Read totals and differences from a graph

2.MD.D.103.MD.B.3 · take · grade 3

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

Liam's team and Mia's team took part in a team quiz match, and the number of questions 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 $5$ , and 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 $2$ , and 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.

Show solution

Understand

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 correct; 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.

Plan

#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 three known Mia-team students to leave Jordan. Reading each circle count straight off the graph supports every step.

Execute

#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.

#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.

#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

Review

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.

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

Standards · min 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.

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