Your learning journey
Use place value to scale and compare decimals, round to stated accuracy, and judge whether a calculation is reasonable.
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
Decimal place: position after the decimal point. Significant figure: a digit counted from the first non-zero digit. Estimate: an approximate calculation. Approximately equal: ≈. Placeholder zero: a zero that preserves position or stated accuracy.
Intentional practice feedback after your attempt
−5 and 12.
Keep signs and operation order separate.
Intentional practice feedback after your attempt
70; 346.
Place determines value.
Intentional practice feedback after your attempt
0.6, because 0.60 > 0.56.
Compare tenths first; digit count is not value.
Present
In 4.063, the digits represent 4 ones, 0 tenths, 6 hundredths and 3 thousandths. Multiplying by ten makes each digit’s value ten times as large; the decimal point marks the boundary between ones and tenths. Pad decimals with trailing zeros to compare equal places: 0.6 = 0.60 > 0.56.
For rounding, identify the retained place and inspect the next digit. At 5 or above, increase the retained digit; otherwise keep it. Carry where needed. For significant figures, begin at the first non-zero digit. Estimate by replacing awkward numbers with convenient approximations, then compare the scale and units of the result.
| Ones | Tenths | Hundredths | Thousandths |
|---|---|---|---|
| 4 | 0 | 6 | 3 |
Read: four ones, zero tenths, six hundredths, three thousandths.
Optional scaffold
Label ones, tenths, hundredths and thousandths.
Intentional practice feedback after your attempt
2 + 0.5 + 0.007; 0.5.
The 5 is in the tenths place.
Optional scaffold
Track the 3 first; preserve the spacing between the digits.
Intentional practice feedback after your attempt
30.6; 0.0306.
Each digit moves into a place worth ten times as much, or one hundredth as much.
Optional scaffold
Retain hundredths; inspect thousandths.
Intentional practice feedback after your attempt
6.29.
The next digit is 6, so increase the hundredths digit.
Optional scaffold
Leading zeros locate the number; start counting at 7.
Intentional practice feedback after your attempt
0.0073.
The first two significant digits are 7 and 3; the next digit is 4.
Apply
Optional scaffold
Use a place-value chart, then cover it.
Intentional practice feedback after your attempt
5.2; 52; 0.052; 0.0052.
Compare how the same digits change value.
Intentional practice feedback after your attempt
9.98; 0.0068; 4.70.
The final zero in 4.70 communicates requested accuracy, although 4.7 is the same value.
Optional scaffold
Write the approximate expression before multiplying.
Intentional practice feedback after your attempt
20 × 5 = 100; exact 97.02. No: 970.2 is about ten times the estimate.
An estimate checks scale; it does not prove every digit correct.
After estimating A3, enter 19.8 × 4.9. Expect 97.02. Compare with 20 × 5 = 100. Read the whole display; do not round intermediate values in a multi-step calculation unless instructed.
Apply and extend
Intentional practice feedback after your attempt
Direct: 2.4. In stages: 2.45 then 2.5. The intermediate rounding changes the final result.
Keep original values until the requested rounding step.
Optional scaffold
Convert the size of the rounding unit as well as the length.
Intentional practice feedback after your attempt
2.0 m = 200 cm; 196 cm to the nearest 10 cm is also 200 cm.
The rounding units match because 0.1 m = 10 cm.
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 useful check must test the original calculation. An inverse check undoes an operation; an estimate checks size. For 18.9 × 3.1, 20 × 3 = 60 suggests an answer near 60, not 6 or 600.
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
0.0050; estimate 400×0.05=20.
Deep challenge
Check after attempting
3.495≤x<3.505; 3.505 rounds to 3.51.