# 2 Using structured resources: arrow cards

Important features of the place value system can be taught using simple everyday objects such as sticks and bundles of sticks. This unit considers resources that are structured in a specific way to further develop students’ understanding of the decimal number system. They are called structured resources and offer the students a way to develop an image of the number system that can help them understand the magnitude of, and manipulate, numbers (Askew et al., 1996).

Activity 1 focuses on using arrow cards. These are very useful for modelling how numbers are written and represented in hundreds, tens and ones, and for demonstrating the value of each digit.

Before attempting to use the activities in this unit with your students, it would be a good idea to complete all, or at least part, of the activities yourself. It would be even better if you could try them out with a colleague, as that will help you when you reflect on the experience. Trying for yourself will mean you get insights into a learner’s experiences that can in turn influence your teaching and your experiences as a teacher. When you are ready, use the activities with your students and once again, reflect on the way the activity went and the learning that happened. This will help you to develop a more learner-focused teaching environment.

## Activity 1: Using arrow cards to teach about place value

### Preparation

Plan how you will organise your students into groups. Prepare sufficient sets of arrow cards for your class to work in groups of three or four. Resource 2 provides some templates to copy or print. Once you have made some sets of cards, you will be able to use them again on many occasions.

Look at the list of statements to use with this activity in Resource 3. Select the statements you will want to use in your lesson. Hand out one full set of cards to each group and ask them to lay the cards neatly in front of them. Allow a few minutes for this – it’s valuable experience for the students simply to handle the cards and look at the numbers on them.

### The activity

Start by drawing the students’ attention to the arrows on the right ends of the cards. These arrows must always be on top of each other when making a number. Demonstrate making two or three numbers, drawing attention to how the number is made up.

For example, Figure 1 shows how the number 364 is made up of 300 + 60 + 4.

Figure 1 The number 364 in arrow cards.

(Source: Wendy Petti, Education World)

Call out the statements that you have selected from Resource 3. Ask each group to prepare their response using the arrow cards and hold it up to show you on a given signal. Many teachers find the phrase ‘3, 2, 1, show!’ works well for this, but you may prefer to use your own signal.

It is important to allow the groups a set amount of time (perhaps 30 seconds or one minute) to prepare their response, and to insist that everyone in the group agrees it is a correct response before holding it up for you to see. This helps to ensure that all of the class remain involved, and also encourages collaborative working and mathematical discussion.

## Reflecting on your teaching practice

When you do such an exercise with your class, reflect afterwards on what went well and what went less well. Consider the questions that led to the students being interested and being able to progress, and those you needed to clarify. Such reflection always helps with finding a ‘script’ that helps you engage the students to find mathematics interesting and enjoyable. If they do not understand and cannot do something, they are less likely to become involved. Use this reflective exercise every time you undertake the activities, noting some quite small things that made a difference.

 Pause for thought Good questions to trigger such reflection are: How did it go with your class? What responses from students were unexpected? What did these responses tell you about the students’ mathematical thinking?Did all the students participate?If not, how could you modify the activity to enable them to participate?What points did you feel you had to reinforce?As well as trying out your own ideas to enable all students to participate, you may want to have a look at the key resource ‘Involving all’ for other suggestions.

1 Place value in the decimal number system

3 Using structured resources: base-ten blocks