multiplying and dividing decimals marta garcia, buncombe county schools amy lehew,...
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![Page 1: Multiplying and Dividing Decimals Marta Garcia, Buncombe County Schools Amy LeHew, Charlotte-Mecklenburg Schools Drew Polly, UNC Charlotte Thursday, October](https://reader035.vdocument.in/reader035/viewer/2022081516/56649ec95503460f94bd76f6/html5/thumbnails/1.jpg)
Multiplying and Dividing DecimalsMarta Garcia, Buncombe County SchoolsAmy LeHew, Charlotte-Mecklenburg SchoolsDrew Polly, UNC Charlotte
Thursday, October 318:30-9:15 Cedar A
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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
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Let’s Get to Work!
Use base ten blocks to justify why 3 x 50 is
ten times larger than 3 x 5.
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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 Marta Garcia, Buncombe County Schools Amy LeHew, Charlotte-Mecklenburg Schools Drew Polly, UNC Charlotte Thursday, October](https://reader035.vdocument.in/reader035/viewer/2022081516/56649ec95503460f94bd76f6/html5/thumbnails/5.jpg)
Associative Property: Why is the Product Ten Times Larger?
6 x 5 = 30
3 groups of 10 Use the thinking on the left to
solve
6 x 50
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• 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
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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
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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
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Proving Equivalence with Decimals
Remember 2 x 30 = 3 x 20
.2 x 30 = 20 x .3
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Comparing Two Generalizations
What’s the “rule”
20 x 30
2 x 3“Count the zeros”
What’s the “rule”
.2 x .3
2 x 3“Count the
decimal places”
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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.
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True or False?
200 divided by 40 = 20 divided by 4
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Dividing Decimals
Explore…
�32 divided by 8
3.2 divided by 8
.32 divided by 8
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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?
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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.”
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Making Connections
�How does the multiplication and division of decimals connect the base ten work from prior grades?
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Questions? Reflections?