Sensim Math · Depth 한국어

3-2 · Data Organization

Determine the value each picture symbol stands for

3.MD.B.3 · take · grade 3

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

▶ Practice — 8 problems

The pictograph shows how much milk the students in Mia's group drank during one week. If Hazel drank 2500 mL2500\ \text{mL} of milk during the week, how many milliliters of milk did all of the students in Mia's group drink during the week altogether?

Milk Each Student Drank

Name Amount of Milk
Mia 22 large symbols, 44 small symbols
Owen 33 large symbols, 33 small symbols
Hazel 55 large symbols
Caleb 44 large symbols, 22 small symbols

In the pictograph, one large symbol stands for an unknown amount, and one small symbol stands for 100 mL100\ \text{mL}.

Milk Each Student Drank Name Amount of Milk Mia Owen Hazel Caleb = unknown amount = 100 mL
Show solution

Understand

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

Givens
  • Symbols (large + small): Mia 2 + 4, Owen 3 + 3, Hazel 5 + 0, Caleb 4 + 2.
  • 1 small carton = 100 mL; 1 large carton = unknown.
  • Hazel drank 2500 mL (her row is 5 large cartons).
Unknowns
  • The total milk all four students drank, in mL (after finding the large-carton value).
Constraints
  • Each large carton has the same fixed value.
  • Hazel's 5 large cartons 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 carton, then total each student and add. Each student's amount is a small subproblem.

Execute

#11 Work Backwards 3.MD.B.3
Hazel's 5 large cartons equal 2500 mL, so one large carton is 2500 / 5 = 500 mL.
2500÷5=500 mL2500 \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 carton and 100 mL per small carton. Mia: 2x500 + 4x100 = 1400. Owen: 3x500 + 3x100 = 1800. Hazel: 2500. Caleb: 4x500 + 2x100 = 2200.
1400, 1800, 2500, 2200 mL1400,\ 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 mL1400 + 1800 + 2500 + 2200 = 7900\ \text{mL}
Combining the four totals is an addition within the thousands using place value.
Answer: 7900 mL

Review

Each student drank between 1400 and 2500 mL, so four students should total roughly 4 x 2000 = 8000 mL; 7900 mL is right in that range. Counting all large cartons (14 x 500 = 7000 mL) plus all small cartons (9 x 100 = 900 mL) also gives 7900 mL.

Organize differently (tool 15): add all large cartons (14 x 500 = 7000) and all small cartons (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-carton value from Hazel's row and reading each student's amount.
  • 3.NBT.A.2 Fluently add and subtract within 1000 — Adding the four students' amounts to get the grand total.
💡 Use Hazel's row to learn one big carton is 500 mL, then add everyone up - Grade 3 graph reading!