Friday, 15 April 2016

Flipping our Classroom: Area Model Multiplication Strategy

We flipped our classroom again this week to enquire into the area model multiplication strategy.   ( Benefits of flipping classroom for enquiry-based maths for percentages )

Usually if we flip, I create a google doc with YouTube links for the children to choose from according to levels of complexity.

This week though, I thought I'd experiment and see what happens by keeping it more open.

For home learning, the children were asked to choose two different YouTubes that explained the strategy and recorded their enquiry (see below):

As we often discuss in class, teaching others is an effective way to deepen our understandings, so when we enquire like this at home I think having them teach their parents is a useful learning strategy.  It also helps parents to gain an understanding of who their child is as a mathematician.

Flipping is an amazing learning strategy. It allows for differentiating different levels of understanding, provides children with the time each needs to comprehend and deepen their understandings, gives them a sense of responsibility and ownership and when sharing findings- extends the learning further as the children are sharing different approaches.

Having the children reflect about what they think of the strategy helps them to internalise the learning they have been doing and also helps them to deepen their understanding of it. Reading through their reflections also serves as a very interesting informal assessment and helps one to gain interesting insights into each child's mathematical mind.

Some of our reflections about the strategy:

° I like this strategy a lot because it focuses on place values and splitting the numbers up. I think it is a great strategy and I want to use it more often!!

° I think it is a very effective strategy because it is very simple and yet it shows you what the numbers really mean.

° I think this strategy is incredibly useful because sometimes you can do it in your head!

° I like how this strategy helps you to visualise what you are doing when you multiply. 

° I wish I had discovered this strategy last year. It finally helps me make sense of what it means when I multiply large numbers.

° I think it is really creative, but I wouldn't use it all the time because it would be harder and take longer with large numbers. 

We sat in a circle with our enquiries.  I began our discussion by finding out who was new to this strategy.  Most were.

To make this a more meaningful and student-owned discussion I then explained that they are to ask our group questions about their enquiries. The student posing the question controlled the discussion by asking those who wanted to answer. I was silent throughout - just listening and making mental notes.

Some of the great questions that emerged:

° Who would use this strategy again and why?

° Why does the strategy work?

° What are the pros and cons to this strategy?

° Do we think we could use this strategy for really large numbers?

° What did our parents think about the strategy?

° How did you feel when you were teaching your parents the strategy?

° Do you think this or the column strategy is faster?

After our discussion, I had already prepared an area model grid, but without the numbers.  Together we thought of how we could find out what the multiplication question was and it's answer.

We worked out that if we counted the number of squares across, we could determine the numbers multiplied.

When multiplying, we were surprised that so many squares existed in each rectangle!

Upon solving it, we came back to the previous discussion question of the pros and cons.  We could see how this strategy helps us to really comprehend what we are doing with the numbers when we multiply them.  

One student remarked how it was the first time she actually could see what multiplication means. That's a powerful moment we thought!

A key factor of enquiry-based learning is giving children the opportunities to take ownership of their learning based upon their own curiosities, so we shared what this strategy makes us wonder.  What are we curious to investigate?

Our ideas we wanted to investigate:

° Can we use this strategy for really large numbers?

° Can we use it to multiply fractions?

° Multiplying decimals?

° If we timed how long it would take to multiply the same number using this strategy, the column strategy and the split strategy, which would be faster?

With these great wonderings, the children chose one they were most interested in and either individually or in small groups they investigated.

Some really wonderful enquiries took place.  A pair seeing if we could use the strategy to multiply decimals had an interesting approach. They decided it would be best to try with easy numbers and gradually build up:

When multiplying a decimal with a decimal though, things become tricky.  When checking their answer with a different strategy, there were different answers. Why?

They were perplexed and thought about finding the difference between the two answers to see if that would give them a clue.  

Eventually, they worked out how they were multiplying the decimals incorrectly. Like in the example above, when they multiplied 0 . 7 by 0. 8 they had thought that was 5.6 rather than 0.56.   They discussed what they needed to do with the place values.  

They then continued on multiplying larger decimals to see if it would continue to work.

When they shared with the class, we thought it was great how they shared the challenge they faced but didn't give up.  In their sharing poster, they even thought it best to explain what they had done wrong as a way for all of us to learn from:

Groups who challenged themselves with using the strategy with large numbers reflected how it was possible and it helped them to practise multiplying numbers with lots of zeros, but it wasn't a good choice compared to the column strategy:

When you constantly give and discuss the message that maths is about creative thinking, wonderful ideas like this group emerge:

After discovering how to use the strategy with multiplying fractions, they wondered if they could create their own strategy:

When they shared their strategy, we could see how the cat's face fractions weren't mathematically correct, but we did love where they took their thinking to try and create their own unique way.  

One student's feedback was: I think all the maths we know today started off with people experimenting like what you did.

How can we not love these realisations being formulated in children's minds?

The group that timed which strategy was faster shared how with 1 and two digit numbers, the area model and column strategy were pretty close.  But when it came to larger numbers, the column strategy was faster:

After sharing our enquiries, I asked what our enquiries helped us to think about:

° When we use numbers, some strategies are more effective than others so we need to think about which is better.

° Maths really is about creative thinking.

° It's important to understand what multiplication really is especially when we use large numbers because it can tricky to comprehend.

° We are able to make our own maths discoveries!

Flipping our classrooms is a powerful tool we can use to help foster enquiry-based learning in maths.  The children came into our learning today with sound understandings and were able to develop these at their own pace.  It opened up the doors for wonderings to be investigated.   

Another benefit to this approach, I think, is that we can have children building upon their number sense in a more meaningful and reflective way at home whilst we might be focusing on different maths units in class.  At the moment, for example, we are currently enquiring into ratios, proportions and rates in class, but at the same time they were building multiplication conceptual understandings at home. 

YouTube is great tool for home learning when we utilise it in these types of ways. 

Other Flipping Classroom Ideas we have done:

Flipping: Introduction to Ratios

Flipping for Percentages

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