Mathematics

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50 mins

Teacher/Student led

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+90 XP

Teacher-led from the board. Pupils do not need a device, but can follow on one.

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IWB/Projector/Large Screen

Place Value Problem Solving and Review

Use place-value clues to solve mystery decimal numbers. Each clue narrows down the possibilities until one answer remains, and discover how clue order affects solving speed.

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

Your turn

Your teacher is running this lesson on the board. Here is the part you can try yourself.

Your written work is on page 12

Place value chart

1 - Getting Started ~3 mins

Here is a mystery number's first clue: "I have three tenths and no hundredths."

Say what you think the number could be. Could there be more than one answer from just this one clue, or does it already pin the number down?

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~8 mins

Three clues narrow one mystery decimal down to a single answer. Read each clue, look at its place-value chart, and keep your own list of the numbers that are still possible.

Clue 1. The number has no units, three tenths and four hundredths. Its thousandths digit is hidden: it could be any digit from 0 to 9, even 0.
Clue 2. The number is between 0.3 and 0.35.
Clue 3. Multiply the number by 100 and you get a whole number.

Which number survives all three clues? Decide before you open the answer.

Show how the clues narrow it down

Clue 1 narrows a lot. Ten numbers fit, one for each digit the hidden thousandths could be: 0.340, 0.341, 0.342 and so on up to 0.349.

Clue 2 narrows nothing, and that is the thing to notice. All ten are already inside those fences, so none are ruled out. It is still a true clue: it would have ruled out 0.36 or 0.4 if they had been on the list. A clue can be true and still do no work.

Clue 3 finishes it. Try every one: 0.341 × 100 = 34.1, 0.342 × 100 = 34.2, and so on up to 0.349 × 100 = 34.9. None of those is a whole number. Only 0.340 × 100 = 34 is.

One number survives all three: 0.340, which we write as 0.34. The hidden digit was 0.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

Today we work through one full mystery number together, clue by clue. Here are the four clues in the order we will meet them:

Clue 1: I have no units and two decimal places. My tenths digit is 4.
Clue 2: When you round me to the nearest tenth, I round up to 0.5.
Clue 3: My hundredths digit is odd.
Clue 4: My tenths digit and my hundredths digit add up to 11.

After each clue we will build one surviving candidate at a time on the place-value mat to check it still fits, and cross off any that the new clue rules out on the board. Predict, before clue 4, how many numbers are still standing.

Show the mystery number

Clue 1 leaves ten numbers, 0.40 to 0.49. Clue 2 leaves 0.45, 0.46, 0.47, 0.48 and 0.49. Clue 3 leaves 0.45, 0.47 and 0.49. Clue 4 leaves one number: 0.47, because 4 + 7 = 11.

Build the surviving candidates

+15 XP

4 - Sketch a Clue Mat in Your Copy ~2 mins

COPYBOOK MOMENT

Illustration for Sketch a Clue Mat in Your Copy In your maths copy, sketch a place-value mat with U, t and h columns for each of the four clues we just worked. Write the candidate decimals that fit that clue underneath your mat, then cross off any that the next clue rules out.

+10 XP

Pupil practice

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

Lesson 12 · Place Value Problem Solving and Review

Download Activity Book page (PDF)

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