Scientific notation: a week of ready-to-teach maths
Five lessons for Year 9 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet with practice and a stretch section, plus size line-up cards, same-number match cards, a mini-check and every answer with its working.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Print the two cut-out sheets, one copy per pair, and cut them before Day 1: the size line-up cards are for Day 1, the same-number match cards for Day 3.
- Days 1 to 3 are worked without calculators, so the point really moves; calculators come out on Days 4 and 5.
- Open the free interactive unit on the board. Every plan says which picture to show and which buttons to press.
The idea in plain words
Real measurements run from the width of an atom to the distance to the Sun, and from a nanosecond to the age of the universe. Scientific notation writes each one as a number that is at least 1 and less than 10, multiplied by a power of ten: 27 000 000 is 2.7 × 10⁷ and 0.000 025 is 2.5 × 10⁻⁵. The power counts the places the point moves, positive for large numbers and negative for small ones (small, not below zero), so it tells the scale at a glance. Numbers are compared by their powers first, and multiplied and divided with the index laws.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 60 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point for two shorter sessions, and every worksheet ends with a stretch section for students who finish early.
How we write these numbers
A power of ten has a raised exponent: 10⁵, 10⁻⁴. Ordinary numbers are spaced in groups of three once a part has five or more digits, the SI way: 300 000 and 0.000 05, but 3000 and 0.0003. The first number of standard form is called the mantissa on the board, as in the interactive unit. Measurements are real ones, rounded as each sheet says.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Students learn and do | On screen |
|---|---|---|---|
| 1 | Too big, too small | Read one strip of sizes from an atom to the Sun, write powers of ten both ways, apply the one-to-ten rule, and line up twelve real lengths by their powers of ten | Why we need scientific notation; The one-to-ten rule |
| 2 | Large numbers | Move the point left to write large numbers in scientific notation and back again, count places rather than zeros, and write real measurements from Australia and space | Moving the decimal point (large) |
| 3 | Small numbers | Move the point right for negative powers, see that negative means small, write tiny measurements from bacteria to light, and play same-number match | Moving the decimal point (small) |
| 4 | Comparing and time scales | Compare numbers by their powers first, turn days, years and lifetimes into seconds, find how many times longer one interval is, and squeeze the universe into a year | A timeline of scales |
| 5 | Calculating with powers of ten | Multiply and divide with the index laws, solve light, Moon and paper-stack problems, read a calculator display, and play the quiz as a class game | Multiplying with the index laws; self-check quiz as a class game |
How the week builds
Day 1 meets powers of ten and the one-to-ten rule; Days 2 and 3 write large and then small measurements in scientific notation and back; Day 4 compares and orders them, with time intervals in seconds; and Day 5 calculates with them. It builds on the index laws with integer exponents earlier in Year 9 and on place value. It prepares measurement and science work where very large and very small quantities are the everyday ones.
Materials for the week (one trip)
- From the classroom: calculators for Days 4 and 5, scissors, envelopes for the cards, this pack printed.
- Cut-out sheet 1, one per pair: 12 size line-up cards (Day 1).
- Cut-out sheet 2, one per pair: 16 same-number match cards (Day 3).
- If you have them: mini whiteboards for quick conversions. No other equipment to buy.
Words for the word wall
scientific notation, standard form, mantissa, power of ten, exponent, index, place value, decimal point, positive exponent, negative exponent, order of magnitude, nanosecond, microsecond, millisecond, interval, scale, compare, index laws
Dear families
This week in maths, Year 9 is writing very large and very small measurements in scientific notation: the distance to the Moon, the width of a hair, the age of the universe and the time a camera flash lasts. The power of ten in each number tells its size at a glance.
Try this at home
- Find a very large or very small number on a packet, a bill or in the news, and write it as a number from 1 to 10 times a power of ten.
- Ask: how many seconds are in an hour? (3600, which is 3.6 × 10³.)
- Ask: which is bigger, 2 × 10⁻³ or 1 × 10⁻²? (1 × 10⁻² = 0.01 is bigger than 0.002.)
- Ask: is 5 × 10⁻⁴ a negative number? (No: it is 0.0005, small but positive.)
My scale diary
Fill one row a day. Write a measurement from class, its ordinary form, and its scientific notation.
| Day | Measurement | Ordinary form | Scientific notation |
|---|---|---|---|
| Monday | |||
| Tuesday | |||
| Wednesday | |||
| Thursday | |||
| Friday |
Too big, too small
Measurements run from the width of an atom to the distance to the Sun. Scientific notation writes each as a number from 1 up to 10 times a power of ten, so the power alone gives the scale.
We are learning to
- write powers of ten as ordinary numbers and back, negative powers included,
- say whether a number is in standard form, and rewrite it if not,
- order real lengths by their powers of ten.
Success criteria
- I can write 10⁻³ as an ordinary number and say why 32 × 10³ is not in standard form.
- I can put six lengths in order by looking at their powers of ten first.
You need
The worksheet; the size line-up cards (cut-out sheet 1), one set per pair, cut out. No calculators today.
Lesson flow (about 60 minutes)
| 12 min | One strip, every size Show the first board picture (see the box). Then write 10⁶ = 1 000 000 and 10⁻³ = 0.001: the power counts the places the point moves from 1. Ask: “Why does 10⁻³ have three decimal places but only two zeros after the point?” |
| 13 min | The one-to-ten rule Show the second picture, then pairs do Parts A and B. Ask: “35 × 10⁴ and 3.5 × 10⁵ are the same number. Which is standard form, and why have a rule at all?” |
| 35 min | Size line-up Part C with the cards: pairs sort by the power first, then the mantissa, and record the order. Early finishers do Part D. Ask: “Which tells you more about a size, the power of ten or the first number?” |
Two shorter sessions instead? Split after Part B; start the second with the strip on the board again.
Watch for these ideas
- Counting zeros instead of places: 10⁻³ = 0.001 has two zeros after the point but the point moves three places.
- Reading 10⁻³ as a negative number: it is small, not below zero.
- Thinking 32 × 10³ is the wrong value: it is the right number, just not in standard form.
Answers
- Part A: 10⁵ = 100 000; 10⁻² = 0.01; 10⁹ = 1 000 000 000; 10⁻⁴ = 0.0001; 10⁰ = 1.
- Part B: 3.2 × 10⁴ yes; 32 × 10³ no, 3.2 × 10⁴; 0.8 × 10⁵ no, 8 × 10⁴; 9.99 × 10⁻² yes; 10 × 10⁶ no, 1 × 10⁷; 1.5 × 10⁻⁸ yes.
- Part C: the card key is with the mini-check answers. Closest to 1 m is a person’s height, 1.7 × 10⁰ m: power 0.
- Part D: (1.5 × 10¹¹) ÷ (1 × 10⁻¹⁰) = 1.5 × 10²¹: the Sun is 21 powers of ten farther than an atom is wide.
Too big, too small
A. Powers of ten, both ways
Write each power of ten as an ordinary number, or each ordinary number as a power of ten.
| 10⁵ | = |
| 10⁻² | = |
| 1 000 000 000 | = |
| 0.0001 | = |
| 10⁰ | = |
B. Standard form or not?
In standard form the first number is at least 1 and less than 10. Tick the ones in standard form; rewrite the others.
| Number | Standard form? | Rewritten, if needed |
|---|---|---|
| 3.2 × 10⁴ | ||
| 32 × 10³ | ||
| 0.8 × 10⁵ | ||
| 9.99 × 10⁻² | ||
| 10 × 10⁶ | ||
| 1.5 × 10⁻⁸ |
C. Size line-up
Put the 12 cards in order from smallest to largest: powers of ten first, then the first numbers. Write the letters in order.
Which card is closest to 1 m? How do you know from its power of ten? ______________________
D. Stretch: how many times?
How many times farther is the Sun from Earth than an atom is wide? Use the powers of ten on the two cards.
Large numbers
A large number goes into standard form by moving the point left until one non-zero digit stands in front of it; the number of places moved is the positive power. Going back, the power says how many places to move the point right.
We are learning to
- write large numbers in scientific notation by counting the places the point moves,
- write a number in scientific notation in full, zeros and all,
- write real large measurements in scientific notation, with their units.
Success criteria
- I can write 46 000 as 4.6 × 10⁴ and say what the 4 in the power counts.
- I can write 2.3 × 10⁶ in full without losing a zero.
You need
The worksheet; mini whiteboards if you have them. No calculators today.
Lesson flow (about 60 minutes)
| 12 min | Slide the point Show the board (see the box). Then Australia’s population, about 27 000 000: the point moves 7 places left, so it is 2.7 × 10⁷. Ask: “27 000 000 has six zeros. Why is the power 7?” |
| 13 min | Both ways Pairs do Parts A and B, one writing and one checking by moving the point back. Ask: “Where does the last zero go when 4.05 × 10⁶ is written in full?” |
| 35 min | Real measurements Part C; early finishers do Part D. Ask: “Why round the land area of Australia? How much is lost by rounding?” |
Two shorter sessions instead? Split after Part B; start the second with the board picture again.
Watch for these ideas
- Counting zeros, not places: 5.07 × 10⁵ has a 0 inside it, and the power still counts places.
- Stopping too soon: 25 × 10⁶ is the right size but not standard form.
- Dropping a zero inside: 4.05 × 10⁶ is 4 050 000, not 405 000.
Answers
- Part A: 8300 = 8.3 × 10³; 507 000 = 5.07 × 10⁵; 12 000 000 = 1.2 × 10⁷; 96 400 000 = 9.64 × 10⁷; 1 000 000 000 000 = 1 × 10¹².
- Part B: 6.2 × 10³ = 6200; 4.05 × 10⁶ = 4 050 000; 7 × 10⁸ = 700 000 000; 1.001 × 10⁴ = 10 010.
- Part C: 344 400 = 3.444 × 10⁵; 7 688 287 = 7.688287 × 10⁶, about 7.69 × 10⁶; 5500 = 5.5 × 10³; 300 000 000 = 3 × 10⁸.
- Part D: a googol is 1 followed by 100 zeros. 25 × 10⁶ = 2.5 × 10⁷; 0.5 × 10⁹ = 5 × 10⁸: the mantissa moves one place and the power changes by one the other way.
Large numbers
A. Into scientific notation
Move the point left until one non-zero digit is in front of it. Count the places.
| 8300 | = |
| 507 000 | = |
| 12 000 000 | = |
| 96 400 000 | = |
| 1 000 000 000 000 | = |
B. Back to ordinary numbers
| 6.2 × 10³ | = |
| 4.05 × 10⁶ | = |
| 7 × 10⁸ | = |
| 1.001 × 10⁴ | = |
C. Real measurements
Write each measurement in scientific notation, with its unit. Round the mantissa where it says so.
| The Great Barrier Reef Marine Park covers about 344 400 km². | |
| The land area of Australia is 7 688 287 km². (Round the mantissa to 2 decimal places.) | |
| The surface of the Sun is at about 5500 °C. | |
| In one second, light travels about 300 000 000 m. |
D. Stretch: googols and fixing
A googol is 10¹⁰⁰. How many zeros does it have in full? Then put 25 × 10⁶ and 0.5 × 10⁹ into standard form, and explain what happens to the power.
Small numbers
A small number goes into standard form by moving the point right until one non-zero digit stands in front of it; the places moved give a negative power. Negative means small, less than one, not below zero.
We are learning to
- write small numbers in scientific notation with a negative power,
- write a number with a negative power in full,
- write tiny real measurements, and match ordinary and scientific forms quickly.
Success criteria
- I can write 0.0082 as 8.2 × 10⁻³ and explain the minus sign.
- I can write 7.4 × 10⁻⁴ in full.
You need
The worksheet; the same-number match cards (cut-out sheet 2), one set per pair, cut out. No calculators today.
Lesson flow (about 60 minutes)
| 12 min | The other way Show the board (see the box). Then a grain of pollen, about 0.000 025 m wide: the point moves 5 places right, so it is 2.5 × 10⁻⁵ m. Ask: “Is 2.5 × 10⁻⁵ a negative number? How do you know?” |
| 13 min | Same-number match Pairs lay the 16 cards face down and turn two at a time, keeping a pair when an ordinary number and a scientific one are the same number. The key is with the mini-check answers. Ask: “Which part of a card tells you at once whether its partner is large or small?” |
| 35 min | Tiny measurements Parts A to C; early finishers do Part D. Ask: “How many zeros come after the point in 3 × 10⁻⁷, and why one fewer than 7?” |
Two shorter sessions instead? Split after the match; start the second with the board picture again.
Watch for these ideas
- Forgetting the minus: 0.004 is 4 × 10⁻³, not 4 × 10³.
- Counting the zeros after the point: 0.004 has two, but the point moves three places.
- Thinking a negative power makes the number negative: 10⁻³ is 0.001, a small positive number.
Answers
- Part A: 0.004 = 4 × 10⁻³; 0.000 61 = 6.1 × 10⁻⁴; 0.07 = 7 × 10⁻²; 0.000 000 3 = 3 × 10⁻⁷; 0.000 015 = 1.5 × 10⁻⁵.
- Part B: 2 × 10⁻³ = 0.002; 8.5 × 10⁻⁶ = 0.000 008 5; 1.2 × 10⁻¹ = 0.12; 4.07 × 10⁻⁵ = 0.000 040 7.
- Part C: 0.000 002 = 2 × 10⁻⁶ m; 0.0001 = 1 × 10⁻⁴ m; 0.000 06 = 6 × 10⁻⁵ g; 0.000 000 53 = 5.3 × 10⁻⁷ m.
- Part D: 3 × 10⁻⁵ = 0.000 03 is larger than 3 × 10⁻⁸ = 0.000 000 03, by 10³ = 1000 times. No: 2 × 10⁻³ = 0.002 is above zero.
Small numbers
A. Into scientific notation
Move the point right until one non-zero digit is in front of it. The power is negative.
| 0.004 | = |
| 0.000 61 | = |
| 0.07 | = |
| 0.000 000 3 | = |
| 0.000 015 | = |
B. Back to ordinary numbers
| 2 × 10⁻³ | = |
| 8.5 × 10⁻⁶ | = |
| 1.2 × 10⁻¹ | = |
| 4.07 × 10⁻⁵ | = |
C. Tiny measurements
Write each measurement in scientific notation, with its unit.
| An E. coli bacterium is about 0.000 002 m long. | |
| A sheet of paper is about 0.0001 m thick. | |
| A grain of table salt has a mass of about 0.000 06 g. | |
| Green light has a wavelength of about 0.000 000 53 m. |
D. Stretch: smaller by how much?
Which is larger, 3 × 10⁻⁵ or 3 × 10⁻⁸, and how many times larger? Is 2 × 10⁻³ a negative number? Explain both.
Comparing and time scales
To compare numbers in scientific notation, compare the powers first; only when the powers match do the first numbers decide. Time intervals from a camera flash to a lifetime compare the same way once they are all in seconds.
We are learning to
- compare and order numbers in scientific notation, large and small,
- turn time intervals into seconds and write them in scientific notation,
- find how many times longer one interval is than another.
Success criteria
- I can explain why 2 × 10⁻² is larger than 9 × 10⁻³.
- I can write a week in seconds in scientific notation.
You need
The worksheet; calculators.
Lesson flow (about 60 minutes)
| 12 min | Powers first Show the board (see the box). Then 4 × 10⁶ against 9 × 10⁵: 10⁶ beats 10⁵, so 4 × 10⁶ is larger even though 9 > 4. A millisecond, 10⁻³ s, is 1000 microseconds, 10⁻⁶ s. Ask: “When do the first numbers decide which is larger?” |
| 13 min | Compare Pairs do Part A, writing each pair in full only to check. Ask: “Which is larger, 10⁻⁵ or 10⁻⁶? Why does −5 beat −6?” |
| 35 min | Seconds and how many times Parts B and C with calculators; early finishers do Part D. Ask: “To find how many times longer, which number goes on top?” |
Two shorter sessions instead? Split after Part A; start the second with the timeline again.
Watch for these ideas
- Comparing the first numbers before the powers: 9 × 10⁵ is smaller than 4 × 10⁶.
- With negative powers, thinking 10⁻⁶ is larger because 6 is larger than 5.
- Dividing the wrong way round for “how many times longer”: the longer interval goes on top.
Answers
- Part A: 6.1 × 10⁴ > 9.8 × 10³; 2.5 × 10⁻³ < 2.5 × 10⁻²; 7 × 10⁵ < 7.1 × 10⁵; 1.2 × 10⁻⁴ > 9 × 10⁻⁵.
- Part B: one day = 86 400 s = 8.64 × 10⁴ s; a heartbeat = 0.8 s = 8 × 10⁻¹ s; one year = 31 536 000 s ≈ 3.15 × 10⁷ s; a camera flash = 0.001 s = 1 × 10⁻³ s; a human lifetime = 2 522 880 000 s ≈ 2.52 × 10⁹ s. Shortest to longest: a camera flash, a heartbeat, one day, one year, a human lifetime.
- Part C: one day ÷ one second = 8.64 × 10⁴; a microsecond ÷ a nanosecond = 1 × 10³; the age of Earth, 4.5 × 10⁹ years ÷ a lifetime of 80 years ≈ 5.63 × 10⁷.
- Part D: 5000 ÷ (1.38 × 10¹⁰) × 3.15 × 10⁷ s ≈ 11.4 s: all of recorded history fits in the last 11 seconds of the year.
Comparing and time scales
A. Which is larger?
Write < or > between each pair. Look at the powers first.
| 6.1 × 10⁴ | 9.8 × 10³ | |
| 2.5 × 10⁻³ | 2.5 × 10⁻² | |
| 7 × 10⁵ | 7.1 × 10⁵ | |
| 1.2 × 10⁻⁴ | 9 × 10⁻⁵ |
B. All in seconds
Write each interval in seconds, in scientific notation (mantissa to 2 decimal places). Then number them from shortest (1) to longest (5).
| Interval | Given as | Seconds | Order |
|---|---|---|---|
| one day | 24 hours | ||
| a heartbeat | 0.8 seconds | ||
| one year | 365 days | ||
| a camera flash | 0.001 seconds | ||
| a human lifetime | 80 years of 365 days |
C. How many times longer?
| How many times longer is one day than one second? | |
| How many times longer is a microsecond than a nanosecond? | |
| How many times longer is the age of Earth, 4.5 × 10⁹ years than a lifetime of 80 years? |
D. Stretch: the universe in a year
The universe is about 1.38 × 10¹⁰ years old. Squeeze all of it into one year of 365 days. Recorded human history is about 5000 years: how many seconds of that year does it take?
Calculating with powers of ten
The index laws do the work: to multiply, multiply the first numbers and add the powers; to divide, divide them and subtract the powers. Then put the answer back into standard form.
We are learning to
- multiply and divide numbers in scientific notation with the index laws,
- solve measurement problems about light, the Moon and paper in scientific notation,
- enter and read scientific notation on a calculator.
Success criteria
- I can work out (3 × 10⁵) × (2 × 10⁻²) and give the answer in standard form.
- I can read 2.5E−3 on a calculator as 2.5 × 10⁻³.
You need
The worksheet; calculators; the unit’s self-check quiz for the game.
Lesson flow (about 60 minutes)
| 10 min | Light from the Sun Show the board (see the box). Then sunlight: the Sun is 1.5 × 10¹¹ m away and light travels 3 × 10⁸ m/s, so the time is 0.5 × 10³ = 5 × 10² s, about 8.3 minutes. Ask: “Why is 0.5 × 10³ not the final answer?” |
| 35 min | Calculate and solve Parts A to C; early finishers do Part D. Check one Part A answer each with the calculator’s EXP or ×10ˣ key. Ask: “Does the answer make sense? Is the stack of paper taller than you?” |
| 15 min | Self-check quiz as a class game Run the unit’s self-check quiz on the board. Teams vote on each answer, then the reason is read aloud. |
Two shorter sessions instead? Split after Part A; start the second with Part B and the quiz.
Watch for these ideas
- Multiplying the powers: 10⁴ × 10³ is 10⁷, not 10¹².
- Leaving 15 × 10³ or 0.5 × 10⁻⁵ as the answer: fix the mantissa and change the power.
- Typing 10 and then EXP on a calculator: 3 × 10 EXP 8 gives 3 × 10⁹, ten times too big.
Answers
- Part A: (2 × 10⁵) × (4 × 10³) = 8 × 10⁸; (5 × 10⁻³) × (3 × 10⁶) = 15 × 10³ = 1.5 × 10⁴; (9 × 10⁸) ÷ (3 × 10²) = 3 × 10⁶; (4 × 10⁻²) ÷ (8 × 10³) = 0.5 × 10⁻⁵ = 5 × 10⁻⁶.
- Part B: 1. 3 × 10⁸ × 60 = 1.8 × 10¹⁰ m. 2. 1 × 10⁻⁴ × 5 × 10³ = 5 × 10⁻¹ m = 0.5 m. 3. 3.84 × 10⁸ ÷ 3 × 10⁸ = 1.28 s. 4. 5.97 × 10²⁴ ÷ 7.35 × 10²² ≈ 81 times.
- Part C: 3.2E5 = 3.2 × 10⁵; 7.05E-4 = 7.05 × 10⁻⁴; 1E12 = 1 × 10¹².
- Part D: a year is about 3.15 × 10⁷ s, so at 14 a student has lived about 14 × 3.15 × 10⁷ ≈ 4.4 × 10⁸ s.
Calculating with powers of ten
A. Multiply and divide
Work out each one without a calculator. Give the answer in standard form.
| (2 × 10⁵) × (4 × 10³) | = |
| (5 × 10⁻³) × (3 × 10⁶) | = |
| (9 × 10⁸) ÷ (3 × 10²) | = |
| (4 × 10⁻²) ÷ (8 × 10³) | = |
B. Problems
Write the calculation first, then the answer in scientific notation with its unit.
| 1. Light travels 3 × 10⁸ m in one second. How far does it travel in one minute? | |
| 2. A sheet of paper is 1 × 10⁻⁴ m thick. How tall is a stack of 5 × 10³ sheets? | |
| 3. The Moon is 3.84 × 10⁸ m away. A radio message travels at the speed of light. How long does it take to reach the Moon? | |
| 4. Earth’s mass is 5.97 × 10²⁴ kg and the Moon’s is 7.35 × 10²² kg. How many times heavier is Earth? |
C. Read the calculator
A calculator shows scientific notation with an E. Write each display in scientific notation.
| 3.2E5 | = |
| 7.05E−4 | = |
| 1E12 | = |
D. Stretch: seconds alive
About how many seconds have you been alive? Estimate a year in seconds first, then write your answer in scientific notation.
Size line-up cards
For Day 1, one set per pair: 12 cards
Line the cards up from the smallest length to the largest. Read the power of ten first, then the first number.
Teacher note: the key is with the mini-check answers, so this sheet can go to pairs whole.
Same-number match cards
For Day 3, one set per pair: 16 cards
Lay the cards face down. Take turns to turn two over. Keep them if they are the same number, one ordinary and one in scientific notation.
Teacher note: the key is with the mini-check answers, so this sheet can go to pairs whole.
What we know: Scientific notation
Work on your own, without a calculator. Show your working.
- Write 52 000 in scientific notation. ______________________
- Write 0.0009 in scientific notation. ______________________
- Write 6.03 × 10⁵ as an ordinary number. ______________________
- Is 0.45 × 10⁴ in standard form? If not, rewrite it. ______________________
- Which is larger, 2 × 10⁻⁷ or 5 × 10⁻⁸? Explain. ______________________
- A millisecond is 10⁻³ s and a nanosecond is 10⁻⁹ s. How many nanoseconds are in a millisecond? ______________________
- Work out (6 × 10⁵) × (3 × 10⁻²) in standard form. ______________________
- A cell is 1 × 10⁻⁵ m wide. How many cells fit side by side along 1 cm, which is 1 × 10⁻² m? ______________________
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers with working
- The point moves 4 places left: 5.2 × 10⁴.
- The point moves 4 places right: 9 × 10⁻⁴.
- Move the point 5 places right: 603 000.
- No: 0.45 is less than 1. 0.45 × 10⁴ = 4.5 × 10³.
- 2 × 10⁻⁷: compare the powers first, and 10⁻⁷ is larger than 10⁻⁸ (0.000 000 2 against 0.000 000 05).
- 10⁻³ ÷ 10⁻⁹ = 10⁶ = 1 000 000.
- 6 × 3 = 18, and 5 + (−2) = 3: 18 × 10³ = 1.8 × 10⁴.
- 10⁻² ÷ 10⁻⁵ = 10³ = 1000 cells.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Standard form | Leaves a mantissa of 10 or more, or under 1 | Writes the first number from 1 up to 10 and fixes one that is not | Explains why the power changes when the mantissa is fixed |
| Large and small | Counts zeros instead of places, or drops the minus | Converts both ways for large and small numbers | Explains that a negative power means small, not below zero |
| Comparing and time | Compares the first numbers before the powers | Orders by powers first and turns intervals into seconds | Finds how many times larger, with the right number on top |
| Calculating | Multiplies the powers, or leaves 15 × 10³ | Uses the index laws to multiply and divide, in standard form | Solves a problem in steps and checks that the answer is sensible |
Eight questions, four ideas. A student at standard answers most questions with working, and every answer is in standard form.
Card keys
Size line-up (Day 1), smallest first: B 1 × 10⁻¹⁰ m, G 1 × 10⁻⁷ m, I 7.5 × 10⁻⁶ m, D 7 × 10⁻⁵ m, K 5 × 10⁻⁴ m, A 1.7 × 10⁰ m, F 5.03 × 10² m, L 2.228 × 10³ m, C 2.508 × 10⁶ m, J 1.27 × 10⁷ m, E 3.84 × 10⁸ m, H 1.5 × 10¹¹ m.
Same-number match (Day 3): 45 000 = 4.5 × 10⁴; 0.0072 = 7.2 × 10⁻³; 3 800 000 = 3.8 × 10⁶; 0.000 05 = 5 × 10⁻⁵; 610 = 6.1 × 10²; 0.29 = 2.9 × 10⁻¹; 920 000 000 = 9.2 × 10⁸; 0.000 000 8 = 8 × 10⁻⁷.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Powers | Large | Small | Compare | Calculate |
|---|---|---|---|---|---|
The five columns are the five days: powers of ten, large numbers, small numbers, comparing and time, and calculating.