# Pattern sniffing with Decimal Subtraction

An idea for a mixed attainment class that came to me about 5 minutes before a lesson today:

1. 3.4 – 3.04
2. 5.2 – 5.02
3. 7.8 – 7.08
4. 8.2 – 8.02

Find other questions like this.  (The “weakest” student in the class told me the pattern before I’d even finished writing the fourth question on the board.)

What do you notice?  Why is the answer to Q2 the same as the answer to Q4?

Can you create a question with 0.54 as an answer?  How many different answers are there to these types of questions?

Then:

1. 5.7 – 5.007
2. 8.3 – 8.003
3. 6.4 – 6.004
4. etc.

These are more tricky and test the skills of column subtraction, something that should be secure by Year 7 but may not be. Maybe an opportunity for collaboration amongst students to show how.

And then finally, try these two calculations. Which is easier and why?

7 – 1.392

6.999 – 1.391

Show on a number line why this works and then try some more.  I think these questions are interesting to explore.  But I would hesitate to recommend it as a must-do method to solve e.g 8-2.5687.  Whether or not it is easier to turn it into 7.999-2.5686 or not is an interesting discussion and one which I would want my students to form their own opinion on, not be too swayed by mine.