Count Equal Squares in Rows and Columns
Draw the stated rows and columns of equal squares.
About 15 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: A rectangle has four rows of three equal squares.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
A rectangle can be partitioned into equal squares with no gaps or overlap. Each row contains the same number of tiles when the grid is rectangular. Count all rows or add equal row counts; the outside rectangle is not another tile to include.
Draw the stated rows and columns of equal squares. Count one row, then add that count for every row. Verify that both row and column descriptions locate the same total tile set.
Draw all rows with the same number of columns. Count tiles, not grid intersections or the outside outline. Make a rectangular grid with the stated row and column counts.
- Make a rectangular grid with the stated row and column counts.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Draw the stated rows and columns of equal squares.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
A rectangle has four rows of three equal squares. Counting 3+3+3+3 gives twelve squares. Counting columns gives four in each of three columns, also twelve. The twelve tiles cover the rectangle; the whole outline does not add a thirteenth tile. Draw all rows with the same number of columns. Count tiles, not grid intersections or the outside outline. Make a rectangular grid with the stated row and column counts.
Check your reasoning
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Helpful tips
- Draw all rows with the same number of columns.
- Count tiles, not grid intersections or the outside outline.
See the answer and explanation
6
Count all equal squares across the complete rows. The result is 6.
Take it further
Four rows of five equal squares contain 20 squares.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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