These are just some simple questions that I ended up writing because I couldn’t find any that contained a suitable mixture. I wanted worded problems that combined % increase, % decrease and % of an amount, but didn’t delve into reverse percentage. Enjoy, use, adapt…
No 1 in a series of posts based on Thinking Mathematically (1985) by Mason, Burton, Stacey
This question prompts learners to come up with their own specific example(s) of a price to apply the discount and sales tax to. It made me think that there are many questions I use in class which I could adapt (i.e. remove the specific example) to get my students better acquainted with this step.
I used £100 and performed the calculation mentally. It prompted me to reflect on how I chose £100 and how I would help my students make good choices for examples.
I think a number of my students might think that they have seen something a bit like this before:
"A price is reduced by 20% in a sale but this price is then reduced by a further 10% by using a voucher code" Amy says that the overall reduction is 30%. Explain why she is wrong.
Depending on the class, I might use these two examples together to highlight the process of moving through from the specific by choosing good examples to the general using basic algebraic notation with decimal multipliers.
In the first example, we need to get to:
0.8 x 1.15 x P = 1.15 x 0.8 x P
In the second case:
0.8 x 0.9 x P ≠ 0.7 x P
These statements alone are insufficient “explanations” in the context of the question, so there could be a good opportunity here to work on some specific exam technique as these types of questions often pose difficulty for students.
This is a simple card sort activity where students fill in the blanks, practising converting between fractions, decimals and percentages and then placing them in order from smallest to largest.
What I particularly like about it is that you can hand out the cards in 3 sets of 5. This could provide differentiation, but more importantly (in my view) it gives the teacher the chance to assess the progress of the students as they go. It’s easy to glance at Set A to see if they have worked it out.
As you circulate the class, helping students you can give out Set B which interleave with Set A to produce this:
And then finally with Set C, you get this:
Here is the pdf as a set of 15 cards, but if you are printing a class set, then I strongly recommend using the Excel version here. This is set up so you print 5 at a time. They come out stacked so that as you cut you have a set of 5 already in a pile without needing to sort them.
Also, if you want to change the actual values and which values you show, you can do that on the spreadsheet too.
I built this a while ago on Geogebra. I usually use it with mini-whiteboards as a flexible way to do AfL on percentage of an amount. You can select what is shown using the tick boxes, usually revealing the “answer” by ticking the third box – “Show amount”.
If you click the image above, it will open in GeoGebra Tube. If you would rather download the .ggb file, click here.