5.3.L
The Standard
divide whole numbers by unit fractions and unit fractions by whole numbers
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students determine how many equal unit-fraction groups fit in a whole number. They also split one unit fraction into equal shares and represent both situations with models and equations.
What Mastery Looks Like
- Given 4 ÷ 1/3, a student models 12 one-third groups and records a quotient of 12. Given 1/3 ÷ 4, the student partitions one-third into four equal parts and records 1/12.
Common Misconceptions
- Students may treat 4 ÷ 1/3 and 1/3 ÷ 4 as the same calculation. They may divide denominators directly or assume division always makes a number smaller.
How to Assess It
- Ask students to draw models and solve 3 ÷ 1/4 and 1/4 ÷ 3. Have them explain in one sentence why the quotients differ.
Lesson moves
Ways to Teach It
Fold four paper strips into thirds and count the pieces, then divide one one-third strip into four equal parts.
Ask, “Why do 4 ÷ 1/3 and 1/3 ÷ 4 have different answers?” Students write and compare explanations.
Match expression cards, quotient cards, and fraction-bar models; students explain each match before keeping the set.
Use 3 liters of juice to fill 1/4-liter cups, then share 1/4 liter equally among three students.
Keep exploring
Related Standards
- 5.3.J
represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pict...
- 3.7.A
represent fractions of halves, fourths, and eighths as distances from zero on a number line
- 3.3.C
explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whol...
- 4.4.E
represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations
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