# Scenario 2: How do I create a contextualised numeracy diagnostic for my painting and decorating programme?

Here’s the next scenario:

*You’re a trades tutor teaching painting and plastering. Your learners are a group of adults with mixed backgrounds and abilities. You suspect that they don’t understand how to work with area calculations.*

**1. Consider what else you now know about your programme and your learners**

Your learners are working towards unit standards and a New Zealand certificate. But you also know that they lack some of the key numeracy skills that they need to work effectively in the industry.

As a former commercial painter and decorator, your reputation is at stake here. You don’t feel that you can recommend any of your students to potential employers unless you feel confident in their abilities to do the work. And being able to work out how much paint is needed for a wall is one thing they need to know above almost anything else.

**2. Revisit your learning outcome for numeracy**

Next, you draft the following learning outcome. This is what you hope your learners to achieve:

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

You’ve included estimation here because as a professional painter you know that after a while you don’t have to calculate everything every time.

With experience, you hope that your trainees will also be able to quickly estimate key measurements that they need with a degree of accuracy.

**3. Unpack the calculation or task**

In order to unpack a calculation you sat down with a colleague, and over coffee asked the following question:

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

Here’s a summary of what you 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.

**4. Develop some diagnostic questions based on what you’ve unpacked**

You’ve worked out what the outcome is that you want to achieve and you’ve unpacked some of the underpinning knowledge and skills. Next, you come up with the following diagnostic questions:

**Numeracy diagnostic for painting and decorating**

*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:*