Shapes, Space and Data
Primary 5 · Mathematics
Shapes, Space and Data
Lesson 3 of 3
14 min
Let's begin
Teacher asks the P5 class one simple question: how did you get to school today?
Thirty children shout at once. Walking! Bicycle! Moto! My uncle's car! It is noise, and nobody learns anything from noise.
So Keza goes to the board and starts making little marks. Ten minutes later the whole class can see the answer at a glance. Today you will learn how she did it — and how to squeeze a pile of numbers down into one number that speaks for all of them.
Data is just a collection of facts — here, thirty answers.
You cannot write fast enough to record thirty shouted answers in words, so you use tally marks. Each time somebody says a thing, you draw one short stroke next to it.
The clever part: when you reach the fifth stroke, you draw it across the other four, like a little gate. Now the marks are grouped in fives and you can count them in fives instead of one by one.
So 7 would be one gate of five, then two more strokes. And 12 would be two gates, then two more strokes.
Count each row of tallies and write the number down. That number is called the frequency — it means how many times.
| How you came to school | Frequency (number of children) |
|---|---|
| Walking | 18 |
| Bicycle | 6 |
| Moto | 4 |
| Car | 2 |
Always check your total: 18 + 6 + 4 + 2 = 30. There are 30 children in the class, so nobody has been lost or counted twice. If your total is wrong, count again before you draw anything.
A bar graph turns those numbers into bars, so that taller instantly means more.
With a scale of 1 square = 2 children: Walking is 9 squares tall (9 × 2 = 18), Bicycle is 3 squares (3 × 2 = 6), Moto is 2 squares (2 × 2 = 4), Car is 1 square (1 × 2 = 2).
Do the opposite. Put your finger on the top of a bar, slide it straight across to the number line, and read the value there.
Always check the scale first. If 1 square = 5 children and a bar is 6 squares tall, that bar means 6 × 5 = 30 children, not 6. Reading the squares instead of the scale is the commonest mistake there is.
On Mugisha's graph, one square stands for 4 mangoes. The bar for Tuesday is 7 squares tall. How many mangoes were sold on Tuesday?
7 squares × 4 mangoes per square = 28 mangoes.
A bar graph is perfect for comparing separate groups — walking against bicycle against moto.
But some data is not separate groups at all. It is one thing being watched as it changes: the midday temperature in Kigali on each day of the week, or the rainfall each month of the year, or a baby goat's weight month by month.
For that you use a line graph. Time goes along the bottom. You mark a dot for each measurement, then join the dots one after another with straight lines.
The joined line does something bars cannot: it shows you the journey. Where the line climbs, the thing is rising. Where it falls, the thing is dropping. Where it is flat, nothing changed.
The rule of thumb: separate groups → bar graph. One thing changing over time → line graph.
Four friends walk home past the mango trees. Uwase picks 3 mangoes, Keza picks 5, Gatete picks 6 and Mutesi picks 2.
That is unfair, and they know it. So they pile every mango into one basket and share them out again, equally.
Step 1: pile them up. 3 + 5 + 6 + 2 = 16 mangoes altogether.
Step 2: share them out. There are 4 friends: 16 ÷ 4 = 4 mangoes each.
If they had all picked the same number, they would each have picked 4. That fair-share number is called the mean, and it is the single number that stands for the whole group.
Mean = total of all the values ÷ how many values there are
Ishimwe's five maths marks are 8, 6, 9, 7 and 10. What is his mean mark?
Step 1 Add them all: 8 + 6 + 9 + 7 + 10 = 40.
Step 2 Count how many marks there are. Five.
Step 3 Divide: 40 ÷ 5 = 8.
His mean mark is 8. Notice it sits comfortably in the middle of his marks — not below the lowest, not above the highest. If your mean ever lands outside that range, you have made a mistake.
Umutoni spends 200 Frw, 350 Frw, 150 Frw and 300 Frw on four days. What is her mean spending per day?
Step 1 Total: 200 + 350 + 150 + 300 = 1,000 Frw.
Step 2 How many days? Four.
Step 3 1,000 ÷ 4 = 250 Frw a day.
She never actually spent exactly 250 Frw on any single day — and that is fine. The mean is not one of the real values. It is the fair-share value that stands for all of them.
The mean of Byiringiro's 5 test marks is 12. What did his marks add up to altogether?
The mean was made by dividing the total by 5. So to get the total back, do the opposite and multiply by 5.
Total = 12 × 5 = 60.
Tip
Mean = pile it up, then share it out
Add every value into one big pile. Count how many values went into the pile. Divide.
Then sanity-check: your mean must land between the smallest and the biggest value. A mean of 25 from the numbers 8, 6, 9, 7, 10 is impossible — you forgot to divide.
For graphs: read the scale before you read the bar. "1 square = 5" changes everything.
Work each one out first. The full answer is written under it.
Now collect your own data. Ask ten people at home or at school their favourite fruit, keep a tally, and draw the bar graph in your book. Give it a title and label both axes.
What you learned today
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