Maryland Math 5.NOS.B.5.d

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.

Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of division.

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 use equal rows or split rectangles to show division. They connect each part of the drawing to an equation and explain what the answer counts.
What Mastery Looks Like: For 156 ÷ 12, a student draws 12 rows split into blocks of 120 and 36. They show 120 ÷ 12 + 36 ÷ 12 = 13 and explain that 13 is the number in each row.
Common Misconceptions: Some students divide 120 by 12 but forget to divide the remaining 36. Others call the 12 rows the answer, or draw parts that do not add to 156.
How to Assess It: Ask students to draw a split rectangle for 156 ÷ 12, write a matching equation, and explain what 13 counts.

Lesson moves

Give pairs 156 counters to arrange in 12 equal rows, then have them separate each row into groups of 10 and 3.
Have students write why splitting a 12-by-13 rectangle into 12-by-10 and 12-by-3 blocks shows 156 ÷ 12 = 13.
Make cards showing 144 ÷ 12, 168 ÷ 12, and matching split rectangles; partners race to pair each equation with its rectangle.
For 156 markers packed equally into 12 boxes, have students draw a split rectangle and label what its 13 columns mean.

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