First published in the SMC Primary Journal Issue 1 (2017)
Two years ago we bought 100 metre sticks. Last year we bought 100 more! Used together with base ten materials, metre sticks are a great resource for teaching key numeracy skills.
The ones we use have the multiples of ten and five written on them but have marks only (no numerals) for the numbers in-between.
These partially numbered metre sticks can be difficult to find. We sourced ours from the Ruler Company – www.rulerco.co.uk.
Number sequence 0 to 100
To familiarise children with the metre stick I like to play the ‘two hands, one piano’ game. This is a simple ‘show-me’ activity where one child ‘plays’ the numbers from 0 to 50, and the other plays the numbers from 50 to 100.
Call out a range of numbers and challenge the children to find them as quickly as possible. I start with the multiples of ten, then extend this to include the multiples of five. Next, children progress to identifying the unmarked numbers. This requires them to count on or back, from the nearest 5 or 10, to find the given number’s position.
Adding and subtracting tens
The children can then move on to using the metre stick, along with base-ten rods, to add and subtract tens. Assuming you have an up-to-date set, each base-ten rod should measure exactly 10cm. So, for example, if one end of the rod is placed on the stick at 15, adding on ten takes you to 25. Taking ten away returns you to 15.
There is general agreement that addition and subtraction are best taught together. The metre stick shows beautifully how the two operations are related. It is also effective in helping children understand why, when they add or subtract ten, only the tens digit changes.
Pattern is a key element of mathematics.. Moving the tens rod along the stick from 42 to 52 to 62 etc. clearly shows a repeating pattern. By using these patterns, children quickly learn how to add or subtract 10, and multiples of ten, to or from any 2-digit number.
For pupils in need of challenge, place two or three metre sticks end to end and explore calculations such as 123 + 70, 156 – 40 etc.
Complements to 100
We will assume for what follows that children already have instant recall of addition facts to ten.
Take two metre sticks, turn one round the other way and place them back to back. Ask the children to observe and describe what they see.
By carefully placing tens rods along the appropriate part of each stick, it should be easy for children to see that, for example, 60 + 40 = 100 because 6 tens and 4 tens equals 10 tens.
This activity can be extended to include the multiples of five, for example 35 + 65 = 100. Two lots of five unit cubes make up the middle ten.
As before, the ‘in-between’ facts can then be explored, for example 64 + 36. The question as to why 36 (not 46) is the complement of 64 generates interesting discussion and is extremely useful when working out change from £1. The metre stick becomes your ‘pound’ and the centimetres your ‘pennies’!
Differences
Difference is often taught as another word for ‘taking away’ but in actual fact these two ideas are quite different.
To find 100 – 70 we start at 100 and count down to 70.
However, the difference between 70 and 100 is the distance on the stick between 70 and 100,
The relationship between addition and subtraction is again highlighted. The children come to understand that the difference between 70 and 100 is 30 because 70 + 30 = 100 and 100 – 30 = 70
Differences between the fives numbers is a good follow-up investigation, again using base-ten rods.
Subtracting 8 or 9
Subtracting ‘near tens’ is something children often find challenging. Turning the metre stick into an elevator illustrates this beautifully!
Stand the stick on its end with zero on the table and 100 in the air. The metre stick now represents a tall skyscraper with 100 floors. A staircase runs from top to bottom and an express lift stops at every tenth floor. So, if you are on floor 50 and want to get to floor 40 you can go down 10 floors in the lift.
However, if you only want to go down 9 floors, the quickest thing to do is to get the lift down ten floors then walk back up one level using the stairs: 50 – 9 = 41
The same method will allow you to subtract 19, 29 or 39, for example by zooming down 40 floors and walking back up 1. This idea can be extended to include subtracting 8, 18, 28…. by zooming down 10, 20 or 30 floors and climbing back up 2 levels.
Once children have grasped this idea they can explore what happens if they start on an ‘in-between’ number and subtract 8 or 9. They can also investigate the patterns that occur when they add near tens by zooming up and walking down.
Well I hope that has got your creative juices flowing! Go and get those metre sticks ordered and get counting.
P.S. The same metre sticks are also great for teaching fractions, decimal fractions and percentages. But that’s a story for another time ….
Author
Rob Porteous, Deputy Head Learning and Teaching, George Watson’s College, Edinburgh;
Creator of Maths Investigations.