PART 2 (find PART 1 HERE)

STEP 1 - STEP 2:

Now they have to find a new way to solve the same grouping. We need to learn a new way. This is where we stopped the lesson although some were starting to have the idea of dividing the numbers... We will resume this task tomorrow.

The idea here is to go through a few more cycles using the same task: i.e. Allow them to divide the numbers and find proportionalities (body:head) adults 7:1 children 4:1 or 5:1 then relate this to fractions if possible. Then disallow this as a solution. Next solution should be drawing pictures/diagrams showing a child as 4 heads or 5 heads tall and an adult as 7 or 8 heads tall. Then take that away and lead them to graphing (body length vs head length) and finding slopes/gradients. Hopefully this should mean that they have a really solid appreciation of proportion before we go to the graph stage.

NEXT DOUBLE LESSON: First we reviewed the previous lessons work as some will have forgotten the point we reached 4 days ago.

STEP 2 - 1 - 2 again: Students were very confident in the use of the language 'X length/size compared to length/size of Y' so I said "language - X compared to Y - is now not allowed, find a new way to express the relationship you observed". As this was the first run through I eventually suggested using pictures/diagrams to explain instead of words. No students had started independently making measurements on the pictures yet which was interesting.

After this I said "ok find a new way, not a diagram and not using words". Students did get stuck at this point again, so I sent them back again to the pictures and to review their other descriptions. As a hint I dropped rulers on the tables... They started measuring and after a little while they started dividing the numbers together. They therefore observed that if they focused on one pair of variables that the 'answers' from dividing the 2 numbers were very different for adults than for young animals. They therefore understood that they could USE these numbers to select members of groups. We discussed this and I allowed them to re-sort the 'young' vs 'adult' groups using the various forms of expressions. They observed that these worked smoothly.

Students came up with several different ways/diagrams etc. that worked. See them HERE.

STEP 3: TEST and REFLECT: Challenge after task has reached this stage just before progressing to graphs (as an extension). Students are asked to organise 5 human skeletons into order of ages. Youngest to oldest or reverse doesn't matter. BUT they must have the calculations done to defend their choice.

This also worked well.

FIND PART 3 HERE

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