5.3.J
The Standard
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 pictorial models, including area models
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students show two division situations with fraction strips, counters, or area drawings. They split one fractional piece into equal shares, and they count how many unit fractions fit inside a whole number.
What Mastery Looks Like
- A student can show that splitting 1/3 into seven equal parts makes pieces of size 1/21. The student can also show that seven wholes contain twenty-one groups of 1/3.
Common Misconceptions
- Students may assume division always makes a number smaller. They may reverse the two numbers, or claim that 1/3 ÷ 7 equals 7/3 instead of 1/21.
How to Assess It
- Ask students to solve 1/4 ÷ 3 and 3 ÷ 1/4. Require a labeled area model and one sentence explaining each quotient.
Lesson moves
Ways to Teach It
Fold a paper strip into fourths, shade one fourth, then split the shaded section into three equal parts to model 1/4 ÷ 3.
Compare 1/5 ÷ 2 and 2 ÷ 1/5, then explain why one quotient is less than one and the other is greater.
Match equation cards with area model cards and quotient cards, then check each match with a partner.
A four-yard ribbon is cut into 1/3-yard pieces. Draw a model and find how many pieces can be cut.
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Related Standards
- 3.3.F
represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines
- 5.3.L
divide whole numbers by unit fractions and unit fractions by whole numbers
- 5.3.F
represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using objects and pictorial models, including...
- 5.3.I
represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models
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