Posted on: November 27th, 2014 by jnovakowski 3 Comments

The students in Gillian Ewart’s grades 5 & 6 class have been beginning to learn about factors and multiples through creating arrays. Last week we decided to play around with the concept of “halving and doubling” as a strategy and how it could help us think about factors. I asked the students to created an array for 8 x 6. This task brought up language around columns and rows and what 8 x 6 would look like.

We then took the students through modelling halving and doubling with their arrays. Halving the numbers of rows and then sliding one half of the rows up to double the amount in each new row.

The big idea here is that the product (48) stays the same and that there is a relationship between halving and doubling. The students began to anticipate what their arrays were going to look like, realizing they were going to need to be creative in order to create their arrays after halving and doubling their 2 x 24 arrays!

As the students built and photographed their arrays, we recorded the corresponding equations on the whiteboard.

We also looked at all the factors we found for 48, beginning to look at factorization and “factor trees”.

As students were halving and doubling, they documented each stage by taking a photograph with the iPad and then labelled their photos using the Skitch app. We asked the students to focus on communicating what they had learned about factors by using arrays. The students then either used PicCollage or ShowMe on the iPads to compile their photographs and share what they had learned.

Here are some examples of the PicCollages the students created:

As students completed their documentation as a way to share their learning, they were asked to choose a new multiplication equation and play around with the idea of halving and doubling their arrays. This is something that the class was going to continue investigating after I left. We could have begun our investigation this way, with students creating different arrays, halving and doubling and seeing if they could generalize what might happen. For this context, we decided that a guided approach to start would provide the students with the language and understanding they needed to be successful when they investigated their own arrays.

This was my last scheduled visit to McNeely and our goal was to introduce a variety of iPad apps to the students so that they would have different ways to communicate their mathematical thinking and learning. I’m looking forward to hearing from the classroom teacher and students as to how this journey continues for them.

~Janice

## 3 Responses

1. Gillian Ewart says:

Thanks Janice! In the spirit of iPad Thursdays, we’ll be exploring multiplying by 10s, 100s, 1000s using iPads and place value blocks. I’ll try to send you some of the finished products.

2. Fred Harwood says:

I wonder if this can be adapted to Russian Peasant multiplication (or a variety of other names) for multiplying any two numbers. Here is a quick video of the method that shows him using all of THE algorithms for checking. But the halving/doubling method is clear.