3 Using structured resources: base-ten blocks

Although arrow cards are very useful for modelling how numbers are written and represented, they do not in themselves help students develop a sense of the size, or magnitude, of a number.

‘Base-ten’ blocks (also known as Dienes blocks) are a very effective resource for developing this sense of number size, because there is a direct and accurate relationship between the size of each block and its value. For example, in Figure 2, which again represents the number 364, it is clear to see that each 100 block is ten times bigger than each 10 block, and that each 10 block is made up of ten ones.

Figure 2 The number three hundred and sixty four represented in base-ten blocks. (Source: Wendy Petti, Education World)

If you don’t have access to base-ten blocks, then bundles of sticks (or straws, or used matches) can also provide a realistic sense of relative size and can be used in a similar way on a place value board like the one shown in Figure 2. However, they are not as strong visually and are less practical – particularly bundles of 100 sticks!

In Case Study 1 below, Class I Mrs Aparajeeta decided to use base-ten blocks to extend her students’ understanding of the decimal number system.

Case Study 1: Mrs Aparajeeta uses base-ten blocks

For the first part of the lesson, Mrs Aparajeeta wanted the students to work in groups of four with base-ten blocks but she did not have enough blocks for every group. Some of the groups therefore worked with base-ten blocks, and the others worked with some sets she had made out of card (using a template similar to the one in Resource 4). Mrs Aparajeeta also made a large set out of card, which she held up when she was talking to the whole class.

I started by writing 243 on the blackboard and asking ‘How many hundreds are in this number?’ After the correct response was given, I asked two students to come to the front of the class and hold up two of the large cardboard ‘hundred’ blocks. I did the same for the tens and the ones, until the number 243 was represented correctly. To consolidate, I represented the number in three columns on the blackboard as follows:

Hundreds Tens Ones
2 4 3

Each group of four was given a large place value board made out of card:

Hundreds Tens Ones

I then asked the students to represent different numbers on their place value board using the base-ten blocks, for example:

• ‘I want you to make the number 324.’
• ‘I want you to make me a number between 240 and 250.’

Altogether I asked the groups to make eight different numbers, so that every student made two each. For each number, I encouraged the other three group members to check that their group’s number had been made correctly.

Because of the limited availability of resources, I did not ask the students to make any numbers greater than 399. This was also helpful because of the limited space, both in the classroom and in the hundreds section on the place value board!

For this lesson, I decided not to include any numbers that included a zero; I would save this for a subsequent lesson.

In the next activity you are asked to try out a similar activity to Mrs Aparajeeta’s using base-ten blocks with your own class.

 Video: Involving all

Activity 2: Using base-ten blocks in class

Preparation

You can organise the activity in a similar way to Mrs Aparajeeta’s lessons as described in Case Study 1. If you don’t have any base-ten blocks, or you do not have enough of them, you will need to make some from card. You will find Resource 4 (a template for base-ten blocks) helpful for this. You will also need to make some place value boards similar to those used by Mrs Aparajeeta.

Before starting the lesson you will need to:

• decide how many students will be in each small group
• think about how you will hand out and collect the resources back in an orderly way; for example, will you set out the base-ten blocks beforehand, or choose one student from each group to collect them from you during the lesson?
• make a list of the numbers you will ask the students to make (including some open instructions, for example ‘a number between 270 and 280’); will you ask the students to make any numbers that include zeros?
• decide how you will ask the groups to share their answers with the rest of the class.
• decide how to introduce the activity. For example, in Case Study 1 Mrs Aparajeeta started by writing a number on the blackboard and getting students to hold large cardboard base-ten blocks to demonstrate how to represent it.

The activity

Now carry out the activity that you planned in part 1.

 Pause for thought How did Activity 2 go with your class? Did you modify your plans for the activity in any way? If so, what was your reasoning for doing so?What questions did you use to probe your students’ understanding when you were talking to small groups?Did all of the students in each group take an active part in the activity?

2 Using structured resources: arrow cards

4 Using a number line to develop understanding of place value