Building place value houses - and number sense.

 

At our Celebration of Learning this week, some of our Autahi students shared their learning about place value houses. This is an essential piece of conceptual understanding that will enable our students to work with numbers of all sizes, in all kinds of ways, in the future. Here's some background on how we're working on this with our students. 

Our number system is based on groups of 10. The number 10 is made of 10 ones. 10 tens make 1 hundred. 10 hundreds make 1 thousand. Using this system, we are able to represent very big numbers and decimals, too. But, to work meaningfully with these numbers, we need to have a clear understanding of what they mean.

This is especially true because we represent all numbers using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In a three-digit number, the numbers that digits represent gets bigger by a power of 10 with each step to the left. For example, reading right to left, 111 is composed of 1 unit, 1 group of ten and 1 group of a hundred. So the 1 in 100 does not mean the number 1: it actually means '1 group of a hundred'.

In a number like 604, zero is playing a role as a 'place holder'. In this case, there are 4 ones, no tens and 6 hundreds. Without the zero, the number would read 64, which would change the 6 into 60 instead of 600 (incorrect by a power of ten).

 

In Autahi, we use physical materials to help our students to grasp these important concepts. In this photo, some of our students are filling up a tens frame (comprised of two rows of 5) with counters to make a group of 10.

We progress from here onto working with with teen numbers, before gradually moving onto twenties and thirties. Here, we're making bundles of 10 pencils. These bundles can be used as groups of ten to build numbers like 15 (1 group of ten and 5 extra ones) or 23 (2 groups of ten and 3 extra ones).

On this chalkboard, the tens house (marked with a t) contains bundles of ten while the ones house (marked with o) is home to single sticks.

By drawing a place value house, we are able to use these materials to represent the numbers we are working on. We learn that ones go in the ones house until we have 10 of them. Then, they become a group of ten and can go and live in the tens house. Once we have 10 groups of ten in the tens house, they become a group of 100 and must go and live in the hundreds house.

Some students will also begin to use place value to help with with addition and subtraction calculations, often with a hundred square for support. A good knowledge of place value helps them to calculate, but also to estimate and have a sense of what answer they might be expecting from a calculation, so they know if they are wide of the mark. The aim is to build firm foundations for a lifetime of working - and playing - with numbers.