Montana Math MT.5.NF.7
The Standard
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions by: Expressing division of a unit fraction by a nonzero whole number and computing such quotients, Expressing division of a whole number by a unit fraction and computing such quotients, and Solving problems in context involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students split a unit fraction into equal parts. They also find how many unit fractions fit in a whole number. They use drawings and equations to solve problems in both directions.
What Mastery Looks Like
- A student can show that 1/3 ÷ 2 = 1/6 and 2 ÷ 1/3 = 6 with labeled drawings. They can explain why the first answer is smaller than 1/3 and the second is larger than 2.
Common Misconceptions
- Students may write 1/4 ÷ 2 = 2/4 because they double the numerator. They may write 2 ÷ 1/4 = 1/8 because they think division always makes an answer smaller.
How to Assess It
- Exit ticket: Draw and label a model for 1/3 ÷ 2 and 2 ÷ 1/3. Write each quotient and explain why the answers differ.
Lesson moves
Ways to Teach It
Fold a paper strip in half, divide one half into three equal pieces, and label each piece 1/6 of the strip.
Ask students to sketch 2 ÷ 1/4 and 1/4 ÷ 2, then write why the answers differ.
Deal a whole-number card and a unit-fraction card; students solve both division orders and check each other's drawings.
Find Browning on the Blackfeet Reservation on a Montana map; sketch a proposed 2-mile walk in 1/4-mile sections and count them.
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