Your learning journey
Diagnose a number error, repair the method, and choose an independent check that tests the original calculation.
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
Diagnostic: evidence used to choose what to reteach. Inverse: an operation that undoes another. Estimate: an approximate check of size. Counterexample: one case disproving an always claim. Evidence: working that supports a conclusion.
Intentional practice feedback after your attempt
−2; 12. Example check: −2 + (−5) = −7.
Record the first error before checking feedback.
Intentional practice feedback after your attempt
12; 1. First divide 18 by 3; first multiply 3 by −2.
Equal-priority operations go left to right.
Intentional practice feedback after your attempt
48; 6.29.
Keep the place-value and rounding decisions visible.
Wider prerequisite screen — ungraded
Plan support for later units. This is not a test of this week’s taught content or an entry-tier decision. Your teacher reviews the responses.
Present
A correct answer copied from feedback does not establish secure understanding. Use attempt → locate the first error → explain and repair → check independently → solve a fresh matched problem after a delay. Match the check to the risk: inverse for an operation, place value for scale, estimate for magnitude, and substitution into the original expression for a missing number.
Keep the original calculation visible. Repeating the same incorrect method is not an independent check. A useful repair names the decision that went wrong and succeeds on a fresh question with the support removed.
Optional scaffold
Rewrite as adding the opposite.
Intentional practice feedback after your attempt
−5; inverse check −5 + (−3) = −8.
The original error treats subtraction as adding the same signed number.
Optional scaffold
Circle multiplication before doing any addition.
Intentional practice feedback after your attempt
−8; 1.
The first error was adding 6 and 2 before multiplying.
Optional scaffold
Compare the result with the starting value.
Intentional practice feedback after your attempt
The number was made ten times smaller instead of one hundred times larger. Correct original: 36. Fresh answer: 72.
Track each digit’s place value.
Optional scaffold
Distinguish reasonable from exact.
Intentional practice feedback after your attempt
No. It supports the scale; an exact calculation or inverse check is still needed.
Different nearby values can all be reasonable.
Apply
Intentional practice feedback after your attempt
−3, checked by −3 + (−6) = −9; 4, checked by (−8) × 4 = −32.
Use the original signed number in the inverse check.
Intentional practice feedback after your attempt
18; −7. First steps 24 ÷ 4 = 6 and 2 × (−6) = −12.
Remove the operation-order prompt once the first step is secure.
Optional scaffold
Name the purpose of each method.
Intentional practice feedback after your attempt
84; 7.39; 80.
Track value, mark the decision digit, then estimate separately.
Core work is non-calculator. After A3, a calculator may confirm 19.7 × 4.2 = 82.74. Estimate first: 20 × 4 = 80. A display can confirm arithmetic, but does not explain an error or prove understanding.
Apply and extend
Intentional practice feedback after your attempt
No. Repeating 2 + 3 × 4 as (2 + 3) × 4 gives 20 twice; the correct value is 14.
A repeated misconception can reproduce the same error.
Optional scaffold
Split 4.2 into 4 + 0.2.
Intentional practice feedback after your attempt
Use exact calculation: 19.7 × 4 = 78.8 and 19.7 × 0.2 = 3.94; sum 82.74.
Estimation cannot distinguish every pair of nearby answers.
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
A factor divides a whole number exactly. The positive factors of 12 are 1, 2, 3, 4, 6 and 12. A prime is an integer greater than 1 with exactly two positive factors. Pair factors systematically to avoid missing one.
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
Subtracting −12 means add 12, so −7+12=5.
Deep challenge
Check after attempting
0.8=4/5, and 35÷5×4=28; or 80% of 35=28.