multiplication & division problem situations something new?

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


Hell’s Library


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.


Time to Fold Some Paper


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.


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 = ☐.


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.


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.


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.


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.


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.”


Time to Fold More Paper


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.


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


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?


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


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.


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?


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

multiplication & division problem situations something new?

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