Multiplication & Division Problem Situations Something New?
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Multiplication & Division Problem Situations
Something New?
June 23, 2011Common Core Leadership in Mathematics (CCLM)
Summer InstituteDeAnn Huinker & Melissa Hedges
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Hell’s Library
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Learning Intention
We are learning to:
Understand the differences among problem types for multiplication and division.
Success Criteria
We will be successful when…
We can pose equal group and compare word problems for multiplication and division.
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Time to Fold Some Paper
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Examine your word problem:
What does the 4 mean?
What does the 7 mean?
4 x 7 = ☐
Pose a word problem for:
Number of Groups
Group Size
The total number of objects in 4 groups of 7 objects each.
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Examine your word problem:What is unknown in your problem:
Number of groups?Group size?
28 ÷ 4 = ☐
Pose a word problem for:
Tell a different story for 28 ÷ 4 = ☐.
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Revisit Grade 3 expectations3OA1
Interpret products of whole numbers, e.g., 5 x 7 as the total number of objects in 5 groups of 7 objects each.
3OA2Interpret whole-number quotients of whole numbers,
e.g., interpret 56 ÷ 8
as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or
as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
28 ÷ 4 = ☐
TotalNumber of shares
or Number of objectsin each shareDivision means to partition
to find the number of shares or find the amount in each share.
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Something new?
Read, highlight, take note:
Grade 4 standards: 4OA1 & 4OA2K-5 OA Progressions: p.29 1st paragraph
Shoulder partners: Summarize the meaning of these standards and implications for curriculum.
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
4OA1Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 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.
4OA2 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.
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
What’s the new thinking being developed in 40A1 & 2?
“This one is 32 feet higher than that one” 40 feet high, the other 8 feet high
Students in earlier grades learned to compare quantities additively….
Students in Grade 4 learn to compare these quantities multiplicatively…..
“This one is 5 times as high as that one.”
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Time to Fold More Paper
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Experiences with Compare Word Problems
Individually pose compare word problems for:
6 x 9 = ☐
54 ÷ 6 = ☐ with Group Size Unknown
54 ÷ 6 = ☐ with Number of Groups Unknown
Use Table 2, p. 89, of CCSSM and/or use Table 3, p.23, of OA Progressions, if needed.
When you have a draft of each, turn and check-in with a partner.
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Connie has 8 times as much money as Melissa. Connie has $56. How much money does Melissa have?
7 x 8 = ☐ Total Unknown
56 ÷ 8 = ☐ Group Size Unknown
56 ÷ 8 = ☐ Number of Groups Unknown
Unknown: Group Size
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Hank is older than Kara. Hank is 56 years old. Kara is 8 years old. How much older is Hank?
7 x 8 = ☐ Total Unknown
56 ÷ 8 = ☐ Group Size Unknown
56 ÷ 8 = ☐ Number of Groups Unknown
Is the answer 48 or 7?
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Building Blocks of Algebra
Understand problem situations
Represent the situation with objects or diagrams
Represent quantitative relationships
with equations
Use properties of operations as the basis for strategies
p.13 OA Progressions
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
RevisitingLearning Intention and Success
Criteria
We were learning to:
Understand the differences among problem types for multiplication and division.
We will be successful when…
We can pose equal group and compare word problems for multiplication and division.
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Revisiting Meaning of Multiplication
Read, highlight, take note:
K-5 OA Progressions: p.33 last paragraph
How does the meaning of multiplication expand across Grade 3 to 4 to 5?
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Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Expanding View of Multiplication
Grade 3: Equal groups
--discrete objects, arrays….
Grade 4: Comparison situations--continuous quantities
Grade 5: Stretches or Shrinks (scale factor)
--Context for reasoning multiplicatively with continuous quantities