Total all categories from a pictograph

3.MD.B.3 · take · grade 3

Archetype: Read and Scale a Data Graph · step in a 21-type progression

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 7 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; about 12 m is sensible for a dozen bouquets.

Make a systematic list (tool 2) of each type's count and a running total before dividing - it confirms 87 flowers, 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 87.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing 87 by 7 for bouquets/remainder and multiplying ribbon lengths.
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting 1224 cm into 12 m 24 cm.

💡 Count the flowers, group by 7, then add up the ribbon and trade every 100 cm for a meter!