At a glance. One lesson of about 60 minutes. It assumes rounding to decimal places from Year 7 and scientific notation from Year 9. Students count significant figures, round to them, estimate with 1 significant figure, and choose a sensible accuracy for an answer.
Calculator: GDC optional. Everything can be done by hand. The optional section shows students who have a GDC how its Sci setting rounds to significant figures and why Fix does not, and how to check an estimate with one line of input.
What students will learn
Know
- The first significant figure is the first digit that is not zero.
- Zeros between digits and a final zero in a decimal are significant; leading zeros are not.
- An estimate rounds every number to 1 significant figure.
Understand
- Significant figures keep the size of a number and state how precisely it is known.
- 0.007 and 0.0070 have the same value but say different things about accuracy.
- An answer should be no more accurate than the data it came from.
Do
- Round a number to a given number of significant figures, keeping its size.
- Estimate a calculation by rounding to 1 significant figure.
- Choose and justify a sensible accuracy for an answer in context.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: counting and rounding to significant figures, and estimating (questions 1 to 9).
- Criterion B. Investigating patterns: the what-if. Students test numbers starting with 1, 5 and 9 and describe how large the change from rounding to 1 significant figure can be.
- Criterion C. Communicating: explaining which zeros are significant, and writing 0.010 rather than 0.01 when 2 significant figures are asked for (the warning card, questions 1 and 9).
- Criterion D. Applying mathematics in real-life contexts: crowd sizes, a tea field and shared juice, where the sensible accuracy depends on the data (questions 5, 6 and 7).
The one thing to do with the figure
Ask for a prediction before every slide. With 38 461 at 3 significant figures, ask: “Which two numbers is it between, and which is nearer?” before anyone moves the slider. Students who chop write 38 400.
Then press 0.0070496 and go from 5 significant figures down to 1. Stop at 2 and ask why the figure shows 0.0070 and not 0.007.
A possible order
| 5 min | Warm-up from the student page, in silence, then answers. |
|---|---|
| 5 min | Hook: the two headlines. Collect predictions for 3 significant figures and for 0.0070. |
| 12 min | The figure with predictions; the key idea; settle the hook. |
| 10 min | Warning card and both worked examples; pairs finish the faded example. |
| 5 min | Question 1, the check. If many choose B or C, return to 0.0070496 in the figure. |
| 18 min | Your turn, Levels 1 to 3, at each student's own pace. |
| 5 min | Something to think about, then the exit ticket, question 9. |
The answers
| Warm-up | 3.5; 4200; 60. |
|---|---|
| Hook | 38 500 (the next digit is 6); 0.0070 has 2 significant figures. |
| Worked examples | 0.050 and 0.0504; the estimate is 900 (exact 908.7…). |
| Faded example | 7100. |
| 1. Counting significant figures | A. B counts a leading zero; C counts every digit; D drops the final zero. |
| 2. Rounding a large number | 64 000. The next digit, 8, rounds the 3 up. |
| 3. Rounding a small number | 0.00683. Leading zeros are not significant. |
| 4. Estimating with 1 significant figure | 400. 50 × 4 ÷ 0.5. |
| 5. An answer to 3 significant figures | 11 600. 11 589.24 rounded. |
| 6. A sensible accuracy | B. A is false precision; C is less accurate than the data; D is a place-value slip. |
| 7. Working backwards from a rounded number | 47 499. One below the halfway point 47 500. |
| 8. Estimating with a small number | 1.2. 0.04 × 600 ÷ 20. |
| 9. Rounding that carries | A. B chops instead of rounding; C drops a significant zero; D keeps one zero too many. |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| B, C or D in question 1 | Counted a leading zero, counted every digit, or dropped the final zero. | Underline the first digit that is not zero and count from there, to the end. |
| 64, 63 000 or 63 900 in question 2 | Lost the size, chopped instead of rounding, or kept 3 significant figures. | Ask: about how many thousand? Then which thousand is nearer? |
| 0.007, 0.00682 or 683 in question 3 | Rounded to decimal places, chopped, or lost the leading zeros. | Circle the first significant figure (the 6) and count three digits from there. |
| 100 or 200 in question 4 | Multiplied by 0.5 instead of dividing, or rounded 0.512 to 1. | Ask how many halves are in 200, and what 0.512 is to 1 significant figure. |
| 11 589, 116 or 11 500 in question 5 | Did not round, lost the size, or chopped. | Ask: about how many thousand square metres? Then round 11 589. |
| A, C or D in question 6 | Copied the display, under-rounded, or slipped a place value. | Ask how accurately the 1.5 L was measured, and whether 7 cups of the answer add back to 1.5 L. |
| 47 500, 47 999 or 47 000 in question 7 | Thinks halfway rounds down, rounds every 47 thousand to 47 000, or gave the reported figure. | Test 47 500 and 47 499 directly: what does each round to? |
| 12 or 480 in question 8 | Rounded 0.0391 to 0.4, or multiplied by 20. | Ask where the first significant figure of 0.0391 is: tenths or hundredths? |
| B, C or D in question 9 | Chopped, dropped a significant zero, or kept too many. | Write the digits 9, 9, 5: round the second 9 up, giving 0.010. Which digits are the first two significant figures? |
Questions worth asking
- Why is 38 461 to 2 significant figures not 38? Listen for “the number has to stay about thirty-eight thousand; the zeros keep it the right size”.
- Are 0.007 and 0.0070 the same number? The same value, but 0.0070 claims more accuracy. A scale that shows 0.0070 is measuring to ten-thousandths.
- When would 1 significant figure be too rough? When the answer is used for a decision that needs precision, such as a dose; an estimate checks size, not digits.
- Why round to 3 significant figures and not 3 decimal places for most answers? Significant figures work the same for 0.00683 and 63 852; decimal places would give 0.007 and 63 852.000.
Differentiation
A way in for anyone stuck
- Give a place-value grid and have students write the number in it, then shade from the first digit that is not zero.
- For each rounding question, write the two candidates and the halfway point first, as the figure does.
- Start with large whole numbers, then move to decimals that start with zeros.
Stretch
- Write down the smallest and largest numbers that round to 0.050 at 2 significant figures.
- Find a calculation where the 1 significant figure estimate is more than 30% away from the exact answer, and explain why.
Students learning in English as an additional language
“Significant” here means “meaningful”: a significant figure tells you something about the size or the accuracy. “Estimate” is both a verb and a noun. Say “to 3 significant figures” in full before abbreviating it to 3 s.f.
| Word | Plain meaning | Example |
|---|---|---|
| significant figure | a digit that tells you something about the size or accuracy of a number, counted from the first digit that is not zero | 0.0305 has 3 |
| round | replace a number by a nearby simpler one with fewer significant figures | 4718 to 2 s.f. is 4700 |
| estimate | a quick approximate answer from rounded numbers | 21.3 × 3.9 is about 20 × 4 = 80 |
| halfway point | the value exactly between the two numbers you could round to | 4750 between 4700 and 4800 |
| accuracy | how close a value is to the true value, shown by how many significant figures it has | 2.40 m, given to 3 significant figures |
| leading zero | a zero before the first digit that is not zero; it only shows place value | the zeros in 0.007 |
Sentence starters for explaining aloud or in writing:
- The first significant figure is …, so …
- It lies between … and …, and it is nearer to …
- A sensible accuracy is … because the data was given to …
Two things not to say
“Zeros don't count.” Some zeros are significant (405, 0.0070); say “leading zeros only place the number”.
“Just cross off the extra digits.” That chops instead of rounding; always look at the next digit.
Questions to set
Extra practice in three tiers, including one question from earlier work for spacing. Every answer has been checked.
1Fluency
The idea on its own, with friendly numbers. Set these first.
- RoundingRound 2.0467 to 3 significant figures.
2.05. - CountingHow many significant figures does 30.05 have?
4.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- ContextA rice harvest in the Mekong Delta is 8.47 tonnes per hectare on a 3.2 hectare farm. Find the harvest to 2 significant figures.
27.104 tonnes, which is 27 tonnes. - Earlier work (Year 9)Write 0.000 52 in scientific notation.
5.2 × 10⁻⁴.
3Challenge
Reasoning, generalizing and working backwards.
- ReasoningA length is 6.0 cm to 2 significant figures. Between which two values must it lie?
From 5.95 cm up to (but not including) 6.05 cm. - EstimatingEstimate √(98.6 × 0.512) by rounding to 1 significant figure.
√(100 × 0.5) = √50, which is about 7.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
The figure works with the keyboard (tab to the slider or a button, then the arrow keys or Enter) and by touch. “Show me the steps” gives the same states in words.
The With a GDC section is closed by default and optional. Students without a GDC lose nothing; every answer is reached by hand.