Place Value Challenge: Always, Sometimes, Never

Year 6 MathsPlace Value3 pages

About this worksheet

Eight statements about large numbers, rounding and negative numbers make up this Year 6 reasoning challenge. Pupils decide whether each one is always, sometimes or never true and prove it in a table with a verdict column and lines for examples. The statements run from rounding to the nearest million to a temperature that falls by 15ยฐC from a single-digit start. Two pages hold the table. A third gives each verdict with a model explanation, and the set fits the England National Curriculum objectives for Year 6 number and place value.

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Curriculum objectives covered

Number - number and place value

โ€œRead, write, order and compare numbers up to 10 000 000 and determine the value of each digitโ€

Statements 2 and 4 turn on digit values, for example the 8 in 4,819,200 being worth 800,000.

Number - number and place value

โ€œRound any whole number to a required degree of accuracyโ€

Statements 1, 6 and 8 test rounding to the nearest 10,000, 100,000 and million.

Number - number and place value

โ€œUse negative numbers in context, and calculate intervals across zeroโ€

Statement 5 adds two negatives and statement 7 takes 15ยฐC off a single-digit temperature.

Number - number and place value

โ€œSolve number and practical problems that involve all of the aboveโ€

Every statement needs a verdict backed by an example or a counter-example.

What's inside this worksheet

Statements 1 to 4

Pupils judge claims about rounding to the nearest million, seven-digit against six-digit numbers, counting on in steps of 100,000 and whether an 8 can be worth more than a 9 in a seven-digit number.

Statements 5 to 8

Adding two negative integers, rounding to the nearest 10,000, a 15ยฐC temperature drop and a number that rounds to 4,000,000. Each row has six lines for working.

Answers

A verdict and a worked example for each, such as 3,620,000 rounding to 4,000,000 but to 3,600,000 to the nearest 100,000.

How teachers use it

Card sort

Cut the eight statements into cards and let groups sort them into always, sometimes and never before anyone writes. Only statements 2 and 7 are always true, so the sort starts an argument straight away.

Counter-example first

Tell pairs they may not write a verdict until they have tried three numbers. Statement 4 is where most pupils change their minds.

Greater depth

Pupils who finish early can rewrite statement 6 so that it becomes always true, then test their version on 2,396,000.

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