Sensim Math · Depth 한국어

4-1 · Bar Graphs

Combine two graphs to find totals

3.MD.B.34.OA.A.3 · adapt · grade 4

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

▶ Practice — 8 problems

Mr. Park's class surveyed the number of each snack they bought at the school store and the price of one of each snack. The results are shown in the two bar graphs below. Find how much money the class spent buying bread.

Number of snacks bought (unit: items)

Snack Crackers Juice Bread Ice cream
Count 1212 1414 1616 1010

Price of one snack (unit: dollars)

Snack Crackers Juice Bread Ice cream
Price $1.00\$1.00 $0.80\$0.80 $0.70\$0.70 $1.20\$1.20

The data are shown as two bar graphs. The first (horizontal) bar graph shows how many of each snack were bought; the second (vertical) bar graph shows the price of one of each snack in dollars.

Number of Snacks Bought 0 10 20 Count (items) Crackers Juice Bread Ice cream Price of One Snack $0 $0.50 $1.00 Crackers Juice Bread Ice cream
Show solution

Understand

Two bar graphs give, for each snack, how many were bought and the price of one snack. We must find the total money spent on bread by combining bread's count with bread's unit price.

Givens
  • Counts bought: crackers 12, juice 14, bread 16, ice cream 10.
  • Prices each: crackers 1.00,juice1.00, juice0.80, bread 0.70,icecream0.70, ice cream1.20.
  • We want the money spent on bread only.
Unknowns
  • The total amount of money the class spent buying bread.
Constraints
  • Bread count and bread price must come from the same snack (bread).
  • Total cost = number bought times price of one.

Plan

#8 Analyze the Units · also uses: #7 Identify Subproblems

The two graphs supply different units - items and dollars-per-item - and linking the right bread values multiplies to dollars. Checking units (items times dollars/item = dollars) confirms the setup, and reading the matching bread bars is the key subproblem.

Execute

#7 Identify Subproblems 3.MD.B.3
From the 'number of snacks bought' graph, bread was bought 16 times.
bread count=16\text{bread count} = 16
The bread bar in the count graph reaches 16 items.
#7 Identify Subproblems 3.MD.B.3
From the 'price of one snack' graph, one bread costs $0.70.
bread price=$0.70\text{bread price} = \$0.70
The bread bar in the price graph reaches 70 cents per item.
#8 Analyze the Units 4.OA.A.3
Total money = number of breads times price of one bread. Units: 16 items times $0.70 per item gives dollars. Compute 16 times 0.70.
16×$0.70=$11.2016 \times \$0.70 = \$11.20
Multiplying a count by a price-per-item always gives total cost in dollars.
Answer: $11.20

Review

16 breads at about 0.70eachshouldbeabitover16times0.70 each should be a bit over 16 times0.70 = 11.20;estimating16times11.20; estimating 16 times0.75 = 12confirms12 confirms11.20 is in the right range and the units are dollars.

Identify subproblems / repeated addition (tool 7): add 0.70sixteentimes,orcompute10breads=0.70 sixteen times, or compute 10 breads =7.00 plus 6 breads = 4.20,totaling4.20, totaling11.20.

Standards · min grade 4

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the bread count and bread unit price from the two bar graphs.
  • 4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Multiplying the bread count by the bread unit price to get the total money spent.
💡 Pull bread's number from one graph and bread's price from the other, then multiply count times price - linking two graphs is just Grade 4 cost = number times price!