Maryland Math 5.NOS.B.5.c

Math5th GradeNumber and Operation Sense

The Standard

5.NOS.B.5: Divide multi-digit whole numbers with up to four-digit dividends and two-digit divisors.

Use properties of operations and/or the inverse relationship between multiplication and division to divide.

Maryland College and Career Ready Standards for Mathematics (2025) · PERFORM OPERATIONS ON MULTI-DIGIT WHOLE NUMBERS AND WITH DECIMALS TO HUNDREDTHS.

Teacher's field guide

What Students Need to Do: Students split a number into parts that are easier to divide, then divide each part by the same number. They use multiplication to find or check the answer.
What Mastery Looks Like: For 156 ÷ 12, a student uses 120 ÷ 12 and 36 ÷ 12 to get 10 + 3. They check that 12 × 13 = 156.
Common Misconceptions: Some students split the divisor instead and treat 156 ÷ 12 as 156 ÷ 10 + 156 ÷ 2. Others divide 48 hundredths as 48 whole ones when working with 6.48 ÷ 3.
How to Assess It: Ask students to solve 156 ÷ 12 by splitting 156 into two useful parts. Have them check their answer with multiplication.

Lesson moves

Give pairs base-ten blocks for 96; have them trade one ten, share the blocks among four groups, and record 80 ÷ 4 + 16 ÷ 4.
Ask: Why can you split 156 into 120 + 36 before dividing by 12, but not split the divisor into 10 + 2?
Make card sets showing 156 ÷ 12, 120 ÷ 12 + 36 ÷ 12, and 12 × 13; students match the cards and explain why.
Cut a 6.48-meter ribbon into three equal pieces on paper; students divide 6 meters and 48 centimeters, then check by multiplying.

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