Formative Instructional and Assessment Tasks

Comparing Products
5.OA.2 - Task 2
Domain / Operations and Algebra
Cluster / Write and interpret numerical expressions
Standard(s) / 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Materials / Paper and pencil
Task / Matt and Susan are looking at the following problem:
How does the product of 60 x 345 compare to the product of 30 x 345?
Susan says she can compare these products without multiplying the numbers out. Explain how she might do this. Draw a picture or pictures to illustrate your explanation.
Solution:
Since 60 is twice 30, the product 60 x 345 is twice the product 60 x 345. We can write this as an equation: 60 x 345 = (2 x 30) x 345 = 2 x (30 x 345).

The area of a 345 by 60 rectangle (60 x 345) is double that of a 345 by 30 rectangle (30 x 345). If we scale the width of the rectangle by a factor of 2, then the area of the resulting rectangle doubles. So, if one of the factors of the product 30 x 345 is scaled by a factor of 2, then the product is scaled by a factor of 2.
Adapted from Illustrative Mathematics (www.illustrativemathematics.org)
Rubric
Level I / Level II / Level III
Limited Performance
·  Student demonstrates little or no understanding of the concept. / Not Yet Proficient
·  Student can explain how to compare the two expressions without evaluating them.
OR
·  Student can draw a picture that illustrates understanding of the concept. / Proficient in Performance
·  Student can explain how to compare the two expressions without evaluating them
·  Student can draw a picture that illustrates understanding of the concept.
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.


Comparing Products

Matt and Susan are looking at the following problem:

How does the product of 60 x 345 compare to the product of 30 x 345?

Susan says she can compare these products without multiplying the numbers out. Explain how she might do this. Draw pictures to illustrate your explanation.

NC DEPARTMENT OF PUBLIC INSTRUCTION FIFTH GRADE