Recently, we did some work around developing learning outcomes with group that had a lot of painters and plasterers in it. This is a summary of my notes relating to how, as a group, we developed a draft learning outcome for an embedded approach to some very specific numeracy skills around measurement and area.

We also looked at what sample diagnostic questions might look like as well as ideas for a short teaching sequence.

I’ve written about embedded learning outcomes before here if this interests you or you need more detail on how we suggest that you write them.

# Write the embedded numeracy learning outcome

Based on the needs of the group and their learners (who were working towards trades qualifications in painting and plastering) we came up with this:

- Estimate and calculate the area of a rectangle in the context of working out the amount of paint needed for a wall.

# Unpack the calculation

In order to unpack a calculation we asked the following question as part of a group discussion:

- What do I need to know in order to do this?

Here’s a summary of what we brainstormed. Learners would need to know how to:

- Estimate and measure length in metres.
- Understand that area is measured in square metres.
- Know how to estimate the area of a wall in square metres.
- Understand and apply the knowledge that to find the area of a rectangle you multiply the length of one side by the other.
- Multiply numbers with decimals.

# Develop some diagnostic questions

Once we determined what the outcome was that we wanted to achieve and what some of the key underpinning knowledge was, we needed to develop some brief diagnostic questions and activities to figure out what the learners actually knew.

The idea was that the tutors and trainers would use these as their pre and post assessments around the actual teaching component. These aren’t necessarily perfect, but here’s what we came up with and feel free to adapt or modify:

- Estimate the length of a wall.
- Measure the length of a wall.
- Draw a square metre on the wall or workshop floor.
- Estimate the area of the wall.
- Answer these questions
- 2 x 4 =
- 2.4 x 3 =
- 24 x 30 =

- Find the area of this rectangle:

# Develop some teaching activities

Here’s a teaching sequence below that we came up with based on the needs of the painters and plasterers in the group. You could also adapt this to many other contexts where area is important, for example carpentry, joinery, engineering, horticulture, and farming.

- Start with an interactive discussion designed to activate learners’ prior knowledge about measurement and area and why it’s important to the job of painting and plastering.
- The point here is to get people talking about what they already know and what, if any experience, they might have estimating, measuring, or calculating area.
- It could be useful to formulate a discussion question (or a series of questions) prior to the teaching. For example, “Who has had to try and work out the amount paint needed for a job? Did you get it right? What happened? Why is it important to check your estimates? What happens when you get it wrong? Why would your boss care about this?”

- Do some teaching around estimating and measuring length.
- This could start with some work around common benchmarks for length, then move on to checking that learners know the correct way to use a tape measure for measuring length in metres, and conclude with learners practising estimating then measuring accessible objects, shapes, and spaces in the workshop, classroom, or training space.

- Do some teaching around estimating, measuring, and calculating area using decimals including with a calculator.
- This could start with some work around using square units of any kind, e.g. on paper grids so that they have to count and then calculate the number of square units need to cover different shapes and areas. Then learners could estimate the area of a large door or table in square metres and share their estimations. You could follow this up by measuring with tape measure, doing the area calculations, and discussion relevant fractions you need to cover the shape.

Feel free to improve on this… Let me know in the comments. Hat tip to Janet Hogan for leading this workshop activity.

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