Your learning journey
Select, explain and check fraction methods; diagnose misconceptions and transfer a repaired method to a fresh problem.
Work without a calculator except for an invited check. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.
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Ready.
Connect & Check
Counterexample: one case that disproves an always claim. Inverse check: reverse an operation. Unit fraction: numerator 1. Systematic list: organised list that avoids omissions and repeats.
Intentional practice feedback after your attempt
3/4; 3.
Use quarters.
Intentional practice feedback after your attempt
2/3: 10/15>9/15.
Use fifteenths.
Intentional practice feedback after your attempt
−5; 11.
Preserve operation order.
Present
A check must test the original meaning. If 1/2+1/3 is given as 2/5, the result is below 1/2 although a positive amount was added. Renaming gives 3/6+2/6=5/6. Subtracting 1/3 from 5/6 returns 1/2.
Attempt without prompts, identify the first incorrect decision, explain the repair, then solve a fresh matched problem. Use common units for +/− and a reciprocal for ÷. List possibilities systematically when the problem asks for combinations.
Optional scaffold
The sum must exceed each positive addend.
Intentional practice feedback after your attempt
7/12.
4/12+3/12 uses equal-sized parts.
Optional scaffold
Convert 3/5 to tenths.
Intentional practice feedback after your attempt
6.
Each tenth fits six times in six tenths.
Optional scaffold
Rename 1/4 as 2/8.
Intentional practice feedback after your attempt
5/8; 5/8+1/4=7/8.
Reverse subtraction with addition.
Optional scaffold
Multiply, then simplify.
Intentional practice feedback after your attempt
1/2 litre.
(2/3)×(3/4)=1/2; the operator scales the quantity.
Apply
Optional scaffold
Start with twelfths.
Intentional practice feedback after your attempt
5/12; 7/12.
Reverse with subtraction or addition.
Intentional practice feedback after your attempt
3/10; 8/15.
Multiplication scales by 3/4; division asks how many 3/4-sized groups fit.
Optional scaffold
The second fraction acts on 9, not 12.
Intentional practice feedback after your attempt
6 litres.
Initially 9 litres; 3 used; 6 remain.
Optional check after A3: 12 × (3 ÷ 4) × (2 ÷ 3) = 6. Use brackets around each fraction and identify what each factor represents before entering it.
Apply and extend
Intentional practice feedback after your attempt
Both equal 1/6.
Both partition one whole into 2×3 equal parts.
Optional scaffold
Use a two-row, three-column table.
Intentional practice feedback after your attempt
R-black, R-grey, R-white, B-black, B-grey, B-white: 6.
Use one shirt at a time; three choices for each. Higher extension H1 generalises this counting pattern.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
Percent means per hundred. Fractions, decimals and percentages can name the same proportion. We will preserve the value while changing the representation.
Retrieve F1 again in one week. Bring your working and one question.
Higher alternative: Product rule for counting
Higher route: replace the 2-minute A3 feedback and the two 4-minute Challenge discussions with this 10-minute taught extension. Retain core P1–P2. Set HX1–HX2 as the final four minutes of that alternative, and use the shared challenges later if needed. The core route remains 60 minutes; the extension is not an additional compulsory ten minutes. Route choice reflects tier curriculum, not temporary support needs.
If every one of 3 shirts can pair with every one of 4 trousers, there are 4 choices for each shirt: 4+4+4=3×4=12 outfits. With 2 shoe choices for every outfit, there are 3×4×2=24 combinations. The product rule applies when the stated number of next choices is available for each earlier choice.
Intentional Higher practice feedback
10; five main courses for each of two starters.
Intentional Higher practice feedback
3 remain; 4×3=12 codes.
HX1–HX2: teacher review. Completion is not mastery.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
Restore a backup
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Optional extension activities
Stretch
Check after attempting
21/36+10/36=31/36.
Deep challenge
Check after attempting
8/12+9/12=17/12>1.