Practice · Total all categories from a pictograph · Sensim Math

Variant 1 answer: 16 m 20 cm (1620 cm)

A flower shop surveyed the flowers it had by type and showed the results in a pictograph. The flowers will be mixed into bouquets of $5$ flowers each, and any leftover flowers will be wrapped one at a time. If $90\ \text{cm}$ of ribbon is needed to make one bouquet and $20\ \text{cm}$ of ribbon is needed to wrap one single flower, how many meters and centimeters of ribbon are needed in all?

Number of Flowers by Type (pictograph)

Type	Number of flowers
Rose	(1 large picture, 8 small pictures)
Tulip	(2 large pictures, 2 small pictures)
Chrysanthemum	(3 large pictures, 4 small pictures)
Lily	(1 large picture, 6 small pictures)

In the pictograph, each large picture stands for $10$ flowers and each small picture stands for $1$ flower.

Show solution

Understand

A pictograph gives the count of each flower type (large picture = 10, small picture = 1). All flowers are grouped into bouquets of 5, with leftovers wrapped singly. A bouquet uses 90 cm of ribbon and each single flower uses 20 cm. We find the total ribbon in meters and centimeters.

Givens

Rose 1 large + 8 small, Tulip 2 large + 2 small, Chrysanthemum 3 large + 4 small, Lily 1 large + 6 small.
1 large picture = 10 flowers, 1 small picture = 1 flower.
Bouquet = 5 flowers, uses 90 cm of ribbon; each leftover single flower uses 20 cm.
100 cm = 1 m.

Unknowns

Total ribbon needed, in meters and centimeters.

Constraints

Flowers are wrapped 5 per bouquet; the remainder are wrapped one at a time.
Total ribbon = (bouquets x 90) + (singles x 20).

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Several steps chain together: read each flower count, find the grand total, divide by the bouquet size for bouquets and remainder, then combine ribbon lengths and convert to m and cm - watching the cm/m units.

Execute

#7 Identify Subproblems 3.MD.B.3

Each large picture is 10 and each small is 1. Rose: 1x10 + 8 = 18, Tulip: 2x10 + 2 = 22, Chrysanthemum: 3x10 + 4 = 34, Lily: 1x10 + 6 = 16.

18,\ 22,\ 34,\ 16

Turning large/small symbols into counts is basic scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add all four counts: 18 + 22 + 34 + 16 = 90 flowers in all.

18 + 22 + 34 + 16 = 90

Adding the category counts to a total within 1000 is Grade 3 addition.

#7 Identify Subproblems 3.OA.A.3

Group 90 flowers by 5: 90 / 5 = 18 with remainder 0, so there are 18 bouquets and 0 single flowers left over.

90 \div 5 = 18\ \text{R}\ 0

Splitting a total into equal groups of 5 with a leftover is a division-with-remainder word problem.

#8 Analyze the Units 3.OA.A.3

18 bouquets x 90 cm = 1620 cm, and 0 singles x 20 cm = 0 cm. Add: 1620 + 0 = 1620 cm.

18 \times 90 = 1620,\ 0 \times 20 = 0,\ 1620 + 0 = 1620\ \text{cm}

Multiplying counts by per-item lengths and adding keeps the cm units consistent.

#8 Analyze the Units 2.MD.A.1

Since 100 cm = 1 m, 1620 cm = 16 m and 20 cm left over.

1620\ \text{cm} = 16\ \text{m}\ 20\ \text{cm}

Trading every 100 cm for 1 m is length-unit sense from Grade 2 measurement.

Answer: 16 m 20 cm (1620 cm)

Review

90 flowers in groups of 5 give 18 bouquets (90 flowers) plus 0 singles = 90, which checks. Ribbon 1620 + 0 = 1620 cm, and 16 m 20 cm = 1620 cm, so the conversion is right.

Make a systematic list (tool 2) of each type's count and a running total before dividing - it confirms the total, then the same division and ribbon arithmetic follow.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each flower-type count from the large/small symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Summing the four counts to the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the total by the bouquet size for bouquets/remainder and multiplying ribbon lengths.
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting the centimeter total into meters and centimeters.

💡 Count the flowers, group by the bouquet size, then add up the ribbon and trade every 100 cm for a meter!

Variant 2 answer: 14 m 60 cm (1460 cm)

A flower shop surveyed the flowers it had by type and showed the results in a pictograph. The flowers will be mixed into bouquets of $8$ flowers each, and any leftover flowers will be wrapped one at a time. If $100\ \text{cm}$ of ribbon is needed to make one bouquet and $30\ \text{cm}$ of ribbon is needed to wrap one single flower, how many meters and centimeters of ribbon are needed in all?

Number of Flowers by Type (pictograph)

Type	Number of flowers
Rose	(4 large pictures, 0 small pictures)
Tulip	(2 large pictures, 6 small pictures)
Chrysanthemum	(1 large picture, 3 small pictures)
Lily	(3 large pictures, 5 small pictures)

In the pictograph, each large picture stands for $10$ flowers and each small picture stands for $1$ flower.

Show solution

Understand

A pictograph gives the count of each flower type (large picture = 10, small picture = 1). All flowers are grouped into bouquets of 8, with leftovers wrapped singly. A bouquet uses 100 cm of ribbon and each single flower uses 30 cm. We find the total ribbon in meters and centimeters.

Givens

Rose 4 large + 0 small, Tulip 2 large + 6 small, Chrysanthemum 1 large + 3 small, Lily 3 large + 5 small.
1 large picture = 10 flowers, 1 small picture = 1 flower.
Bouquet = 8 flowers, uses 100 cm of ribbon; each leftover single flower uses 30 cm.
100 cm = 1 m.

Unknowns

Total ribbon needed, in meters and centimeters.

Constraints

Flowers are wrapped 8 per bouquet; the remainder are wrapped one at a time.
Total ribbon = (bouquets x 100) + (singles x 30).

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Several steps chain together: read each flower count, find the grand total, divide by the bouquet size for bouquets and remainder, then combine ribbon lengths and convert to m and cm - watching the cm/m units.

Execute

#7 Identify Subproblems 3.MD.B.3

Each large picture is 10 and each small is 1. Rose: 4x10 + 0 = 40, Tulip: 2x10 + 6 = 26, Chrysanthemum: 1x10 + 3 = 13, Lily: 3x10 + 5 = 35.

40,\ 26,\ 13,\ 35

Turning large/small symbols into counts is basic scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add all four counts: 40 + 26 + 13 + 35 = 114 flowers in all.

40 + 26 + 13 + 35 = 114

Adding the category counts to a total within 1000 is Grade 3 addition.

#7 Identify Subproblems 3.OA.A.3

Group 114 flowers by 8: 114 / 8 = 14 with remainder 2, so there are 14 bouquets and 2 single flowers left over.

114 \div 8 = 14\ \text{R}\ 2

Splitting a total into equal groups of 8 with a leftover is a division-with-remainder word problem.

#8 Analyze the Units 3.OA.A.3

14 bouquets x 100 cm = 1400 cm, and 2 singles x 30 cm = 60 cm. Add: 1400 + 60 = 1460 cm.

14 \times 100 = 1400,\ 2 \times 30 = 60,\ 1400 + 60 = 1460\ \text{cm}

Multiplying counts by per-item lengths and adding keeps the cm units consistent.

#8 Analyze the Units 2.MD.A.1

Since 100 cm = 1 m, 1460 cm = 14 m and 60 cm left over.

1460\ \text{cm} = 14\ \text{m}\ 60\ \text{cm}

Trading every 100 cm for 1 m is length-unit sense from Grade 2 measurement.

Answer: 14 m 60 cm (1460 cm)

Review

114 flowers in groups of 8 give 14 bouquets (112 flowers) plus 2 singles = 114, which checks. Ribbon 1400 + 60 = 1460 cm, and 14 m 60 cm = 1460 cm, so the conversion is right.

Make a systematic list (tool 2) of each type's count and a running total before dividing - it confirms the total, then the same division and ribbon arithmetic follow.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each flower-type count from the large/small symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Summing the four counts to the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the total by the bouquet size for bouquets/remainder and multiplying ribbon lengths.
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting the centimeter total into meters and centimeters.

💡 Count the flowers, group by the bouquet size, then add up the ribbon and trade every 100 cm for a meter!

Variant 3 answer: 11 m 30 cm (1130 cm)

A flower shop surveyed the flowers it had by type and showed the results in a pictograph. The flowers will be mixed into bouquets of $7$ flowers each, and any leftover flowers will be wrapped one at a time. If $85\ \text{cm}$ of ribbon is needed to make one bouquet and $22\ \text{cm}$ of ribbon is needed to wrap one single flower, how many meters and centimeters of ribbon are needed in all?

Number of Flowers by Type (pictograph)

Type	Number of flowers
Rose	(2 large pictures, 5 small pictures)
Tulip	(3 large pictures, 2 small pictures)
Chrysanthemum	(1 large picture, 4 small pictures)
Lily	(1 large picture, 8 small pictures)

In the pictograph, each large picture stands for $10$ flowers and each small picture stands for $1$ flower.

Show solution

Understand

A pictograph gives the count of each flower type (large picture = 10, small picture = 1). All flowers are grouped into bouquets of 7, with leftovers wrapped singly. A bouquet uses 85 cm of ribbon and each single flower uses 22 cm. We find the total ribbon in meters and centimeters.

Givens

Rose 2 large + 5 small, Tulip 3 large + 2 small, Chrysanthemum 1 large + 4 small, Lily 1 large + 8 small.
1 large picture = 10 flowers, 1 small picture = 1 flower.
Bouquet = 7 flowers, uses 85 cm of ribbon; each leftover single flower uses 22 cm.
100 cm = 1 m.

Unknowns

Total ribbon needed, in meters and centimeters.

Constraints

Flowers are wrapped 7 per bouquet; the remainder are wrapped one at a time.
Total ribbon = (bouquets x 85) + (singles x 22).

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Several steps chain together: read each flower count, find the grand total, divide by the bouquet size for bouquets and remainder, then combine ribbon lengths and convert to m and cm - watching the cm/m units.

Execute

#7 Identify Subproblems 3.MD.B.3

Each large picture is 10 and each small is 1. Rose: 2x10 + 5 = 25, Tulip: 3x10 + 2 = 32, Chrysanthemum: 1x10 + 4 = 14, Lily: 1x10 + 8 = 18.

25,\ 32,\ 14,\ 18

Turning large/small symbols into counts is basic scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add all four counts: 25 + 32 + 14 + 18 = 89 flowers in all.

25 + 32 + 14 + 18 = 89

Adding the category counts to a total within 1000 is Grade 3 addition.

#7 Identify Subproblems 3.OA.A.3

Group 89 flowers by 7: 89 / 7 = 12 with remainder 5, so there are 12 bouquets and 5 single flowers left over.

89 \div 7 = 12\ \text{R}\ 5

Splitting a total into equal groups of 7 with a leftover is a division-with-remainder word problem.

#8 Analyze the Units 3.OA.A.3

12 bouquets x 85 cm = 1020 cm, and 5 singles x 22 cm = 110 cm. Add: 1020 + 110 = 1130 cm.

12 \times 85 = 1020,\ 5 \times 22 = 110,\ 1020 + 110 = 1130\ \text{cm}

Multiplying counts by per-item lengths and adding keeps the cm units consistent.

#8 Analyze the Units 2.MD.A.1

Since 100 cm = 1 m, 1130 cm = 11 m and 30 cm left over.

1130\ \text{cm} = 11\ \text{m}\ 30\ \text{cm}

Trading every 100 cm for 1 m is length-unit sense from Grade 2 measurement.

Answer: 11 m 30 cm (1130 cm)

Review

89 flowers in groups of 7 give 12 bouquets (84 flowers) plus 5 singles = 89, which checks. Ribbon 1020 + 110 = 1130 cm, and 11 m 30 cm = 1130 cm, so the conversion is right.

Make a systematic list (tool 2) of each type's count and a running total before dividing - it confirms the total, then the same division and ribbon arithmetic follow.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each flower-type count from the large/small symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Summing the four counts to the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the total by the bouquet size for bouquets/remainder and multiplying ribbon lengths.
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting the centimeter total into meters and centimeters.

💡 Count the flowers, group by the bouquet size, then add up the ribbon and trade every 100 cm for a meter!

Variant 4 answer: 12 m 18 cm (1218 cm)

A flower shop surveyed the flowers it had by type and showed the results in a pictograph. The flowers will be mixed into bouquets of $6$ flowers each, and any leftover flowers will be wrapped one at a time. If $75\ \text{cm}$ of ribbon is needed to make one bouquet and $18\ \text{cm}$ of ribbon is needed to wrap one single flower, how many meters and centimeters of ribbon are needed in all?

Number of Flowers by Type (pictograph)

Type	Number of flowers
Rose	(1 large picture, 2 small pictures)
Tulip	(2 large pictures, 8 small pictures)
Chrysanthemum	(3 large pictures, 1 small picture)
Lily	(2 large pictures, 6 small pictures)

In the pictograph, each large picture stands for $10$ flowers and each small picture stands for $1$ flower.

Show solution

Understand

A pictograph gives the count of each flower type (large picture = 10, small picture = 1). All flowers are grouped into bouquets of 6, with leftovers wrapped singly. A bouquet uses 75 cm of ribbon and each single flower uses 18 cm. We find the total ribbon in meters and centimeters.

Givens

Rose 1 large + 2 small, Tulip 2 large + 8 small, Chrysanthemum 3 large + 1 small, Lily 2 large + 6 small.
1 large picture = 10 flowers, 1 small picture = 1 flower.
Bouquet = 6 flowers, uses 75 cm of ribbon; each leftover single flower uses 18 cm.
100 cm = 1 m.

Unknowns

Total ribbon needed, in meters and centimeters.

Constraints

Flowers are wrapped 6 per bouquet; the remainder are wrapped one at a time.
Total ribbon = (bouquets x 75) + (singles x 18).

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Several steps chain together: read each flower count, find the grand total, divide by the bouquet size for bouquets and remainder, then combine ribbon lengths and convert to m and cm - watching the cm/m units.

Execute

#7 Identify Subproblems 3.MD.B.3

Each large picture is 10 and each small is 1. Rose: 1x10 + 2 = 12, Tulip: 2x10 + 8 = 28, Chrysanthemum: 3x10 + 1 = 31, Lily: 2x10 + 6 = 26.

12,\ 28,\ 31,\ 26

Turning large/small symbols into counts is basic scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add all four counts: 12 + 28 + 31 + 26 = 97 flowers in all.

12 + 28 + 31 + 26 = 97

Adding the category counts to a total within 1000 is Grade 3 addition.

#7 Identify Subproblems 3.OA.A.3

Group 97 flowers by 6: 97 / 6 = 16 with remainder 1, so there are 16 bouquets and 1 single flowers left over.

97 \div 6 = 16\ \text{R}\ 1

Splitting a total into equal groups of 6 with a leftover is a division-with-remainder word problem.

#8 Analyze the Units 3.OA.A.3

16 bouquets x 75 cm = 1200 cm, and 1 singles x 18 cm = 18 cm. Add: 1200 + 18 = 1218 cm.

16 \times 75 = 1200,\ 1 \times 18 = 18,\ 1200 + 18 = 1218\ \text{cm}

Multiplying counts by per-item lengths and adding keeps the cm units consistent.

#8 Analyze the Units 2.MD.A.1

Since 100 cm = 1 m, 1218 cm = 12 m and 18 cm left over.

1218\ \text{cm} = 12\ \text{m}\ 18\ \text{cm}

Trading every 100 cm for 1 m is length-unit sense from Grade 2 measurement.

Answer: 12 m 18 cm (1218 cm)

Review

97 flowers in groups of 6 give 16 bouquets (96 flowers) plus 1 singles = 97, which checks. Ribbon 1200 + 18 = 1218 cm, and 12 m 18 cm = 1218 cm, so the conversion is right.

Make a systematic list (tool 2) of each type's count and a running total before dividing - it confirms the total, then the same division and ribbon arithmetic follow.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each flower-type count from the large/small symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Summing the four counts to the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the total by the bouquet size for bouquets/remainder and multiplying ribbon lengths.
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting the centimeter total into meters and centimeters.

💡 Count the flowers, group by the bouquet size, then add up the ribbon and trade every 100 cm for a meter!

Variant 5 answer: 14 m 10 cm (1410 cm)

A flower shop surveyed the flowers it had by type and showed the results in a pictograph. The flowers will be mixed into bouquets of $9$ flowers each, and any leftover flowers will be wrapped one at a time. If $120\ \text{cm}$ of ribbon is needed to make one bouquet and $35\ \text{cm}$ of ribbon is needed to wrap one single flower, how many meters and centimeters of ribbon are needed in all?

Number of Flowers by Type (pictograph)

Type	Number of flowers
Rose	(3 large pictures, 3 small pictures)
Tulip	(1 large picture, 1 small picture)
Chrysanthemum	(2 large pictures, 7 small pictures)
Lily	(2 large pictures, 5 small pictures)

In the pictograph, each large picture stands for $10$ flowers and each small picture stands for $1$ flower.

Show solution

Understand

A pictograph gives the count of each flower type (large picture = 10, small picture = 1). All flowers are grouped into bouquets of 9, with leftovers wrapped singly. A bouquet uses 120 cm of ribbon and each single flower uses 35 cm. We find the total ribbon in meters and centimeters.

Givens

Rose 3 large + 3 small, Tulip 1 large + 1 small, Chrysanthemum 2 large + 7 small, Lily 2 large + 5 small.
1 large picture = 10 flowers, 1 small picture = 1 flower.
Bouquet = 9 flowers, uses 120 cm of ribbon; each leftover single flower uses 35 cm.
100 cm = 1 m.

Unknowns

Total ribbon needed, in meters and centimeters.

Constraints

Flowers are wrapped 9 per bouquet; the remainder are wrapped one at a time.
Total ribbon = (bouquets x 120) + (singles x 35).

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Several steps chain together: read each flower count, find the grand total, divide by the bouquet size for bouquets and remainder, then combine ribbon lengths and convert to m and cm - watching the cm/m units.

Execute

#7 Identify Subproblems 3.MD.B.3

Each large picture is 10 and each small is 1. Rose: 3x10 + 3 = 33, Tulip: 1x10 + 1 = 11, Chrysanthemum: 2x10 + 7 = 27, Lily: 2x10 + 5 = 25.

33,\ 11,\ 27,\ 25

Turning large/small symbols into counts is basic scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add all four counts: 33 + 11 + 27 + 25 = 96 flowers in all.

33 + 11 + 27 + 25 = 96

Adding the category counts to a total within 1000 is Grade 3 addition.

#7 Identify Subproblems 3.OA.A.3

Group 96 flowers by 9: 96 / 9 = 10 with remainder 6, so there are 10 bouquets and 6 single flowers left over.

96 \div 9 = 10\ \text{R}\ 6

Splitting a total into equal groups of 9 with a leftover is a division-with-remainder word problem.

#8 Analyze the Units 3.OA.A.3

10 bouquets x 120 cm = 1200 cm, and 6 singles x 35 cm = 210 cm. Add: 1200 + 210 = 1410 cm.

10 \times 120 = 1200,\ 6 \times 35 = 210,\ 1200 + 210 = 1410\ \text{cm}

Multiplying counts by per-item lengths and adding keeps the cm units consistent.

#8 Analyze the Units 2.MD.A.1

Since 100 cm = 1 m, 1410 cm = 14 m and 10 cm left over.

1410\ \text{cm} = 14\ \text{m}\ 10\ \text{cm}

Trading every 100 cm for 1 m is length-unit sense from Grade 2 measurement.

Answer: 14 m 10 cm (1410 cm)

Review

96 flowers in groups of 9 give 10 bouquets (90 flowers) plus 6 singles = 96, which checks. Ribbon 1200 + 210 = 1410 cm, and 14 m 10 cm = 1410 cm, so the conversion is right.

Make a systematic list (tool 2) of each type's count and a running total before dividing - it confirms the total, then the same division and ribbon arithmetic follow.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each flower-type count from the large/small symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Summing the four counts to the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the total by the bouquet size for bouquets/remainder and multiplying ribbon lengths.
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting the centimeter total into meters and centimeters.

💡 Count the flowers, group by the bouquet size, then add up the ribbon and trade every 100 cm for a meter!

Variant 6 answer: 12 m 24 cm (1224 cm)

A flower shop surveyed the flowers it had by type and showed the results in a pictograph. The flowers will be mixed into bouquets of $7$ flowers each, and any leftover flowers will be wrapped one at a time. If $95\ \text{cm}$ of ribbon is needed to make one bouquet and $28\ \text{cm}$ of ribbon is needed to wrap one single flower, how many meters and centimeters of ribbon are needed in all?

Number of Flowers by Type (pictograph)

Type	Number of flowers
Rose	(3 large pictures, 2 small pictures)
Tulip	(1 large picture, 5 small pictures)
Chrysanthemum	(2 large pictures, 1 small picture)
Lily	(1 large picture, 9 small pictures)

In the pictograph, each large picture stands for $10$ flowers and each small picture stands for $1$ flower.

Show solution

Understand

A pictograph gives the count of each flower type (large picture = 10, small picture = 1). All flowers are grouped into bouquets of 7, with leftovers wrapped singly. A bouquet uses 95 cm of ribbon and each single flower uses 28 cm. We find the total ribbon in meters and centimeters.

Givens

Rose 3 large + 2 small, Tulip 1 large + 5 small, Chrysanthemum 2 large + 1 small, Lily 1 large + 9 small.
1 large picture = 10 flowers, 1 small picture = 1 flower.
Bouquet = 7 flowers, uses 95 cm of ribbon; each leftover single flower uses 28 cm.
100 cm = 1 m.

Unknowns

Total ribbon needed, in meters and centimeters.

Constraints

Flowers are wrapped 7 per bouquet; the remainder are wrapped one at a time.
Total ribbon = (bouquets x 95) + (singles x 28).

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Several steps chain together: read each flower count, find the grand total, divide by the bouquet size for bouquets and remainder, then combine ribbon lengths and convert to m and cm - watching the cm/m units.

Execute

#7 Identify Subproblems 3.MD.B.3

Each large picture is 10 and each small is 1. Rose: 3x10 + 2 = 32, Tulip: 1x10 + 5 = 15, Chrysanthemum: 2x10 + 1 = 21, Lily: 1x10 + 9 = 19.

32,\ 15,\ 21,\ 19

Turning large/small symbols into counts is basic scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add all four counts: 32 + 15 + 21 + 19 = 87 flowers in all.

32 + 15 + 21 + 19 = 87

Adding the category counts to a total within 1000 is Grade 3 addition.

#7 Identify Subproblems 3.OA.A.3

Group 87 flowers by 7: 87 / 7 = 12 with remainder 3, so there are 12 bouquets and 3 single flowers left over.

87 \div 7 = 12\ \text{R}\ 3

Splitting a total into equal groups of 7 with a leftover is a division-with-remainder word problem.

#8 Analyze the Units 3.OA.A.3

12 bouquets x 95 cm = 1140 cm, and 3 singles x 28 cm = 84 cm. Add: 1140 + 84 = 1224 cm.

12 \times 95 = 1140,\ 3 \times 28 = 84,\ 1140 + 84 = 1224\ \text{cm}

Multiplying counts by per-item lengths and adding keeps the cm units consistent.

#8 Analyze the Units 2.MD.A.1

Since 100 cm = 1 m, 1224 cm = 12 m and 24 cm left over.

1224\ \text{cm} = 12\ \text{m}\ 24\ \text{cm}

Trading every 100 cm for 1 m is length-unit sense from Grade 2 measurement.

Answer: 12 m 24 cm (1224 cm)

Review

87 flowers in groups of 7 give 12 bouquets (84 flowers) plus 3 singles = 87, which checks. Ribbon 1140 + 84 = 1224 cm, and 12 m 24 cm = 1224 cm, so the conversion is right.

Make a systematic list (tool 2) of each type's count and a running total before dividing - it confirms the total, then the same division and ribbon arithmetic follow.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each flower-type count from the large/small symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Summing the four counts to the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the total by the bouquet size for bouquets/remainder and multiplying ribbon lengths.
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting the centimeter total into meters and centimeters.

💡 Count the flowers, group by the bouquet size, then add up the ribbon and trade every 100 cm for a meter!

Variant 7 answer: 13 m 25 cm (1325 cm)

A flower shop surveyed the flowers it had by type and showed the results in a pictograph. The flowers will be mixed into bouquets of $6$ flowers each, and any leftover flowers will be wrapped one at a time. If $80\ \text{cm}$ of ribbon is needed to make one bouquet and $25\ \text{cm}$ of ribbon is needed to wrap one single flower, how many meters and centimeters of ribbon are needed in all?

Number of Flowers by Type (pictograph)

Type	Number of flowers
Rose	(2 large pictures, 4 small pictures)
Tulip	(3 large pictures, 1 small picture)
Chrysanthemum	(1 large picture, 7 small pictures)
Lily	(2 large pictures, 3 small pictures)

In the pictograph, each large picture stands for $10$ flowers and each small picture stands for $1$ flower.

Show solution

Understand

A pictograph gives the count of each flower type (large picture = 10, small picture = 1). All flowers are grouped into bouquets of 6, with leftovers wrapped singly. A bouquet uses 80 cm of ribbon and each single flower uses 25 cm. We find the total ribbon in meters and centimeters.

Givens

Rose 2 large + 4 small, Tulip 3 large + 1 small, Chrysanthemum 1 large + 7 small, Lily 2 large + 3 small.
1 large picture = 10 flowers, 1 small picture = 1 flower.
Bouquet = 6 flowers, uses 80 cm of ribbon; each leftover single flower uses 25 cm.
100 cm = 1 m.

Unknowns

Total ribbon needed, in meters and centimeters.

Constraints

Flowers are wrapped 6 per bouquet; the remainder are wrapped one at a time.
Total ribbon = (bouquets x 80) + (singles x 25).

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Several steps chain together: read each flower count, find the grand total, divide by the bouquet size for bouquets and remainder, then combine ribbon lengths and convert to m and cm - watching the cm/m units.

Execute

#7 Identify Subproblems 3.MD.B.3

Each large picture is 10 and each small is 1. Rose: 2x10 + 4 = 24, Tulip: 3x10 + 1 = 31, Chrysanthemum: 1x10 + 7 = 17, Lily: 2x10 + 3 = 23.

24,\ 31,\ 17,\ 23

Turning large/small symbols into counts is basic scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add all four counts: 24 + 31 + 17 + 23 = 95 flowers in all.

24 + 31 + 17 + 23 = 95

Adding the category counts to a total within 1000 is Grade 3 addition.

#7 Identify Subproblems 3.OA.A.3

Group 95 flowers by 6: 95 / 6 = 15 with remainder 5, so there are 15 bouquets and 5 single flowers left over.

95 \div 6 = 15\ \text{R}\ 5

Splitting a total into equal groups of 6 with a leftover is a division-with-remainder word problem.

#8 Analyze the Units 3.OA.A.3

15 bouquets x 80 cm = 1200 cm, and 5 singles x 25 cm = 125 cm. Add: 1200 + 125 = 1325 cm.

15 \times 80 = 1200,\ 5 \times 25 = 125,\ 1200 + 125 = 1325\ \text{cm}

Multiplying counts by per-item lengths and adding keeps the cm units consistent.

#8 Analyze the Units 2.MD.A.1

Since 100 cm = 1 m, 1325 cm = 13 m and 25 cm left over.

1325\ \text{cm} = 13\ \text{m}\ 25\ \text{cm}

Trading every 100 cm for 1 m is length-unit sense from Grade 2 measurement.

Answer: 13 m 25 cm (1325 cm)

Review

95 flowers in groups of 6 give 15 bouquets (90 flowers) plus 5 singles = 95, which checks. Ribbon 1200 + 125 = 1325 cm, and 13 m 25 cm = 1325 cm, so the conversion is right.

Make a systematic list (tool 2) of each type's count and a running total before dividing - it confirms the total, then the same division and ribbon arithmetic follow.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each flower-type count from the large/small symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Summing the four counts to the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the total by the bouquet size for bouquets/remainder and multiplying ribbon lengths.
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting the centimeter total into meters and centimeters.

💡 Count the flowers, group by the bouquet size, then add up the ribbon and trade every 100 cm for a meter!

Variant 8 answer: 15 m 50 cm (1550 cm)

A flower shop surveyed the flowers it had by type and showed the results in a pictograph. The flowers will be mixed into bouquets of $8$ flowers each, and any leftover flowers will be wrapped one at a time. If $110\ \text{cm}$ of ribbon is needed to make one bouquet and $24\ \text{cm}$ of ribbon is needed to wrap one single flower, how many meters and centimeters of ribbon are needed in all?

Number of Flowers by Type (pictograph)

Type	Number of flowers
Rose	(3 large pictures, 0 small pictures)
Tulip	(1 large picture, 9 small pictures)
Chrysanthemum	(2 large pictures, 3 small pictures)
Lily	(3 large pictures, 7 small pictures)

In the pictograph, each large picture stands for $10$ flowers and each small picture stands for $1$ flower.

Show solution

Understand

A pictograph gives the count of each flower type (large picture = 10, small picture = 1). All flowers are grouped into bouquets of 8, with leftovers wrapped singly. A bouquet uses 110 cm of ribbon and each single flower uses 24 cm. We find the total ribbon in meters and centimeters.

Givens

Rose 3 large + 0 small, Tulip 1 large + 9 small, Chrysanthemum 2 large + 3 small, Lily 3 large + 7 small.
1 large picture = 10 flowers, 1 small picture = 1 flower.
Bouquet = 8 flowers, uses 110 cm of ribbon; each leftover single flower uses 24 cm.
100 cm = 1 m.

Unknowns

Total ribbon needed, in meters and centimeters.

Constraints

Flowers are wrapped 8 per bouquet; the remainder are wrapped one at a time.
Total ribbon = (bouquets x 110) + (singles x 24).

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

Several steps chain together: read each flower count, find the grand total, divide by the bouquet size for bouquets and remainder, then combine ribbon lengths and convert to m and cm - watching the cm/m units.

Execute

#7 Identify Subproblems 3.MD.B.3

Each large picture is 10 and each small is 1. Rose: 3x10 + 0 = 30, Tulip: 1x10 + 9 = 19, Chrysanthemum: 2x10 + 3 = 23, Lily: 3x10 + 7 = 37.

30,\ 19,\ 23,\ 37

Turning large/small symbols into counts is basic scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add all four counts: 30 + 19 + 23 + 37 = 109 flowers in all.

30 + 19 + 23 + 37 = 109

Adding the category counts to a total within 1000 is Grade 3 addition.

#7 Identify Subproblems 3.OA.A.3

Group 109 flowers by 8: 109 / 8 = 13 with remainder 5, so there are 13 bouquets and 5 single flowers left over.

109 \div 8 = 13\ \text{R}\ 5

Splitting a total into equal groups of 8 with a leftover is a division-with-remainder word problem.

#8 Analyze the Units 3.OA.A.3

13 bouquets x 110 cm = 1430 cm, and 5 singles x 24 cm = 120 cm. Add: 1430 + 120 = 1550 cm.

13 \times 110 = 1430,\ 5 \times 24 = 120,\ 1430 + 120 = 1550\ \text{cm}

Multiplying counts by per-item lengths and adding keeps the cm units consistent.

#8 Analyze the Units 2.MD.A.1

Since 100 cm = 1 m, 1550 cm = 15 m and 50 cm left over.

1550\ \text{cm} = 15\ \text{m}\ 50\ \text{cm}

Trading every 100 cm for 1 m is length-unit sense from Grade 2 measurement.

Answer: 15 m 50 cm (1550 cm)

Review

109 flowers in groups of 8 give 13 bouquets (104 flowers) plus 5 singles = 109, which checks. Ribbon 1430 + 120 = 1550 cm, and 15 m 50 cm = 1550 cm, so the conversion is right.

Make a systematic list (tool 2) of each type's count and a running total before dividing - it confirms the total, then the same division and ribbon arithmetic follow.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each flower-type count from the large/small symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Summing the four counts to the total.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the total by the bouquet size for bouquets/remainder and multiplying ribbon lengths.
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting the centimeter total into meters and centimeters.

💡 Count the flowers, group by the bouquet size, then add up the ribbon and trade every 100 cm for a meter!

Total all categories from a pictograph · 8 practice problems

Generated variants — 8

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Standards · min grade 3