Fractions, Shapes and Data
Primary 3 · Mathematics
Fractions, Shapes and Data
Lesson 3 of 3
13 min
Let's begin
"Which fruit do you like best?" asks the teacher. Twenty-seven hands shoot up at once, everybody shouting mango, banana, avocado!
Nobody can remember all that noise. So the teacher picks up the chalk and starts drawing little lines on the board. Those little lines are called tally marks, and they are about to make your life much easier.
A tally mark is just a straight line: |
Every time somebody says "mango", you draw one line. Three mango lovers gives you | | |
But if 27 children answer, you end up with a long fence of lines and you will lose your place counting them.
Here is the trick everybody uses. You draw four lines standing up. Then the fifth line lies down across the other four, like a stick tying a bundle of firewood.
That bundle is worth 5. On this screen we cannot lean a line over, so we will write a full bundle of five like this:
||||/
Four standing lines and the fifth one crossing them. Whenever you see ||||/, count 5.
Now counting is fast, because you count the bundles in fives and then add the loose lines at the end.
Here is the board after all 27 children in the P3 class have answered.
| Fruit | Tally | Number |
|---|---|---|
| Mango | ||||/ ||||/ | | 11 |
| Banana | ||||/ ||| | 8 |
| Avocado | ||||/ | 5 |
| Pineapple | ||| | 3 |
Check the mango row with me. There are 2 bundles and 1 loose line.
Count the bundles in fives: 5, 10. Now count on the loose line: 11.
Check the banana row: 1 bundle and 3 loose lines. 5... then 6, 7, 8.
And look at pineapple: only 3 lines, so no bundle at all. You only tie a bundle when you reach 5.
Numbers in a table are correct, but they are not exciting. A picture graph lets you see the answer in one glance. You draw one picture for each thing counted.
Let one star stand for one child.
| Fruit | Children (each ★ = 1 child) |
|---|---|
| Mango | ★★★★★★★★★★★ |
| Banana | ★★★★★★★★ |
| Avocado | ★★★★★ |
| Pineapple | ★★★ |
You did not have to read a single number to know that mango wins. The longest row wins!
A good picture graph always has three things:
Now the graph works for you. Look at it and answer:
Which fruit is the class favourite? Mango. Its row is the longest, with 11 stars.
Which fruit is the least popular? Pineapple. Its row is the shortest, with only 3 stars.
How many more children chose mango than banana? This word more means take away. 11 - 8 = 3 children.
How many children voted altogether? Add every row: 11 + 8 = 19, then 19 + 5 = 24, then 24 + 3 = 27 children. That matches the class size, so we know nobody was missed.
Imagine 20 children love mango. Drawing 20 stars takes forever. So we make each star worth more:
Key: each ★ = 2 children.
Now 20 children need only 10 stars, because 10 × 2 = 20.
And it works backwards too. If the banana row has 4 stars and each star is worth 2 children, then 4 × 2 = 8 children chose banana.
So always, always read the key first. The same 4 stars can mean 4 children or 8 children. Only the key knows.
Tip
Count tallies in fives, then count on. Point at each bundle and say 5, 10, 15... then add the loose lines one by one.
And read the key before you read the graph. A star is only worth what the key says it is worth.
On her walk to school, Umutoni counted the animals she passed. Here is her tally.
| Animal | Tally |
|---|---|
| Cow | ||||/ || |
| Goat | ||||/ ||||/ |
| Chicken | |||| |
| Dog | || |
How many goats did she see?
Answer: 10. Two bundles: 5, 10.
How many chickens did she see?
Answer: 4. There are four lines but no line crossing them, so it is not a bundle of 5.
Which animal did she see the most of?
Answer: goats, with 10. Cows come second with 7 (5 and then 6, 7).
How many more goats than cows?
Answer: 3. Goats 10, cows 7, and 10 − 7 = 3.
Umutoni draws a picture graph where each ★ = 2 animals. How many stars must she draw in the goat row?
Answer: 5 stars, because 5 × 2 = 10 goats.
How many animals did she count altogether?
Answer: 23. 7 + 10 = 17, then 17 + 4 = 21, then 21 + 2 = 23.
What you learned today
Quick check
How many does this tally show? ||||/ ||||/ |||
