Decimals on the Number Line to Thousandths

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Sketch the Line in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Here is a stretch of number line that runs from 0.4 up to 0.5. Where do you think 0.45 would sit on it? And here is a harder one: where would 0.456 go?

Tip

Have a good look before anyone answers.

Teacher Notes

Sketch the short 0.4 to 0.5 line on the board as pupils settle. Take two or three hands-up answers for 0.45 (most will land it near the middle), then pose 0.456 and pause. Do not resolve it yet — the point is to leave them wondering how we place a number with three decimal places when the marks only go to tenths.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~8 mins

Here are three number lines, each showing a tighter stretch than the last. Notice how the marks get finer on each one, and see where each decimal lands.

Teacher Notes

First line, 0 to 1, marks are tenths. 0.7 sits seven steps along. Ask the class to point to where 0.7 goes before revealing the marker.

Name the zoom every time it happens, and say zoom in, not change the scale.

Second line, 0.3 to 0.4, marks now hundredths. Count on: 0.31, 0.32, 0.33, 0.34. Point out that these marks only reach hundredths, so a three-place number like 0.385 falls between marks. Ask where 0.385 would go, take two predictions, revoice one aloud, somewhere between 0.38 and 0.39, before revealing the next.

Third line, 0.38 to 0.39, marks now thousandths. Count on with the class: 0.381, 0.382, 0.383, 0.384, 0.385, landing on the fifth mark past 0.38. This is the key one, same number they just predicted.

Big idea: each zoom makes the marks ten times finer, so there is always room.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

Key point

First, a quick check on trailing zeros. Watch the board: I place 0.5, then 0.50, then 0.500 — all three land on exactly the same point, because a trailing zero adds no value. Five tenths, fifty hundredths, five hundred thousandths: same spot, written three ways.

Now we work on the 0.3 to 0.4 line, with each small mark worth one thousandth. We will place three decimals in this order: 0.305, then 0.342, then 0.388. Watch how each one climbs a little higher along the same line.

Placing thousandths on the 0.3 to 0.4 line

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Open by building the trailing-zero equivalence on the board: place 0.5, then 0.50, then 0.500 and show all three landing on one point. This is the same equivalence idea the lesson keeps returning to, so use the 0.5 family here too.

Then set the line to run 0.3 to 0.4 with minor marks every thousandth. Call 0.305 first, then 0.342, then 0.388, in that order — each higher than the last so pupils can predict its rough position before placing.

Before each placement, ask the class to point roughly where it should go, then let one pupil drag the marker.
As you place, have the pupil count aloud by thousandths from the nearest tenth.

+15 XP

4 - Sketch the Line in Your Copy ~3 mins

COPYBOOK MOMENT

Illustration for Sketch the Line in Your Copy In your maths copy, use a ruler to sketch a number line from 0.3 to 0.4 with a mark every 0.01. That gives you eleven evenly spaced marks: 0.30, 0.31, 0.32, all the way up to 0.40.

These marks only reach hundredths, so our three thousandths decimals sit between two marks. For each one, first draw a small arrow to the nearest hundredth mark, then draw a tiny dot to show roughly where it lands between the marks.

0.305 sits between 0.30 and 0.31, halfway between them (five thousandths along).
0.342 sits between 0.34 and 0.35, close to 0.34.
0.388 sits between 0.38 and 0.39, close to 0.39.

Teacher Notes

Walk the room glancing at whether the ruler line runs 0.3 to 0.4 with ten evenly spaced hundredth marks — this is whole-class copybook practice, not marking. The point is that thousandths sit between hundredth marks, so pupils should place a small dot between two marks, not try to draw a thousandths scale by hand. Nudge anyone who places a dot on a mark rather than between two.

+10 XP

5 - Class Challenge ~8 mins

Key point

Today we work through these placements together on the same 0.3 to 0.4 line: place 0.305, then place 0.342, then place 0.388 — and finally the trickiest one, find a decimal that sits between 0.34 and 0.345.

Place decimals on the 0.3 to 0.4 line

Teacher Notes

These are the practice questions — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

The first three are exact-position placements — pupils read off how many thousandths past the nearest tenth or hundredth.
The last one is a range task: any decimal strictly between 0.34 and 0.345 counts, so more than one answer is right. Ask a second pupil for a different valid answer to make the 'always room in between' idea land.

Use the Check button as part of the narration — 'yes, that's it' on a green tick.

+15 XP

Pupil practice

Module 1 · Place Value, Decimals and the Number System Number

Lesson 8 · Decimals on the Number Line to Thousandths

Download Activity Book page (PDF)

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Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~8 mins

3 - Try It Together ~11 mins

Placing thousandths on the 0.3 to 0.4 line

4 - Sketch the Line in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Place decimals on the 0.3 to 0.4 line

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