100 Days, 10 groups of 10 Cupcakes

We've reached the milestone of 100 days at school. This is no small feat: time to celebrate!

Actually, we've been counting up to our first 100 days at school since the beginning of this school year. We track it each morning on our giant 100 square.

According to our revised Maths curriculum, children are expected to be familiar with numbers 0 to 20 in the first six months at school. After a year at school, they should be familiar with numbers to 100. In practice, this means being able to count and sequence (put in order) forwards and backwards, and also have an understanding of the beginnings of place value. Place value is the value of the digits in a number, according to where they are placed. So, the 1 in teen numbers means 'a group of 10'. The 1 in 100 means 'a group of 100'. We also encourage our students to see that the 10 in 100 means 'ten groups of 10'.

Since one hundred is such a big number to grasp, breaking it down into groups of 10 makes a lot of sense: 10 is a number we're familiar with.

 The tens frames that run alongside our 100 square show how each row of the tens frame make a group of ten: each decade (10, 20, 30, 40 etc.) is a ten. Two digit numbers are comprised of a number of tens and some ones (42 is 4 tens and 2 ones).

We've been practising making groups of 100 things, but arranged in groups of 10.

We have also applied the same thinking to our baking to celebrate 100 days at school. We aimed to bake 10 groups of 10 cupcakes.

After baking and decorating, our yummy cupcakes are ready to eat. We will arrange them in array of 10 groups of 10 before the party. The different coloured icing will help us to see the groups.

Then, we will experiment with how many we have when we eat one, then another and then another...

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.