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.
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.
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:
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 |
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:
Now carry out the activity that you planned in part 1.
![]() Pause for thought
|
OpenLearn - Using structured resources to develop understanding: place value Except for third party materials and otherwise, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence, full copyright detail can be found in the acknowledgements section. Please see full copyright statement for details.