Your learning journey
Interpret ratios, simplify them and share quantities using equal parts while distinguishing part-to-part from part-to-whole.
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
Ratio: ordered comparison of quantities. Part-to-part: compares one component with another. Part-to-whole: compares a component with the total. Equal parts: units of a common size used to share.
Intentional practice feedback after your attempt
2/3; 6.
Divide both entries by the same factor.
Intentional practice feedback after your attempt
20.
Five parts of 10; choose two.
Intentional practice feedback after your attempt
32.
One quarter is 8.
Present
Red:blue = 2:3 means for every two equal red parts there are three equal blue parts. There are five parts altogether, so red is 2/5 of the whole, not 2/3. Scaling both terms by the same positive factor preserves the ratio.
Keep the named order and convert quantities to matching units before simplifying. To share a total, add ratio parts, divide the total by that sum, then multiply for each share. If one share or the difference is given, match it to its number of parts first.
Optional scaffold
Keep the order unchanged.
Intentional practice feedback after your attempt
3:5.
Divide both terms by 5.
Optional scaffold
Add the ratio terms.
Intentional practice feedback after your attempt
3/7 and 4/7.
Seven parts make the whole.
Optional scaffold
Check shares sum to £56.
Intentional practice feedback after your attempt
£24 and £32.
Seven parts at £8 each.
Optional scaffold
Divide the known share by its own ratio term.
Intentional practice feedback after your attempt
A=15; total=50.
35 corresponds to seven parts.
Apply
Optional scaffold
Use a common factor.
Intentional practice feedback after your attempt
All 2:3.
The relative amounts, not the absolute sizes.
Intentional practice feedback after your attempt
45 and 27; B=35.
The second problem gives a share, not the total.
Optional scaffold
Total includes both ingredients.
Intentional practice feedback after your attempt
150 ml concentrate and 600 ml water.
Five parts at 150 ml; sum 750 ml.
Optional check after A3: 750÷5×1=150; 750÷5×4=600. Check 150+600=750 and 150:600=1:4. A correct sum alone does not establish the ratio.
Apply and extend
Intentional practice feedback after your attempt
A=8 is correct. Total=20, so A is 2/5 of the total.
2/3 compares A with B, not A with A+B.
Optional scaffold
Subtract the ratio terms first.
Intentional practice feedback after your attempt
Difference is 2 parts=14; one part=7; A=21, B=35.
The given difference is not the total.
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
In direct proportion, multiplying one quantity by a factor multiplies the other by the same factor. A scale drawing uses one constant length ratio. Match units before writing a scale such as 1:500.
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.
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Optional extension activities
Stretch
Check after attempting
Nine parts at £14: £28, £42, £56; total £126.
Deep challenge
Check after attempting
Equalise B at 10: A:B=6:10 and B:C=10:15, so 6:10:15.