NY Next Generation Math NY-5.NF.5

NY-5.NF.5 is a cluster heading. These are the individual standards under it.

• NY-5.NF.5.a

  Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

01

What Students Need to Do

Students interpret multiplication as resizing a quantity. They predict whether a product is larger, smaller, or equal to a given factor from whether the other factor is greater than, less than, or equal to one.

02

What Mastery Looks Like

The student explains without calculating that 8 times 3/2 is greater than 8 and 8 times 3/4 is less than 8. The student recognizes multiplication by an equivalent form of one leaves a value unchanged.

03

Common Misconceptions

Students may believe multiplication always makes a number larger. They may compare a product to the wrong factor or ignore whether the scaling factor is above or below one.

04

How to Assess It

Without calculating, ask students to compare 12 times 5/6 and 12 times 7/4 with 12 and justify both comparisons.

1. 01

   Resize paper strips by fractional scale factors and compare each new length with the original strip.

2. 02

   Ask students to explain why multiplying by 2/3 shrinks a positive quantity even though multiplication is used.

3. 03

   Play product-size sort using multiplication cards with factors below one, equal to one, and above one.

4. 04

   Predict how a fractional scale factor changes a recipe batch, map distance, or image size.

• NY-3.OA.5

  Apply properties of operations as strategies to multiply and divide.

• NY-4.OA.1

  Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.