Meaningful maths learning

Today we focused on maths, as both myself and Archana were in class together (the only day this week). Archana modelled taking a small group using materials, focusing on place value. The students were asked to solve a word problem based around 72x9. They really struggled with this, so Archana bought it back down to 9x7. The aim was for them to use bundles of ice cream sticks (bundles of 10) to get a tidy number, then take away one from each bundle (to get 9). This strategy would allow students to use multiplicative thinking with larger numbers.

Both groups of students we tried this with really struggled, and it became evident that the students did not have a good understanding of their place value. They could say this is tens, this is hundreds, this is thousands (etc), they could not use that knowledge in practice. 

So, we began a whole class place value session using different materials. 

We had cubes, popsicle sticks and round beads to use. The class was split into groups, each group using a different materials. 

We started with showing the number 94. 

Students had to make 9 groups/bundles of 10, then 4 ones (not that we told them that).

Then we moved into hundreds - students had to make 133. This meant they had to make 10 groups/bundles of 10, group those together to make 1 bundle/group of 100, then make 3 groups/bundles of 10, and leave 3 ones out as well (not that we told them that).

We continued on using bigger numbers, once students showed they had some understanding of 10x10=100, groups of ten etc. 

In the end, we got students to show the number 1028, using materials. We had three groups doing this, so we had to beg, borrow and steal materials from other teachers so each group had enough 'things' to make 1028. We used everything we could, and still had one group using felt tips to make one group of 100 as well. 

Making lots of one hundred.

Students in the process of making their 1028 - starting with making bundles of ten, then putting ten lots of ten together to make a lot of one hundred.  

Here is two lots of one hundred (the cubes), four lots of one hundred (in bundles of sticks), three lots of ten and 8 ones. Total number 638.

After each group showed their number, the rest of the class came over and saw what the group had done. We counted the bundles together, and checked they had the right number of each one, hence the right number shown.

Checking how many bundles of 100 this group made. The discussion then went into how many bundles of hundreds would there be in 2,000, 3,000, 4,000 etc.

1028 - 10 bundles of 100, 2 bundles of 10, 8 ones.

Here are ten lots of one hundred, two rows of ten and eight single blocks. Total number 1028.

The students were engaged, motivated and learning for over an hour and a half! It was an awesome lesson, which laid the ground work for the next few weeks of place value based learning. It got them to have some understanding of place value in practice; how many hundreds are in thousands etc.

A major part of this lesson was students trying it for themselves - neither teacher modelled or explained how to make bundles of ten, or that 10 bundles of 10 made 100, or how to lay them out in order from hundreds-tens-ones to make it easier to count them up. They did it themselves, and we facilitated them through the process by leading them with larger numbers. By giving students a chance to try their own thinking, and to learn from each other, they held the power over their learning. When they succeeded, it was to their credit, not because they copied the teachers example. 

And hence, their learning was more meaningful and they will remember it more than if it was very teacher-dictated.