Morning Prompt: What volume of water should we consume per day?

As we are exploring volume, our morning prompt for when the children entered our room at the beginning of the day whilst organising themselves to get ready was four beakers with different volumes of water.

Here is the invitation to the prompt:

And here is what the volumes looked like.

The first had 250mL, the second had 500mL, the third had 750mL and the fourth 1 . 5 litres.

It was really interesting to observe and listen into the reasoning discussions they were having amongst each other.

Some children drew upon prior knowledge about how much water adults need to consume and so they adjusted that amount to what they thought a child might require.

Some tried to estimate how much they personally would drink in a day and tried to match that estimate with a volume.

A few children began discussing whether they had to actually drink that volume or could the water also be included in the food they eat. 

Some others used reasoning skills to try to determine whether it would be 750 mL or 1. 5 litres. They had already eliminated the two smaller volumes as they felt they drank that much before lunch time. Their gut instinct was telling them that the 1 . 5 litres looked like A LOT of water, so perhaps it was more reasonable to think the 750 mL would be the amount.

One student had remembered reading that adults need to drink 8 cups per day, so he found a cup at our sink and brought it over beside the litre beaker to estimate how many cups that would equate to. He later decided to return to the sink and poured 8 cups of water into another litre jug to test his hypothesis.

Some of our thoughts:

I liked this strategy of comparing his water bottle to the volumes of water shown:

Sharing prior knowledge about water being found in food:

Testing his own hypothesis based on prior knowledge:

There was a lot of genuine engagement and sharing of theories with this prompt. 

Later in the day, we discussed what we already knew about why we need to constantly drink water throughout the day.

In our class, we have a volunteer who is our 'Rehydrator of the Week'. Throughout the day, this person will raise their water bottle and shout out 'Cheers!' to the class.  When we hear that, we all raise our water bottles and say 'Cheers!' and then thank the rehydrator for reminding us to have a drink.

This is a fun routine we have, but it also (hopefully) is helping to create a habit for the children to be conscious of drinking water regularly. 

Over the year, we have discussed often the impacts of drinking water often to help our brains think to their best ability etc.

We also have a class 'energiser'. This person's responsibility is if they feel we have been sitting down for too long, they invite us to the front of the room and will demonstrate three body movements which we copy. The purpose of this is to help circulate the blood in our bodies which e understand carries oxygen to our brains that helps us to think more effectively. I'm hoping this routine will help create positive habits of staying alert and healthy.

We then watched this TedTalk about the benefits of drinking water and discussed some of the information it shared and our wonderings that emerged from it.

We then looked at our water volume prompt and shared some of the strategies we used to determine how much water we should drink.  Some of us were pretty shocked to see it was approximately 1 . 5 litres because it does, indeed look a lot!

In our discussion, some children shared some personal action plans to try to ensure they do drink more water throughout the day which was great to hear (even without our class rehydrator reminding us)

Another suggested we find a way to measure how much water we consume per day to see if we ae being healthy or not and so next week, we will use that idea and try to create a way to record this. This is a great example of giving children opportunities to take action with their learning. It will be interesting to see how our class decides to go about this.

I think these morning prompt routines are a really effective way to engage children in mathematical thinking. They are not mandatory to participate in which I think makes them work better. The children who choose to participate are genuinely engaged and that engagement (I suspect) creates more interest in those other children who might normally pass on the maths thinking opportunity. 

Measuring Volume Morning Prompt

For our morning walk in prompt when the children first enter our room and get organsied for the day, I set up two shapes that had the same volume.

With our morning prompts, children do not have to participate, but nearly all of them do at their own choice.

The question posed was which had a greater volume.

I wanted to give the children an opportunity to solidify their newly discovered strategy of measuring the volume of rectangular prisms. We hadn't looked at this for a few weeks so I was curious to see who would remember the formula and / or what other strategies would emerge.

Most of the children who participated could recognise that the two shapes had the same volume.  Most used the formula, but others chose other strategies. This become a useful informal assessment to see what each child was doing mathematically.


Some samples:

Later in the day, we revisited the prompt and discussed strategies we used. This was a helpful way for children to hear how others approach mathematical thinking.

It also ended up creating an interesting investigation which we decided to add to our wonder wall:   What other prisms can we create that have an equal volume?

I think some very interesting number connections could be explored with that and so I'm excited to see who will choose to explore it and what they discover.

Estimating Volume Morning Prompt

Providing children with invitations in the morning when the first enter the classroom can be an engaging way to appreciate mathematical thinking in different contexts.

As we are currently exploring measuring volume and capacity, I found a small jar of sweets and when the children entered, they could choose to try to estimate how many sweets were in the jar.

On their sticky note, they were asked to explain the strategy they used to estimate.

Later in the day when we visited the maths prompt, children were able to verbally share the startegies they used. Some very interesting strategies and connections were explored.


Some examples of estimating strategies:

 

 

 

As the sticky notes were scatttered all over the board, a classmate suggested we arrange the numbers in order to make it easier to see how estimates. We agreed this was a good idea and so some of us arranged them in teens, twenties, and thirties/forties.

What is the range of estimates?

- We determined the range was 30.



Why?

- Because the smallest estimate was 12 and the largest was 42.



So, what does the range tell us?

- The difference between the highest and lowest.

- How big of a difference people estimated.


Can we explain what the range is in other ways?

- The range can tell us the middle amounts.


It was then time for the exciting part- counting the sweets to see who would win.

We counted 19 sweets.

No one had estimated exactly 19 sweets, so, who wins?

- Whoever was the closest.

We had two students estimate 20 so they won the sweets.

We wanted to hear again what strategy they used, so those learners shared again the strategy they used when estimating.


When counting the sweets, some wonderings emerged which we have added to our wonder wall:

- Do the companies count out the sweets per jar?

- How do they know how many sweets to put in the jar?

- The jar says it is 45 grams, so do they measure the mass of the sweets?

- Do they just estimate the number of sweets?

- Would all the jars have exactly 19 sweets?


And some theories were discussed:

- The jar was packed full, so maybe they are thinking of the volume of sweets- the maximum amount that fits in.

- Since it says 45 grams, I think they must weigh the sweets but they round them up or down so if the sweets weighed 48 grams they would say that is close enough.




Obviously, the opportunity to win some sweets enticed the children a lot. 

Having regular maths prompts / invitations as part of a morning routine can (even without winning sweets) help engage children in creating or testing mathematical strategies in relaxed and real life context ways.

They can also serve as an interesting informal assessment when spending time listening to or reading strategies each child is trialling to use. Often, they come up with really creative ideas that can be tapped into for further investigations.

Form: What is a cubic centimetre like?

Using the PYP key concepts are a fabulous tool for helping children delve deeper into mathematical concepts.

Today we explored the cubic centimetre.

Looking at the PYP key concepts, we thought about which might be the most useful to use first to help us gain a deep understanding of cubic centimetres. Some of is thought 'connection' and explained why they thought so. Others suggested we use 'function' and a few felt perhaps 'causation'  Most of those thought 'form' would be the most useful.  After hearing everyone's reasons, we decided to use 'form' today.

Looking at a plastic cubic centimetre, we used the think-pair-share routine to explore it.

Eventually, our class sharing looked like this:

Though a simple learning experience, it generated a lot of interesting discussions. There was some debate over whether it has to be a cube in shape. To help, we made a cube that was 1 cubic centimetre.  We then squished it down.  Is it taking up the same amount of space? - Yes.  So, what does this tell us? - It is still 1 cubic centimetre because it is the same amount of space; therfore a cubic centimetre does not need to be a cube in shape.

We then found objects in the room and estimated and then measured their volume using cubic centimetre cubes.


We can sometimes overlook the key concept 'form' as being a bit basic. However, when we encourage children to really stretch their minds whilst using it, great understandings and wonderings can be explored. 


To read more about using the key concepts, click the link below:

The Power of Using the PYP Key Concepts in Maths

Creative Volume Problem Solving

Giving children opportunities to problem solve creatively is a key element of mathematical thinking we need to be constantly valuing in our classrooms rather than 'getting answers'.


To help with this, partners were given a thesaurus and an atlas to examine and were asked: 

Which do we estimate takes up the most amount of space? 

(I didn't want to use the term 'volume' just yet to allow the children to gain a better understanding of what volume actually is and I had chosen two books which looked like they had a pretty similar volume)

Without using any resources, rich discussions took place as partners discussed and created estimating strategies.  They then individually recorded their thoughts using the sentence starter:

I estimate that the thesaurus / atlas takes up more space because.......

Giving children sentence starters like this, I think, helps them develop stronger communication skills and also gives them an opportunity to deepen their own thinking without being influenced by others.

After they wrote their thoughts, we discussed together.

Firstly, we showed hands how many of us thought the thesaurus took up more space (4), the atlas (11) and the same amount (5).


     

Students were invited to share why they thought so and some very creative thinking and strategies emerged.

We first heard from those we thought the thesaurus takes up more space:

- I visualised smooshing the book down as if it was playdough and I could see it taking up more space than the atlas.

- I can see the thesaurus is much thicker so I can sense it takes up more space.

- I visualised taking out all the pages of both books and lining those pages up side by side. I could see that the pages of the thesaurus would be much longer so that makes me think it takes up more space.


We then heard from some students who thought the atlas takes up more space:

- I imagined cutting the atlas in half and stacking both halves on top of each other. By doing that I could visualise it being thicker and so taking up more space. 

- I drew a dot at the halfway mark of pages on the side of the thesaurus. I then placed the atlas beside it and imagined doubling it. By doing that I could visualise it taking up more space.

- I opened the thesaurus up at exactly halfway and placed it spread out on top of the atlas.  I then looked at them at table level and could see clearly that the atlas took up more space.  

- When I placed the thesaurauas on top of the atlas, I could see it is almost half the area size of it. So, I visualised doubling that and then tried to estimate the thickness of both to see which might take more space. I'm not exactly sure, but I think I can see the atlas taking up more space.


We then heard from those who thought they took up an equal amount of space.
They had used similar estimating strategies and some had thought about estimating the width and length to mentally calculate which took up more space. That was interesting to me because up till then no one had suggested the books being rectangular prisms nor formulas for measuring the volume of those shapes.



I then asked, what mathematical concept are we using when we measure how much space an object takes up?


A few of us shared how it is volume.


What things in our room have volume?

- chairs, tables, our bodies etc were shared.




What about the air in our room? Does it have volume? 

That question raised a lot of different opinions. When asked why we thought so, someone shared how a balloon gives us evidence that air has volume. 


Another shared how fire 'breathes in' oxygen and when there is no oxygen left in a room a fire goes out so that must prove air has volume because when there is no more of it, it has an impact on fire. Amazing thinking! :)

Another wondered, but what about in space? There is no oxygen there so does space have no volume?

We wondered about that..........

We then began investigating:

How many different strategies can you create to measure the volume of each book?


The 'how many' part of investigations really opens up possibilities for children to stretch their minds.  We are not valuing an answer; instead we are are valuing creative thinking.

We discussed how creative thinking is a key element in maths and that it doesn't matter in this learning experience if the strategy is effective or not. What we are doing is thinking creatively.


Partners were given string, MAB units, longs and flats as well as being able to use rulers or any other object in our room to explore the measuring.




Loads of very impressive creative strategies emerged.....

Some students counted the number of pages inside both books and did calculations to try to find out which had the most number of pages and then doubled / halved the number to see if it would help them measure their volumes.

One student found a connection between numbers and others were discussing the difference in volume they felt they had measured between the two books. 

Some cut the string to use as a measuring tool when comparing.

 This student thought about whether if he rolled a bottle once, then placed the measurement using a pencil and then rolled it again to measure whether it would help him measure the volume of both books or not.  He wasn't sure if it would help, but his idea intrigued many of his classmates and me.

Lots of very rich mathematical theories, reasonings and knowledge were being shared whilst partners created different strategies.

We did a gallery walk hearing the different strategies and were amazed that the incredibly creative ideas that emerged.

I think this was a pretty successful investigation and introduction to volume which we will expand upon in further learning experiences.  

Divergent Thinking: How many ways can we measure the volume of the odd shape?

Maths often requires creative thinking. 

Giving divergent thinking opportunities where we try to generate creative ideas by exploring many possible solutions is a useful way to show children how maths is about thinking creatively.  It also takes anxiety away from some children who harbour misconceptions that maths is all about being 'right / wrong' that they may have been taught previously.




To help us with divergent thinking (and to solidify our new understanding that 1 millilitre = 1 cubic centimetre), I made this odd-looking 3D shape by connecting boxes:

      


How many different ways can we measure the volume of the shape in litres?

The group explored the shape and came up with these amazing ideas:


° measure the volume of each box in cubic centimetres, add together and convert to litres

° create different prisms that connect part of two or three boxes to measure then add together

° fill a bathtub with water.  Submerge the shape in it.  Measure how much water overflowed from the bath and that will tell the volume.

° fill the shape up with water and then measure how much water was used

° make the same shape with base 10 /MAB blocks and then calculate how many cubic centimetres it is. Then convert to litres. 

° use a Hoover to suck out all the air in the shape. Then blow the air into a balloon. Put the balloon into a container of water and measure how much the water rose. 






After generating these possibilities, we then evaluated each and discussed which we thought would be the easiest and the most complex by arranging them in order.


In our oral reflection together we discussed what we gained from this learning experience and how it helps us with other areas of maths.  

A student explained how in maths there are usually many different strategies to solve problems. We should try to find different strategies and then evaluate which are better to use for those situations. Such a great connection!

The children also shared how they enjoyed the learning experience because they liked how they could think of 'mad' ideas and they were deemed good. 

Fun, Engaging Way to Consolidate Learning

To help us reflect on what we have discovered in our unit exploring the following central idea: 

I thought of a way we could consolidate our understandings in a fun way.

Partners were given a Venn diagram and 10 minutes to add as many things as they could to compare / contrast measuring volume with measuring capacity.

To make it a bit more fun, each time they recorded a thought on their Venn diagram, they earned 1 cubic centimetre.  The partners would use them to build a cuboid.  We would then see which partners were able to build the cuboid with the largest volume. (We needed a quick discussion to remember the difference between a cuboid and rectangular prism)

To make it even more interesting, a student suggested that they could earn two cubic centimetres for each idea they could add to the middle section- what volume and capacity has in common. 

We liked that idea a lot so agreed to it. 


This activity was a really engaging way to consolidate what they had learnt during our unit as well as expanding understandings by discussing with a classmate.  It also helped students to deepen their understandings of what measuring volume / capacity is about and identify connections.

Some sample Venn diagrams:

The other interesting thinking involved was how to build a completed cuboid using the cubic cms earned. As they continued being able to add cubes, students experimented with different ways to build the shape. 

When the time was up, they could only measure the volume of a completed cuboid. Therefore if they were missing one cube, they would have to take away some of the cubes:

This pair had to take the 3 cubic centimetres away to measure a cuboid:

When the ten minutes was up, we measured and shared the volume of the cuboids we managed to create:

To conclude our enquiry into volume / capacity, we then decided on an investigation we wanted to explore in depth.  These will be done either in small groups or individually.

To help decide, we used a Google form and nominated one investigation that grabbed our interest.  These were some of the wonderings students had created during our unit and had placed on our wonder wall.  They were chosen because I felt they could create some deep investigations.

They also had the option to add their own idea for an investigation.

Our choices for our personal maths enquiries:

(17 responses)

CONNECTIONS: How are cubic cm / m connected with ml / litres?	1
STRATEGIES: How can we measure the volume of other prisms? eg, hexagonal prisms etc	6
CREATIVITY: How many 3D shapes can I make with a volume of 24 cubic centimetres?	5
STRATEGIES: What is the volume of the oddly shaped prism in litres?	1
PATTERNS: What patterns exist when we multiply the L / H / W of a prism by the same number?	4
Other	0

Giving students opportunities to take their own learning further in a more independent way is a key element to creating an enquiry-based maths learning environment. 

The children gain a wonderful sense of pride and confidence in the types of mathematicians they are.