Topic C

TOPIC C: Division with a Unit Fraction and a Whole Number

Dear Family,

Your student is learning to divide a whole number by a unit fraction and to divide a unit

fraction by a whole number. A unit fraction, such as 1/3 ,1/8 ,or 1/15 , is exactly 1 of a specific

fractional unit. They begin by exploring division when the divisor represents the size of

each group, and then when the divisor represents the number of groups. Students use tape

diagrams and number lines to reason about division. Your student makes connections about

the size of quotients, or answers. They see that the quotient of a whole number and a unit

fraction is greater than the dividend, and that the quotient of a unit fraction and a whole

number is less than the dividend. Students solve real-world problems involving fractions with

multiplication and division.

KEY TERMS

convert

cup

denominator

gallon

mixed number

numerator

ounce

pint

pound

product

quart

quotient

whole number

AT HOME ACTIVITY

Find a sample of our lessons below to help support MATH TALK at home.

Students also have these in their APPLY workbook.

Lesson 12

Divide a nonzero whole number by a unit fraction to find the number of groups.

I can interpret a unit fraction divisor as the size of the group by asking, How many ____ are in ____? I can use this interpretation to find a quotient that represents the number of groups. I can use a tape diagram to both model and divide.

Lesson 13

Divide a nonzero whole number by a unit fraction to find the size of the group.

I can interpret a unit fraction divisor as the number of groups by asking, ____ is ____ of what number? I can use this interpretation to find a quotient that represents the size of the group. I can use a tape diagram and a number line to both model and divide.

Lesson 14

Divide a unit fraction by a nonzero whole number.

I can interpret a whole number divisor as the number of groups when the dividend is a unit fraction by asking, ____ is ____ groups of what? I can use this interpretation to find a quotient that represents the size of the group. When I model with a tape diagram, I need to show the total units in 1 so I can accurately identify the quotient.

Lesson 15

Divide by whole numbers and unit fractions.

I can use the Read–Draw–Write process to solve problems involving dividing by whole numbers and unit fractions. I can reason about the size of the quotient based on the dividend and the divisor to check the reasonableness of my answer.

Lesson 16

Reason about the size of quotients of whole numbers and unit fractions and quotients of unit fractions and whole numbers.

I can reason about the size of quotients when I divide a whole number by a unit fraction or divide a unit fraction by a whole number. I can explain this reasoning by drawing representations or writing explanations. I can use this reasoning to compare the values of expressions without evaluating.

Lesson 17

Solve word problems involving fractions with multiplication and division.

By using information from a word problem, I can decide which operation to use to solve the problem. I can discuss with classmates about why someone may have chosen a different operation or a different pathway to the solution.

Solve word problems involving fractions with multiplication and division.

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