Your learning journey
Calculate exactly with fractions using all four operations and explain why each method works.
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
Common denominator: shared unit for addition or subtraction. Reciprocal: number that multiplies with a non-zero number to make 1. Exact answer: no rounding. Cancellation: dividing factors by a common factor.
Intentional practice feedback after your attempt
3/6; 2/6.
Scale both entries.
Intentional practice feedback after your attempt
3/2.
Two halves plus one half.
Intentional practice feedback after your attempt
2/5.
Divide by 3.
Present
Addition and subtraction count equal units: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Multiplication can mean a fraction of a fraction: half of three quarters is three eighths. Division asks how many groups fit: 3/4 ÷ 1/4 = 3.
For + or −, rename with a common denominator. For ×, multiply numerators and denominators; cancel common factors if useful. For ÷ by a non-zero fraction, multiply by its reciprocal because that makes the divisor 1. Convert mixed numbers first; simplify and check size.
Optional scaffold
Use LCM of 4 and 3.
Intentional practice feedback after your attempt
3/12+4/12=7/12.
Count twelfths.
Optional scaffold
Rename in twelfths.
Intentional practice feedback after your attempt
7/12.
10/12−3/12.
Optional scaffold
Cancel a factor 3, not terms in a sum.
Intentional practice feedback after your attempt
2/5.
Two thirds of three fifths is six fifteenths.
Optional scaffold
Invert the divisor only.
Intentional practice feedback after your attempt
5/6.
(2/3)×(5/4)=10/12.
Apply
Optional scaffold
Name the operation before choosing a method.
Intentional practice feedback after your attempt
5/6; 1/6; 1/6; 3/2.
The operation changes the meaning.
Intentional practice feedback after your attempt
7/10; 13/24; 1/6; 2.
Simplify exact results; check division by multiplication.
Optional scaffold
The fraction of a piece is not the leftover length.
Intentional practice feedback after your attempt
3 complete pieces; 1/4 m remains.
(5/2)÷(3/4)=10/3=3 1/3; three pieces use 9/4 m.
Optional check after A2: use brackets around each fraction, for example (5 ÷ 6) ÷ (5 ÷ 12) = 2. Check the result by multiplying by 5/12. Retain exact fractions when requested.
Apply and extend
Intentional practice feedback after your attempt
No: (1/2)×(1/3)=1/6, smaller than both.
Multiplying by a number between 0 and 1 scales down.
Optional scaffold
Use quarters as the common unit.
Intentional practice feedback after your attempt
3/4 contains 1 1/2 halves; (3/4)÷(1/2)=3/2; (3/2)×(1/2)=3/4.
Half-sized units fit twice as often.
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
An independent check uses the meaning of the original problem. Estimate the size, reverse an operation, or represent equal parts. Repeating the same mistaken procedure is not a check.
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
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
11/24 and 3/5.
Deep challenge
Check after attempting
Division by 2/5 multiplies by 5/2: 3/4×5/2=15/8.