Your learning journey
Explain equivalence, simplify fractions, convert mixed and improper forms and compare fractions exactly.
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
Numerator: number of parts counted. Denominator: equal parts in one whole. Equivalent: same value. Improper fraction: numerator at least denominator. Mixed number: whole number plus proper fraction.
Intentional practice feedback after your attempt
6.
Common factors 1,2,3,6.
Intentional practice feedback after your attempt
23.
Multiply before adding.
Intentional practice feedback after your attempt
0.6.
0.60 > 0.56.
Present
Splitting each of three equal parts into two makes six equal parts. Thus 2/3 = 4/6. Multiplying numerator and denominator by the same non-zero number multiplies by 1, preserving the value. Adding the same number to both does not usually do this.
Simplify by a common factor, preferably the HCF. For a mixed number, multiply wholes by the denominator, then add the numerator. For comparison, use equal denominators and compare numerators; keep the same whole.
Optional scaffold
Multiply both entries by 4.
Intentional practice feedback after your attempt
12/20.
Each fifth is split into four twentieths.
Optional scaffold
Find HCF of 15 and 25.
Intentional practice feedback after your attempt
3/5.
Divide numerator and denominator by 5.
Optional scaffold
3×5+2 gives the numerator.
Intentional practice feedback after your attempt
17/5.
Three wholes contain fifteen fifths.
Optional scaffold
Use eighths to compare.
Intentional practice feedback after your attempt
2 4/5; 3/4 is larger because 6/8 > 5/8.
Remainder stays over the original denominator.
Apply
Optional scaffold
Scale both entries together.
Intentional practice feedback after your attempt
3/6; 5/10; both simplify to 3/5.
Equivalent forms can look different.
Intentional practice feedback after your attempt
17/6; 4 3/4; 2/3=8/12 < 9/12=3/4.
Common units make the comparison meaningful.
Optional scaffold
Convert one whole to fourths.
Intentional practice feedback after your attempt
Yes: 1 3/4 = 4/4+3/4 = 7/4 litres.
Same value and units.
Optional check: enter 2 ÷ 3 and 4 ÷ 6. Matching displays support the equivalence, but the exact fraction argument explains why. Do not replace exact fractions with rounded decimals.
Apply and extend
Intentional practice feedback after your attempt
3/5=18/30; 4/6=20/30, so not equal.
Adding changes the ratio of parts.
Optional scaffold
Use twelfths rather than sixths.
Intentional practice feedback after your attempt
For example 7/12: 1/2=6/12 < 7/12 < 8/12=2/3.
Other valid fractions with exact justification accepted.
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
Adding fractions combines counts of equal-sized parts. Rename unlike fractions using a common denominator first. We will also interpret multiplication as a fraction of an amount and division as how many groups fit.
Retrieve F1 again in one week. Bring your working and one question.
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
3/5; examples 6/10 and 9/15.
Deep challenge
Check after attempting
Multiplier 7, so denominator 56.