Here is my thinking process:
For the 1st weigh, it can only represent 1 weight.
For the 2nd weigh, it can represent 2*1+1 = 3 different weights.
For the 3rd weigh, it can represent 2*(1+3)+1 = 9 different weights.
For the 4th weigh, it can represent 2*(1+3+9)+1 = 27 different weights.
And what's nice is that 1+3+9+27 = 40, so the 1st weigh should have a weight of 1gram, 2nd weigh is 3 grams, 3rd weigh is 9 grams, and the 4th weigh is 27 grams. There should be only one set of solutions, otherwise, some weights are skipped while the maximum possible weights are still 40.
Extension: Say you want to buy x grams of herb, what is the minimal number of weighs that you need?
Yiwen, you should also post your group microteaching lesson plan here. The following is my response to your group's plan:
ReplyDeleteThanks Amrit, Chloe, Yiwen and Roya! Looks like an interesting lesson. I'm glad that you're thinking about what the students will be doing. Have you planned out how the four of you are going to co-teach this lesson? That ought to be included in your lesson plan as well.
Some suggestions: (1) I would spend less than 5 minutes with students looking at the first worksheet, and get on to the idea of slope as rise/run earlier. (2) How will you distribute worksheets online? (3) I think that 5 minutes and the start and end is a bit too long, given that this is just a 20 minute lesson. Make sure that you give time to establishing the link between hiking in the mountains and calculating slope as rise/run. I would think that 2 minutes at the end is probably adequate...? (depending on what kind of assessment and wrap-up you're planning, of course!)
Thanks for this interesting solution to the scale problem, Yiwen!
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