Atom 3 - Identifying What Lengths...

What lengths do you need to work out the area of a trapezium?

Podcast is AI generated. Interactive transcript available here.

Previously we looked at a Routine Atomisation for finding the area of a trapezium using the formula:

What is Atomisation?

I said that atom 3 was one of only two new atoms, and that it was a very powerful atom to focus on; an atom that is often overlooked or not given enough time.

If you do an image search for 'area of a trapezium worksheets,’ you will find that nearly every one of them presents trapezia with three lengths labelled.

This is very typical of area worksheets for all shapes: present only the values necessary for calculating the area.

Because of this, many students implicitly learn the rule: “When I’m asked for to find an area, I times together all the numbers.”

But then, they also get mixed up and confused: for the trapezium I need to add something first… for perimeter I need to add something… am I adding or timesing… more than two numbers have been given, what do I do?

The exact nature of the confusion varies depending on lots of factors, but it results in some version of students giving up and adding everything, multiplying every number, dividing by two at random, or old faithful: head on desk.

Atom 3 is one part of the secret to undoing this confusion, or avoiding it outright.

The goal of atom 3 is to identify what lengths will find the area of a trapezium.

There are a few different ways you can frame the question:

1. Are these the correct lengths? Yes / No

2. Circle the correct lengths

3. State the correct lengths

4. What are a1, a2 and b?

Whichever you choose, they all share one common, fundamental, important feature that is missing from the I Do / We Do worked example problem pair model:

Every one them isolates this one concept, and gives students the chance to both practise it to mastery in the moment, and practise it to memory long into the future.

Below is an example of what the atom looks like once it’s isolated.

The prompt has changed from ‘what is area of the shape?’ to just ‘what are the values of a1, a2 and b?’

The formula is now provided; no more needing to retrieve it from memory.

The ‘right answer’ isn’t the area of the trapezium, it’s just the values of the three lengths they need, with the parallel sides correctly distinguished from the distance between them.

There’s no need to process any arithmetic.

It’s up to you how much you ask your kids to practise this; the amount of practice needed can vary a lot depending on the class (their prior knowledge, ability, rate of learning.)

But, even at the low end, isolating the atom like this gives you the chance to present a wide variety of contexts to students.

For example here, each time the task is just to identify the three values you need to calculate the area:

There’s a huge variety of orientations and trapezia shape across those four tasks, including a right-trapezia, a (near) isosceles trapezium, and an obtuse trapezium. And that might be, say, a minutes’ work; around ten seconds per question. So lots of practice in a short space of time at the thing that matters most when learning how to find the area of a trapezium, the plutonium atom.

Focusing on a single atom like this also gives you laser precise insight into whether or not your students can identify the correct three lengths, no matter how complicated or unusual the diagram looks. If you know they have thoroughly mastered this, then you can be confident this isn’t what’s getting in the way if they still struggle to find trapezia area.

Assuming students can recall the correct formula, and assuming all prior knowledge is mastered, this is the only new thing they need to learn; this is where most of the difficulty would lie.

But not all of it.

To understand students’ next challenge we’ll need to look at Chaining in a future post.

Until then, here’s a free worksheet generator that will be available for the next few months. The visual design isn’t perfect, but it works, and it generates infinite practice tasks for this atom - you can practise it as much as needed until all students can respond to six tasks in around a minute.