4 · Balancing Equations
See an equation as a balance scale: whatever you do to one side, do to the other.
What your child learns
- Both sides of an equation are equal
- Use inverse operations to isolate the variable
- Keep the balance by changing both sides the same way
Example
x + 3 = 8 → take 3 from both sides → x = 5.
Mini lesson: Equality & Balancing
Goal: Understand an equation as a balance: whatever you do to one side, do to the other.
- Adding, subtracting, multiplying or dividing both sides by the same number keeps it true.
- Use the inverse (opposite) operation to get the letter on its own.
Worked example
Solve x + 4 = 9 with a balance.
- Left: x and 4 coins. Right: 9 coins.
- Take 4 coins from BOTH sides.
- x = 5
Common mistakes
- Changing only one side.
- Using the same operation instead of the opposite one.
Practice questions
A taste of the questions in BloomTracks – the app makes fresh ones every time and adjusts the level as your child answers.
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Question 1 · Level 1
The scale is balanced. Each purple box is x and each coin is 1. What is x?
Show the answer
Answer: 6
x + 1 = 7. Remove 1 from each side: x = 6.
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Question 2 · Level 3
The scale is balanced. What is x?
Show the answer
Answer: 4
2x + 2 = 10 → 2x = 8 → x = 4.
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Question 3 · Level 5
x + y = 19 and x = y + 1. What is x?
Show the answer
Answer: 10
2y + 1 = 19 → y = 9 → x = 9 + 1 = 10.
Try it at home
Use a kitchen scale or two hands to 'balance' objects.
Key takeaway
An equation stays true as long as you treat both sides fairly.
Practise 4 · balancing equations with Bloomie
Bloomie reads every question aloud, listens to spoken answers and adapts the difficulty one question at a time.