Groups, Sharing and Halves
Primary 2 · Mathematics
Groups, Sharing and Halves
Lesson 1 of 3
13 min
Let's begin
At Kimironko market, Mugisha helps his aunt sell avocados. She does not throw them in a heap. She makes tidy little piles, and every pile has 2 avocados in it.
A customer asks, "How many avocados do you have?" Mugisha starts counting one by one. His aunt laughs. "There is a faster way," she says. Today you will learn it too.
Groups are equal when every group has the same number of things.
Mugisha made 3 piles. Each pile has 2 avocados:
pile 1: 2 avocados pile 2: 2 avocados pile 3: 2 avocados
Every pile has 2. So these are equal groups. We say: 3 groups of 2.
Now count the avocados, but jump 2 at a time:
2... 4... 6.
Mugisha has 6 avocados. He did not count to six one by one. He counted only three times!
Another way to say 3 groups of 2 is to add 2 three times:
2 + 2 + 2 = 6
That works. But look what happens with 6 piles of 2. You would have to write:
2 + 2 + 2 + 2 + 2 + 2 = 12
That is a long sentence for such a small idea. Mathematicians got tired of writing it. So they made a shorter way.
The sign × means groups of. We read it as times.
Instead of 2 + 2 + 2 = 6, we write:
3 × 2 = 6
Read it out loud: three times two equals six. It means three groups of two.
The first number tells you how many groups. The second number tells you how big each group is.
So the long one becomes short:
6 × 2 = 12
Same answer. Much less writing.
To find the 2 times facts, just count in twos. Use your fingers and say them:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
Here it is at work. There are 7 desks in the classroom. 2 children sit at each desk. How many children?
Count in twos, seven times: 2, 4, 6, 8, 10, 12, 14.
So 7 × 2 = 14 children.
Now count in fives. One open hand is 5 fingers, so this one is easy to see:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
Look at the last digit of every answer: 5, 0, 5, 0, 5, 0... A 5 times answer always ends in 5 or in 0. That is a good way to check yourself.
Try one. Keza buys 4 mandazi. Each mandazi costs 5 Frw. How much does she pay?
Count in fives, four times: 5, 10, 15, 20.
So 4 × 5 = 20. Keza pays 20 Frw.
This is the friendliest table of all. Count in tens:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100.
Do you see the secret? The answer is your number with a 0 stuck on the end. 6 becomes 60. 9 becomes 90.
Umutoni buys 6 sweets. Each sweet costs 10 Frw. She pays 6 × 10 = 60 Frw.
Picture 2 rows of 5 beans:
2 × 5 = 10
Now turn the paper sideways. The very same beans are now 5 rows of 2:
5 × 2 = 10
Nothing was added and nothing was taken away, so the answer cannot change. 2 × 5 and 5 × 2 both make 10.
This is useful, because it means you can pick the easier way to count.
Take 2 × 9. Counting in nines is hard. So swap it round and do 9 × 2 instead: count in twos nine times. 2, 4, 6, 8, 10, 12, 14, 16, 18.
So 2 × 9 = 18 and 9 × 2 = 18. You are allowed to swap whenever it helps you.
Tip
Skip-count on your fingers. Put up one finger each time you say a number. For 4 × 5, say "5, 10, 15, 20" and stop when 4 fingers are up. The last number you said is the answer: 20. That works for the 2s, the 5s and the 10s.
Skip-count on your fingers. Do not rush. Then tap Show answer to check.
Write 5 + 5 + 5 as a times sentence.
Answer: 3 × 5 = 15. There are three groups, and each group is 5.
6 × 2 = ?
Answer: 12. Count in twos six times: 2, 4, 6, 8, 10, 12.
8 × 10 = ?
Answer: 80. Stick a 0 on the end of the 8.
Ishimwe carries 3 bunches of bananas. Each bunch has 5 bananas. How many bananas?
Answer: 15 bananas. 3 × 5 = 15. Count 5, 10, 15.
Gatete says 7 × 5 = 34. Is he right?
Answer: No. A 5 times answer must end in 5 or 0, and 34 ends in 4. Count in fives seven times: 5, 10, 15, 20, 25, 30, 35. The answer is 35.
What you learned today
Quick check
4 groups of 5. How do you write it?
