# Using Maths pedagogy to inform my Science teaching

This is quite a niche blog, perhaps only of interest to Science and Maths teachers (if I am lucky). This blog owes a huge hat tip to @BenRogersEdu, @emc2andallthat and @mrbartonmaths. Ben’s blog, here, provided the nudge to trial bar modelling (along with @emc2andallthat’s blog and @DSGhataura’s tweets). Craig Barton’s wonderful book (How I wish I had taught Maths) is a must read for any Science teacher (and of course, Maths- and any other teacher to be honest) and I have more takeaways coming in a future blog.

As soon as I read Ben’s blog on bar modelling, I twigged that this would be a great way to (re)teach moles, molar mass and mass equations. It was time to revisit this with my Year 11 Applied Higher tier pupils and I didn’t want to focus on the (hated) formula triangle and just plugging the numbers in without any conceptual understanding. In the mock exam paper, all bar one of the Higher tier pupils struggled with this concept.

After reviewing the concept of moles, relative molecular mass and molar mass:

We moved onto calculating the number of moles from a known mass of given compound. This is where the bar modelling came in to play.

The question was, if you have 20g of Helium, how many moles do you have? I modelled this on the board (the key being -the mass goes on top, the molar mass on the bottom) :

Pupils then tried an example on their own (how many moles in 232g of Sodium Chloride):

Then another practice question:

and their response:

What I really like about using bar modelling for this concept is that if the top (the mass they have) is smaller than the bottom, they can see that they don’t have enough for a single mole so the answer will be a fraction/decimal/less than 1. When the top (the mass they have) is bigger than the bottom, then they can see they have more than 1 mole. Even when working with “difficult numbers” a quick sketch of a bar model can help to give a check as to whether their answer is plausible (thanks @ejsearle for that turn of phrase).

I gave the pupils a homework to pull together some key ideas and to give them the opportunity to practice bar modelling.

I was pleased to see most pupils continued with the bar modelling. My only feedback was (for the final question) to the pupil on the left to try to make the bars closer to scale and the pupil on the right to sketch the bars so they have something to check against for how plausible their answer is. The bar model would show: less than a mole and a really small fraction of a mole at that. Therefore 0.09 moles is very much plausible.

Interestingly, the one pupil that nailed this in the mock wasn’t fussed with the bar model and didn’t want to use it. If they don’t use it then I hope they can visualize the likely ratio and check their answer in their head.

I knew after dipping my toe into bar modelling that I wanted to continue to use it. As part of our final unit we are looking at materials, their properties and their uses. Density is property that is always important in choosing materials for a purpose. Density also comes up in the Maths GCSE. Because of this, I wanted to ensure that my pupils had a good conceptual understanding of density (rather than just thinking it means heavy or not and plugging the numbers into a calculator). I also wanted to avoid the dreaded formula triangle (I am not a fan as you may be aware by now).

After clarifying what mass and volume are and how they are measured we completed the following worksheet. This is where the reading of Craig Barton’s book came to the fore. I wanted pupils to understand density relative to water density and whether objects would float or sink. This is the handout:

The “me” section was completed by me (who else) on the board and pupils mirrored what I did (this is similar to the worked example-problem pair that Craig advocates).

I was very selective in my worked examples. I chose something that floats, something that sinks and water. This would give the density numbers an anchor for relative comparison.

Pupils then did their examples. I was even more selective for these. As covered by @mrbartonmaths’s book, I wanted minimally different examples. I wanted them to see what the pattern of density would be when the mass is the same but the volume occupied gets bigger in successive examples. Or smaller. Or the mass increases in successive examples but the volume is the same. I also wanted them to use the bar model so they could visualize what this would look like (in terms of ratio). From my worked example we could visualize that “top heavy” models (mass in g greater than volume in cm3) sinks (density more than 1) and “bottom heavy” (density less than 1) floats.

Pupils completed this side well (though if I was being fussy I would want scaling to look more like the middle example).

By choosing these examples I was hoping (and I obviously drew their attention) they would see what happens when mass only changes between the examples and what happens when volume only changes between the examples.

Then onto some questions.

Every single pupil had a, b and c as floaters and also that a and c could be the same substance.

Question 2 really allowed us to explore what the unit g/cm3 actually means as both a and c have different masses and different volumes but each cm3 of a and c has the same mass.

Then the pupils moved onto the “boundary examples”. This is another idea stolen from Craig Barton’s book. He defines boundary examples as weird questions or normal looking questions with weird results. In Science I tend to think of them as “worst case scenario” exam questions that are at the very boundary of what we would expect. Now most pupils quickly twigged that 1kg had to be changed to 1000g (you could argue that by calling this a boundary example I have alerted pupils that there is something more at play here than a standard density question). From here they had no problem.

What was interesting is that a small number of pupils had put 1 on the top of the bar model and 90 on the bottom and had then calculated the answer as 0.17 g/cm3. If they compared their answer to their bar model they would have seen that their answer was plausible. However, one pupil in particular knew her answer wasn’t correct as the bar model was showing it would float and she knew that lead would sink. It was very bottom heavy and this couldn’t be right, she reasoned, as she knew that lead sinks. I would argue that without the bar model, many of the pupils dividing 1 by 90 would have been less likely to spot that the answer is wrong. By including the bar model, if the number (less than 1) doesn’t jump out as wrong then the bar model might. It did with a number of my pupils.

The secondary boundary example also gave some problems. The most common mistake was to divide 72 by 3. This then led most to realise they had made an error. Or some tried some further mathematics to make the answer “work”.

Many pupils did get the answer right but it reminded us that they will be expected to apply their mathematical knowledge in their Science exams and to not just assume that each question will be standard and straight forward (so watch out for boundary questions).

We finished the lesson with a multiple choice question that I scanned using plickers. Their results will dictate how I start next lesson. The question was:

I didn’t let the pupils look back at their worksheet (perhaps a mistake) and I was a little disappointed with the results. The plickers results were:

The fact that a few pupils went for C and D shows that this concept is not fully understood by too many of the group. We will review this answer tomorrow. After Easter break I will set 2 questions, one where volume stays the same but mass increases and another where mass stays the same between 2 objects but the volume increases.

I already have my question planned. It will be:

Object R and P have the same mass. Object R’s volume is 4 times greater than object Ps.

**A** the density of object R is 4 times smaller than object P.

**B** the density of object R is 4 times greater than object P.

**C **it depends on the material

**D** The density of the 2 objects will be identical

I will scan their answers in using plickers then I will give them the opportunity to check the left hand side of the worksheet we did today and then re-scan if anyone has changed their minds.

I will be aiming for 100% (despite the time they have had to forget).

Thanks so much for reading this far. As ever, constructive critique is always welcome.

(all work shared with pupil permission).

Thanks for sharing this. It looks like a good application of bar modelling. One question, do you think that bar modelling is particularly effective at certain ability levels, or is it useful across the board. -you mentioned one pupil who nailed it but didn’t want to use it. I know that’s a very small sample(!) but just wondered whether you had any instinctive feeling about the general applicability to all pupils.

Hi Brian. Thank you so much for reading. Interestingly, the pupil that didn’t want to use bar modelling with moles really liked using them for density as the visual image of top heavy (sink and a number greter than 1) or bottom heavy (float and number greater han 1) really helped him check his answer. He also liked bar modelling to write chemical formulae from tables of ions (not included in blog).

I am 100% convinced that they can be useful for pupils of any attainment. I told the class that using them for density (or moles) won’t get the any extra marks but will help them check the plausibility of their answers and increase their chances of getting it right. They all agreed that no matter how well they were doing in Science, there is always the danger that a miscalculation will be written down but doddling a quick barmodel gives something to compare it to.

I also think it has helped all pupils (bar one with the moles) with their conceptual understanding.

That is the long answer. In short, I really think it is a good technique to show all pupils.

Damian

Thanks, your blog gave me the nudge to work on this. Just updated all my Year 7 physics lessons on Power, efficiency, and speed. Looking forward to using this in other areas. I also bought Mr Barton’s fantastic book and I’m halfway through. Fantastic stuff for a biologist, it really has transformed how I think when planning lessons with maths elements.