**Thanks to maths consultant, Caroline Clissold for this month's maths blog which explores the methods she uses to plan a series of maths lessons.**

When I work with teachers we plan using the headings:

• Let’s engage and explore

• Let’s learn

• Let’s practise

• Let’s apply

I adapted these headings from the Rising Stars Mathematics Teacher’s Guide and pupil text books and they are extremely useful terms to work with.

When starting a new unit of work, we always begin with a **Let’s engage and explore** session in which we assess what the children already know. An engage and explore session involves such things as revealing the new mathematics, using multiple representations and making connections. It can also identify misconceptions which some children may be able to address themselves or which will be noted so that we can come back to them in the following **Let’s learn** session.

I’ll give an example of how this worked recently in Year 2. The children were beginning a unit of work on fractions. The first explore session focussed on half. The children worked in groups of four to explore half of lots of things on their tables. For example, 1m length of ribbon, 4 packets of noodles, 15cm strips of paper, 1.5l bottle of water and measuring jug, metre stick, ruler, counters, a large ball of plasticine, money and scales. They initially began by making two piles of the objects that could physically be placed in two piles. Then they found half of the ribbon and the strip of paper by folding. They rolled the plasticine into a worm-like length and cut it in half. Some of them used the scales to weigh each half. Some of the children estimated what half of the 1.5l bottle of water and then used the measuring jugs to find out how many millilitres half was. Several children knew how to read the scales on the measuring jug and the weighing scales and could explain how to do this to the others in their group. They noticed the numbers on the ruler and metre stick and could find how many centimetres were half of each. We talked about the 1.5l bottle of water. One child knew that 0.5 was equivalent to half and that there was one and a half litres of water. We discussed how to find half of that volume. They weren’t sure how many millilitres were equivalent to a litre but knew that there were either 100 or 1000. Once we had established that there were 1000, they could halve that and also halve 500. We modelled half of all these different measures using the bar model.

It was fascinating to observe how much knowledge the children had that we hadn’t anticipated. In this unit, the second session was another **Let’s engage and explore** session, which was a repeat of the first but this time the focus was on quarters and the relationship between halves and quarters.

Next came a **Let’s learn** lesson in which we confirmed concepts from the exploration sessions, introduced the precise mathematical vocabulary that the children needed to know, addressed any misconceptions and made generalisations, for example, that two quarters are equivalent to one half. We focussed on the part, part whole model as shown above using place value counters. After the **Let’s learn** session the children practised what they had learned. **Let’s practice** sessions are a very important part of developing understanding. They involve variation, practice within different contexts and opportunities to develop fluency. The children used different numbers of cubes this time and wrote number statements identifying how many cubes made up one quarter and one half of the whole. They also practiced using money.

The next two sessions were **Let’s apply** sessions, where we were aiming to deepen the children’s understanding through connecting the unfamiliar with the familiar and also through non-routine problem solving. We asked, for example, if we know that ¼ + ¾ = 1 whole, what else do we know? The idea was to find out if they could translate their learning about commutativity and inverse in the addition and subtraction of whole numbers to the addition and subtraction of fractions. We also had a **Let’s apply** lesson where we used the part, part whole model to solve problems such as, in a tin of sweets, half the sweets were chocolates, one quarter were toffees and the rest were custard creams. There were 15 custard creams. How many sweets were in the tin? The children used a strip of paper to represent the tin of sweets and folded it to make the parts. After working through the problem together they worked on some problems in pairs. The problem was the same but in the new ones the number of custard creams varied.

We then wanted to see if the children could use their understanding of part, part whole for halves and quarters and apply it to the addition and subtraction of other fractions. This session was a mixture of **Let’s learn** and **Let’s apply**. For example, they made three fifths using two different coloured cubes. They could tell us that 3/5 add 2/5 equals one whole and therefore 2/5 add 3/5 equals one whole, that one whole subtract 3/5 equals 2/5 and one whole subtract 2/5 equals 3/5. They repeated this for other fractions.

The unit continued for about three weeks in this manner and by the end all the children had mastered the part, part whole element of fractions.

You may have noticed that I refer to sessions and not lessons. The reason for that is a session could last longer than one lesson.

Since adopting the idea of **Let’s engage and explore, Let’s learn, Let’s practice** and **Let’s apply**, I have noticed a difference in the children’s confidence, their willingness to have a go and their achievement. I would really recommend giving it a try and find out just how much the children in your class can achieve. Let us know if you do, we would love to hear about what happened!

*Rising Stars Mathematics* is a primary textbook programme written for the new curriculum. Find out more and download a free sample activity pack.