3. How Many Squares?
How many rectangles could you make?
Children are not expected to learn the definition of the term 'area', but develop a sense of the concept through suitable examples. Give them many opportunities in the classroom to compare things in terms of area and guess which is bigger. Things like stamps, leaves, footprints, walls of the classroom etc. can be compared.
Look at these interesting stamps
Collect some old stamps. Place them on the square grid and find their area and perimeter.
Guess
Trace your hand on the squared sheet on the next page.
How will you decide whose hand is bigger - your hand or your friend's hand?
What is the area of your hand? _______ square cm.
What is the area of your friend's hand? _______ square cm.
My Footprints
At this stage children need not count each square. Encourage them to identify the largest squares and rectangles within a footprint to know their area and then count small squares for irregular shapes. Though area of a rectangle will be done in chapter 11, some children may discover themselves that they can find the area faster through multiplication.
How Many Squares in Me?
In this exercise children are expected to notice the geometrical symmetry of the shapes to find out their area. Encourage children to evolve their own strategies. Rounding off is not needed in these examples.
Try Triangles
Help Sadiq in finding some more such triangles. Draw at least 5 more.
Complete the Shape
Suruchi drew two sides of a shape. She asked Asif to complete the shape with two more sides, so that its area is 10 square cm
Measure the side of a small square on the squared paper given below. Make as many shapes as possible using 5 such squares. Three are drawn for you.
Did you get all the 12 shapes using 5 squares?
Draw all the 12 shapes on a sheet of cardboard and cut them.
Try to arrange your 12 shapes in some other way to make a 10 * 6 rectangle. Could you do it?
Try another puzzle
You have to make a 5*12 rectangle with these 12 shapes. There are more than 1000 ways to do it. If you can find even one, that's great!
Here is a chessboard. Play this game with your partner, with one set of 12 shapes.
The first player picks one shape from the set and puts it on the board covering any five squares.
The other player picks another shape and puts it on the board, but it must not overlap the first shape.
Keep taking turns until one of you can't go any further.
Whoever puts the last piece wins!
Remember the floor patterns in Math-Magic Book 4 (pages117-119). You had to choose the correct tile which could be repeated to make a pattern so that there were no gaps left.
Encourage children to try to do these 'pentomino' puzzles at home. Such exercises can be designed for shapes with 6 squares (hexominoes) in which case there will be 35 different shapes possible.
Ziri went to a shop and was surprised to see the different designs of tiles on the floor.
Aren't these beautiful!
Can you find the tile which is repeated to make each of these floor patterns?
Circle a tile in each pattern.
After looking at the patterns Ziri wanted to make her own yellow tile. You too make a tile this way.
Step 1: Take a piece of cardboard or thick paper. Draw a square of side 3 cm on it.
Step 2: Draw a triangle on any one of the sides of this square.
Step 3: Draw another triangle of the same size on another side of the square. But this time draw it inside the square.
Step 4: Cut this shape from the cardboard. Your tile is ready! What is it's area?
Make a pattern using your tile. Trace the shape to repeat it on a page, but remember there must be no gaps between them.
Ziri made a pattern using her yellow tiles.(You know the area of her tile.)
Answer these --
Practice time
Ziri tried to make some other tiles. She started with a square of 2 cm side and made shapes like these.
Look at these carefully and find out:
In Class III and IV basic shapes like squares, rectangles, hexagons, triangles, circles etc were used to examine which of those can tile and which do not tile to make floor patterns. Children must now be able to modify basic shapes to create different tiling shapes. In the exercise above they may create new shapes out of a square that do not tile even though their area remains the same as that of the square from which they are made.