← 3-2 · Determine the value each picture symbol stands for · Read and Scale a Data Graph

Determine the value each picture symbol stands for · 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: 4300 g

The pictograph shows how much each person has. If Finn has $900\ \text{g}$ , how much do all of the people have altogether?

Amount Each Person Has

Name	Amount
Eve	$2$ large symbols, $3$ small symbols
Finn	$3$ large symbols
Gus	$4$ large symbols, $4$ small symbols
Hana	$1$ large symbols, $6$ small symbols

In the pictograph, one large symbol stands for an unknown amount, and one small symbol stands for $100\ \text{g}$ .

Show solution

Understand

A pictograph shows each person's amount in large and small symbols. A small symbol is 100 g; a large symbol is an unknown amount. Finn's row is 3 large symbols and equals 900 g, which lets us find the large-symbol value, then we total everyone.

Givens

Symbols (large + small): Eve 2 + 3, Finn 3 + 0, Gus 4 + 4, Hana 1 + 6.
1 small symbol = 100 g; 1 large symbol = unknown.
Finn has 900 g (row is 3 large symbols).

Unknowns

The total amount all four people have, in g (after finding the large-symbol value).

Constraints

Each large symbol has the same fixed value.
Finn's 3 large symbols total 900 g.

Plan

#11 Work Backwards · also uses: #7 Identify Subproblems

Use Finn's known total to back out the value of one large symbol, then total each person and add. Each person's amount is a small subproblem.

Execute

#11 Work Backwards 3.MD.B.3

Finn's 3 large symbols equal 900 g, so one large symbol is 900 / 3 = 300 g.

900 \div 3 = 300\ \text{g}

Finding what one symbol stands for from a known row total is the heart of reading a scaled pictograph.

#7 Identify Subproblems 3.MD.B.3

Use 300 g per large symbol and 100 g per small symbol. Eve: 2x300 + 3x100 = 900. Finn: 900. Gus: 4x300 + 4x100 = 1600. Hana: 1x300 + 6x100 = 900.

900,\ 900,\ 1600,\ 900\ \text{g}

Multiplying each symbol count by its value and adding is direct scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add the four amounts: 900 + 900 + 1600 + 900 = 4300 g.

900 + 900 + 1600 + 900 = 4300\ \text{g}

Combining the four totals is an addition using place value.

Answer: 4300 g

Review

Counting all large symbols (10 x 300 = 3000) plus all small symbols (13 x 100 = 1300) also gives 4300 g, matching the grand total 4300 g.

Organize differently (tool 15): add all large symbols (10 x 300 = 3000) and all small symbols (13 x 100 = 1300) separately, then 3000 + 1300 = 4300.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the large-symbol value from Finn's row and reading each person's amount.
3.NBT.A.2 Fluently add and subtract within 1000 — Adding the four people's amounts to get the grand total.

💡 Use Finn's row to learn one big symbol is 300 g, then add everyone up - Grade 3 graph reading!

Variant 2 answer: 4900 mL

The pictograph shows how much each person has. If Nia has $1500\ \text{mL}$ , how much do all of the people have altogether?

Amount Each Person Has

Name	Amount
Max	$3$ large symbols, $4$ small symbols
Nia	$5$ large symbols
Ola	$2$ large symbols, $2$ small symbols
Pip	$4$ large symbols, $1$ small symbols

In the pictograph, one large symbol stands for an unknown amount, and one small symbol stands for $100\ \text{mL}$ .

Show solution

Understand

A pictograph shows each person's amount in large and small symbols. A small symbol is 100 mL; a large symbol is an unknown amount. Nia's row is 5 large symbols and equals 1500 mL, which lets us find the large-symbol value, then we total everyone.

Givens

Symbols (large + small): Max 3 + 4, Nia 5 + 0, Ola 2 + 2, Pip 4 + 1.
1 small symbol = 100 mL; 1 large symbol = unknown.
Nia has 1500 mL (row is 5 large symbols).

Unknowns

The total amount all four people have, in mL (after finding the large-symbol value).

Constraints

Each large symbol has the same fixed value.
Nia's 5 large symbols total 1500 mL.

Plan

#11 Work Backwards · also uses: #7 Identify Subproblems

Use Nia's known total to back out the value of one large symbol, then total each person and add. Each person's amount is a small subproblem.

Execute

#11 Work Backwards 3.MD.B.3

Nia's 5 large symbols equal 1500 mL, so one large symbol is 1500 / 5 = 300 mL.

1500 \div 5 = 300\ \text{mL}

Finding what one symbol stands for from a known row total is the heart of reading a scaled pictograph.

#7 Identify Subproblems 3.MD.B.3

Use 300 mL per large symbol and 100 mL per small symbol. Max: 3x300 + 4x100 = 1300. Nia: 1500. Ola: 2x300 + 2x100 = 800. Pip: 4x300 + 1x100 = 1300.

1300,\ 1500,\ 800,\ 1300\ \text{mL}

Multiplying each symbol count by its value and adding is direct scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add the four amounts: 1300 + 1500 + 800 + 1300 = 4900 mL.

1300 + 1500 + 800 + 1300 = 4900\ \text{mL}

Combining the four totals is an addition using place value.

Answer: 4900 mL

Review

Counting all large symbols (14 x 300 = 4200) plus all small symbols (7 x 100 = 700) also gives 4900 mL, matching the grand total 4900 mL.

Organize differently (tool 15): add all large symbols (14 x 300 = 4200) and all small symbols (7 x 100 = 700) separately, then 4200 + 700 = 4900.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the large-symbol value from Nia's row and reading each person's amount.
3.NBT.A.2 Fluently add and subtract within 1000 — Adding the four people's amounts to get the grand total.

💡 Use Nia's row to learn one big symbol is 300 mL, then add everyone up - Grade 3 graph reading!

Variant 3 answer: 2860 coins

The pictograph shows how much each person has. If Jay has $400\ \text{coins}$ , how much do all of the people have altogether?

Amount Each Person Has

Name	Amount
Ivy	$4$ large symbols, $1$ small symbols
Jay	$2$ large symbols
Kit	$3$ large symbols, $3$ small symbols
Liv	$5$ large symbols, $2$ small symbols

In the pictograph, one large symbol stands for an unknown amount, and one small symbol stands for $10\ \text{coins}$ .

Show solution

Understand

A pictograph shows each person's amount in large and small symbols. A small symbol is 10 coins; a large symbol is an unknown amount. Jay's row is 2 large symbols and equals 400 coins, which lets us find the large-symbol value, then we total everyone.

Givens

Symbols (large + small): Ivy 4 + 1, Jay 2 + 0, Kit 3 + 3, Liv 5 + 2.
1 small symbol = 10 coins; 1 large symbol = unknown.
Jay has 400 coins (row is 2 large symbols).

Unknowns

The total amount all four people have, in coins (after finding the large-symbol value).

Constraints

Each large symbol has the same fixed value.
Jay's 2 large symbols total 400 coins.

Plan

#11 Work Backwards · also uses: #7 Identify Subproblems

Use Jay's known total to back out the value of one large symbol, then total each person and add. Each person's amount is a small subproblem.

Execute

#11 Work Backwards 3.MD.B.3

Jay's 2 large symbols equal 400 coins, so one large symbol is 400 / 2 = 200 coins.

400 \div 2 = 200\ \text{coins}

Finding what one symbol stands for from a known row total is the heart of reading a scaled pictograph.

#7 Identify Subproblems 3.MD.B.3

Use 200 coins per large symbol and 10 coins per small symbol. Ivy: 4x200 + 1x10 = 810. Jay: 400. Kit: 3x200 + 3x10 = 630. Liv: 5x200 + 2x10 = 1020.

810,\ 400,\ 630,\ 1020\ \text{coins}

Multiplying each symbol count by its value and adding is direct scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add the four amounts: 810 + 400 + 630 + 1020 = 2860 coins.

810 + 400 + 630 + 1020 = 2860\ \text{coins}

Combining the four totals is an addition using place value.

Answer: 2860 coins

Review

Counting all large symbols (14 x 200 = 2800) plus all small symbols (6 x 10 = 60) also gives 2860 coins, matching the grand total 2860 coins.

Organize differently (tool 15): add all large symbols (14 x 200 = 2800) and all small symbols (6 x 10 = 60) separately, then 2800 + 60 = 2860.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the large-symbol value from Jay's row and reading each person's amount.
3.NBT.A.2 Fluently add and subtract within 1000 — Adding the four people's amounts to get the grand total.

💡 Use Jay's row to learn one big symbol is 200 coins, then add everyone up - Grade 3 graph reading!

Variant 4 answer: 5200 mL

The pictograph shows how much each person has. If Wes has $600\ \text{mL}$ , how much do all of the people have altogether?

Amount Each Person Has

Name	Amount
Val	$5$ large symbols, $2$ small symbols
Wes	$2$ large symbols
Xan	$4$ large symbols, $3$ small symbols
Yas	$3$ large symbols, $5$ small symbols

In the pictograph, one large symbol stands for an unknown amount, and one small symbol stands for $100\ \text{mL}$ .

Show solution

Understand

A pictograph shows each person's amount in large and small symbols. A small symbol is 100 mL; a large symbol is an unknown amount. Wes's row is 2 large symbols and equals 600 mL, which lets us find the large-symbol value, then we total everyone.

Givens

Symbols (large + small): Val 5 + 2, Wes 2 + 0, Xan 4 + 3, Yas 3 + 5.
1 small symbol = 100 mL; 1 large symbol = unknown.
Wes has 600 mL (row is 2 large symbols).

Unknowns

The total amount all four people have, in mL (after finding the large-symbol value).

Constraints

Each large symbol has the same fixed value.
Wes's 2 large symbols total 600 mL.

Plan

#11 Work Backwards · also uses: #7 Identify Subproblems

Use Wes's known total to back out the value of one large symbol, then total each person and add. Each person's amount is a small subproblem.

Execute

#11 Work Backwards 3.MD.B.3

Wes's 2 large symbols equal 600 mL, so one large symbol is 600 / 2 = 300 mL.

600 \div 2 = 300\ \text{mL}

Finding what one symbol stands for from a known row total is the heart of reading a scaled pictograph.

#7 Identify Subproblems 3.MD.B.3

Use 300 mL per large symbol and 100 mL per small symbol. Val: 5x300 + 2x100 = 1700. Wes: 600. Xan: 4x300 + 3x100 = 1500. Yas: 3x300 + 5x100 = 1400.

1700,\ 600,\ 1500,\ 1400\ \text{mL}

Multiplying each symbol count by its value and adding is direct scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add the four amounts: 1700 + 600 + 1500 + 1400 = 5200 mL.

1700 + 600 + 1500 + 1400 = 5200\ \text{mL}

Combining the four totals is an addition using place value.

Answer: 5200 mL

Review

Counting all large symbols (14 x 300 = 4200) plus all small symbols (10 x 100 = 1000) also gives 5200 mL, matching the grand total 5200 mL.

Organize differently (tool 15): add all large symbols (14 x 300 = 4200) and all small symbols (10 x 100 = 1000) separately, then 4200 + 1000 = 5200.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the large-symbol value from Wes's row and reading each person's amount.
3.NBT.A.2 Fluently add and subtract within 1000 — Adding the four people's amounts to get the grand total.

💡 Use Wes's row to learn one big symbol is 300 mL, then add everyone up - Grade 3 graph reading!

Variant 5 answer: 4590 beads

The pictograph shows how much each person has. If Abe has $1800\ \text{beads}$ , how much do all of the people have altogether?

Amount Each Person Has

Name	Amount
Zoe	$3$ large symbols, $3$ small symbols
Abe	$6$ large symbols
Cy	$2$ large symbols, $4$ small symbols
Deb	$4$ large symbols, $2$ small symbols

In the pictograph, one large symbol stands for an unknown amount, and one small symbol stands for $10\ \text{beads}$ .

Show solution

Understand

A pictograph shows each person's amount in large and small symbols. A small symbol is 10 beads; a large symbol is an unknown amount. Abe's row is 6 large symbols and equals 1800 beads, which lets us find the large-symbol value, then we total everyone.

Givens

Symbols (large + small): Zoe 3 + 3, Abe 6 + 0, Cy 2 + 4, Deb 4 + 2.
1 small symbol = 10 beads; 1 large symbol = unknown.
Abe has 1800 beads (row is 6 large symbols).

Unknowns

The total amount all four people have, in beads (after finding the large-symbol value).

Constraints

Each large symbol has the same fixed value.
Abe's 6 large symbols total 1800 beads.

Plan

#11 Work Backwards · also uses: #7 Identify Subproblems

Use Abe's known total to back out the value of one large symbol, then total each person and add. Each person's amount is a small subproblem.

Execute

#11 Work Backwards 3.MD.B.3

Abe's 6 large symbols equal 1800 beads, so one large symbol is 1800 / 6 = 300 beads.

1800 \div 6 = 300\ \text{beads}

Finding what one symbol stands for from a known row total is the heart of reading a scaled pictograph.

#7 Identify Subproblems 3.MD.B.3

Use 300 beads per large symbol and 10 beads per small symbol. Zoe: 3x300 + 3x10 = 930. Abe: 1800. Cy: 2x300 + 4x10 = 640. Deb: 4x300 + 2x10 = 1220.

930,\ 1800,\ 640,\ 1220\ \text{beads}

Multiplying each symbol count by its value and adding is direct scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add the four amounts: 930 + 1800 + 640 + 1220 = 4590 beads.

930 + 1800 + 640 + 1220 = 4590\ \text{beads}

Combining the four totals is an addition using place value.

Answer: 4590 beads

Review

Counting all large symbols (15 x 300 = 4500) plus all small symbols (9 x 10 = 90) also gives 4590 beads, matching the grand total 4590 beads.

Organize differently (tool 15): add all large symbols (15 x 300 = 4500) and all small symbols (9 x 10 = 90) separately, then 4500 + 90 = 4590.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the large-symbol value from Abe's row and reading each person's amount.
3.NBT.A.2 Fluently add and subtract within 1000 — Adding the four people's amounts to get the grand total.

💡 Use Abe's row to learn one big symbol is 300 beads, then add everyone up - Grade 3 graph reading!

Variant 6 answer: 7900 mL

The pictograph shows how much each person has. If Hazel has $2500\ \text{mL}$ , how much do all of the people have altogether?

Amount Each Person Has

Name	Amount
Mia	$2$ large symbols, $4$ small symbols
Owen	$3$ large symbols, $3$ small symbols
Hazel	$5$ large symbols
Caleb	$4$ large symbols, $2$ small symbols

In the pictograph, one large symbol stands for an unknown amount, and one small symbol stands for $100\ \text{mL}$ .

Show solution

Understand

A pictograph shows each person's amount in large and small symbols. A small symbol is 100 mL; a large symbol is an unknown amount. Hazel's row is 5 large symbols and equals 2500 mL, which lets us find the large-symbol value, then we total everyone.

Givens

Symbols (large + small): Mia 2 + 4, Owen 3 + 3, Hazel 5 + 0, Caleb 4 + 2.
1 small symbol = 100 mL; 1 large symbol = unknown.
Hazel has 2500 mL (row is 5 large symbols).

Unknowns

The total amount all four people have, in mL (after finding the large-symbol value).

Constraints

Each large symbol has the same fixed value.
Hazel's 5 large symbols total 2500 mL.

Plan

#11 Work Backwards · also uses: #7 Identify Subproblems

Use Hazel's known total to back out the value of one large symbol, then total each person and add. Each person's amount is a small subproblem.

Execute

#11 Work Backwards 3.MD.B.3

Hazel's 5 large symbols equal 2500 mL, so one large symbol is 2500 / 5 = 500 mL.

2500 \div 5 = 500\ \text{mL}

Finding what one symbol stands for from a known row total is the heart of reading a scaled pictograph.

#7 Identify Subproblems 3.MD.B.3

Use 500 mL per large symbol and 100 mL per small symbol. Mia: 2x500 + 4x100 = 1400. Owen: 3x500 + 3x100 = 1800. Hazel: 2500. Caleb: 4x500 + 2x100 = 2200.

1400,\ 1800,\ 2500,\ 2200\ \text{mL}

Multiplying each symbol count by its value and adding is direct scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add the four amounts: 1400 + 1800 + 2500 + 2200 = 7900 mL.

1400 + 1800 + 2500 + 2200 = 7900\ \text{mL}

Combining the four totals is an addition using place value.

Answer: 7900 mL

Review

Counting all large symbols (14 x 500 = 7000) plus all small symbols (9 x 100 = 900) also gives 7900 mL, matching the grand total 7900 mL.

Organize differently (tool 15): add all large symbols (14 x 500 = 7000) and all small symbols (9 x 100 = 900) separately, then 7000 + 900 = 7900.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the large-symbol value from Hazel's row and reading each person's amount.
3.NBT.A.2 Fluently add and subtract within 1000 — Adding the four people's amounts to get the grand total.

💡 Use Hazel's row to learn one big symbol is 500 mL, then add everyone up - Grade 3 graph reading!

Variant 7 answer: 4300 points

The pictograph shows how much each person has. If Sue has $1200\ \text{points}$ , how much do all of the people have altogether?

Amount Each Person Has

Name	Amount
Ray	$2$ large symbols, $6$ small symbols
Sue	$4$ large symbols
Tom	$3$ large symbols, $1$ small symbols
Uma	$5$ large symbols, $3$ small symbols

In the pictograph, one large symbol stands for an unknown amount, and one small symbol stands for $10\ \text{points}$ .

Show solution

Understand

A pictograph shows each person's amount in large and small symbols. A small symbol is 10 points; a large symbol is an unknown amount. Sue's row is 4 large symbols and equals 1200 points, which lets us find the large-symbol value, then we total everyone.

Givens

Symbols (large + small): Ray 2 + 6, Sue 4 + 0, Tom 3 + 1, Uma 5 + 3.
1 small symbol = 10 points; 1 large symbol = unknown.
Sue has 1200 points (row is 4 large symbols).

Unknowns

The total amount all four people have, in points (after finding the large-symbol value).

Constraints

Each large symbol has the same fixed value.
Sue's 4 large symbols total 1200 points.

Plan

#11 Work Backwards · also uses: #7 Identify Subproblems

Use Sue's known total to back out the value of one large symbol, then total each person and add. Each person's amount is a small subproblem.

Execute

#11 Work Backwards 3.MD.B.3

Sue's 4 large symbols equal 1200 points, so one large symbol is 1200 / 4 = 300 points.

1200 \div 4 = 300\ \text{points}

Finding what one symbol stands for from a known row total is the heart of reading a scaled pictograph.

#7 Identify Subproblems 3.MD.B.3

Use 300 points per large symbol and 10 points per small symbol. Ray: 2x300 + 6x10 = 660. Sue: 1200. Tom: 3x300 + 1x10 = 910. Uma: 5x300 + 3x10 = 1530.

660,\ 1200,\ 910,\ 1530\ \text{points}

Multiplying each symbol count by its value and adding is direct scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add the four amounts: 660 + 1200 + 910 + 1530 = 4300 points.

660 + 1200 + 910 + 1530 = 4300\ \text{points}

Combining the four totals is an addition using place value.

Answer: 4300 points

Review

Counting all large symbols (14 x 300 = 4200) plus all small symbols (10 x 10 = 100) also gives 4300 points, matching the grand total 4300 points.

Organize differently (tool 15): add all large symbols (14 x 300 = 4200) and all small symbols (10 x 10 = 100) separately, then 4200 + 100 = 4300.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the large-symbol value from Sue's row and reading each person's amount.
3.NBT.A.2 Fluently add and subtract within 1000 — Adding the four people's amounts to get the grand total.

💡 Use Sue's row to learn one big symbol is 300 points, then add everyone up - Grade 3 graph reading!

Variant 8 answer: 2880 stickers

The pictograph shows how much each person has. If Ben has $800\ \text{stickers}$ , how much do all of the people have altogether?

Amount Each Person Has

Name	Amount
Ann	$3$ large symbols, $2$ small symbols
Ben	$4$ large symbols
Cara	$2$ large symbols, $5$ small symbols
Dan	$5$ large symbols, $1$ small symbols

In the pictograph, one large symbol stands for an unknown amount, and one small symbol stands for $10\ \text{stickers}$ .

Show solution

Understand

A pictograph shows each person's amount in large and small symbols. A small symbol is 10 stickers; a large symbol is an unknown amount. Ben's row is 4 large symbols and equals 800 stickers, which lets us find the large-symbol value, then we total everyone.

Givens

Symbols (large + small): Ann 3 + 2, Ben 4 + 0, Cara 2 + 5, Dan 5 + 1.
1 small symbol = 10 stickers; 1 large symbol = unknown.
Ben has 800 stickers (row is 4 large symbols).

Unknowns

The total amount all four people have, in stickers (after finding the large-symbol value).

Constraints

Each large symbol has the same fixed value.
Ben's 4 large symbols total 800 stickers.

Plan

#11 Work Backwards · also uses: #7 Identify Subproblems

Use Ben's known total to back out the value of one large symbol, then total each person and add. Each person's amount is a small subproblem.

Execute

#11 Work Backwards 3.MD.B.3

Ben's 4 large symbols equal 800 stickers, so one large symbol is 800 / 4 = 200 stickers.

800 \div 4 = 200\ \text{stickers}

Finding what one symbol stands for from a known row total is the heart of reading a scaled pictograph.

#7 Identify Subproblems 3.MD.B.3

Use 200 stickers per large symbol and 10 stickers per small symbol. Ann: 3x200 + 2x10 = 620. Ben: 800. Cara: 2x200 + 5x10 = 450. Dan: 5x200 + 1x10 = 1010.

620,\ 800,\ 450,\ 1010\ \text{stickers}

Multiplying each symbol count by its value and adding is direct scaled-pictograph reading.

#7 Identify Subproblems 3.NBT.A.2

Add the four amounts: 620 + 800 + 450 + 1010 = 2880 stickers.

620 + 800 + 450 + 1010 = 2880\ \text{stickers}

Combining the four totals is an addition using place value.

Answer: 2880 stickers

Review

Counting all large symbols (14 x 200 = 2800) plus all small symbols (8 x 10 = 80) also gives 2880 stickers, matching the grand total 2880 stickers.

Organize differently (tool 15): add all large symbols (14 x 200 = 2800) and all small symbols (8 x 10 = 80) separately, then 2800 + 80 = 2880.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the large-symbol value from Ben's row and reading each person's amount.
3.NBT.A.2 Fluently add and subtract within 1000 — Adding the four people's amounts to get the grand total.

💡 Use Ben's row to learn one big symbol is 200 stickers, then add everyone up - Grade 3 graph reading!