Maryland Math 5.NOS.D.13

5.NOS.D.13 is a cluster heading. These are the individual standards under it.

• 5.NOS.D.13.a

  Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.

• 5.NOS.D.13.b

  Apply and extend whole number multiplication strategies (e.g. area model, partial products).

01

What Students Need to Do

Students multiply fractions, including improper fractions and mixed numbers. They use a split rectangle or partial products. They estimate with benchmark numbers to check their answers.

02

What Mastery Looks Like

A student can split 1 1/2 × 1 1/4 into four area pieces and find 1 7/8. They can explain why the answer lies between 1 1/2 and 2 1/4.

03

Common Misconceptions

Some students multiply the whole number parts and fraction parts separately, getting 1 1/8 for 1 1/2 × 1 1/4. Others think multiplying by any fraction makes a number smaller.

04

How to Assess It

Ask students to draw a split rectangle for 1 1/2 × 1 1/4, label each area, and find the product. Have them explain why their answer is near 2.

1. 01

   On grid paper, draw a 1 1/2 by 1 1/4 rectangle, split it at whole units, label each area, and add them.

2. 02

   Ask, "Why is 1 1/2 × 1 1/4 greater than 1 1/2 but less than 2 1/4?"

3. 03

   Put 5/4, 3/2, and 7/4 on cards; partners draw two, estimate the product, then use partial products to check.

4. 04

   Show a recipe card listing 3/4 cup oats per batch; students calculate the amount for 1 1/2 batches and check against one cup.

• 5.NOS.D.12

  Apply and extend previous understandings of multiplication to multiply a fraction by a fraction.

• 5.NOS.D.11

  Apply and extend previous understandings of multiplication to multiply a whole number by a fraction (c/d × b).

• 4.NOS.E.12

  Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract fractions with like denominators.