Your learning journey
Convert between fractions, decimals and percentages, and compare proportions on a consistent basis.
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
Percentage: parts per hundred. Proportion: part relative to the whole. Terminating decimal: ends after finitely many places. Recurring decimal: a digit or block repeats indefinitely.
Intentional practice feedback after your attempt
1/4; 3/4.
Divide numerator and denominator by 25.
Intentional practice feedback after your attempt
7; 0.35.
Use place value.
Intentional practice feedback after your attempt
2.
Multiply by 10/3.
Present
25% means 25/100, so it equals 1/4 and 0.25. Decimal to percentage multiplies the numerical value by 100 and adds %. Fraction to decimal uses division. The percentage sign changes the unit: 0.25 is 25%, not 0.25%.
Choose a useful route: common denominator 100 for simple fractions, numerator ÷ denominator otherwise. Keep recurring values exact; 1/3 is 0.333… recurring, not exactly 0.33. Compare by changing all values into one form.
Optional scaffold
Multiply both entries by 5.
Intentional practice feedback after your attempt
0.35; 35%.
7/20=35/100.
Optional scaffold
Keep all three decimal places when forming the fraction.
Intentional practice feedback after your attempt
3/8; 37.5%.
375/1000 simplifies by 125.
Optional scaffold
Divide the percentage number by 100.
Intentional practice feedback after your attempt
3/2; 1.5.
A percentage can exceed one whole.
Optional scaffold
(7÷10)×100.
Intentional practice feedback after your attempt
70%.
Compare the part with its own whole.
Apply
Optional scaffold
Write each over 100.
Intentional practice feedback after your attempt
40%; 4%; 0.4%; 140%.
Multiplying by 100 preserves proportion when the % unit is introduced.
Intentional practice feedback after your attempt
0.375; 37.5%; 13/20; 3/5,61%,0.62.
The ordered percentages are 60%,61%,62%.
Optional scaffold
Simplify each part/whole fraction.
Intentional practice feedback after your attempt
A: 75%, compared with B:70%.
Different totals require proportions, not just scores.
Optional check after A3: (18 ÷ 24) × 100 = 75 and (14 ÷ 20) × 100 = 70. Enter the part divided by the whole. A decimal display of 1÷3 is rounded; it does not make 0.33 exact.
Apply and extend
Intentional practice feedback after your attempt
No: 33%=33/100; 1/3−33/100=1/300.
1/3=33 1/3%; an approximation must be labelled.
Optional scaffold
Start with 1 1/2 wholes.
Intentional practice feedback after your attempt
For example 150%=1.5=3/2, one and a half of the reference whole.
Other equivalent examples above 1 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
To find a fraction of an amount, divide by the denominator then multiply by the numerator. A percentage is the same kind of operator: 35% of an amount means multiply it by 35/100.
Retrieve F1 again in one week. Bring your working and one question.
Higher alternative: Recurring decimals as exact fractions
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.
Let x=0.272727… with 27 repeating forever. Multiplying by 100 shifts one full repeating block: 100x=27.272727…. Subtract x: 99x=27 because the repeating tails cancel exactly. Therefore x=27/99=3/11. Multiplying by 100 is chosen because the block has two digits. This uses exact infinite repetition, not a rounded display.
Intentional Higher practice feedback
6; 6; 6/9=2/3.
Intentional Higher practice feedback
Multiply by 100; 99x=45; x=45/99=5/11.
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
Original Reach for the Star. Not an official or endorsed Pearson resource. Separate teacher package contains assessment solutions. Local saving is browser-dependent; no account or dashboard service is included.
Optional extension activities
Stretch
Check after attempting
7/20=0.35=35%; order 0.3,32%,7/20.
Deep challenge
Check after attempting
0.125×100=12.5%, not 1.25%.