Reason about the location of any number with up to 2 decimal places in the linear number system (1)

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Description

Pupils need to become familiar with the relative positons, on a number line, of numbers with 1 and 2 decimal places. They will need to see number lines with both tenths and intermediate hundredths values marked, and learn, for example, that 0.5 is the same as 0.50 and 3 is the same as 3.0 or 3.00. Pupils should recognise the magnitude and position of a given decimal fraction, irrespective of the precision it is given to, for example, 5 tenths lies between 0.45 and 0.55 on the number line below, whether it is represented as 0.5 or 0.50. Pupils need to be able to identify or place decimal fractions on number lines marked in tenths and/or hundredths. They should use efficient strategies and appropriate reasoning, including identifying the midpoints or working backwards from a whole number or a multiple of one tenth. Pupils need to be able to estimate the value or position of decimal fractions on unmarked or partially marked numbers lines, using appropriate proportional reasoning, rather than counting on from a start point or back from an end point. For example, here pupils should reason: “8.6 is about here on the number line because it’s just over half way”. Here, pupils should reason: “8.75 is about here on the number line because it’s the midpoint of 8.7 and 8.8.” Pupils must also be able to identify which whole numbers, or which pair of multiples of 0.1, a given decimal fraction is between. To begin with, pupils can use a number line for support. In this example, for the number 8.61, pupils must identify the previous and next whole number, and the previous and next multiple of 0.1.

Language focus:

“a is 0.14 because it is 1 hundredth less than the midpoint of 0.1 and 0.2, which is 0.15.”

“b is 0.41 because it is 1 hundredth more than 0.4.”

By the end of year 5 pupils need to be able to complete this type of task without the support of a number line. Pupils should then learn to round a given decimal fraction to the nearest whole number by identifying the nearest of the pair of whole numbers that the decimal fraction is between. Similarly, pupils should learn to round to the nearest multiple of 0.1. They should understand that they need to examine the digit in the place to the right of the unit they are rounding to, for example when rounding to the nearest whole number, pupils must examine the digit in the tenths place. Again, pupils can initially use number lines for support, but should be able to round without that support by the end of year 5.

Language focus:

“The previous whole number is 8. The next whole number is 9.”

“The previous multiple of 0.1 is 8.6. The next multiple of 0.1 is 8.7.”

“The closest whole number is 9.”

“8.61 rounded to the nearest whole number is 9.”

Finally, pupils should also be able to count forwards and backwards from any decimal fraction in steps of 1, 0.1 or 0.01. Pay particular attention to counting over ‘boundaries’, for example:     • 2.1, 2.0, 1.9      • 2.85, 2.95, 3.05

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