Your learning journey
Calculate with signed products, quotients and mixed operations; justify the order and check with an inverse.
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
Product: result of multiplication. Quotient: result of division. Factor: a number being multiplied. Brackets group a calculation. A square multiplies a number by itself.
Intentional practice feedback after your attempt
3 and 3.
Use addition of the opposite for the subtraction.
Intentional practice feedback after your attempt
24 and 4.
Division undoes multiplication.
Intentional practice feedback after your attempt
3 × 3 = 9.
The exponent 2 means two equal factors, not double.
Present
Three lots of −4 give −12. To keep distribution valid, (−3) × (4 + (−4)) must be zero. Since (−3) × 4 = −12, (−3) × (−4) must be +12. Division reverses multiplication: −24 ÷ 6 = −4 because 6 × (−4) = −24. Division by zero is undefined.
Brackets first; then powers; then multiplication and division from left to right; then addition and subtraction from left to right. Equal-priority operations are not separate alphabetical steps.
Optional scaffold
Write four signed terms before adding.
Intentional practice feedback after your attempt
−12.
Four groups of −3 have a total of −12.
Optional scaffold
The second product must cancel −12.
Intentional practice feedback after your attempt
12; 0; 10.
Distribution over 4 + (−4) = 0 explains the sign.
Optional scaffold
Write (−6) × □ = −24.
Intentional practice feedback after your attempt
4; (−6) × 4 = −24.
The divisor times the quotient must equal the dividend.
Optional scaffold
Underline 3 × (−2) first.
Intentional practice feedback after your attempt
−6; 1.
Multiply before adding.
Apply
Optional scaffold
Keep the magnitude 12; justify the sign.
Intentional practice feedback after your attempt
12, −12, −12, 12.
Changing one factor’s sign changes the product’s sign; changing both restores it.
Intentional practice feedback after your attempt
12; 3; 15.
Use left-to-right order at equal priority; brackets change grouping.
Optional scaffold
Multiply the repeated payment before combining the changes.
Intentional practice feedback after your attempt
−7 + 3 × 4 − 9 = −4, so −£4.
Payments are positive changes. Check −4 + 9 − 12 = −7.
Optional check only: estimate the sign, then enter (−18) ÷ (−3) + 2 × 4 using brackets and the negative-number key. Expect 14. Calculator models differ; demonstrate your own.
Apply and extend
Intentional practice feedback after your attempt
−5 and 6. The claim works for a product of two negative numbers, not every operation.
State the operation before using a sign rule.
Optional scaffold
Write each as a multiplication before applying the leading minus.
Intentional practice feedback after your attempt
9 and −9. (−3)² = (−3) × (−3); −3² means −(3 × 3).
A power acts on its base; brackets show that the negative sign belongs to the base.
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
Each place to the left is ten times the value. For example, 2.47 × 10 = 24.7: the digits take places worth ten times as much. Estimate an answer before using a calculator.
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
−8×−2+5=21.
Deep challenge
Check after attempting
(6+2)×5−4=36.