Maryland Math 3.NOS.E.9.c

Math3rd GradeNumber and Operation Sense

The Standard

3.NOS.E.9: Recall or quickly derive multiplication and division facts within 100 (e.g., factors less than or equal to 10 and quotients less than or equal to 10).

Use properties of operations (e.g., to solve 8 × 7, think of (5 × 7) + (3 × 7)) to multiply.

Maryland College and Career Ready Standards for Mathematics (2025) · MULTIPLY AND DIVIDE WITHIN 100.

Teacher's field guide

What Students Need to Do: Students break one factor into smaller parts, multiply each part, then add the products. They use an array or an equation to show why the answer stays the same.
What Mastery Looks Like: A student can solve 8 × 7 by finding 5 × 7 and 3 × 7, then adding 35 + 21. They can point to the two parts of an array and explain why they still make eight rows of seven.
Common Misconceptions: Some students write (5 × 7) + 3 and forget to multiply the second part. Others use 3 × 8 for the second part, instead of 3 × 7.
How to Assess It: Exit ticket: Solve 6 × 8 by splitting 6 into two parts. Write both smaller multiplication facts and show how you get the total.

Lesson moves

Build eight rows of seven counters, separate five rows from three rows, and add the two products.
Ask, “Why does (5 × 7) + (3 × 7) give the same answer as 8 × 7?” Have students draw and label an array.
Give pairs multiplication cards, such as 7 × 8 and 9 × 6, and have them race to solve each by splitting a factor.
Show nine boxes with six crayons each, then ask students to count them by splitting the boxes into groups of five and four.

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