Multiplying Decimals

As part of our Unit of Inquiry exploring forces, today we were going to find out how much we would weigh on different planets- the kids love it! 

Part of that requires multiplying their body mass with decimals.

So, to better understand what we will be doing with the numbers, we began with this lead in:

We used the think-pair-share strategy.  Firstly the children jotted down different ways. They then shared with their table group and then we discussed and shared ideas as whole class.  Some of the key understandings included:

We have done this a few times over the year and each time additionally unique perceptions are shared which I find really interesting. I can see how some children's conceptual understandings and abilities to express have expanded and deepened. 


The whole class sharing raised some interesting discussions such as a child sharing how decimal numbers are like negative numbers.  

- Are they? What do we think about that?

Some of us agreed, some disagreed and many were unsure.

Another asked: Can we have negative decimals?

- Can we?

We thought of having a temperature of   - 1 . 5 ° C

Does this prove we can have negative decimals?

Does this mean a decimal is a negative number?

A student shared a theory that: 

This really got us wondering: Can a demoninator be zero?

We chatted about what this might mean- Can we have zero whole parts?  Could this represent a decimal as a negative number?

It was a very interesting thought and I explained that we will definitely come back to this in a few weeks when we explore negative numbers. 

Some of us still weren't 100% sure about decimals being negative numbers or not and that is ok. I think it's good to keep wonderings floating in our minds to think more about later. 



Having tuned our minds back into what a decimal is, we then looked at the following: 

I posed this question to help build number sense and to also value creating theories which we are always doing. 

We showed with thumps up, down or sideways what we our theory was.

There was a mixed initial thought to this.

To help each of us find out for ourselves, the following was posed: 

Asking 'How many different ways......' is a great way to encourage deeper thinking and creativity.

If we ask children to think of one way / one answer, we are limiting their potential to discover different ways of thinking.

Again, we used the think-pair-share routine. 

It was interesting to be able to walk around and chat / observe the different ways the children were trying to visualise it. 

One children shared a great hypothesis:

When we multiply numbers, the answer is bigger so my theory is that the answer to 5 x 0 . 5 will be bigger.

This completely makes sense and I love how she has drawing upon prior conceptual knowledge to create and test a theory.

After a while, the children shared with ther table partners their visual ways. Each table group were asked to select one of the visualisations that they thought the whole class would benefit from seeing. 

Together we discussed the following shared:

We appreciated all the different ways we could visualise the numbers.

We then repeated with a larger decimal:

Again, we first estimated and then tested by visually drawing what it looks like in different ways.

Some of the table sharing included:

We really loved the creative story behind the one below. He explained how there were 5 whole people at the airport and each carried a bag that was 0 . 25 of their body mass:

Valuing creativity and visualising in maths can greatly help children to make stronger number sense like these examples show. 

Lastly, the children created and visually showed their own number sums. Afterwards, they shared and discussed these with their table partners:

Some wanted to challenge themselves further by multiplying a decimal with a decimal to see what it looks like:

And this student found it very interesting to discover how small the number would be when multiplying 5 by 0 . 0000002. We giggled about it being about half the size of a ladybird's poo :P

Before moving on to multiplying the gravitational force of our mass to see how much we would weigh on different planets, I asked if we had some wonderings we wanted to explore next week and so we have the folllowing to find out about: 

I think this has helped us launch into some really interesting wonderings to explore that will further help develop our number sense with decimals and fractions. 

FInding the Fraction of a Quantity Investigation

Today we started exploring how to find the fraction of a quantity which is a key way we use fractions in everyday life. 

To find out strategies the children already knew and to give them an opportunity to create their own strategies, we looked at the following situation:

Developing number sense requires children to constantly estimate and get a feeling for numbers, so before we started working it out, the children were asked to identify their 'gut instinct' of which they feel might be cheaper and to write a star beside it to test later.  

We then had time either using strategies we already knew or trying to create strategies to help find out. 

For those children who could find a successful strategy easily, their challenge was to try to create another strategy that might also work. I think that giving children opportunities like this helps develop their creative thinking whilst also helping them to delve deeper into mathematical understandings. 

As they were creating strategies, this was a great opportunity to discuss with children their thinking and to find a few interesting startegies that could be shared with the class.

I found the following, wrote them up and then those children shared their strategy with the class who then gave feedback on what they thought of it:

After discussing these strategies, we then needed to discuss which t-shirt was actually cheaper since we had different ideas.


Some children hadn't realised they needed to subtract the fraction from the original price so listening to others explain why helped them to see the mathematical thinking needed:

Looking at the various thinking that took place can greatly help create a picture of where each child is at, whether they prefer visualising or not and any misconceptions they might be harbouring such as the last sample where the child is thinking a third equates to 25%. 

We then extended this understanding with our next situation:

Again, to help develop their number sense, before applying any strategies, the children drew a star next to their estimate or 'gut feeling' for which was greater. 


This question helped identify misconceptions some children were harbouring and we used some of those ideas to help deepen learning of everyone in our discussion.

We are constantly reminding oursleves that mistakes are great when we take the time to think why they are mistakes and how sharing mistakes can help deepen everyone else's understandings.


This was a great example:

Quite a few children had explored this as a strategy. Others were able to explain how we either need to 'stretch out' the fifths or 'shrink' the tenths so they are the same sized whole. 

Some thought of comparing the two fractions to a half as a strategy which we thought was an interesting idea: 

Students were then invited to share stratgeies of how we can find the fraction of the amount that helped us to determine which was more. 

We really loved this classmates' visual strategy:

We thought this was an interesting strategy too:

Lots of questions were asked when a student shared this strategy:

Finally, this student's strategy was chosen to be shared:

We then practised a few 'fractions of an amount' questions and reflected in our Maths Reflection Diary:  


Maths Reflection Diary Link

Valuing Creative Thinking in Maths

What message do we want to impress upon children of what maths is about?

When our children leave our year level, what would we like them to feel mathematical thinking is about?  How would we like their perspectives on maths to have grown, deepened and changed by the time they move up a year level at the end of the academic year?

This year, one of my goals is to help the children in my class to appreciate the wonders of number relationships and connections. That our number system isn't something to fear, but to play and make discoveries about. I also hope to impress the idea that mathematical thinking isn't about getting an answer. An answer is merely a byproduct of the rich process we can take our minds when creating and evaluating strategies. 

To help deepen our understanding that maths is about creative thinking, today we looked at the following context problem:

Stuffed with Pizza

Andrés and Margarita are stuffed with pizza!

Andrés ate one-quarter of a cheese pizza. He then ate three-eighths of a pepperoni pizza  and finally ate one-half of a mushroom pizza.

Margarita ate five-eighths of a cheese pizza followed by another half of the mushroom pizza.

All the pizzas were the same size. Andrés says he ate more pizza than Margarita because Margarita did not

eat any pepperoni pizza. Margarita says they each ate the same amount of pizza.

Who is correct?   /    How many different strategies can you create to solve it?

The key to opening up an investigation like this, I think, is changing the last part to state 'how many different strategies.........'

If we present children with closed problems where the answer is deemed what we are valuing, then we can only expect children to think the correct answer is what is important.

When presented with this problem, I asked my class, "What do we think we are valuing in this investigation?"

As we have been doing learning experiences like this a lot of the year, happily, we were able to identify that we are valuing creative thinking. Others thought we are valuing how there are many different ways to solve a problem and that they are all good. Another shared how in maths we should try to evaluate different strategies to see which are more effective and why that is so.

When I hear the children sharing these understandings, I feel like the big messages of the year are settling in their minds and this is also observable by their much more positive perspectives on maths.

If we as teachers, feed children the perpetual message that maths is about answering closed questions, then it is no wonder why so many children develop negative attitudes towards it. If we help children see how maths is about being creative, they more freely take risks with their thinking and begin enjoying where their minds take them.

Children buddied up with their table partner to create different strategies to solve the problem. Loads of rich and deep discussions took place. Loads of trial and error and lots of peer teaching of some misconceptions being harboured also took place. Listening in to the diverse discussions, it made me realise how all this amazingthinking and learning could never be taking place with a traditional chalk-n-talk maths lesson. Real mathematical thinking was taking place and children were feeling passionate about their creativity.

After some time, partners then published some of their strategies on paper and these were then shared around the room. As others read their strategies, they used post it notes to give constructive feedback. This strategy further helped us to see even more possible ways we can visualise and problem solve in maths.

Some of our ideas:

After sharing our strategies, we then used Padlet to write a short reflection about this learning experience. Here are some responses:

When we read reflections like this, we have to know we are doing something right in our classrooms......