Here is a photo of a pencil lying along a ruler. The tip is sitting somewhere between the 16 and 17 centimetre marks. How long is this pencil, as exactly as you can read it? Hands up: what number would you write down?
Watch closely at the front. The ruler has long lines for the centimetres and tiny lines in between — ten millimetres in every centimetre. We will measure a few real objects against it, so watch where each one ends and where the eye needs to be to read it true.
Now it is your turn at your own desk. Take your own ruler and measure three things: your pencil, your eraser, and your maths copy. For each one, read it to the nearest millimetre.
Say each length aloud two ways: in centimetres with a decimal (like 13.8 cm) and in whole millimetres (like 138 mm). Remember to look straight down, eye square over the mark, before you read. Each pupil's pencil, eraser and copy are different lengths, so readings will not match.
In your maths copy, sketch ONE of the readings you just took. Write the length two ways underneath your sketch: in centimetres with a decimal, and in whole millimetres. Then circle the millimetre digit on each one.
Watch this worked example first. A pencil that ends four small marks past 12 is written two ways:
Circle the millimetre digit on both: the 4 after the decimal point in 12.4 cm, and the last digit 4 in 124 mm. Those two circled digits are the same millimetre count. Now sketch one of your own readings and do the same.
Before the stations, watch one worked reading together. An object ends between two tiny millimetre marks, past the 8.6 line but not quite at 8.7. It sits closer to 8.6, so the nearest millimetre is 8.6 cm (or 86 mm). When an end falls between two marks, choose the nearer one, not a half.
Six real objects are set out as stations at the front: a crayon, an eraser, a glue stick, a highlighter, a marker, and a colour pencil. In your maths copy, rule three columns and head them Object, cm, mm. When it is your turn at a station, measure that object with your own ruler to the nearest millimetre.
Write each object's name and its length two ways in your copy: in centimetres with a decimal and in whole millimetres. Look straight down, eye square over the mark, every time. If the end sits between two marks, take the nearer mark. At the end we will read each one aloud and agree the true length.
Where did the reading get harder today? Was it the longest objects, the ones whose end fell between two marks, or the ones where it was tricky to look straight down? Where does the precision start to drop off?
Next we will take these millimetre, centimetre and metre readings and convert between them — moving the digits along as we change from one unit to the next.
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