Sensim Math · Depth 한국어

2-2 · Tables and Graphs

Complete a table from its graph and back

2.MD.D.103.MD.B.3 · take · grade 3

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

▶ Practice — 8 problems

Mr. Park's class surveyed the students' favorite fruits and recorded the results in a table and a picture graph. Complete both the table and the graph.

Number of students by favorite fruit (table)

Fruit Apple Tangerine Banana Grape Total
Number of students 55 33 1818

Number of students by favorite fruit (graph)

The vertical axis shows the number of students from 11 to 66, one student per cell, and the horizontal axis lists the fruits (apple, tangerine, banana, grape). Only the grape column has circles drawn, filling cells 1,2,3,41, 2, 3, 4 from the bottom (44 circles); the apple, tangerine, and banana columns are empty.

(1) How many circles are in the grape column, and so how many students like grapes?

(2) Find the number of students who like tangerines. (=18−5−3−□)(=18-5-3-\square)

(3) Complete both the table and the graph.

Number of students by favorite fruit (table) Fruit Apple Tang. Banana Grape Students 5 3 Total 18 Number of students by favorite fruit (graph) 1 2 3 4 5 6 Students Fruit Apple Tang. Banana Grape
Show solution

Understand

A favorite-fruit survey is shown in both a table and a picture graph. The table gives apple 5, banana 3, total 18, with tangerine and grape blank. The graph shows only grape drawn with 4 circles. I must complete both the table and the graph.

Givens
  • Table: apple = 5, banana = 3, total = 18; tangerine and grape blank.
  • Graph: grape column has 4 circles drawn (one circle = 1 student); apple, tangerine, banana columns empty.
Unknowns
  • Number who like grapes (from the graph).
  • Number who like tangerines (the missing table value).
  • The completed table and graph.
Constraints
  • Each circle stands for 1 student.
  • The four fruit counts must add to the total of 18.

Plan

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

The graph supplies the grape value the table is missing, and the table's total supplies the tangerine value the graph is missing. Moving each fact between the two representations and using the total fills in everything.

Execute

#15 Organize Information in More Ways 2.MD.D.10
The grape column has 4 circles, and one circle is one student, so 4 students like grapes. Write 4 in the grape cell of the table.
Counting the drawn circles transfers the grape count into the table.
#7 Identify Subproblems 2.OA.A.1
The four counts add to 18. Subtract the known ones: tangerine = 18 - 5 - 3 - 4 = 6 students.
18−5−3−4=618 - 5 - 3 - 4 = 6
Total minus the three known fruits leaves the tangerine count.
#15 Organize Information in More Ways 2.MD.D.10
Completed table: apple 5, tangerine 6, banana 3, grape 4, total 18. For the graph draw circles bottom-up: apple 5, tangerine 6, banana 3, grape 4.
5+6+3+4=185 + 6 + 3 + 4 = 18
Each table value becomes that many circles in its column, keeping the two views consistent.
Answer: Tangerine = 6 students (grape = 4); completed counts: apple 5, tangerine 6, banana 3, grape 4, total 18.

Review

The completed counts sum to 5 + 6 + 3 + 4 = 18, matching the given total, so the table and graph agree.

Add the three knowns first (5 + 3 + 4 = 12), then 18 - 12 = 6 for tangerine — same result.

Standards · min grade 2

  • 2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading grapes from the graph circles and drawing each completed count back onto the graph.
  • 2.OA.A.1 Solve one- and two-step word problems using addition and subtraction within 100 — Using the total of 18 with subtraction to find the missing tangerine count.
💡 This only needs Grade 2 graph-reading and subtraction — let the table and graph fill in each other!