Choosing mathematical tools

Question 1

Jamie measured a rectangular tabletop to be 9 cm long and 6 cm wide. He multiplies 9 × 6 = 54 cm². To check his work, he takes a ruler and a sheet of squared paper where each tiny square is 1 cm². Which statement correctly describes how he should verify the area?

Accepted Answer

Draw the rectangle with the measured sides on the grid and count only the whole squares that are completely inside; the count should be 54.

Answer

Count every square that the rectangle touches, even if it only covers a part of the square, and add them together; this will give a number larger than 54.

Answer

Simply multiply the number of squares along the length (9) by the number along the width (6) without drawing anything; the product is automatically the area.

Answer

Find the perimeter (9 + 6 + 9 + 6 = 30 cm) and then divide by 2; the result 15 cm² is the verified area.

Question 2

You measured a rectangle that is 5 cm long and 3 cm wide. After multiplying 5 × 3 you get 15 cm². Which method would best let you check this answer using a ruler and squared paper?

Accepted Answer

Draw the rectangle on squared paper and count the squares inside.

Answer

Do the multiplication again in your head.

Answer

Enter 5 × 3 into a calculator.

Answer

Write the numbers 5 and 3 on a list.

Question 3

Sam draws a rectangle on graph paper. The rectangle is 6 squares long and 4 squares high. He first finds the area by multiplying 6 × 4. To check his answer using the ruler and the squared paper, what should Sam do next?

Accepted Answer

Count how many small squares are inside the rectangle.

Answer

Add the lengths of all four sides together.

Answer

Use a calculator to multiply 6 × 4 again.

Answer

Measure the diagonal of the rectangle with the ruler.

Try three questions

Jamie measured a rectangular tabletop to be 9 cm long and 6 cm wide. He multiplies 9 × 6 = 54 cm². To check his work, he takes a ruler and a sheet of squared paper where each tiny square is 1 cm². Which statement correctly describes how he should verify the area?

You measured a rectangle that is 5 cm long and 3 cm wide. After multiplying 5 × 3 you get 15 cm². Which method would best let you check this answer using a ruler and squared paper?

Sam draws a rectangle on graph paper. The rectangle is 6 squares long and 4 squares high. He first finds the area by multiplying 6 × 4. To check his answer using the ruler and the squared paper, what should Sam do next?

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