Multiplication & Division Problem Situations Something New? June 23, 2011 Common Core Leadership in Mathematics (CCLM) Summer Institute DeAnn Huinker & Melissa Hedges

Hell’s Library

Learning Intention Success Criteria 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

4 x 7 = ☐ What does the 4 mean? What does the 7 mean? The total number of objects in 4 groups of 7 objects each. Pose a word problem for: 4 x 7 = ☐ Group Size Number of Groups Examine your word problem: What does the 4 mean? What does the 7 mean?

28 ÷ 4 = ☐ Tell a different story for 28 ÷ 4 = ☐. Pose a word problem for: 28 ÷ 4 = ☐ Examine your word problem: What is unknown in your problem: Number of groups? Group size? Tell a different story for 28 ÷ 4 = ☐.

Revisit Grade 3 expectations 3OA1 Interpret products of whole numbers, e.g., 5 x 7 as the total number of objects in 5 groups of 7 objects each. 3OA2 Interpret 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 = ☐ Number of shares or Number of objects in each share Total Division 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 & 4OA2 K-5 OA Progressions: p.29 1st paragraph Shoulder partners: Summarize the meaning of these standards and implications for curriculum.

4OA1 Interpret a multiplication equation as a comparison, e. g 4OA1 Interpret 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? Students in earlier grades learned to compare quantities additively…. “This one is 32 feet higher than that one” 40 feet high, the other 8 feet high 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.

7 x 8 = ☐ Total Unknown 56 ÷ 8 = ☐ Group Size Unknown 56 ÷ 8 = ☐ Number of Groups Unknown Connie has 8 times as much money as Melissa. Connie has $56. How much money does Melissa have? Unknown: Group Size

Is the answer 48 or 7? 7 x 8 = ☐ Total Unknown 56 ÷ 8 = ☐ Group Size Unknown 56 ÷ 8 = ☐ Number of Groups Unknown Hank is older than Kara. Hank is 56 years old. Kara is 8 years old. How much older is Hank? 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

Revisiting Learning 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