Your learning journey
Work without a calculator, except for the optional check. Type a minus with your keyboard (-); it means the same as −. Try each question before opening a prompt or practice explanation. Read your explanation aloud if that helps.
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Ready.
Connect & Check
Integer: a whole number including negative whole numbers and zero. Ascending: least to greatest. Opposite: same distance from zero, other side.
Optional scaffold
Mark −5 and −1 on a number line.
Intentional practice feedback after your attempt
−5, −1, 0, 2
Ascending means least to greatest. A number farther left is smaller.
Optional scaffold
What added to 3 gives 8?
Intentional practice feedback after your attempt
5; 5 + 3 = 8
Subtraction and addition undo one another.
Optional scaffold
Imagine temperatures of −2°C and −7°C.
Intentional practice feedback after your attempt
−2, because it is farther right on the number line.
A larger digit does not make a negative number greater.
Present
A sign belongs to a number; an operation tells you what to do. Adding a positive moves right. Adding a negative moves left. Subtraction adds the opposite: a − b = a + (−b). Adding b back returns a, so the inverse operation checks the result.
Start −3, move five units right, finish 2. Check 2 − 5 = −3.
Optional scaffold
Move 4 units to zero, then 2 more.
Intentional practice feedback after your attempt
2; start at −4, move 6 units right.
Adding a positive number moves right. Cross zero carefully.
Optional scaffold
First reach zero, then move 3 more units.
Intentional practice feedback after your attempt
−3; 5; left; −3 + 5 = 2.
Adding a negative number moves left by its distance from zero.
Optional scaffold
Rewrite subtraction as adding the opposite.
Intentional practice feedback after your attempt
−8; −8 + 5 = −3.
Subtracting a positive number moves left.
Optional scaffold
What number plus −5 equals −3?
Intentional practice feedback after your attempt
5; 2
Subtracting a negative adds its opposite. The inverse check explains why.
Apply
Optional scaffold
Read “subtract negative seven” aloud before rewriting.
Intentional practice feedback after your attempt
(a) 11 (b) −3 (c) −3 (d) 11
The operation and the sign of the second number both matter.
Optional scaffold
Use your own number line if needed, then try again without it.
Intentional practice feedback after your attempt
(a) 3 (b) −15 (c) 3; e.g. 3 + (−9) = −6.
Only one feature varies at a time. Explain why (a) and (c) agree.
Optional scaffold
Find the temperature after the rise before applying the fall.
Intentional practice feedback after your attempt
−4 + 9 − 3 = 2°C. Check: 2 + 3 − 9 = −4.
An increase is a positive change; a decrease is a negative change.
Optional calculator check for A3: estimate the sign first. Use your calculator’s negative-number key (−), +/− or neg for the starting −4, then + 9 − 3. Models differ; ask your teacher to demonstrate. The display should show 2. Include °C in the contextual answer.
Apply and extend
Optional scaffold
Try subtracting a negative number.
Intentional practice feedback after your attempt
For example, 1 − (−2) = 3, and 3 > 1. One counterexample disproves “always”.
A counterexample must contradict the stated claim, not just give another calculation.
Optional scaffold
Think about positive, zero and negative values of b.
Intentional practice feedback after your attempt
Exactly when b < 0. Subtracting a negative adds a positive amount. b = 0 leaves a unchanged; b > 0 decreases it.
Use a general argument and consider zero. This extension is available to either tier.
Stretch is available to either tier. Support needs and qualification tier are separate. A counterexample must contradict the claim.
Recall & Review
Retrieval without notes
Enter a number, decimal, simple fraction such as 3/2, or mixed number such as 1 1/2. Equivalent exact values are accepted. If your notation is not recognised, it is referred for review, not marked wrong. There are 6 retrieval points; these do not include method marks.
Not checked.
Independent exit evidence
P1–P2: five minutes, without notes. Total 4 marks. Your teacher reviews the method and explanation. No assessment solutions are embedded here.
Recall & Review and prepare
Read: 3 × 4 means three groups of four, giving 12. Division undoes multiplication: 12 ÷ 3 = 4. In 2 + 3 × 4, multiply first to obtain 14. L002 explains multiplication/division of signed numbers and operation priority.
Repeat F1 tomorrow and in one week. Bring one question and your working.
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
−26; for example (−18+27)−35=9−35=−26.
Deep challenge
Check after attempting
False: −8−(−3)=−5, still negative.