← 3-2 · Translate between table and pictograph · Read and Scale a Data Graph

Translate between table and pictograph · 8 practice problems

3.MD.B.33.NBT.A.2

Generated variants — 8

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: Oak = 650, Pine = 700

The amounts for each item were surveyed and shown in a table and a pictograph. Complete the table and the pictograph.

Amount by Item (table)

Item	Maple	Oak	Pine	Birch	Total
Amount	830			720	2900

Amount by Item (pictograph)

Item	Amount
Maple
Oak	(6 large pictures, 5 small pictures)
Pine
Birch

In the pictograph, each large picture stands for $100$ and each small picture stands for $10$ .

Show solution

Understand

A table and a matching pictograph show the same data for Maple, Oak, Pine, Birch. The table gives Maple = 830, Birch = 720 and total 2900, with two cells blank. The pictograph's only filled row, Oak, shows 6 large pictures (100 each) and 5 small pictures (10 each). Completing the table means finding Oak and Pine.

Givens

Table: Maple = 830, Birch = 720, Total = 2900.
Pictograph legend: 1 large picture = 100, 1 small picture = 10.
Oak row (from figure): 6 large pictures and 5 small pictures.
The table and pictograph show the same data.

Unknowns

Oak's amount and Pine's amount (to complete the table).

Constraints

The four amounts must add to 2900.
Pictograph amounts come from the large/small picture values.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Translate the pictograph picture into a number (Oak), then treat 'find Pine' as the remaining subproblem using the total. This is moving between two representations of the same data.

Execute

#15 Organize Information in More Ways 3.MD.B.3

Oak shows 6 large pictures and 5 small pictures. Each large is 100 and each small is 10: 6 x 100 = 600 and 5 x 10 = 50, so Oak = 600 + 50 = 650.

6 \times 100 + 5 \times 10 = 600 + 50 = 650

Turning scaled picture symbols into a count is exactly what a scaled pictograph teaches in Grade 3.

#7 Identify Subproblems 3.NBT.A.2

The four amounts add to 2900. Subtract the three known amounts: 2900 - 830 - 720 - 650 = 700, so Pine = 700.

2900 - 830 - 720 - 650 = 700

Subtracting the known parts from a known total is Grade 3 place-value work.

#15 Organize Information in More Ways 3.MD.B.3

Convert each amount back into pictures: Maple 830 = 8 large + 3 small; Oak 650 = 6 large + 5 small; Pine 700 = 7 large + 0 small; Birch 720 = 7 large + 2 small.

100\ \text{per large},\ 10\ \text{per small}

Going from a number back to the right count of large and small symbols is the reverse of reading a pictograph.

Answer: Oak = 650, Pine = 700

Review

Add all four: 830 + 650 + 700 + 720 = 2900, which matches the given total exactly, so the table is consistent.

Subproblem order can vary: add the three other amounts first, then subtract from 2900 to get Pine - same result.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the filled row from the scaled symbols and converting amounts back into symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting the known amounts from 2900 to find Pine.

💡 Each big picture is 100 and each little picture is 10 - count them up, then the total fills in the rest!

Variant 2 answer: South = 250, West = 280

The amounts for each item were surveyed and shown in a table and a pictograph. Complete the table and the pictograph.

Amount by Item (table)

Item	North	South	East	West	Total
Amount	360		410		1300

Amount by Item (pictograph)

Item	Amount
North
South	(2 large pictures, 5 small pictures)
East
West

In the pictograph, each large picture stands for $100$ and each small picture stands for $10$ .

Show solution

Understand

A table and a matching pictograph show the same data for North, South, East, West. The table gives North = 360, East = 410 and total 1300, with two cells blank. The pictograph's only filled row, South, shows 2 large pictures (100 each) and 5 small pictures (10 each). Completing the table means finding South and West.

Givens

Table: North = 360, East = 410, Total = 1300.
Pictograph legend: 1 large picture = 100, 1 small picture = 10.
South row (from figure): 2 large pictures and 5 small pictures.
The table and pictograph show the same data.

Unknowns

South's amount and West's amount (to complete the table).

Constraints

The four amounts must add to 1300.
Pictograph amounts come from the large/small picture values.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Translate the pictograph picture into a number (South), then treat 'find West' as the remaining subproblem using the total. This is moving between two representations of the same data.

Execute

#15 Organize Information in More Ways 3.MD.B.3

South shows 2 large pictures and 5 small pictures. Each large is 100 and each small is 10: 2 x 100 = 200 and 5 x 10 = 50, so South = 200 + 50 = 250.

2 \times 100 + 5 \times 10 = 200 + 50 = 250

Turning scaled picture symbols into a count is exactly what a scaled pictograph teaches in Grade 3.

#7 Identify Subproblems 3.NBT.A.2

The four amounts add to 1300. Subtract the three known amounts: 1300 - 360 - 410 - 250 = 280, so West = 280.

1300 - 360 - 410 - 250 = 280

Subtracting the known parts from a known total is Grade 3 place-value work.

#15 Organize Information in More Ways 3.MD.B.3

Convert each amount back into pictures: North 360 = 3 large + 6 small; South 250 = 2 large + 5 small; East 410 = 4 large + 1 small; West 280 = 2 large + 8 small.

100\ \text{per large},\ 10\ \text{per small}

Going from a number back to the right count of large and small symbols is the reverse of reading a pictograph.

Answer: South = 250, West = 280

Review

Add all four: 360 + 250 + 410 + 280 = 1300, which matches the given total exactly, so the table is consistent.

Subproblem order can vary: add the three other amounts first, then subtract from 1300 to get West - same result.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the filled row from the scaled symbols and converting amounts back into symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting the known amounts from 1300 to find West.

💡 Each big picture is 100 and each little picture is 10 - count them up, then the total fills in the rest!

Variant 3 answer: Blue = 180, Green = 190

The amounts for each item were surveyed and shown in a table and a pictograph. Complete the table and the pictograph.

Amount by Item (table)

Item	Red	Blue	Green	Gold	Total
Amount	240			310	920

Amount by Item (pictograph)

Item	Amount
Red
Blue	(18 large pictures, 0 small pictures)
Green
Gold

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

Show solution

Understand

A table and a matching pictograph show the same data for Red, Blue, Green, Gold. The table gives Red = 240, Gold = 310 and total 920, with two cells blank. The pictograph's only filled row, Blue, shows 18 large pictures (10 each) and 0 small pictures (1 each). Completing the table means finding Blue and Green.

Givens

Table: Red = 240, Gold = 310, Total = 920.
Pictograph legend: 1 large picture = 10, 1 small picture = 1.
Blue row (from figure): 18 large pictures and 0 small pictures.
The table and pictograph show the same data.

Unknowns

Blue's amount and Green's amount (to complete the table).

Constraints

The four amounts must add to 920.
Pictograph amounts come from the large/small picture values.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Translate the pictograph picture into a number (Blue), then treat 'find Green' as the remaining subproblem using the total. This is moving between two representations of the same data.

Execute

#15 Organize Information in More Ways 3.MD.B.3

Blue shows 18 large pictures and 0 small pictures. Each large is 10 and each small is 1: 18 x 10 = 180 and 0 x 1 = 0, so Blue = 180 + 0 = 180.

18 \times 10 + 0 \times 1 = 180 + 0 = 180

Turning scaled picture symbols into a count is exactly what a scaled pictograph teaches in Grade 3.

#7 Identify Subproblems 3.NBT.A.2

The four amounts add to 920. Subtract the three known amounts: 920 - 240 - 310 - 180 = 190, so Green = 190.

920 - 240 - 310 - 180 = 190

Subtracting the known parts from a known total is Grade 3 place-value work.

#15 Organize Information in More Ways 3.MD.B.3

Convert each amount back into pictures: Red 240 = 24 large + 0 small; Blue 180 = 18 large + 0 small; Green 190 = 19 large + 0 small; Gold 310 = 31 large + 0 small.

10\ \text{per large},\ 1\ \text{per small}

Going from a number back to the right count of large and small symbols is the reverse of reading a pictograph.

Answer: Blue = 180, Green = 190

Review

Add all four: 240 + 180 + 190 + 310 = 920, which matches the given total exactly, so the table is consistent.

Subproblem order can vary: add the three other amounts first, then subtract from 920 to get Green - same result.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the filled row from the scaled symbols and converting amounts back into symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting the known amounts from 920 to find Green.

💡 Each big picture is 10 and each little picture is 1 - count them up, then the total fills in the rest!

Variant 4 answer: Plum = 730, Pear = 610

The amounts for each item were surveyed and shown in a table and a pictograph. Complete the table and the pictograph.

Amount by Item (table)

Item	Apple	Pear	Plum	Grape	Total
Amount	520			640	2500

Amount by Item (pictograph)

Item	Amount
Apple
Pear
Plum	(7 large pictures, 3 small pictures)
Grape

In the pictograph, each large picture stands for $100$ and each small picture stands for $10$ .

Show solution

Understand

A table and a matching pictograph show the same data for Apple, Pear, Plum, Grape. The table gives Apple = 520, Grape = 640 and total 2500, with two cells blank. The pictograph's only filled row, Plum, shows 7 large pictures (100 each) and 3 small pictures (10 each). Completing the table means finding Plum and Pear.

Givens

Table: Apple = 520, Grape = 640, Total = 2500.
Pictograph legend: 1 large picture = 100, 1 small picture = 10.
Plum row (from figure): 7 large pictures and 3 small pictures.
The table and pictograph show the same data.

Unknowns

Plum's amount and Pear's amount (to complete the table).

Constraints

The four amounts must add to 2500.
Pictograph amounts come from the large/small picture values.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Translate the pictograph picture into a number (Plum), then treat 'find Pear' as the remaining subproblem using the total. This is moving between two representations of the same data.

Execute

#15 Organize Information in More Ways 3.MD.B.3

Plum shows 7 large pictures and 3 small pictures. Each large is 100 and each small is 10: 7 x 100 = 700 and 3 x 10 = 30, so Plum = 700 + 30 = 730.

7 \times 100 + 3 \times 10 = 700 + 30 = 730

Turning scaled picture symbols into a count is exactly what a scaled pictograph teaches in Grade 3.

#7 Identify Subproblems 3.NBT.A.2

The four amounts add to 2500. Subtract the three known amounts: 2500 - 520 - 640 - 730 = 610, so Pear = 610.

2500 - 520 - 640 - 730 = 610

Subtracting the known parts from a known total is Grade 3 place-value work.

#15 Organize Information in More Ways 3.MD.B.3

Convert each amount back into pictures: Apple 520 = 5 large + 2 small; Pear 610 = 6 large + 1 small; Plum 730 = 7 large + 3 small; Grape 640 = 6 large + 4 small.

100\ \text{per large},\ 10\ \text{per small}

Going from a number back to the right count of large and small symbols is the reverse of reading a pictograph.

Answer: Plum = 730, Pear = 610

Review

Add all four: 520 + 610 + 730 + 640 = 2500, which matches the given total exactly, so the table is consistent.

Subproblem order can vary: add the three other amounts first, then subtract from 2500 to get Pear - same result.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the filled row from the scaled symbols and converting amounts back into symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting the known amounts from 2500 to find Pear.

💡 Each big picture is 100 and each little picture is 10 - count them up, then the total fills in the rest!

Variant 5 answer: Lake = 290, Vale = 420

The amounts for each item were surveyed and shown in a table and a pictograph. Complete the table and the pictograph.

Amount by Item (table)

Item	Hill	Lake	Vale	Wood	Total
Amount	560			430	1700

Amount by Item (pictograph)

Item	Amount
Hill
Lake	(2 large pictures, 9 small pictures)
Vale
Wood

In the pictograph, each large picture stands for $100$ and each small picture stands for $10$ .

Show solution

Understand

A table and a matching pictograph show the same data for Hill, Lake, Vale, Wood. The table gives Hill = 560, Wood = 430 and total 1700, with two cells blank. The pictograph's only filled row, Lake, shows 2 large pictures (100 each) and 9 small pictures (10 each). Completing the table means finding Lake and Vale.

Givens

Table: Hill = 560, Wood = 430, Total = 1700.
Pictograph legend: 1 large picture = 100, 1 small picture = 10.
Lake row (from figure): 2 large pictures and 9 small pictures.
The table and pictograph show the same data.

Unknowns

Lake's amount and Vale's amount (to complete the table).

Constraints

The four amounts must add to 1700.
Pictograph amounts come from the large/small picture values.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Translate the pictograph picture into a number (Lake), then treat 'find Vale' as the remaining subproblem using the total. This is moving between two representations of the same data.

Execute

#15 Organize Information in More Ways 3.MD.B.3

Lake shows 2 large pictures and 9 small pictures. Each large is 100 and each small is 10: 2 x 100 = 200 and 9 x 10 = 90, so Lake = 200 + 90 = 290.

2 \times 100 + 9 \times 10 = 200 + 90 = 290

Turning scaled picture symbols into a count is exactly what a scaled pictograph teaches in Grade 3.

#7 Identify Subproblems 3.NBT.A.2

The four amounts add to 1700. Subtract the three known amounts: 1700 - 560 - 430 - 290 = 420, so Vale = 420.

1700 - 560 - 430 - 290 = 420

Subtracting the known parts from a known total is Grade 3 place-value work.

#15 Organize Information in More Ways 3.MD.B.3

Convert each amount back into pictures: Hill 560 = 5 large + 6 small; Lake 290 = 2 large + 9 small; Vale 420 = 4 large + 2 small; Wood 430 = 4 large + 3 small.

100\ \text{per large},\ 10\ \text{per small}

Going from a number back to the right count of large and small symbols is the reverse of reading a pictograph.

Answer: Lake = 290, Vale = 420

Review

Add all four: 560 + 290 + 420 + 430 = 1700, which matches the given total exactly, so the table is consistent.

Subproblem order can vary: add the three other amounts first, then subtract from 1700 to get Vale - same result.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the filled row from the scaled symbols and converting amounts back into symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting the known amounts from 1700 to find Vale.

💡 Each big picture is 100 and each little picture is 10 - count them up, then the total fills in the rest!

Variant 6 answer: Moon = 380, Star = 610

The amounts for each item were surveyed and shown in a table and a pictograph. Complete the table and the pictograph.

Amount by Item (table)

Item	Sun	Moon	Star	Sky	Total
Amount	670			540	2200

Amount by Item (pictograph)

Item	Amount
Sun
Moon	(3 large pictures, 8 small pictures)
Star
Sky

In the pictograph, each large picture stands for $100$ and each small picture stands for $10$ .

Show solution

Understand

A table and a matching pictograph show the same data for Sun, Moon, Star, Sky. The table gives Sun = 670, Sky = 540 and total 2200, with two cells blank. The pictograph's only filled row, Moon, shows 3 large pictures (100 each) and 8 small pictures (10 each). Completing the table means finding Moon and Star.

Givens

Table: Sun = 670, Sky = 540, Total = 2200.
Pictograph legend: 1 large picture = 100, 1 small picture = 10.
Moon row (from figure): 3 large pictures and 8 small pictures.
The table and pictograph show the same data.

Unknowns

Moon's amount and Star's amount (to complete the table).

Constraints

The four amounts must add to 2200.
Pictograph amounts come from the large/small picture values.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Translate the pictograph picture into a number (Moon), then treat 'find Star' as the remaining subproblem using the total. This is moving between two representations of the same data.

Execute

#15 Organize Information in More Ways 3.MD.B.3

Moon shows 3 large pictures and 8 small pictures. Each large is 100 and each small is 10: 3 x 100 = 300 and 8 x 10 = 80, so Moon = 300 + 80 = 380.

3 \times 100 + 8 \times 10 = 300 + 80 = 380

Turning scaled picture symbols into a count is exactly what a scaled pictograph teaches in Grade 3.

#7 Identify Subproblems 3.NBT.A.2

The four amounts add to 2200. Subtract the three known amounts: 2200 - 670 - 540 - 380 = 610, so Star = 610.

2200 - 670 - 540 - 380 = 610

Subtracting the known parts from a known total is Grade 3 place-value work.

#15 Organize Information in More Ways 3.MD.B.3

Convert each amount back into pictures: Sun 670 = 6 large + 7 small; Moon 380 = 3 large + 8 small; Star 610 = 6 large + 1 small; Sky 540 = 5 large + 4 small.

100\ \text{per large},\ 10\ \text{per small}

Going from a number back to the right count of large and small symbols is the reverse of reading a pictograph.

Answer: Moon = 380, Star = 610

Review

Add all four: 670 + 380 + 610 + 540 = 2200, which matches the given total exactly, so the table is consistent.

Subproblem order can vary: add the three other amounts first, then subtract from 2200 to get Star - same result.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the filled row from the scaled symbols and converting amounts back into symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting the known amounts from 2200 to find Star.

💡 Each big picture is 100 and each little picture is 10 - count them up, then the total fills in the rest!

Variant 7 answer: Tulip = 560, Lily = 490

The amounts for each item were surveyed and shown in a table and a pictograph. Complete the table and the pictograph.

Amount by Item (table)

Item	Rose	Lily	Tulip	Daisy	Total
Amount	470			380	1900

Amount by Item (pictograph)

Item	Amount
Rose
Lily
Tulip	(5 large pictures, 6 small pictures)
Daisy

In the pictograph, each large picture stands for $100$ and each small picture stands for $10$ .

Show solution

Understand

A table and a matching pictograph show the same data for Rose, Lily, Tulip, Daisy. The table gives Rose = 470, Daisy = 380 and total 1900, with two cells blank. The pictograph's only filled row, Tulip, shows 5 large pictures (100 each) and 6 small pictures (10 each). Completing the table means finding Tulip and Lily.

Givens

Table: Rose = 470, Daisy = 380, Total = 1900.
Pictograph legend: 1 large picture = 100, 1 small picture = 10.
Tulip row (from figure): 5 large pictures and 6 small pictures.
The table and pictograph show the same data.

Unknowns

Tulip's amount and Lily's amount (to complete the table).

Constraints

The four amounts must add to 1900.
Pictograph amounts come from the large/small picture values.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Translate the pictograph picture into a number (Tulip), then treat 'find Lily' as the remaining subproblem using the total. This is moving between two representations of the same data.

Execute

#15 Organize Information in More Ways 3.MD.B.3

Tulip shows 5 large pictures and 6 small pictures. Each large is 100 and each small is 10: 5 x 100 = 500 and 6 x 10 = 60, so Tulip = 500 + 60 = 560.

5 \times 100 + 6 \times 10 = 500 + 60 = 560

Turning scaled picture symbols into a count is exactly what a scaled pictograph teaches in Grade 3.

#7 Identify Subproblems 3.NBT.A.2

The four amounts add to 1900. Subtract the three known amounts: 1900 - 470 - 380 - 560 = 490, so Lily = 490.

1900 - 470 - 380 - 560 = 490

Subtracting the known parts from a known total is Grade 3 place-value work.

#15 Organize Information in More Ways 3.MD.B.3

Convert each amount back into pictures: Rose 470 = 4 large + 7 small; Lily 490 = 4 large + 9 small; Tulip 560 = 5 large + 6 small; Daisy 380 = 3 large + 8 small.

100\ \text{per large},\ 10\ \text{per small}

Going from a number back to the right count of large and small symbols is the reverse of reading a pictograph.

Answer: Tulip = 560, Lily = 490

Review

Add all four: 470 + 490 + 560 + 380 = 1900, which matches the given total exactly, so the table is consistent.

Subproblem order can vary: add the three other amounts first, then subtract from 1900 to get Lily - same result.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the filled row from the scaled symbols and converting amounts back into symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting the known amounts from 1900 to find Lily.

💡 Each big picture is 100 and each little picture is 10 - count them up, then the total fills in the rest!

Variant 8 answer: Dalkom = 690, Manna = 730

The amounts for each item were surveyed and shown in a table and a pictograph. Complete the table and the pictograph.

Amount by Item (table)

Item	Singsing	Manna	Dalkom	Haengbok	Total
Amount	780			800	3000

Amount by Item (pictograph)

Item	Amount
Singsing
Manna
Dalkom	(6 large pictures, 9 small pictures)
Haengbok

In the pictograph, each large picture stands for $100$ and each small picture stands for $10$ .

Show solution

Understand

A table and a matching pictograph show the same data for Singsing, Manna, Dalkom, Haengbok. The table gives Singsing = 780, Haengbok = 800 and total 3000, with two cells blank. The pictograph's only filled row, Dalkom, shows 6 large pictures (100 each) and 9 small pictures (10 each). Completing the table means finding Dalkom and Manna.

Givens

Table: Singsing = 780, Haengbok = 800, Total = 3000.
Pictograph legend: 1 large picture = 100, 1 small picture = 10.
Dalkom row (from figure): 6 large pictures and 9 small pictures.
The table and pictograph show the same data.

Unknowns

Dalkom's amount and Manna's amount (to complete the table).

Constraints

The four amounts must add to 3000.
Pictograph amounts come from the large/small picture values.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Translate the pictograph picture into a number (Dalkom), then treat 'find Manna' as the remaining subproblem using the total. This is moving between two representations of the same data.

Execute

#15 Organize Information in More Ways 3.MD.B.3

Dalkom shows 6 large pictures and 9 small pictures. Each large is 100 and each small is 10: 6 x 100 = 600 and 9 x 10 = 90, so Dalkom = 600 + 90 = 690.

6 \times 100 + 9 \times 10 = 600 + 90 = 690

Turning scaled picture symbols into a count is exactly what a scaled pictograph teaches in Grade 3.

#7 Identify Subproblems 3.NBT.A.2

The four amounts add to 3000. Subtract the three known amounts: 3000 - 780 - 800 - 690 = 730, so Manna = 730.

3000 - 780 - 800 - 690 = 730

Subtracting the known parts from a known total is Grade 3 place-value work.

#15 Organize Information in More Ways 3.MD.B.3

Convert each amount back into pictures: Singsing 780 = 7 large + 8 small; Manna 730 = 7 large + 3 small; Dalkom 690 = 6 large + 9 small; Haengbok 800 = 8 large + 0 small.

100\ \text{per large},\ 10\ \text{per small}

Going from a number back to the right count of large and small symbols is the reverse of reading a pictograph.

Answer: Dalkom = 690, Manna = 730

Review

Add all four: 780 + 730 + 690 + 800 = 3000, which matches the given total exactly, so the table is consistent.

Subproblem order can vary: add the three other amounts first, then subtract from 3000 to get Manna - same result.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the filled row from the scaled symbols and converting amounts back into symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting the known amounts from 3000 to find Manna.

💡 Each big picture is 100 and each little picture is 10 - count them up, then the total fills in the rest!