therefore our actual product will be greater than 60,000.

T: Work with a partner to solve using the standard algorithm.

S: (Solve to find 74,104.) T: Look back to our estimated product. Is our answer reasonable? Turn and talk.

S: Yes, it’s greater like we thought it would be. Our answer makes sense

11 of 17

Concept Development Problem 1

T: (Write 314 × 236 on the board.) Round each factor to estimate the product. Turn and talk.

S: 314 is closer to 3 hundreds than 4 hundreds on the number line. 236 is closer to 2 hundreds than 3 hundreds on the number line.

T: Multiply your rounded factors to estimate the product. What is 300 times 200?

S: Hundreds times hundreds makes ten thousands. 3 × 2 is 6. So, we’ll get 6 ten thousands, or 60,000.

T: Express 60,000 as a multiplication expression with an exponent.

S: 6 × 10⁴ .

T: I noticed that we rounded both of our factors down to the nearest hundred. Will our actual product be more than or less than our estimated product? Why? Tell a neighbor.

S: The answer should be more than 60,000. Our actual factors are greater, therefore our actual product will be greater than 60,000.

T: Work with a partner to solve using the standard algorithm.

S: (Solve to find 74,104.) T: Look back to our estimated product. Is our answer reasonable? Turn and talk.

S: Yes, it’s greater like we thought it would be. Our answer makes sense

12 of 17

Concept Development Problem 2

1,882 x 296

Round each factor and estimate the product. Will the product be greater than or less than your estimate? Turn and talk.

Work independently to solve.

Share answers.

Is our product reasonable considering our estimate?

T: (Write 1,882 × 296 on the board.) Round each factor and estimate the product. Will the actual product be greater than or less than your estimate? Turn and talk.

S: 1,882 rounds to 2,000. 296 rounds up to 300. The estimated product is 600,000. We rounded both factors up this time. Since our actual factors are less than 2,000 and 300, our actual product must be less than 600,000.

T: Work independently to solve 1,882 × 296. S: (Solve.)

T: What is the product of 1,882 and 296? S: 557,072.

T: Is our product reasonable considering our estimate? Turn and talk.

S: Yes, it is close to 600,000, but a bit less than our estimated product like we predicted it would be. Possibly have students compare the estimates of Problems 1 and 2.

NOTES ON MULTIPLE MEANS OF ACTION AND EXPRESSION: If students are not yet ready for independent work, have them work in pairs and talk as they estimate, solve, and check their solutions. These types of strategy-based discussions deepen understanding for students and allow them to see problems in different ways.

13 of 17

Concept Development Problem 3

4,902 x 408

Work independently to find an estimated product.

Read the estimated multiplication sentence without the product.

(Write 4,902 × 408 on the board.) Work independently to find an estimated product for this problem.

T: (Pause.) Let’s read the estimated multiplication sentence without the product.

S: 4,902 × 408 is about as much as 5,000 × 400.

T: As I watched you work, I saw that some of you said our estimated product was 200,000, and others said 2,000,000. One is 10 times as much as the other. Analyze the error with your partner

S: 5,000 × 400 is like (5 × 1,000) × (4 × 100). That’s like (5 × 4) × 100,000, so 20 copies of 1 hundred thousand. That’s 20 hundred thousands which is 2 million.

T: Simply counting the zeros in our factors is not an acceptable strategy. We should always be aware of our units and how many of those units we are counting.

T: Should our actual product be more or less than our estimated product? How do you know? Turn and talk.

S: We rounded one factor up and one factor down. Our actual product could be more or less. We can’t really tell yet, since we rounded 4,902 up and 408 down. Our actual product might be more or less than 2,000,000, but it should be close.

T: Work independently to solve 4,902 × 408.

S: (Solve to find 2,000,016.)

T: Is the actual product reasonable?

S: Yes.

14 of 17

Problem Set

15 of 17

Debrief

What is the benefit of estimating before solving?

Look at Problems 1 (b) and (c).

What do you notice about the estimated products?
Analyze why the estimates are the same, yet the products are so different.
How could the cost of the chairs have been found using the unit form mental math strategy?

Any combination of the questions below may be

used to lead the discussion.

16 of 17

Debrief

In Problem 4, Carmella estimated that she had 3,000 cards.

How did she most likely round her factors?
Would rounding the number of boxes of cards to 20 have been a better choice? Why or why not?
Do we always have to round to a multiple of 10, 100, or 1,000?
Is there a number between 10 and 20 that would have been a better choice for Carmella?

Can you identify a situation in a real-life example where overestimating would be most appropriate?

Can you identify a situation in the real world where underestimation would be most appropriate?

In Problem 4, Carmella estimated that she had 3,000 cards.
How did she most likely round her factors?
Would rounding the number of boxes of cards to 20 have been a better choice?
Why or why not? (Students might consider that she is done collecting cards and will not need any more space.

Others might argue that she is still collecting and could use more room for the future.)

Do we always have to round to a multiple of 10, 100, or 1,000?
Is there a number between 10 and 20 that would have been a better choice for Carmella?
Can you identify a situation in a real-life example where overestimating would be most appropriate?
Can you identify a situation in the real world where underestimation would be most appropriate? (For example, ordering food for a party where 73 people are invited. The answer, of course, depends on the circumstances, budget, the likelihood of the attendance of all who were invited, etc.)

17 of 17

Exit Ticket