Sensim Math · Depth 한국어

2-2 · Measuring Length

Cut a rectangle into a grid of cards

2.G.A.23.MD.C.7 · adapt · grade 3

Archetype: Tile and Cut Figures with Congruent Pieces · step in a 5-type progression

▶ Practice — 8 problems

A rectangular sheet of paper is 30 cm30\ \text{cm} wide and 20 cm20\ \text{cm} tall. It is cut into identical squares that are each 5 cm5\ \text{cm} on a side.

Find the total number of identical squares that can be made.

5 cm 5 cm 30 cm 20 cm
Show solution

Understand

A 30 cm by 20 cm rectangular sheet is cut into identical 5 cm squares. We need the total number of squares.

Givens
  • The sheet is 30 cm wide and 20 cm tall.
  • Each square is 5 cm on a side.
  • The figure shows the sheet divided into a 6-by-4 grid of 5 cm squares.
Unknowns
  • The total number of identical 5 cm squares cut from the sheet.
Constraints
  • Squares tile the rectangle exactly (5 divides both 30 and 20 evenly), with no leftover.

Plan

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

Break it into two subproblems: how many squares fit across the width, and how many fit down the height. Then a rows-times-columns array gives the total, matching the grid in the figure.

Execute

#7 Identify Subproblems 2.G.A.2
The width is 30 cm and each square is 5 cm wide, so divide to find the columns.
30÷5=630 \div 5 = 6
Partitioning a length into equal 5 cm pieces is a Grade 2 measurement idea.
#7 Identify Subproblems 2.G.A.2
The height is 20 cm and each square is 5 cm tall, so divide to find the rows.
20÷5=420 \div 5 = 4
Same partitioning idea applied to the vertical side gives the number of rows.
#7 Identify Subproblems 3.MD.C.7
The squares form a 6-column by 4-row array, so multiply to count them all.
6×4=246 \times 4 = 24
An array of equal squares is counted by multiplication, just like finding area in unit squares.
Answer: 24 squares

Review

The figure shows exactly 6 columns and 4 rows; counting the grid cells gives 24, confirming the array. The unit (squares, a count) matches the question.

Use area (tool 8, Analyze Units): total area 30x20 = 600 cm^2, each square 5x5 = 25 cm^2, and 600 / 25 = 24.

Standards · min grade 3

  • 2.G.A.2 Partition a rectangle into rows and columns of same-size squares — Finding how many 5 cm squares fit along the width and height.
  • 3.MD.C.7 Relate area to multiplication and addition operations — Counting the full grid of squares as a rows-by-columns array.
💡 Count squares across and down, then multiply — the same row-by-column array thinking behind area!