Grade by Grade
C. Algebra · Patterns, Equality and Coding

Equal and Not Equal: Keeping the Balance

C2.2 C2.3About 35 minutes
Learning goals
  • I know that the equal sign (=) means the same amount as.
  • I can tell if two addition or subtraction expressions are equal or not equal.
  • I can use the not equal sign (≠).
  • I can find a missing number to make both sides balance.
  • I can show the same number in different ways, up to 50.

Words to know

equal
The same amount.
equal sign =
A sign that means is the same amount as.
not equal sign ≠
A sign that means is not the same amount as.
expression
Numbers joined with + or −, like 3 + 2 or 7 − 1.
balance
When both sides have the same amount, so neither side is heavier.
equivalent
Worth the same amount, even if it looks different.

The seesaw game

Have you been on a seesaw? If two friends are the same weight, the seesaw stays level. It balances. If one side is heavier, that side goes down.

The equal sign (=) works like a balanced seesaw. It tells us that the amount on the left side is the same as the amount on the right side.

An empty wooden seesaw in a park, sitting perfectly level.
When a seesaw is level, both sides balance, just like the two sides of an equal sign. AI-generated image
3 + 24 + 1
3 + 2 is 5. 4 + 1 is 5. Both sides are the same, so the scale is balanced: 3 + 2 = 4 + 1.

Big idea

The equal sign does not mean the answer comes next. It means the same amount as.

So all of these are true:

  • 5 = 3 + 2
  • 3 + 2 = 5
  • 3 + 2 = 4 + 1
  • 5 = 5

Not equal

If the two sides are different amounts, they are not equal. We use the sign ≠. It is an equal sign with a line through it.

6 + 3 ≠ 10 − 2 because 6 + 3 is 9 and 10 − 2 is 8. 9 and 8 are not the same.

6 + 310 − 2
6 + 3 is 9. 10 − 2 is 8. The side with 9 is heavier and goes down. 6 + 3 ≠ 10 − 2.
Worked example

Equal or not equal?

Is 5 + 3 equal to 6 + 2?

  1. Work out the left side: 5 + 3 = 8.
  2. Work out the right side: 6 + 2 = 8.
  3. Compare: 8 and 8 are the same.

Equal! 5 + 3 = 6 + 2

🍎🍎🍎🍎🍎🍏🍏🍏🍊🍊🍊🍊🍊🍊🍋🍋
Left side: 5 red apples and 3 green apples make 8. Right side: 6 oranges and 2 lemons make 8. Both sides have 8 pieces of fruit.
Worked example

Addition and subtraction

Is 7 − 2 equal to 4 + 1?

  1. Left side: start at 7 and take away 2. 7 − 2 = 5.
  2. Right side: 4 + 1 = 5.
  3. 5 and 5 are the same.

Equal! 7 − 2 = 4 + 1

Worked example

A smart shortcut

Is 4 + 6 equal to 6 + 4?

  1. Both sides use the same two numbers, 4 and 6.
  2. You can add numbers in any order and get the same total. 4 + 6 = 10 and 6 + 4 = 10.

Equal! 4 + 6 = 6 + 4. Switching the order of numbers you add does not change the total.

Finding the missing number

Sometimes one number is hidden. Find it so both sides balance!

Worked example

Make it balance

4 + ___ = 3 + 5

  1. Work out the side you know: 3 + 5 = 8.
  2. Now the left side must also make 8: 4 + ___ = 8.
  3. Count on from 4 to 8: 5, 6, 7, 8. That is 4 more.
  4. Check: 4 + 4 = 8 and 3 + 5 = 8. Balanced!

The missing number is 4. 4 + 4 = 3 + 5

012345678910+4
From 4, it takes a jump of 4 to get to 8.

Same number, different ways

A number can be shown in many equivalent ways. They all look different, but they are all worth the same.

Here are some ways to show 25:

  • 20 + 5
  • 10 + 10 + 5
  • 5 + 5 + 5 + 5 + 5
  • 30 − 5
  • 2 tens and 5 ones
25 is 10 + 10 + 5.
Worked example

Money that is equal

A toonie is worth 2 dollars. A loonie is worth 1 dollar. How many loonies equal 3 toonies?

  1. 1 toonie = 2 loonies.
  2. 3 toonies = 2 + 2 + 2 loonies.
  3. 2 + 2 + 2 = 6.

3 toonies = 6 loonies. Both are worth 6 dollars.

Worked example

Bigger numbers

Is 20 + 10 equal to 15 + 15?

  1. Left side: 20 + 10. Two tens and one more ten is 3 tens = 30.
  2. Right side: 15 + 15. 10 + 10 = 20, and 5 + 5 = 10. 20 + 10 = 30.
  3. 30 and 30 are the same.

Equal! 20 + 10 = 15 + 15

Your turn

1

Equal or not equal? 2 + 6 and 4 + 4

2

Equal or not equal? 9 − 3 and 5 + 2

3

Equal or not equal? 10 − 5 and 1 + 4

4

True or false? 7 = 7

5

True or false? 6 = 2 + 3

6

Find the missing number: 5 + ___ = 4 + 6

7

Find the missing number: 20 + 10 = ___ + 15

8

Write 2 different ways to make 40.

Just for fun

Why is the equal sign so calm?

Because it always keeps things balanced!

Hands-on activity

Make a hanger balance

You need: a clothes hanger, 2 paper cups, string or tape, and many objects that are all the same (like paper clips, LEGO bricks of one size, or dry pasta pieces).

  1. Hang the two cups from each end of the hanger. Hang the hanger on a doorknob.
  2. Put 3 paper clips and then 2 more in the left cup.
  3. Put 4 paper clips and then 1 more in the right cup.
  4. Does it balance? (It should! 3 + 2 = 4 + 1.)
  5. Now try 6 + 1 on one side and 3 + 2 on the other. Which side goes down? Why?
  6. Make up your own equal and not equal puzzles for a grown-up to solve.

Math talk

Ask: How do you know the two sides are equal? Can you prove it a different way? You might count, draw, use a ten frame, or use a fact you already know.

More practice: warm-up

1

Equal or not equal? 3 + 3 and 5 + 1

2

True or false? 9 = 4 + 5

3

Which sign goes in the box, = or ≠? 2 + 2 ☐ 5

4

Count each side. Are they equal?

Left: 🍎🍎🍎 🍎🍎

Right: 🍊🍊🍊🍊 🍊

5

Find the missing number: 5 = 3 + ___

More practice: on your own

1

Equal or not equal? 10 − 4 and 3 + 3

2

Equal or not equal? 8 + 1 and 10 − 3

3

Find the missing number: ___ + 3 = 2 + 6

4

Find the missing number: 10 + 10 = 25 − ___

5

A toonie is worth 2 dollars and a loonie is worth 1 dollar. Is 1 toonie and 1 loonie equal to 3 loonies?

Challenge

1

Find the mistake! Kim wrote 13 in the blank: 4 + ___ = 3 + 6. What did she do wrong? What is the right answer?

2

Write 3 different ways to make 20. Then use two of them to write a true equation with =.

3

Plate A has 🍪🍪🍪🍪🍪🍪 and Plate B has 🍪🍪🍪🍪. How many cookies should you move from Plate A to Plate B so the plates are equal? Explain.

Check your understanding

Quiz

1.

What does the = sign mean?

2.

Which is true?

3.

Which sign goes in the box? 8 − 1 ☐ 4 + 4

4.

Find the missing number: 6 + ___ = 5 + 3

5.

Which is not a way to make 30?

6.

Which is true?

7.

Find the missing number: 10 + ___ = 5 + 15

For parents and teachers

Many children (and adults!) believe the equal sign means write the answer here. That makes problems like 4 + ___ = 3 + 5 or 7 = 7 very confusing. This lesson builds the correct idea: = means the same amount as, like a balanced scale.

Common mistakes

  • Writing 8 in 4 + ___ = 3 + 5 (adding 3 + 5 and stopping). Ask: Is 4 + 8 the same amount as 3 + 5?
  • Saying 5 = 3 + 2 is "backwards" or wrong. Show both sides with objects: they balance.
  • Adding all the numbers on both sides together. Cover one side with a hand and work out each side separately.

How to help

  • Use a pan balance, a hanger balance or a seesaw at the park.
  • Use loonies and toonies: Is 1 toonie equal to 2 loonies? Is it equal to 3 loonies?
  • Write puzzles on sticky notes: Is 6 + 1 equal to 5 + 2? and let your child prove it with objects.