# Section Four: The format of the Let’s Think Maths activities

Each of the Let’s Think Maths lessons is outlined on two double-page spreads, which are followed by any notesheets that you may need for teaching the lesson.

Before teaching a lesson, you will need to read the Teaching Notes spread as well as the ‘Before you teach’ section from the first page of the Background Notes. You may find it helpful to add your own notes to these pages, either before or after you have taught a lesson.

The Background Notes double-page spread (the narrative overview of the lesson and the diagram which provides information on ‘Children’s Thinking and Abstract of the Activity’) will probably be something you return to over time. The information in them is generally more helpful after you have taught the lesson or set of lessons from the same mathematical reasoning strand (see Section five).

The notesheets are for children’s rough workings. These should not be collected or marked. Teachers often just ask the children to make notes on large pieces of paper, using the notesheets as prompts.

The Background Notes pages

The Background Notes form the first two pages of each lesson. They are not intended to stand alone but should be viewed together with the Teaching Notes and notesheets (if the lesson includes any), to get a more complete idea of the flow of ideas in the lesson.

These pages include a narrative description and a levels diagram, as shown in the example on page 20.

The narrative description

The first paragraph of each lesson provides a very brief sketch of the aim of the lesson, naming the ‘big ideas’ involved. In Lesson 3, we are told that the intention is to provide children with an opportunity to explore different methods for finding perimeter and area of rectangles. This is followed by a short description of the flow of the lesson.

The main description of lesson aims is presented in boxes, and is preceded by a reminder about the structure of each episode, each of which includes an introduction, paired or group work and whole-class sharing. As with most Primary Let’s Think Maths lessons, Lesson 3 has two episodes. The first episode introduces ideas that are explored in greater depth in the second episode. The last box contains a brief note regarding the final reflection phase.

Immediately below the box is the section ‘Before you teach’ which tells you some of the key things to consider before teaching the lesson. It highlights some of the main concerns that may arise and what should be avoided (for example, don’t hurry the initial phases to arrive at the formal mathematics). Here we also point to particular strategies or misconceptions that need to be addressed (such as counting squares rather than edges to find perimeter). This section

also indicates any specific knowledge or experience that the children may need before a lesson. This will help ensure that the main purpose and flow of the lesson is not disrupted on the day.Property of Let’s Think Forum – not to be copied or reproduced without permission

The levels diagram – Children’s Thinking and Abstract of the Activity

The diagram on the second page of the Background Notes is a flow diagram to be read from the bottom up. It parallels the narrative on the previous facing page and gives an idea of the cognitive demand of each stage of the activity, in terms of Piagetian levels. It should be noted that these levels are only for teacher guidance.. The levels shown provide an indication of what type of thinking is being promoted. The narrative portion of the diagram provides further indication of what is taking place in each of the episodes.

In the ‘Largest rectangle’ the lesson begins with tasks at a lower level of cognitive demand. The children talk about rules in the final sharing phase of the first episode. The rules then become the means for moving on to the second episode, the different stages of which are also roughly equated to Piagetian levels. This episode is more demanding, particularly in terms of cognition (concrete generalisation moving to early formal).

The Teaching Notes pages

The Teaching Notes pages are two facing pages that include both general information and specific guidance for teaching the lesson. See the example on page 21.

General preparation

The first page includes information to help prepare for the lesson:

Aims – a brief indication of the lesson’s main thinking points and mathematical content.

Resources – a list of the special resources needed. ‘Largest Rectangle’, for example, asks for special paper and the rectangles notesheets.

Organisation – which size and ability range of groups have worked well during the trialling of each lesson

Vocabulary – key mathematical vocabulary for the lesson. Note: this is not a key focus in the lesson and the ideas are generally introduced in the context of children’s everyday language

Lesson delivery

The bottom of the first page of the two-page teaching spread provides material for introducing the lesson activity to the whole class, denoted as ‘Whole class preparation’. Suggestions for opening questions, such as, ‘Is a square a rectangle?’ are given in italics. Other general suggestions for conducting this preparation phase are given in roman type face.

The second page of the teaching spread provides background and suggestions for questions for continuing with the first episode. ‘Paired Work’ or ‘Group Work’ is the first construction phase, during which the children work on the initial stages of a task together. This is followed by the

Class Sharing’ phase. During this phase, the class talks about what they have discovered. The first episode ends with the children sharing the rules they have found (in the case of Lesson 3, using words and, if suggested by the children, letters for length and width).Property of Let’s Think Forum – not to be copied or reproduced without permission

The lesson carries on with the second episode . Note: depending on the time available, you may need to bring things to a close well before getting into the later work. If you do, the final questions should be adjusted to ask the children to reflect on where they have reached and what they have found, as well as how have they addressed the initial questions.

The notesheets

Some lessons use two or three notesheets while others use none. The notesheets are there to support the delivery of the lesson. Remember that these are provided for children’s rough workings and should not be collected or marked.