Good Learning Co.
SavannahYear 8
← Maths
MathsNumber sense25 min★ difficulty

Place value with big and small numbers

The same ten digits describe the width of an atom and the distance to the Moon. Place value is the trick that makes that possible.

Part of your national curriculum
  • Number: Understand and use place value for decimals, measures and integers of any size

Lesson overview

What you'll learn in this lesson

Understand and use place value for decimals, measures and integers of any size

Key learning points

  • • Columns keep growing
  • • Worked example
  • • Reading measures

This lesson at a glance

  • 25 minutes
  • 14 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

decimalsmeasuresintegerscolumnsgrowing

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%
1

Watch & discover

Part 1 of 14

Watch first

Place value with big and small numbers

An English teaching video on this topic from MathTalk. Watch it, then scroll down for the lesson.

In a nutshell

Understand and use place value for decimals, measures and integers of any size

2

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · Columns keep growing

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 14

Learn

Columns keep growing

Each column is ten times the one to its right: units, tens, hundreds, thousands, and so on forever. Moving left multiplies by 10; moving right divides by 10. So 4,000,000 is 4 × 1,000,000, and 0.004 is 4 ÷ 1,000.

4

Explore the idea

Part 4 of 14

Learn

Worked example

Multiply 3.6 by 100. Each digit shifts two columns left: 3.6 × 100 = 360. Now divide 360 by 1000: each digit shifts three columns right, giving 360 ÷ 1000 = 0.36.

5

Quick check

Part 5 of 14

Quick check

What is 3.6 × 100?

6

Reset break

Part 6 of 14

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
7

Quick check

Part 7 of 14

Quick check

What is 250 mg in grams?

8

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Reading measures

A short piece of teaching, then a check to make sure it has landed.

9

Explore the idea

Part 9 of 14

Learn

Reading measures

A distance of 1.5 km is 1,500 m because kilo means ×1000. A mass of 250 mg is 0.25 g because milli means ÷1000. Matching the prefix to the place-value shift avoids silly errors.

10

Quick check

Part 10 of 14

Quick check

Which is bigger, 0.09 or 0.1?

11

Challenge round

Part 11 of 14

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

12

Challenge round

Part 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Each digit shifts two ____ left: 3.6 × 100 = 360.

13

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Place value with big and small numbers

3 questions, marked with the reasoning shown. No timer.

  1. 1. What is 3.6 × 100?

  2. 2. What is 250 mg in grams?

  3. 3. Which is bigger, 0.09 or 0.1?

14

Lesson round-up

Part 14 of 14

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 14 · Watch & discover

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    Understand and use place value for decimals, measures and integers of any size

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