I am often asked what makes a perfect mathematics lesson. This is a difficult question to answer, as I’m not sure that there is one best lesson. It really depends on what you want to achieve, as the purpose of a mathematics lesson determines its structure. I find that kids adapt well to different types of lessons, as long as they know why they are doing them.

Start by working out what you want to achieve in your mathematics lesson today:

- To challenge and stretch thinking, to experiment with new concepts – use unfamiliar and complex problem-solving lesson to experiment with new concepts
- To build accuracy and efficiency – an explicit teaching or mastery lesson structure will help build fluency
- To connect and generalize – lessons that focus on questioning to build connections in as many ways as possible are a good choice
- To work on logical structuring and our process – Start by comparing processes to find similarities and differences, to decide which is best in each circumstance, and to build reasoning skills

Next, it is important to set the scene for students and explain what we will be doing today.

- Today we will be experimenting with new concepts in maths. It is our brain-growing of maths lesson today, so I want you to think hard and try out lots of different ideas.
- Today we will be sharing of strategies from the previous problem and working out which suits each different set of circumstances. I want you to find the similarities between each different process.
- Today we will be building connections from our learning yesterday to as many new ideas as we can. I want you to look for connections between this process and others that we have already learned about.
- Today we will be building our accuracy and efficiency in strategies that we have already learned about. I want you to practice using the process enough times to build your confidence and accuracy, so that it becomes automatic.

Finally, set success criteria in line with your purpose:

- I struggled with a challenging problem and persisted multiple times
- I experimented with a new concept and worked out a way forward
- I tried something that was difficult for me
- I solved a problem in at least two different ways
- I proved that a wrong answer was incorrect
- I set out my steps logically
- I connected the area model for multiplication to area of a rectangle
- I found that multiplying the base by the height of a rectangle determines its area, just like in an array
- I connected the area of a rectangle to a triangle
- I remembered to write the formula at the start of each question
- I wrote one step on each separate line
- I remembered to include the units

Have a great time and remember to let me know how it goes.

*Tierney*

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