Chapter 9: Patterns and Pre-Algebra
Patterns, Function Machines and Simple Equations
Spot the rule, apply it consistently, and use inverse operations to find missing numbers.
AI teacher
Press Start to hear a short classroom-style explanation. If sound is unavailable, the full script is shown below.
Voice: Browser voice
Workbook pages
Fun Maths Book 2 pages 111-120
Continue sequences, use function machines, and solve simple equations.
AI explanation
The AI teacher shows sequences as repeated moves and function machines as input-output machines. Equations are taught as balanced scales where the same value must stay on both sides.
- 1A sequence follows a rule.
- 2Rules can add, subtract, multiply or divide.
- 3A function machine changes every input in the same way.
- 4To solve an equation, use the inverse operation.
Think with the AI teacher
Today we will look for rules. Algebra begins when we notice what changes and what stays the same.
Question 1
Pause 4sIn 100, 96, 92, 88, what changes each time?
After thinking
The number decreases by 4 each time.
Great pattern spotting. The rule is subtract 4.
Question 2
Pause 5sA machine doubles then adds 1. What should happen to every input?
After thinking
Every input follows the same two steps: double, then add 1.
Yes. A function rule must be consistent.
Question 3
Pause 4sIf x + 9 = 17, what operation would undo adding 9?
After thinking
Subtracting 9 undoes adding 9.
Excellent. Inverse operations help us solve equations.
Deep structure
What children discover
Children discover that algebra is not guessing; it is using rules, balance and inverse operations.
Common mistake
Children may guess missing numbers instead of identifying the rule or inverse operation.
Future connection
Patterns and equations prepare students for sequences, functions, graphs, formulae and later algebra.
Animated demonstration
See the maths move
Number cards move through an animated function machine, then a balance scale solves missing-number equations.
x 2, + 1
Guided examples
Negative common difference
Continue the sequence: 100, 96, 92, 88, ...
- 1.Find the difference: 96 - 100 = -4.
- 2.The rule is subtract 4 each time.
- 3.Subtract 4 from 88.
Simple equation
Solve 3x = 24.
- 1.3x means 3 times x.
- 2.Use the inverse operation: divide by 3.
- 3.24 รท 3 = 8.
Interactive practice
Try it now
Write the rule in words before continuing any sequence or solving any function machine.
What is the next number? 45, 40, 35, 30, ...
A function machine doubles the input then adds 1. What is the output for 6?
Solve x + 9 = 17.
Review
Say what inverse operation means before solving the workbook equations.
Parent signal
If the child guesses equations, ask what operation would undo the one shown.
Brilliant rule spotting. You are starting to think like an algebra student.