Minds On

How many will fit?

Explore the following image. What do you notice? What do you wonder?

A square is beside a rectangle. They are the same height. The rectangle is 3 squares longer than the individual square

How many squares do we need to completely cover the rectangle?

How do you know?

How could you check?

Press ‘Answer’ to find out how many squares are needed to cover the rectangle.

4 squares are needed to cover the rectangle.

We could guess how many are needed.

Or we could measure by using cut-outs of the small square.

A square is beside a rectangle. The rectangle is covered by 4 transparent squares.

Action

Measuring how much space

When we examine different shapes and objects, one thing we can measure is how much surface there is!

A gift box with two of its sides highlighted. 2 arrows point to the highlighted sides and a label says “faces of an object are surfaces”

Surface is the amount of space that makes up the faces of a shape or object.

We can use everyday shapes and items to help us measure how much surface an object has.

Let’s explore!

Examine the following image.

How many small squares do we need to completely cover the large rectangle?

A square is beside a rectangle. It is half as tall as the rectangle. The rectangle is 4 squares longer than the individual square

You may use the following activity to help you answer. Count as you place a blue square over each of the dark purple squares.

Press ’Answer’ to learn how many squares are needed to cover the rectangle.

10 squares are needed to cover the rectangle.

  • 5 squares can cover the top of the rectangle
  • 5 squares can cover the bottom of the rectangle
A 7 by 7 grid with 10 squares highlighted. The highlighted squares are in 2 rows of 5 squares each and form a rectangle

Choosing a measuring tool

When choosing a tool to measure the surfaces of objects there are a few things we need to know.

Let’s examine the image and learn!

When measuring the surface of an object, the items we are using need to be placed side by side, without overlapping, and without leaving any space or gaps between them. The items we use to measure an object must also be the same size and shape. For example, we can measure a rectangle using another shape, like a square. But we can’t measure a rectangle using several different shapes at once. Finally, the items we use to measure a shape need to cover the shape without going outside of it. An example is shown of 5 squares lined up inside a rectangle, covering the bottom half of the rectangle. The squares do not go beyond the edges of the rectangle.

Try it

Let’s guess!

How many squares can fit inside the rectangle shape? Some squares have already been placed to help you answer.

A rectangle is partially covered by 6 squares: 3 squares cover the top section, and 4 squares cover the left side of the rectangle.

Press ’Answer’ to learn how many squares are needed to cover the rectangle.

12 squares are needed to cover the rectangle.

  • 4 squares can cover the left side
  • 4 squares can cover the middle
  • 4 squares can cover the right side

4 squares + 4 squares + 4 squares = 12 squares total!

A rectangle covered with 12 squares

Consolidation

Let’s help Teacher A!

Teacher A wants to cover their bulletin board with pieces of square construction paper.

There are many colours to choose from.

The paper is all the same size though!

Can you help them find out how many total pieces of paper they will need to cover the whole bulletin board? You may use any colours that you like!

Use the following activity to help you answer or another method of your choice. Count as you place each square on the bulletin board.

Student Success

Think

How many pieces of paper did it take to cover the whole bulletin board?

Could we cover the bulletin board with something other than paper?

Record your thinking using a method of your choice.

Reflection

How do you feel about what you have learned in this activity? Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

I feel...

Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.