Math · Unit 11

Pre-Algebra

Variables, expressions, order of operations and equations

Algebra begins the moment a letter stands in for a number, and the conceptual jump is from calculating an answer to describing a relationship.

The unit covers variables and expressions, order of operations, arithmetic with integers, solving one-step equations, and inequalities.

This unit breaks down into 21 short steps and 120 questions, starting at difficulty 3 and building to 4. Below you can see exactly what it covers, how the path is structured, and worked examples with explanations.

Steps: 21
Questions: 120
Difficulty: 3-4

What this unit covers

One-Step Equations
Order of Operations
Working with Integers
Variables and Expressions
Inequalities

Where this fits

Needs Integers and Number Theory. It is the direct prerequisite for Algebra.

Where people slip

The equals sign does not mean here comes the answer. It asserts that two things are the same, and everything in algebra depends on treating it that way.

How the unit is structured

Pre-Algebra runs as 21 short steps that unlock in order. 15 are practice rounds and 6 are challenge rounds that pull together everything before them. Questions start at difficulty 3 and climb to 4 as you progress.

Step 1 · easierStep 21 · harder

Challenge rounds

Example questions

30 real questions from this unit, with the answer and the reason behind it, grouped by what they practise. There are 120 in the unit altogether.

Inequalities

Choose all that applyLevel 3
1. Which values make x > 4 true? Choose all.
- 5correct
- 6correct
- 4
- 2
Only numbers greater than 4 work, so 5 and 6.
Fact or fibLevel 3
2. -3 is greater than -5.
Answer: True
On the number line -3 sits to the right of -5, so it is greater.
Fill the blankLevel 3
3. The statement 8 > 3 is read '8 is ____ than 3'.
- greatercorrect
- less
- equal
- smaller
The > symbol means greater than.
Multiple choiceLevel 3
4. Which value of x makes x > 5 true?
- 7correct
- 5
- 3
- 1
Only 7 is greater than 5; 5 is not greater than itself.
Odd one outLevel 3
5. Which symbol is NOT an inequality symbol?
- =correct
- <
- >
- <=
The equals sign shows equality, not an inequality.
Build the sentenceLevel 4
6. Build a true sentence about inequalities.
Answer: An inequality compares two values that are not equal
Inequalities show when values are not equal.

One-Step Equations

Build the sentenceLevel 3
7. Build a true sentence about solving equations.
Answer: Do the same thing to both sides
Keeping both sides equal is the key to solving equations.
Choose all that applyLevel 3
8. Which equations have the solution x = 3? Choose all.
- x + 4 = 7correct
- 2x = 6correct
- x / 3 = 1correct
- x - 5 = 8
Each true one gives x = 3 when solved.
Fact or fibLevel 3
9. The solution to 2x = -10 is x = -5.
Answer: True
Divide by 2: -10 / 2 = -5.
Fill the blankLevel 3
10. If 3x = 21, then x = ____.
- 7correct
- 18
- 24
- 63
Divide 21 by 3 to get x = 7.
Guess the numberLevel 3
11. Solve x - 7 = 8. What is x?
Answer: 15
Add 7 to both sides: 8 + 7 = 15.
Match the pairsLevel 3
12. Match each equation to its solution.
Answer: x + 2 = 9 = x = 7; x - 1 = 4 = x = 5; 2x = 6 = x = 3
Undo the operation to find each x.

Order of Operations

Build the sentenceLevel 3
13. Build a true sentence about the order of operations.
Answer: Always do multiplication before addition
Multiplication comes before addition in the order of operations.
Fact or fibLevel 3
14. 6 + 4 / 2 = 5.
Answer: False
Divide first: 4 / 2 = 2, then 6 + 2 = 8, not 5.
Choose all that applyLevel 4
15. Which expressions equal 20? Choose all.
- 4 x (2 + 3)correct
- 2^2 x 5correct
- 30 - 2 x 5correct
- 6 + 2 x 5
Three evaluate to 20; 6 + 2 x 5 = 16.
Fill the blankLevel 4
16. Following the order of operations, 20 - 3^2 = ____.
- 11correct
- 14
- 289
- 9
Square first: 3^2 = 9, then 20 - 9 = 11.
Guess the numberLevel 4
17. Evaluate 5 + 2 x 6 - 3.
Answer: 14
Multiply first: 2 x 6 = 12, then 5 + 12 - 3 = 14.
Multiple choiceLevel 4
18. What is 12 - 2 x 3 + 4?
- 10correct
- 34
- 6
- 4
Multiply first: 2 x 3 = 6, then 12 - 6 + 4 = 10.

Variables and Expressions

Build the sentenceLevel 3
19. Build a true sentence about variables.
Answer: A variable stands for an unknown number
A variable is a symbol for an unknown number.
Choose all that applyLevel 3
20. Which of these are like terms with 3x? Choose all.
- 5xcorrect
- -2xcorrect
- 3
- x^2
Like terms have the same variable x to the first power.
Fill the blankLevel 3
21. A letter that stands for an unknown number is called a ____.
- variablecorrect
- constant
- coefficient
- sum
A variable is a letter that represents an unknown value.
Match the pairsLevel 3
22. Match each phrase to its expression.
Answer: 5 more than x = x + 5; twice x = 2x; x divided by 4 = x / 4
Translate the words into symbols.
Multiple choiceLevel 3
23. Evaluate 3x + 2 when x = 6.
- 20correct
- 24
- 11
- 36
Put 6 in for x: 3 times 6 is 18, plus 2 makes 20.
Fact or fibLevel 4
24. The expression 3(x + 2) expands to 3x + 6.
Answer: True
Distribute the 3 to both terms: 3x + 6.

Working with Integers

Multiple choiceLevel 3
25. What is -15 / 3?
- -5correct
- 5
- -12
- -18
A negative divided by a positive is negative: -15 / 3 = -5.
Odd one outLevel 3
26. Which expression has a NEGATIVE result?
- 3 - 8correct
- -2 + 5
- 4 - 1
- -3 x -2
3 - 8 = -5, while the others are all positive.
Build the sentenceLevel 4
27. Build a true sentence about subtracting negatives.
Answer: Subtracting a negative is the same as adding
Subtracting a negative turns into addition.
Choose all that applyLevel 4
28. Which results are positive? Choose all.
- -3 x -4correct
- -6 + 10correct
- 5 - 9
- -2 x 3
-3 x -4 = 12 and -6 + 10 = 4 are positive.
Fact or fibLevel 4
29. (-2)^3 = -8.
Answer: True
-2 x -2 x -2 = -8, because three negative factors give a negative.
Fill the blankLevel 4
30. -9 + 4 - 2 = ____.
- -7correct
- -3
- 7
- -11
Work left to right: -9 + 4 = -5, then -5 - 2 = -7.

Where these questions come from. Each unit starts as a plan of the concepts it should cover and the difficulty it should span. Questions are written against that plan with AI assistance, then checked by a validator that rejects anything without a single defensible answer, an explanation, or plausible wrong options. How we write questions sets out the whole process, and corrections are fixed in the bank and reach the site and the app the same day.

How you practise

This unit mixes 14 different question formats, so you are recalling and applying rather than recognising the same layout every time.

Build the sentence
Choose all that apply
Fact or fib
Fill the blank
Guess the number
Match the pairs
Multiple choice
Odd one out
Picture question
Put in order
Sort into groups
Spell it
True or false
Type the answer

Practise Pre-Algebra

120 questions across 21 steps. Start with step one and crawl at your own pace.

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Read about Pre-Algebra

Explainers from our blog on what this unit covers. Each one ends with real questions from the bank.

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