Groups or Group Size?
Twenty-four counters are placed 4 in each bag. What does the quotient tell us?
The quotient tells the number of bags, or equal groups. 24 ÷ 4 = 6 bags.
A tape diagram has a total of 20. Each part is 5. How many equal parts should it have?
Four equal parts, each labeled 5. 20 ÷ 5 = 4.
Complete the unknown-factor equation and division equation: ? × 4 = 20 and 20 ÷ 4 = ?
The unknown factor is 5. 5 × 4 = 20 and 20 ÷ 4 = 5.
Fifteen apples are packed 3 in each bag. How many bags are needed?
5 bags. 15 ÷ 3 = 5 and 5 × 3 = 15.
Twenty pencils are packed 5 in each cup. In 20 ÷ 5 = 4, what does 4 represent?
Four represents the number of cups, or equal groups.
Eighteen stickers are shared equally among 3 students. What does the quotient tell us?
The quotient tells the number of stickers each student receives. 18 ÷ 3 = 6 stickers each.
Twenty-one objects are shared into 3 equal groups. What labels belong on the tape diagram?
Label the whole 21. Partition it into 3 equal parts. Each part is 7.
The unknown factor is 5. 5 × 4 = 20 and 20 ÷ 4 = 5.
30 ÷ 6 = 5 and 30 ÷ 5 = 6.
Twenty-four papers are shared equally into 6 piles. How many papers are in each pile?
4 papers per pile. 24 ÷ 6 = 4 and 6 × 4 = 24.
Twenty pencils are shared equally among 4 cups. In 20 ÷ 4 = 5, what does 5 represent?
Five represents the number of pencils in each cup, or the group size.
Forty crayons are placed 5 in each cup. Name the group size and the number of groups.
Group size: 5 crayons. Number of groups: 8 cups. 40 ÷ 5 = 8.
A tape diagram has 6 equal parts and a total of 42. Write the division and multiplication equations.
42 ÷ 6 = 7 and 6 × 7 = 42.
Use an unknown-factor equation to solve 32 ÷ 4.
? × 4 = 32. The unknown factor is 8, so 32 ÷ 4 = 8.
Forty balloons are arranged in bunches of 5. How many bunches are made?
8 bunches. 40 ÷ 5 = 8 and 8 × 5 = 40.
Thirty chairs are arranged in rows of 5. Choose the equation and label the quotient.
30 ÷ 5 = 6 rows. The quotient represents the number of rows.
Thirty-six blocks are shared into 6 equal towers. What information is known, and what is unknown?
Known: total of 36 and 6 groups. Unknown: group size. 36 ÷ 6 = 6 blocks per tower.
The total is 28 and the group size is 4. Describe how to draw the tape diagram.
Draw equal parts labeled 4 until the total reaches 28. The tape has 7 parts. 28 ÷ 4 = 7.
Write the complete multiplication and division fact family for 7, 8, and 56.
7 × 8 = 56, 8 × 7 = 56, 56 ÷ 7 = 8, and 56 ÷ 8 = 7.
Thirty-six pencils are shared equally among 4 tables. How many pencils does each table receive?
9 pencils per table. 36 ÷ 4 = 9 and 4 × 9 = 36.
Compare these stories: 24 cookies with 6 in each box, and 24 cookies shared into 6 boxes. How does the meaning of 4 change?
In the first story, 4 means boxes. In the second, 4 means cookies in each box. Both use 24 ÷ 6 = 4.
The equation is 24 ÷ 6 = 4. Give two different questions that this equation could answer.
Ask for the number of groups when 6 is the group size. Ask for the group size when 6 is the number of groups.
A student draws 3 parts labeled 8 for this story: 24 objects are placed in groups of 3. Explain the error.
The drawing represents 3 groups of 8. The story needs 8 groups with 3 in each group. 24 ÷ 3 = 8.
Explain why solving 45 ÷ 5 is the same as finding the unknown factor in ? × 5 = 45.
Both questions ask how many groups of 5 make 45. The unknown factor and quotient are both 9.
Forty-eight markers are packed 6 per box. Three boxes are already filled. How many more boxes are needed?
48 ÷ 6 = 8 boxes in all. 8 − 3 = 5 more boxes.
A student says, “The divisor always tells the number of groups.” Is the student correct? Explain.
A student says, “The divisor always tells the number of groups.” Is the student correct? Explain.