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Basic Algebra Foundations
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Basic Algebra Foundations
Show your working for solving questions. Use inverse operations to find unknown values.
Understanding Equations
1.What does the equals sign mean in the equation 8 + 3 = 11?
- The answer must come after it
- The expressions on both sides have the same value
- It tells you to add the numbers
2.Complete: 9 + 6 = .
3.Complete: 14 − = 8.
4.Complete: + 7 = 16.
5.Complete: 18 = 11 + .
Solving One-Step Equations
6.Solve x + 8 = 17. Show the inverse operation you use.
7.Solve 3p = 21. Show your working.
8.Solve r − 6 = 9. Show your working.
9.Solve 5k = 35. Show your working.
10.Select every equation that is true when x = 7.
- x + 4 = 11
- 2x = 14
- x − 3 = 5
- x + 2 = 10
Properties of Operations
11.Select each equation that shows the commutative property (changing the order of the terms or factors without changing the result).
- 6 × c = c × 6
- d + 9 = 9 + d
- 3(q + 2) = 3q + 6
- 8 + t = t + 8
12.Expand 3(a + 4).
13.Expand 5(b + 2).
14.Expand 2(c + 7).
15.Match each expression to its meaning.
- 4d
- m + 6
- 3(n + 2)
- p − 8
- Eight less than p
- Four times d
- Six more than m
- Three times the sum of n and 2
Visual Algebra
16.Use a sketch of algebra tiles or another clear model to represent x + 4 = 9. Label the value of x.
17.Draw a model showing two equal groups of n making 12 altogether. What is n?
18.In an equation, what does keeping both sides balanced mean when you solve it?
Challenge Questions
19.Wiremu had some shells. She gave 5 away and then had 12 left. Write an equation using s for the number of shells she started with, and find s.
20.Solve 4x + 3 = 23. Show your working.
21.Select all expressions equivalent to 5a + 10.
- 5(a + 2)
- 10 + 5a
- 5a + 4 + 6
- 5(a + 10)
22.A student says the solution to 2y = 18 is y = 9. Check the claim by substituting 9 for y, and state whether it is correct.
4 printable pages
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