4.1 Investigate and approximate the area of polygons

Mathematics

Grade 4

Space and shape, patterns, data handling

Module 14

Investigate and approximate the area of polygons

Activity 1:

To investigate and approximate the area of polygons (using square grids and tiling) in order to develop an understanding of square units [LO 4.8]

• You know that when we tessellate, a flat space is completely covered without any overlapping and without spaces being left.

1. Square blocks covered by your hand.

1.1 On the grid paper below, carefully place your hand with the fingers spread out. Trace around your hand with your pencil, stopping at the wrist. Lift your hand. You will see a beautiful outline of your hand. We want to find out how many square blocks your hand covers.

1.2 Put a dot in each full block as you count it, and write down the total number of full blocks covered by your hand in the table on the next page. Now look for places where half a block is covered. Two half blocks will make a whole block, so put a dot in each and count them as one whole block. Write down the total. Now combine those less than a half with those more than a half to make more wholes. Write down that total. Now add the totals. That should give you an approximate idea of how many blocks are covered by your hand.

Square blocks covered by my hand.

1.3 Now colour in the shape of your hand on the paper.

2. Count the square blocks covered by the following shape in the same way. First count the whole blocks. Then combine bits to make whole blocks. (Put dots in the blocks as you count them, if it helps.)

Total number of blocks covered: …………………. square blocks.

3. Count the blocks covered by the following polygons:

3. 1 _________ square blocks

3.2 _______________square blocks

Measure the square blocks with your ruler. They are 1 cm long and 1 cm wide, so instead of calling them “square blocks”, we can call them SQUARE CENTIMETRES.

4. Now find the number of square centimetres covered by each of the following polygons:

4.1_____________ square cm

4.2_______________ square cm

5. Let’s pretend that you have made a doll’s house for a younger cousin. You have covered the floor of the bathroom with paper on which you have drawn 1 cm square blocks. There is a bath mat on the floor as shown below. How many of the tiles are covered by the bath mat?

• Explain to a friend how you calculated your answer.
• Write down how you calculated your answer. Also write down your answer. Remember to write “square cm” with your answer. 6. In the family room there is a mat that is 4 m long and 3 m wide.

6.1 Draw a diagram to show what the mat looks like and label the length and the width.

6.2 Calculate how many square metres of floor are covered by the mat. Write down your calculation and the answer. Remember to write “square metres” with the answer.

6.3 Now draw blocks on your diagram so that it is four blocks long and three blocks wide. Check your answer for 6.2.

7. Dad uses 36 square tiles to tile the floor of a square braai area. He starts to tile the floor by placing 6 tiles next to each other along the edge of this floor.