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Balancing Equations Activity

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Balancing Equations Activity

Solve each equation by keeping both sides equal. Show your working where asked.

Understanding equality

1.What does the equal sign tell you in the statement 9 + 4 = 8 + 5?

The calculation on the left must be done first
The expressions on each side have the same value
The numbers on the left should be added to the right
The answer is always written on the right

2.A balance has 3 identical x-tiles and 4 unit tiles on the left pan, and 19 unit tiles on the right pan. Write an equation to represent the balanced scale.

3.Select every statement that is correct about an equation.

Both expressions have the same value
Adding the same amount to both sides keeps the equation balanced
The equal sign means that the next number is the answer
Subtracting the same amount from both sides keeps the equation balanced

Solve one-step equations

Use an inverse operation to find the value of the variable.

4.Solve x + 8 = 21.

5.Solve 6y = 42.

6.Solve m − 9 = 14.

7.Solve p ÷ 5 = 7.

8.For the equation 4 + n = 15, state the inverse operation used to isolate n and give the value of n.

Reasoning with equations

9.Match each equation to its solution.

a + 6 = 17
b − 3 = 9
5c = 20
d ÷ 4 = 3

10.Tane says 7 + 5 = 6 + 6 is true because both sides have a value of 12. Is Tane correct? Explain using the values of both sides.

11.Complete the sentence using the words equal, inverse and unknown: To solve an equation, find the value.

12.Complete the sentence using the words equal, inverse and unknown: Both sides of an equation must be .

13.Complete the sentence using the words equal, inverse and unknown: An operation can undo the operation applied to the variable.

Challenge

14.Write three different true equations that each have a solution of x = 10. Use a different operation in each equation: addition, subtraction and multiplication.

15.Finn solves 3x + 2 = 17 by subtracting 2 from both sides, then dividing both sides by 3. What value does she get for x? Show the two balanced equations in her working.