Chapter 9: Problem Solving and Reasoning
Problem Solving and Reasoning
Break unfamiliar problems into known information, target information, method choice and a final check.
AI maths coach
Step-by-step teaching, practice and checkpoint.
Voice: Browser voice
Voice: Browser voice
Workbook pages
Fun Maths Book 3 pages 101-114
Solve multi-step word problems, ratio and fraction applications, financial reasoning and logic puzzles.
Think first
Good mathematicians decide what the question is asking before they calculate.
- 1What information do we already know?
- 2What are we trying to find?
- 3Which representation could help: bar model, table, diagram or equation?
- 4Does the final answer fit the story and units?
Visual teaching
See the method
A word problem is unpacked into known values, a bar model, operations and a final checked answer.
5 : 2
Worked examples
A recipe uses flour and sugar in the ratio 5 : 2. If it uses 350 g of flour, how much sugar is needed?
Step 1: What information is given?
Flour : sugar = 5 : 2, and flour is 350 g.
Why: The ratio tells us how the two amounts compare.
Step 2: What does 350 g represent?
350 g represents 5 flour parts.
Why: The first ratio number matches flour because the words are flour then sugar.
Step 3: Find one part.
350 ÷ 5 = 70 g.
Why: Finding one part lets us scale to sugar.
Be careful: Do not divide by 2 first; 2 is the sugar part.
Step 4: Find the sugar amount.
Sugar is 2 parts, so 2 x 70 = 140 g.
Why: Scale one part to the required number of parts.
Common mistake: Mixing up the order of the ratio parts.
A jacket costs $80. It is reduced by 25%. What is the sale price?
Step 1: What are we trying to find?
We need the sale price after the discount.
Why: The discount is not the final price; it is the amount removed.
Step 2: Find the discount.
25% is one quarter, and one quarter of $80 is $20.
Why: Using a friendly percentage makes the calculation easier.
Step 3: Subtract the discount.
$80 - $20 = $60.
Why: A reduced price is lower than the original price.
Common mistake: Writing $20 as the sale price instead of the discount.
Three notebooks cost $18. A student buys 5 notebooks and pays with $40. How much change should they get?
Step 1: What information do we know?
3 notebooks cost $18, and the student buys 5 notebooks.
Why: We need a unit cost before finding the cost of 5.
Step 2: Find the cost of one notebook.
$18 ÷ 3 = $6.
Why: Unit cost helps us scale to any number of notebooks.
Step 3: Find the cost of 5 notebooks.
5 x $6 = $30.
Why: Multiply the unit cost by the number bought.
Step 4: Now find the change.
$40 - $30 = $10.
Why: Change is money paid minus the cost.
Common mistake: Stopping at $30 and forgetting the question asks for change.
Guided practice
If 3 parts equal 45, what is 1 part?
Independent practice
Your turn
A problem has several steps. What should you do first?
If 3 parts equal 45, what is 1 part?
A 10% discount on $90 is...
Mini checkpoint
Check your thinking
A 10% discount on $90 is...
A box has 24 pencils. 3/8 are blue. How many are blue?
A problem has several steps. What should you do first?
Key idea
Problem solving starts before calculation: understand, represent, choose a method, solve and check. Name the known information, name the target, choose a useful model, and check the final answer in the story.
Parent signal
Strong reasoning answers include units and a sentence, not just a final number.