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Read totals and differences from a graph · 8 practice problems

2.MD.D.102.OA.A.1

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Generated variants — 8

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

Variant 1 medium

Liam's team and Mia's team took part in a team quiz match, and the number of questions answered correctly each student answered correctly was recorded in two picture graphs. If Liam's team answered $2$ more questions correctly than Mia's team in total, find how many questions Jordan answered correctly.

Liam's team: questions answered correctly per student

The vertical axis shows the number of correct questions from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Liam, Noah, Owen, Jacob). Liam has $2$ circles, Noah has $4$ , Owen has $5$ , Jacob has $3$ .

Mia's team: questions answered correctly per student

The vertical axis shows the number of correct questions from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Sophia, Ethan, Jordan, Emma). Sophia has $4$ circles, Ethan has $2$ , Emma has $3$ ; Jordan's column is empty.

(1) (Total correct for Liam's team) $=$ (Liam) $+$ (Noah) $+$ (Owen) $+$ (Jacob) $=\square$

(2) (Total correct for Mia's team) $=\square-2=\square$

(3) Therefore Jordan answered $\square-$ (Sophia) $-$ (Ethan) $-$ (Emma) $=\square$ questions correctly.

Your answer

Show solution

1 · Understandwhat's really being asked

Two picture graphs show how many questions each student answered correctly. Liam's team total is 2 more than Mia's team total. Jordan's column on Mia's team is blank; I need to find how many questions Jordan got right.

Givens

Liam's team: Liam 2, Noah 4, Owen 5, Jacob 3 correct.
Mia's team: Sophia 4, Ethan 2, Emma 3; Jordan unknown (blank column).
Liam's team answered 2 more correct in total than Mia's team.

Unknowns

The number of questions Jordan answered correctly.

Constraints

Each circle on a graph stands for 1 correct question.
A team total is the sum of every student's correct answers.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

This breaks into clear subproblems: add Liam's team total, subtract 2 to get Mia's team total, then subtract the known Mia's team students to leave Jordan. Reading each circle count straight off the graph supports every step.

3 · Execute3 carry out the plan

1Total for Liam's team

#7 Identify Subproblems 2.MD.D.10

Add the four students' correct answers: 2 + 4 + 5 + 3 = 14.

2 + 4 + 5 + 3 = 14

Reading each column's circles and adding is exactly interpreting a picture graph.

2Total for Mia's team

#7 Identify Subproblems 2.OA.A.1

Liam's team is 2 more than Mia's team, so Mia's team total is 14 - 2 = 12.

14 - 2 = 12

'2 more' means subtract 2 to go back to the smaller total — a Grade 2 word-problem move.

3Find Jordan's count

#7 Identify Subproblems 2.OA.A.1

Mia's team total minus the three known students leaves Jordan: 12 - 4 - 2 - 3 = 3.

12 - 4 - 2 - 3 = 3

Subtracting the known parts from the whole gives the missing part.

Answer: 3 questions

4 · Reviewdoes it hold up?

Check the totals: Mia's team would be 4 + 2 + 3 + 3 = 12, and Liam's team is 14, which is 2 more — exactly matching the condition. Jordan's 3 is a sensible count, between 1 and 5 like the others.

Another way: Subtract the three known Mia's team students from Liam's team's total first (14 - 4 - 2 - 3 = 5), then subtract the extra 2 from the difference (5 - 2 = 3) to get Jordan.

Standardsmin grade 2

2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading each student's circle count from the two picture graphs.
2.OA.A.1 Solve one- and two-step word problems using addition and subtraction within 100 — Using 'team total' and the 2-more relationship with addition and subtraction to find Jordan.

💡Takeaway. This only needs Grade 2 graph-reading and add/subtract — find the totals, then fill the missing part!

Variant 2 medium

Tigers and Lions took part in a team quiz match, and the number of goals scored each student answered correctly was recorded in two picture graphs. If Tigers answered $2$ more goals correctly than Lions in total, find how many goals Mia answered correctly.

Tigers: goals scored per student

The vertical axis shows the number of correct goals from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Ian, Jen, Kai, Leo). Ian has $4$ circles, Jen has $4$ , Kai has $3$ , Leo has $5$ .

Lions: goals scored per student

The vertical axis shows the number of correct goals from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Mia, Nia, Oma, Pam). Nia has $4$ circles, Oma has $5$ , Pam has $2$ ; Mia's column is empty.

(1) (Total correct for Tigers) $=$ (Ian) $+$ (Jen) $+$ (Kai) $+$ (Leo) $=\square$

(2) (Total correct for Lions) $=\square-2=\square$

(3) Therefore Mia answered $\square-$ (Nia) $-$ (Oma) $-$ (Pam) $=\square$ goals correctly.

Your answer

Show solution

1 · Understandwhat's really being asked

Two picture graphs show how many goals each student answered correctly. Tigers total is 2 more than Lions total. Mia's column on Lions is blank; I need to find how many goals Mia got right.

Givens

Tigers: Ian 4, Jen 4, Kai 3, Leo 5 correct.
Lions: Nia 4, Oma 5, Pam 2; Mia unknown (blank column).
Tigers answered 2 more correct in total than Lions.

Unknowns

The number of goals Mia answered correctly.

Constraints

Each circle on a graph stands for 1 correct question.
A team total is the sum of every student's correct answers.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

This breaks into clear subproblems: add Tigers total, subtract 2 to get Lions total, then subtract the known Lions students to leave Mia. Reading each circle count straight off the graph supports every step.

3 · Execute3 carry out the plan

1Total for Tigers

#7 Identify Subproblems 2.MD.D.10

Add the four students' correct answers: 4 + 4 + 3 + 5 = 16.

4 + 4 + 3 + 5 = 16

Reading each column's circles and adding is exactly interpreting a picture graph.

2Total for Lions

#7 Identify Subproblems 2.OA.A.1

Tigers is 2 more than Lions, so Lions total is 16 - 2 = 14.

16 - 2 = 14

'2 more' means subtract 2 to go back to the smaller total — a Grade 2 word-problem move.

3Find Mia's count

#7 Identify Subproblems 2.OA.A.1

Lions total minus the three known students leaves Mia: 14 - 4 - 5 - 2 = 3.

14 - 4 - 5 - 2 = 3

Subtracting the known parts from the whole gives the missing part.

Answer: 3 goals

4 · Reviewdoes it hold up?

Check the totals: Lions would be 3 + 4 + 5 + 2 = 14, and Tigers is 16, which is 2 more — exactly matching the condition. Mia's 3 is a sensible count, between 1 and 5 like the others.

Another way: Subtract the three known Lions students from Tigers's total first (16 - 4 - 5 - 2 = 5), then subtract the extra 2 from the difference (5 - 2 = 3) to get Mia.

Standardsmin grade 2

2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading each student's circle count from the two picture graphs.
2.OA.A.1 Solve one- and two-step word problems using addition and subtraction within 100 — Using 'team total' and the 2-more relationship with addition and subtraction to find Mia.

💡Takeaway. This only needs Grade 2 graph-reading and add/subtract — find the totals, then fill the missing part!

Variant 3 medium

North team and South team took part in a team quiz match, and the number of questions answered correctly each student answered correctly was recorded in two picture graphs. If North team answered $2$ more questions correctly than South team in total, find how many questions Wes answered correctly.

North team: questions answered correctly per student

The vertical axis shows the number of correct questions from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Ray, Sue, Tom, Uma). Ray has $5$ circles, Sue has $2$ , Tom has $4$ , Uma has $3$ .

South team: questions answered correctly per student

The vertical axis shows the number of correct questions from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Vic, Wes, Xan, Yumi). Vic has $2$ circles, Xan has $4$ , Yumi has $1$ ; Wes's column is empty.

(1) (Total correct for North team) $=$ (Ray) $+$ (Sue) $+$ (Tom) $+$ (Uma) $=\square$

(2) (Total correct for South team) $=\square-2=\square$

(3) Therefore Wes answered $\square-$ (Vic) $-$ (Xan) $-$ (Yumi) $=\square$ questions correctly.

Your answer

Show solution

1 · Understandwhat's really being asked

Two picture graphs show how many questions each student answered correctly. North team total is 2 more than South team total. Wes's column on South team is blank; I need to find how many questions Wes got right.

Givens

North team: Ray 5, Sue 2, Tom 4, Uma 3 correct.
South team: Vic 2, Xan 4, Yumi 1; Wes unknown (blank column).
North team answered 2 more correct in total than South team.

Unknowns

The number of questions Wes answered correctly.

Constraints

Each circle on a graph stands for 1 correct question.
A team total is the sum of every student's correct answers.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

This breaks into clear subproblems: add North team total, subtract 2 to get South team total, then subtract the known South team students to leave Wes. Reading each circle count straight off the graph supports every step.

3 · Execute3 carry out the plan

1Total for North team

#7 Identify Subproblems 2.MD.D.10

Add the four students' correct answers: 5 + 2 + 4 + 3 = 14.

5 + 2 + 4 + 3 = 14

Reading each column's circles and adding is exactly interpreting a picture graph.

2Total for South team

#7 Identify Subproblems 2.OA.A.1

North team is 2 more than South team, so South team total is 14 - 2 = 12.

14 - 2 = 12

'2 more' means subtract 2 to go back to the smaller total — a Grade 2 word-problem move.

3Find Wes's count

#7 Identify Subproblems 2.OA.A.1

South team total minus the three known students leaves Wes: 12 - 2 - 4 - 1 = 5.

12 - 2 - 4 - 1 = 5

Subtracting the known parts from the whole gives the missing part.

Answer: 5 questions

4 · Reviewdoes it hold up?

Check the totals: South team would be 2 + 5 + 4 + 1 = 12, and North team is 14, which is 2 more — exactly matching the condition. Wes's 5 is a sensible count, between 1 and 5 like the others.

Another way: Subtract the three known South team students from North team's total first (14 - 2 - 4 - 1 = 7), then subtract the extra 2 from the difference (7 - 2 = 5) to get Wes.

Standardsmin grade 2

2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading each student's circle count from the two picture graphs.
2.OA.A.1 Solve one- and two-step word problems using addition and subtraction within 100 — Using 'team total' and the 2-more relationship with addition and subtraction to find Wes.

💡Takeaway. This only needs Grade 2 graph-reading and add/subtract — find the totals, then fill the missing part!

Variant 4 medium

Red team and Blue team took part in a team quiz match, and the number of points scored each student answered correctly was recorded in two picture graphs. If Red team answered $2$ more points correctly than Blue team in total, find how many points Hana answered correctly.

Red team: points scored per student

The vertical axis shows the number of correct points from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Ava, Ben, Cara, Dan). Ava has $3$ circles, Ben has $5$ , Cara has $4$ , Dan has $2$ .

Blue team: points scored per student

The vertical axis shows the number of correct points from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Eli, Fay, Gus, Hana). Eli has $5$ circles, Fay has $3$ , Gus has $2$ ; Hana's column is empty.

(1) (Total correct for Red team) $=$ (Ava) $+$ (Ben) $+$ (Cara) $+$ (Dan) $=\square$

(2) (Total correct for Blue team) $=\square-2=\square$

(3) Therefore Hana answered $\square-$ (Eli) $-$ (Fay) $-$ (Gus) $=\square$ points correctly.

Your answer

Show solution

1 · Understandwhat's really being asked

Two picture graphs show how many points each student answered correctly. Red team total is 2 more than Blue team total. Hana's column on Blue team is blank; I need to find how many points Hana got right.

Givens

Red team: Ava 3, Ben 5, Cara 4, Dan 2 correct.
Blue team: Eli 5, Fay 3, Gus 2; Hana unknown (blank column).
Red team answered 2 more correct in total than Blue team.

Unknowns

The number of points Hana answered correctly.

Constraints

Each circle on a graph stands for 1 correct question.
A team total is the sum of every student's correct answers.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

This breaks into clear subproblems: add Red team total, subtract 2 to get Blue team total, then subtract the known Blue team students to leave Hana. Reading each circle count straight off the graph supports every step.

3 · Execute3 carry out the plan

1Total for Red team

#7 Identify Subproblems 2.MD.D.10

Add the four students' correct answers: 3 + 5 + 4 + 2 = 14.

3 + 5 + 4 + 2 = 14

Reading each column's circles and adding is exactly interpreting a picture graph.

2Total for Blue team

#7 Identify Subproblems 2.OA.A.1

Red team is 2 more than Blue team, so Blue team total is 14 - 2 = 12.

14 - 2 = 12

'2 more' means subtract 2 to go back to the smaller total — a Grade 2 word-problem move.

3Find Hana's count

#7 Identify Subproblems 2.OA.A.1

Blue team total minus the three known students leaves Hana: 12 - 5 - 3 - 2 = 2.

12 - 5 - 3 - 2 = 2

Subtracting the known parts from the whole gives the missing part.

Answer: 2 points

4 · Reviewdoes it hold up?

Check the totals: Blue team would be 5 + 3 + 2 + 2 = 12, and Red team is 14, which is 2 more — exactly matching the condition. Hana's 2 is a sensible count, between 1 and 5 like the others.

Another way: Subtract the three known Blue team students from Red team's total first (14 - 5 - 3 - 2 = 4), then subtract the extra 2 from the difference (4 - 2 = 2) to get Hana.

Standardsmin grade 2

2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading each student's circle count from the two picture graphs.
2.OA.A.1 Solve one- and two-step word problems using addition and subtraction within 100 — Using 'team total' and the 2-more relationship with addition and subtraction to find Hana.

💡Takeaway. This only needs Grade 2 graph-reading and add/subtract — find the totals, then fill the missing part!

Variant 5 medium

Star team and Moon team took part in a team quiz match, and the number of points scored each student answered correctly was recorded in two picture graphs. If Star team answered $2$ more points correctly than Moon team in total, find how many points Gem answered correctly.

Star team: points scored per student

The vertical axis shows the number of correct points from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Abe, Bea, Cy, Deb). Abe has $3$ circles, Bea has $3$ , Cy has $4$ , Deb has $4$ .

Moon team: points scored per student

The vertical axis shows the number of correct points from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Edo, Fox, Gem, Hil). Edo has $4$ circles, Fox has $2$ , Hil has $4$ ; Gem's column is empty.

(1) (Total correct for Star team) $=$ (Abe) $+$ (Bea) $+$ (Cy) $+$ (Deb) $=\square$

(2) (Total correct for Moon team) $=\square-2=\square$

(3) Therefore Gem answered $\square-$ (Edo) $-$ (Fox) $-$ (Hil) $=\square$ points correctly.

Your answer

Show solution

1 · Understandwhat's really being asked

Two picture graphs show how many points each student answered correctly. Star team total is 2 more than Moon team total. Gem's column on Moon team is blank; I need to find how many points Gem got right.

Givens

Star team: Abe 3, Bea 3, Cy 4, Deb 4 correct.
Moon team: Edo 4, Fox 2, Hil 4; Gem unknown (blank column).
Star team answered 2 more correct in total than Moon team.

Unknowns

The number of points Gem answered correctly.

Constraints

Each circle on a graph stands for 1 correct question.
A team total is the sum of every student's correct answers.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

This breaks into clear subproblems: add Star team total, subtract 2 to get Moon team total, then subtract the known Moon team students to leave Gem. Reading each circle count straight off the graph supports every step.

3 · Execute3 carry out the plan

1Total for Star team

#7 Identify Subproblems 2.MD.D.10

Add the four students' correct answers: 3 + 3 + 4 + 4 = 14.

3 + 3 + 4 + 4 = 14

Reading each column's circles and adding is exactly interpreting a picture graph.

2Total for Moon team

#7 Identify Subproblems 2.OA.A.1

Star team is 2 more than Moon team, so Moon team total is 14 - 2 = 12.

14 - 2 = 12

'2 more' means subtract 2 to go back to the smaller total — a Grade 2 word-problem move.

3Find Gem's count

#7 Identify Subproblems 2.OA.A.1

Moon team total minus the three known students leaves Gem: 12 - 4 - 2 - 4 = 2.

12 - 4 - 2 - 4 = 2

Subtracting the known parts from the whole gives the missing part.

Answer: 2 points

4 · Reviewdoes it hold up?

Check the totals: Moon team would be 4 + 2 + 2 + 4 = 12, and Star team is 14, which is 2 more — exactly matching the condition. Gem's 2 is a sensible count, between 1 and 5 like the others.

Another way: Subtract the three known Moon team students from Star team's total first (14 - 4 - 2 - 4 = 4), then subtract the extra 2 from the difference (4 - 2 = 2) to get Gem.

Standardsmin grade 2

2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading each student's circle count from the two picture graphs.
2.OA.A.1 Solve one- and two-step word problems using addition and subtraction within 100 — Using 'team total' and the 2-more relationship with addition and subtraction to find Gem.

💡Takeaway. This only needs Grade 2 graph-reading and add/subtract — find the totals, then fill the missing part!

Variant 6 medium

Green team and Gold team took part in a team quiz match, and the number of goals scored each student answered correctly was recorded in two picture graphs. If Green team answered $2$ more goals correctly than Gold team in total, find how many goals Fia answered correctly.

Green team: goals scored per student

The vertical axis shows the number of correct goals from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Ari, Bri, Coe, Dia). Ari has $2$ circles, Bri has $3$ , Coe has $5$ , Dia has $4$ .

Gold team: goals scored per student

The vertical axis shows the number of correct goals from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Eko, Fia, Gia, Hue). Eko has $3$ circles, Gia has $4$ , Hue has $2$ ; Fia's column is empty.

(1) (Total correct for Green team) $=$ (Ari) $+$ (Bri) $+$ (Coe) $+$ (Dia) $=\square$

(2) (Total correct for Gold team) $=\square-2=\square$

(3) Therefore Fia answered $\square-$ (Eko) $-$ (Gia) $-$ (Hue) $=\square$ goals correctly.

Your answer

Show solution

1 · Understandwhat's really being asked

Two picture graphs show how many goals each student answered correctly. Green team total is 2 more than Gold team total. Fia's column on Gold team is blank; I need to find how many goals Fia got right.

Givens

Green team: Ari 2, Bri 3, Coe 5, Dia 4 correct.
Gold team: Eko 3, Gia 4, Hue 2; Fia unknown (blank column).
Green team answered 2 more correct in total than Gold team.

Unknowns

The number of goals Fia answered correctly.

Constraints

Each circle on a graph stands for 1 correct question.
A team total is the sum of every student's correct answers.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

This breaks into clear subproblems: add Green team total, subtract 2 to get Gold team total, then subtract the known Gold team students to leave Fia. Reading each circle count straight off the graph supports every step.

3 · Execute3 carry out the plan

1Total for Green team

#7 Identify Subproblems 2.MD.D.10

Add the four students' correct answers: 2 + 3 + 5 + 4 = 14.

2 + 3 + 5 + 4 = 14

Reading each column's circles and adding is exactly interpreting a picture graph.

2Total for Gold team

#7 Identify Subproblems 2.OA.A.1

Green team is 2 more than Gold team, so Gold team total is 14 - 2 = 12.

14 - 2 = 12

'2 more' means subtract 2 to go back to the smaller total — a Grade 2 word-problem move.

3Find Fia's count

#7 Identify Subproblems 2.OA.A.1

Gold team total minus the three known students leaves Fia: 12 - 3 - 4 - 2 = 3.

12 - 3 - 4 - 2 = 3

Subtracting the known parts from the whole gives the missing part.

Answer: 3 goals

4 · Reviewdoes it hold up?

Check the totals: Gold team would be 3 + 3 + 4 + 2 = 12, and Green team is 14, which is 2 more — exactly matching the condition. Fia's 3 is a sensible count, between 1 and 5 like the others.

Another way: Subtract the three known Gold team students from Green team's total first (14 - 3 - 4 - 2 = 5), then subtract the extra 2 from the difference (5 - 2 = 3) to get Fia.

Standardsmin grade 2

2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading each student's circle count from the two picture graphs.
2.OA.A.1 Solve one- and two-step word problems using addition and subtraction within 100 — Using 'team total' and the 2-more relationship with addition and subtraction to find Fia.

💡Takeaway. This only needs Grade 2 graph-reading and add/subtract — find the totals, then fill the missing part!

Variant 7 medium

Eagles and Hawks took part in a team quiz match, and the number of questions answered correctly each student answered correctly was recorded in two picture graphs. If Eagles answered $2$ more questions correctly than Hawks in total, find how many questions Hugo answered correctly.

Eagles: questions answered correctly per student

The vertical axis shows the number of correct questions from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Ada, Bo, Cleo, Dex). Ada has $5$ circles, Bo has $4$ , Cleo has $5$ , Dex has $4$ .

Hawks: questions answered correctly per student

The vertical axis shows the number of correct questions from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Eve, Fin, Gio, Hugo). Eve has $5$ circles, Fin has $5$ , Gio has $4$ ; Hugo's column is empty.

(1) (Total correct for Eagles) $=$ (Ada) $+$ (Bo) $+$ (Cleo) $+$ (Dex) $=\square$

(2) (Total correct for Hawks) $=\square-2=\square$

(3) Therefore Hugo answered $\square-$ (Eve) $-$ (Fin) $-$ (Gio) $=\square$ questions correctly.

Your answer

Show solution

1 · Understandwhat's really being asked

Two picture graphs show how many questions each student answered correctly. Eagles total is 2 more than Hawks total. Hugo's column on Hawks is blank; I need to find how many questions Hugo got right.

Givens

Eagles: Ada 5, Bo 4, Cleo 5, Dex 4 correct.
Hawks: Eve 5, Fin 5, Gio 4; Hugo unknown (blank column).
Eagles answered 2 more correct in total than Hawks.

Unknowns

The number of questions Hugo answered correctly.

Constraints

Each circle on a graph stands for 1 correct question.
A team total is the sum of every student's correct answers.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

This breaks into clear subproblems: add Eagles total, subtract 2 to get Hawks total, then subtract the known Hawks students to leave Hugo. Reading each circle count straight off the graph supports every step.

3 · Execute3 carry out the plan

1Total for Eagles

#7 Identify Subproblems 2.MD.D.10

Add the four students' correct answers: 5 + 4 + 5 + 4 = 18.

5 + 4 + 5 + 4 = 18

Reading each column's circles and adding is exactly interpreting a picture graph.

2Total for Hawks

#7 Identify Subproblems 2.OA.A.1

Eagles is 2 more than Hawks, so Hawks total is 18 - 2 = 16.

18 - 2 = 16

'2 more' means subtract 2 to go back to the smaller total — a Grade 2 word-problem move.

3Find Hugo's count

#7 Identify Subproblems 2.OA.A.1

Hawks total minus the three known students leaves Hugo: 16 - 5 - 5 - 4 = 2.

16 - 5 - 5 - 4 = 2

Subtracting the known parts from the whole gives the missing part.

Answer: 2 questions

4 · Reviewdoes it hold up?

Check the totals: Hawks would be 5 + 5 + 4 + 2 = 16, and Eagles is 18, which is 2 more — exactly matching the condition. Hugo's 2 is a sensible count, between 1 and 5 like the others.

Another way: Subtract the three known Hawks students from Eagles's total first (18 - 5 - 5 - 4 = 4), then subtract the extra 2 from the difference (4 - 2 = 2) to get Hugo.

Standardsmin grade 2

2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading each student's circle count from the two picture graphs.
2.OA.A.1 Solve one- and two-step word problems using addition and subtraction within 100 — Using 'team total' and the 2-more relationship with addition and subtraction to find Hugo.

💡Takeaway. This only needs Grade 2 graph-reading and add/subtract — find the totals, then fill the missing part!

Variant 8 medium

West team and East team took part in a team quiz match, and the number of points scored each student answered correctly was recorded in two picture graphs. If West team answered $2$ more points correctly than East team in total, find how many points Val answered correctly.

West team: points scored per student

The vertical axis shows the number of correct points from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Ola, Pia, Roy, Sia). Ola has $4$ circles, Pia has $5$ , Roy has $4$ , Sia has $3$ .

East team: points scored per student

The vertical axis shows the number of correct points from $1$ to $5$ , one per cell, and the horizontal axis lists the students (Tia, Uri, Val, Zoe). Tia has $5$ circles, Uri has $2$ , Zoe has $3$ ; Val's column is empty.

(1) (Total correct for West team) $=$ (Ola) $+$ (Pia) $+$ (Roy) $+$ (Sia) $=\square$

(2) (Total correct for East team) $=\square-2=\square$

(3) Therefore Val answered $\square-$ (Tia) $-$ (Uri) $-$ (Zoe) $=\square$ points correctly.

Your answer

Show solution

1 · Understandwhat's really being asked

Two picture graphs show how many points each student answered correctly. West team total is 2 more than East team total. Val's column on East team is blank; I need to find how many points Val got right.

Givens

West team: Ola 4, Pia 5, Roy 4, Sia 3 correct.
East team: Tia 5, Uri 2, Zoe 3; Val unknown (blank column).
West team answered 2 more correct in total than East team.

Unknowns

The number of points Val answered correctly.

Constraints

Each circle on a graph stands for 1 correct question.
A team total is the sum of every student's correct answers.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #1 Draw a Diagram

This breaks into clear subproblems: add West team total, subtract 2 to get East team total, then subtract the known East team students to leave Val. Reading each circle count straight off the graph supports every step.

3 · Execute3 carry out the plan

1Total for West team

#7 Identify Subproblems 2.MD.D.10

Add the four students' correct answers: 4 + 5 + 4 + 3 = 16.

4 + 5 + 4 + 3 = 16

Reading each column's circles and adding is exactly interpreting a picture graph.

2Total for East team

#7 Identify Subproblems 2.OA.A.1

West team is 2 more than East team, so East team total is 16 - 2 = 14.

16 - 2 = 14

'2 more' means subtract 2 to go back to the smaller total — a Grade 2 word-problem move.

3Find Val's count

#7 Identify Subproblems 2.OA.A.1

East team total minus the three known students leaves Val: 14 - 5 - 2 - 3 = 4.

14 - 5 - 2 - 3 = 4

Subtracting the known parts from the whole gives the missing part.

Answer: 4 points

4 · Reviewdoes it hold up?

Check the totals: East team would be 5 + 2 + 4 + 3 = 14, and West team is 16, which is 2 more — exactly matching the condition. Val's 4 is a sensible count, between 1 and 5 like the others.

Another way: Subtract the three known East team students from West team's total first (16 - 5 - 2 - 3 = 6), then subtract the extra 2 from the difference (6 - 2 = 4) to get Val.

Standardsmin grade 2

2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading each student's circle count from the two picture graphs.
2.OA.A.1 Solve one- and two-step word problems using addition and subtraction within 100 — Using 'team total' and the 2-more relationship with addition and subtraction to find Val.

💡Takeaway. This only needs Grade 2 graph-reading and add/subtract — find the totals, then fill the missing part!

Where next?

← Back to the problem: Read totals and differences from a graph