Montana Math MT.K.OA.3

MathKindergartenOperations and Algebraic Thinking

The Standard

Decompose numbers less than or equal to 10 into pairs in multiple ways.

2026 Montana Mathematics Content Standards

Teacher's field guide

What Students Need to Do: Students split up to 10 objects into two groups and find different ways to do it. They show each pair with objects, drawings, or numbers, including a pair with zero in one group.
What Mastery Looks Like: For 8, a student can show 0 and 8, 1 and 7, and 3 and 5. They can check that each pair still makes 8.
Common Misconceptions: Students may think both groups need at least one object. Some count an object in both groups or change the total while making a new pair. Others find one pair and think they are done.
How to Assess It: Give students this exit ticket: “Show two different ways to split 7 dots into two groups. Draw and label each group.”

Lesson moves

Give pairs seven two-color counters to shake, sort by color, and record three different red and yellow pairs.
Ask, “Mia says 4 and 3 is the only way to make 7. Can you draw another way and explain it?”
Play Make 9: roll a die, place that many counters on a nine-frame, and count the empty spaces.
Draw two lunch containers and give students eight paper apple slices to divide between them in three different ways.

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