**Story:**

Swish, twirl, swoosh. Welcome to the ribbon artistic gymnastics! One problem - moments before the event, your dog just ate your ribbon! Oh gosh - why did you bring a dog to the Olympics! It's okay, it's okay. I know what you can do. You can just measure a new ribbon and off you go to compete. But wait, the dog has also chewed off the start of your measuring tape. What is wrong with this dog! Oh no...what can you do? The judges are so fussy - if it is even off by 1cm, the ribbon will be disqualified. Think, think!

You find a new ribbon on the floor. But you need to check its length. Remember, the start of your measuring tape has vanished. But, there is surely a way to measure it.

Write down proof about the measurements of your new ribbon for the judges, but __find at least 5 different equations that prove it__, because those judges are so fussy that measuring once will not be enough.

**Tools: **

Ribbons cut to varying lengths (under 20cm for most students).

Measuring tapes stuck down to desks with Blu Tack or similar.

**Main event**

Record all start and end points of your ribbon along the measuring tape, proving its length. For example, for an 8cm ribbon:

48 - 40 = 8

56 - 48 = 8

90 - 82 = 8

114 - 106 = 8

83 - 75 = 8

Next, change ribbons and repeat, choosing your favourite ribbon by the end of the lesson.

**Pro tip: **Did you know that you can do this to solve really tricky subtraction problems.

For example, 62 - 37 seems difficult. But you can instead +3 to both sides of the equation, keeping the difference (the ribbon's length) the same. This would transform into 65 - 40, which is just 25, too easy! The change transforms the problem from an ugly duckling to a beautiful swan, using the transformation (pump it up) strategy.

Let's try another, like 106 - 88. Take away 6 from both numbers, which keeps the difference (ribbon length) the same, making the new equation 100 - 82, which is a difference of 18 (from the 82, 8 more to get to 90, then 10 more to get to 100).

Or add 2 to both sides, making the new problem 108 - 90 (which is also 18: From 90, 10 more to get to 100, then 8 more to 108, so 18 altogether as the difference).

Or even 10 005 - 8965. Take away 6 from each, transforming the equation to 9999 - 8959, which is easy to solve vertically. This completely avoids the need to work with the internal zero renaming.

Or take away 5 from each to make it 10 000 - 8960, which is just 40 more to get from 8960 to 9000 and 1000 more to then get to 10 000, so 1040 is the answer (jump the difference strategy, following an initial transformation). This is called transformation, but we like to think of it as turning an ugly duckling equation into a beautiful swan - transforming it!

**Extension: **Try it with decimals - the ribbon is 0.08m.

Equations would then be:

0.48 - 0.4 = 0.08, and so on.

This works beautifully if you have a decimal conversions measuring tape (which has decimals/metres on side A and centimetres/whole numbers on side B). These are exclusive to our Top Ten Toolbox range, custom-made by our Australian numeracy coaches.

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