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Lesson 8: I can fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product 5th Grade Module 2 – Lesson 8

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5th Grade Module 2 – Lesson 8

Lesson 8: I can fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check

for reasonableness of the product

5th Grade Module 2 – Lesson 8

State in Exponential Form

102

Say the base.Say the exponent.

Say 10 squared as a multiplication

sentence starting with 10

10 x 10 = 100

Say it as a number sentence without

using a multiplication

sentence

10 squared = 100

5th Grade Module 2 – Lesson 8

State in Exponential Form

103

Say the base.Say the exponent.

Say 10 to the third as a multiplication sentence starting

with 10

10 x 10 x 10 = 100

Say it as a number sentence without

using a multiplication

sentence

10 to the third = 1000

5th Grade Module 2 – Lesson 8

State in Exponential Form

104

Say the base.Say the exponent.

Say 10 to the fourth as a multiplication sentence starting

with 10

10 x 10 x10 x 10 = 10,000

Say it as a number sentence without

using a multiplication

sentence

10 to the fourth = 10,000

5th Grade Module 2 – Lesson 8

State in Exponential Form

105

Say the base.Say the exponent.

Say 10 to the fifth as a multiplication sentence starting

with 10

10 x 10 x 10 x 10 x 10 = 100

Say it as a number sentence without

using a multiplication

sentence

10 to the fifth =

100,000

5th Grade Module 2 – Lesson 8

State in Exponential Form

107

Say the base.Say the exponent.

Say 10 to the seventh as a

multiplication sentence starting

with 10

10 x 10 x 10 x 10 x 10 x 10 x

10= 100

Say it as a number sentence without

using a multiplication

sentence

10 to the seventh = 10,000,00

0

5th Grade Module 2 – Lesson 8

Multiply Using the Area Model with a Zero in One Factor

287 x 64 ≈ ___ x ___ = ____300 60 18,000

On your boards, write the multiplication sentence rounding

each factor to arrive at a reasonable estimate of the product.

5th Grade Module 2 – Lesson 8

Application Problem

Erin and Frannie entered a rug design contest. The rules stated that the rug’s dimensions must be 32 inches x 45 inches and that they must use rectangles. They drew the following for their entries. Show at least 3 other designs they could have entered in the contest and calculate the area of each section and the total of your rugs.

5th Grade Module 2 – Lesson 8

5th Grade Module 2 – Lesson 8

314 x 236

Round each factor to estimate the

product.

Turn and talk.

estimate the product.

What is 300 x 200?

300 x 200 = 60,000

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

6 x 104

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?

The answer should be more because our actual

factors are more than what we rounded to!

Solve using the standard algorithm.

Look back at our estimate. Is our answer reasonable?

5th Grade Module 2 – Lesson 8

1,882 x 296

Round each factor and estimate the product.

Will the actual answer be greater than or less than

2,000 x 300

Work independently to solve for the actual answer.

Is the product reasonable?

5th Grade Module 2 – Lesson 8

4,902 x 408

Find the estimated product for this

problem.

Let’s read the estimated multiplication sentence

without the product.

4,902 x 408 is about as much as 5,000 x

400

Some of you estimated the product to be 200,000.

What is the error?

We cannot simply count the zeros! You must

Should our actual product be more or less than our actual

product? Turn and talk!

We rounded one factor up and one factor down. We can’t really tell but it

should be close!

5th Grade Module 2 – Lesson 8

Complete Pages 2.B.75 - 2.B.76 You will have 10 minutes to work.

5th Grade Module 2 – Lesson 8

Debrief•How can estimating before solving help us?

•Look at Problem 1(b) and (c). What do you notice about estimated products? Analyze why the estimates are the same but the products are so different.

•How could the cost of the chairs have been found using the unit form mental math strategy?

5th Grade Module 2 – Lesson 8

Debrief•In Problem 3, 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?

5th Grade Module 2 – Lesson 8

Debrief

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

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

5th Grade Module 2 – Lesson 11

EXITTICKETPage 2.B.77