## Session 1: Classifying mathematical objects and interpreting multiple representations

Before trying out activities with learners, it may be a good idea to try them out for yourself to get a feel for how the learners might react.

### Activity 1

Here is an activity for you to have a go at. It is taken from the Professional Development section of *Improving learning in mathematics* and has been used extensively with teachers. It would be good if you could do the activity with a colleague but if you can't, don't worry.

The idea of this activity is to find several reasons for each mathematical object in a group of three being different from the others. You should write down your reasons, with justifications, or discuss them if you are working with a colleague. Try to imagine what reasons your learners might give.

There is an example below:

You may be able to think of many other reasons for this set.

**Task:** In the link below there are more for you to try. Make a note of your reasoning

Classifying mathematical objects

Source: *Improving learning in mathematics* PD3.2 Classifying mathematical objects, page 31

### Reflection on the activity:

## Now reflect on this activity

Please record your thoughts

### Activity 2

Mathematical concepts can be represented in many ways: words, diagrams, algebraic symbols, tables, graphs and so on. These can sometimes be very confusing, so activities that help learners with these different representations will allow them to construct meanings and links between the underlying concepts

What follows are two examples, A and B, of activities that can help learners interpret different representations of the same concept. One is concerned with interpreting algebraic expressions and the other with comparing fractions. You may wish to choose just one of these to try, or you can do both if you wish. The activity can be done on screen. Try to act the role of the learner as you try the activity and think about how it confronts and exposes common misinterpretations and misconceptions. If you are able to look at this with a colleague, it would be helpful to discuss the implications for learners.

#### A. Interpreting algebraic expressions

This activity is intended to help learners to translate between words, symbols, and area representations of algebraic expressions, recognise the order of operations, recognise equivalent expressions, and understand the distributive laws of multiplication and division over addition (expansion of brackets).

**Task:** There are three sets of cards that can be matched together. You will be able to drag them on the screen and match as many equivalents as you can. Whilst you are doing the activity you might want to think about what sort of responses your learners would make.

#### B Comparing fractions

This session is designed to help learners to:

- interpret a fraction using number line and area models
- compare and order fractions.

**Task:** There are three sets of cards that can be matched together. You will be able to drag them on the screen into matching sets. Whilst you are doing the activity you might want to think about what sort of responses your learners would make.

## Now you have tried one of these activities, think about the possible benefits to your learners of this kind of activity

Please record your thoughts

### If you would like to do more

- You may like to try and devise your own classification activity using other mathematical objects, such as numbers, equations or functions. You could try one of these activities with your learners.
- There are a number of classifying activities in the
*Improving learning in mathematics*teaching sessions. If you wish to look at one of these, SS1 Classifying shapes is a good one to start with. This can be accessed using the link below.

Other sessions contained within Improving learning in mathematics that use multiple representations activities include:

- A1 Interpreting Algebraic Expressions
- SS7 Transforming Shapes
- S5 Interpreting bar charts, pie charts, box and whisker plots...

These can all be found on the Teaching Activities section of *Improving learning in mathematics*

The *Improving learning in mathematics* resource has professional development sessions to use with colleagues. You might want to look at this one:

Getting started

which can be found in the *Improving learning in mathematics* Professional Development Materials.