multiplying and dividing decimals

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Multiplying and Dividing Decimals Marta Garcia, Buncombe County Schools Amy LeHew, Charlotte-Mecklenburg Schools Drew Polly, UNC Charlotte Thursday, October 31 8:30-9:15 Cedar A

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Multiplying and Dividing Decimals. Marta Garcia, Buncombe County Schools Amy LeHew, Charlotte-Mecklenburg Schools Drew Polly, UNC Charlotte Thursday, October 31 8:30-9:15 Cedar A. Goals of the Session. Today we will: - PowerPoint PPT Presentation

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Page 1: Multiplying and Dividing Decimals

Multiplying and Dividing DecimalsMarta Garcia, Buncombe County SchoolsAmy LeHew, Charlotte-Mecklenburg SchoolsDrew Polly, UNC Charlotte

Thursday, October 318:30-9:15 Cedar A

Amy Lehew
What progression will they look at? Will we have copied the parts of NBT needed?
Marta Garcia
I think we decided we don't have time for progressions.
Amy Lehew
This could take 20+ minutes. Would we rather have participants doing some of the math involved or creating a progression?
Amy Lehew
Is this too much info for this venue?
Marta Garcia
Delete this slide!
Page 2: Multiplying and Dividing Decimals

Goals of the Session

Today we will:Explore multiplication of decimals and connect

the multiplication work of whole numbers to decimals

Explore division of decimals and connect the division work of whole numbers to decimals

Page 3: Multiplying and Dividing Decimals

Let’s Get to Work!

Use base ten blocks to justify why 3 x 50 is

ten times larger than 3 x 5.

Page 4: Multiplying and Dividing Decimals

Grade 3

3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Use base ten blocks to justify why 3 x 50 is ten times larger than 3 x

5

Page 5: Multiplying and Dividing Decimals

Associative Property: Why is the Product Ten Times Larger?

6 x 5 = 303 groups of 10 Use the

thinking on the left to

solve

6 x 50

Page 6: Multiplying and Dividing Decimals

• CCSS.Math.Content.4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

• CCSS.Math.Content.4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1

Page 7: Multiplying and Dividing Decimals

What does it mean to be Ten Times Bigger?

Student responses to how many times greater is

4 x 100 than 4 x 10?�4 x 100 is 360 times bigger than 4 x 10

4 x 100 is 90 times bigger than 4 x 10� �4 x 100 is 100 times bigger than 4 x 10

Page 8: Multiplying and Dividing Decimals

5th Grade

�5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used

Page 9: Multiplying and Dividing Decimals

Proving Equivalence with Decimals

Remember 2 x 30 = 3 x 20

.2 x 30 = 20 x .3

Page 10: Multiplying and Dividing Decimals

Comparing Two Generalizations

What’s the “rule”

20 x 30

2 x 3“Count the zeros”

What’s the “rule”

.2 x .32 x 3

“Count the decimal places”

Page 11: Multiplying and Dividing Decimals

Understanding the Standards

�4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

�5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Page 12: Multiplying and Dividing Decimals

True or False?

200 divided by 40 = 20 divided by 4

Page 13: Multiplying and Dividing Decimals

Dividing Decimals

Explore…�32 divided by 8

3.2 divided by 8

.32 divided by 8

Page 14: Multiplying and Dividing Decimals

Sally … Making Sandwiches

�We have 99.99 grams of peanut butter to use to make sandwiches. If we put 0.3 grams on each sandwich, how many sandwiches can we make?

�“I know that I can move the decimal in both numbers one spot to the right to make 99.9 divided by 3. I then just divided and got my answer 33.3. We can make 33.3 sandwiches.

��What did Sally do mathematically when she moved the decimal?

�What does Sally “understand” about place value?�What question could we ask Sally to assess her

understanding?

Page 15: Multiplying and Dividing Decimals

Comparing Two Generalizations

What’s the “rule”

80,000 divided by 400

“Just cross out the zeros”

What’s the “rule”

8.88 divided by 0.4“Just move the

decimal.”

Page 16: Multiplying and Dividing Decimals

Making Connections

�How does the multiplication and division of decimals connect the base ten work from prior grades?

Page 17: Multiplying and Dividing Decimals

Questions? Reflections?

Page 18: Multiplying and Dividing Decimals

Contact Information

Marta- [email protected] [email protected] [email protected]