Can You See a Pattern?

Today both year 8 groups were asked to discuss and solve a number of Algebraic patterning tasks. These started off with basic colour patterns and gradually built up to number patterns and representations where they needed to work out the rule/formula/relationship of that sequence.

Patterning is, "critical to the development of mathematical concepts and algebraic thinking and reasoning. General mathematical processes of representation, symbolization, abstraction, generalization and proof rely on initial pattern recognition and application in a variety of shapes, counting, spatial arrays or geometric patterns" (Bobis, Mulligan & al, 2013, pg 54).

As they worked in a group, it allowed every member of the group to contribute. In Group 3, one person made a suggestion of the relationship between the first three numbers in:

1, 2, 3, 5, 8, 13, 21, __

which helped others in the group to explore that idea further which eventually ended with the discovery of the pattern and the answer.

Below is a picture of some of the tasks I used today.

It's All About the Money

Last week my Year 8 groups and my Year 5 group were using play money. Money is good to use because it relates to real life. Everyone of my students has had experience at some point of handling money and buying or selling goods in exchange for money. 

My year 5's role played 'Shop Keepers'. They took turns being a shop keeper and had to sell an item to a customer. The problem for them in this challenge was working out how much change to give back i.e. if a drink cost $3.80 and they were given a $10 note, how much change do they give back? This involves using knowledge of place value, counting, addition, subtraction, parts of a whole (fractions) and decimals

My year 8's were first asked to count the pile of money put in front of them then they were asked to use money to solve addition and subtraction story problems involving money. 

Here are a couple of photos of one of my year 8 groups engaged in using their money to solve a problem.

My year 5 students (below) playing 'Shopkeepers'

Show Me Some More Strategies!

Below is a Show Me video of my Year 2/3 group having a lesson on place value. 

We have been looking at adding the tens first then the ones using place value blocks. We have also been using uni-link cubes and Popsicle sticks so they become familiar with seeing tens and ones in various forms. 

In this video, I am asking them to partition (break up) the numbers, which will help them as they move towards stage 5 and eventually stage 6 strategies. In this video I gave them more than ten ones (units) so that they would need to identify that there were another ten within those ones that needed to be added to the existing tens. They became a little confused at the end but as you can see they did work it out. The next step is to begin to withdraw the materials (blocks) and add in numbers so they can make the connection between the concrete materials and abstract numbers. We will try this then I will post the next video just keep checking back : )