Chapter 5: Algebra, Equations, and Patterns
Algebra, Equations and Patterns
Use algebra as a clear thinking system: replace variables carefully, keep equations balanced, and describe pattern rules precisely.
AI maths coach
Step-by-step teaching, practice and checkpoint.
Voice: Browser voice
Voice: Browser voice
Workbook pages
Fun Maths Book 3 pages 49-61
Substitute values, solve equations, continue sequences and describe coordinate pattern rules.
Think first
Good mathematicians decide what the question is asking before they calculate.
- 1Is the letter standing for a known value or an unknown value?
- 2What operation is happening to the variable?
- 3Which inverse operation will undo that step?
- 4Does the rule work when we check it in the original question?
Visual teaching
See the method
A letter tile is replaced by a number, then a balance scale solves an equation and a sequence path reveals its rule.
Worked examples
Find 4x + 7 when x = 6.
Step 1: First, what information is given?
The expression is 4x + 7, and the value of x is 6.
Why: Substitution means replacing the letter with the value we are given.
Step 2: What does 4x mean?
4x means 4 times x, so 4x becomes 4 x 6.
Why: In algebra, a number beside a letter means multiplication.
Be careful: Do not read 4x as the two-digit number 46.
Step 3: Which operation should happen first?
Calculate multiplication first: 4 x 6 = 24.
Why: Multiplication comes before addition in the order of operations.
Step 4: Now finish the expression.
24 + 7 = 31.
Why: After replacing and multiplying, only addition remains.
Common mistake: Writing 46 + 7 because 4x was mistaken for 46.
Solve 3x - 5 = 22.
Step 1: What are we trying to find?
We need the value of x that makes both sides equal.
Why: Solving an equation means finding the unknown value.
Step 2: Which operation should we undo first?
The expression subtracts 5, so add 5 to both sides: 3x = 27.
Why: Adding 5 undoes subtracting 5, and doing it to both sides keeps the equation balanced.
Be careful: Do not add 5 to only one side.
Step 3: What operation is still attached to x?
3x means 3 times x, so divide both sides by 3.
Why: Division by 3 undoes multiplication by 3.
Step 4: Now write and check the value.
27 divided by 3 is 9, so x = 9.
Why: This value should make the original equation true.
Common mistake: Doing the operations in the wrong order and dividing before undoing the -5.
The sequence is 5, 11, 17, 23, ... What is the 8th term?
Step 1: What information do we already know?
The first term is 5, and each term increases by 6.
Why: A sequence rule tells us how the terms change.
Step 2: What are we trying to find?
We need the 8th term, not just the next term.
Why: Jumping to a later term needs a rule, not repeated guessing.
Step 3: How many jumps are needed from the 1st term to the 8th term?
From term 1 to term 8 there are 7 jumps.
Why: The first term is already counted, so the number of jumps is one less than the term number.
Be careful: A common mistake is doing 8 jumps instead of 7.
Step 4: Use the rule to calculate.
7 jumps of 6 is 42. Then 5 + 42 = 47.
Why: Start at the first term and add the repeated change.
Common mistake: Finding only the next term, 29, instead of the 8th term.
Guided practice
Solve 4n + 3 = 27.
Independent practice
Your turn
Find 2a + 3 when a = 8.
Solve x + 14 = 31.
What is the next term? 5, 11, 17, 23, ...
Mini checkpoint
Check your thinking
Find 3a - 5 when a = 9.
Solve 5x + 4 = 39.
A sequence starts 4, 9, 14, 19, ... What is the 7th term?
Key idea
Algebra becomes manageable when you decide whether you are substituting, solving, or finding a pattern rule. Replace known values carefully, keep equations balanced with inverse operations, and check pattern rules against the original sequence.
Parent signal
If the child guesses equations, ask which inverse operation undoes the step shown.