Enquiry into Imperial v Metric Systems

As a provocation into the imperial / metric systems, we used the see-think-wonder routine with a partner based on this infographic and conversion chart:

This aroused a lot of curiosity amongst the children as they began seeing connections, got confused by other connections, questioned why and wondered, wondered, wondered........


They were hooked!


We then discussed with other partners what we had recorded in our see-think-wonder and then as a whole class.


Some samples:

Using this thinking-routine helped the children to:

° confirm connections and/or prior knowledge
° aroused curiosity
° helped construct meaning / understanding
° gave opportunities to create theories
° created a rich base for our enquiry 




We started discussing our theories about why such a big change in measuring systems.  To help construct this understanding I wrote:

                                         km       m      cm      mm

Partners had some time thinking about the connections between them. Students began explaining to us how we convert them.  

What did we notice?

- They are all base 10 numbers!  x 10  x 100  x 1000


Could this be the reason why the metric system was created?

After analysing the complexity of the imperial measurements, we felt that seemed very likely!

Some students extended & shared with us understandings further to discover how the metric system aligns with our base 10 number system:

We then consolidated our thoughts further to see how the metric system does align with our base 10 number system:

So, what do we want to find out?

Loads!

° Which countries use the imperial and which the metric?

Such a great question, so we googled a map:



This created lots of questions!!



Some of our big questions we want to discover include:

° Why does America still use the imperial system?

° Who created the metric system?

° Is it confusing for Americans to use the imperial lengths when they need to convert?

° How do we know if a unit of measurement is imperial or metric?

° Are there other measurement systems used in the world?



With these, children will partner up and share their findings based on questions they want to discover.  

Measuring Decimal Lengths

To help us enquire further into our central idea:
        

.......we have taken a segway into measuring length to help us understand how we use decimals in real life situations.  In word problems related to length that the children pose for others to solve, we have been finding out how to convert, add, subtract, multiply and divide decimals. Learning how to manipulate decimals with practical examples helps children to understand not only the skill process, but more importantly the why behind the skill.

To practise converting decimal lengths, the children were given lengths of different snake species in the world.  They converted the average length of the snake species and the longest length recorded. We were really amazed at these lengths and wondered how we might react if we came across one in the wild.

Decimal Snake Lengths Google Doc

After this, we were given a choice of activities to investigate:

Easier:

Choose one of the snakes.

Find the average length of the baby.

Make the average length of the baby using a paper strip.  Record the length in metres, centimetres and millimetres.

Make the average length of the adult using a paper strip.  Record the length in metres, centimetres and millimetres.

(This activity was aimed to help some of the children still new to the idea of converting decimal lengths from metres to centimetres etc.  It was also hoped that it would help them to visualise what 4 metres etc actually looks like)

               

We were amazed at the size of an average baby anaconda, an average adult and the longest length recorded!  The children creating this needed to convert the lengths from decimal metres to centimetres (and millimetres as an extension option) and then showed us how they calculated the difference between the decimal lengths.

                               

( Comparing the sizes of an average baby and adult of king cobra and a python)

More Challenging:

Choose one of the snakes.

Think of 10 snake lengths that could show how it got the average length.

Make the snake lengths using paper strips. Record the length in metres, centimetres and millimetres.

(It was hoped that this would make an interesting review on averages that we have been learning about this year and help some children gain a deeper understanding of what an average actually is)

Even More Challenging:

Create a visual graph that shows the distances and compass directions some of us migrated from before arriving in Lausanne.

You need a map ratio key so others can understand.  

You also need a compass rose (directions).

Places we are from link

( To do this activity, the children needed to create map ratio scales, use an atlas to find the directions of the cities we come from Lausanne where we live and thought a lot about using millimetres to help create strips of paper that would accurately represent the distance)

The majority of children were keen to do the last activity and some chose the first.

 

Distances and directions some of us come from with a ratio map scale. I thought this was a really creative way to present her maths findings.

These children decided to show the distances as a column graph.  I think maths thinking is so much better when we give children the opportunity to choose how to tackle an activity rather than constantly being told exactly what to do.  I wouldn't have thought of a column graph, but these children did and it made perfect sense to record the findings this way. 

I really loved the thought that went into this ratio map scale of distances and compass directions we come from:

A close upè of the centre:

Look how far away Melbourne is compared to other cities we come from!

When sharing our maths thinking, we asked questions of strategies they used, how did they know they were accurately showing the lengths and what they were proud of achieving.

In our whole class reflection, children brought up how this helped them to understand further that maths thinking IS creative thinking and they also mentioned how they appreciate being given options of what sort of activities to investigate and to investigate in ways they think is best.  Sounds like what real mathematicians do do to me!

Human Body Ratio Lengths

To arouse curiosity, we started by investigating for 5 mins with a partner what this saying means using tape measures:

We then grouped together and shared what we had discovered.  Some of us felt we need to round measurements up or down for it to make sense and we then discussed how a tailor or dressmaker might use this knowledge in their jobs. 

I introduced the concept of ratios and we might choose to use these as a way of expressing the lengths found. 

What does it make us curious about?

We wanted to find out other connections the human body might have with measurements, so that's what we did.  To help with our investigations, we first brainstormed body parts that we might not know the names of:

Partners were so excited each time they made a discovery of relationships body lengths had!

        

After 10 or so minutes of measuring, we started adding and grouping our discoveries on post it notes to the board under the ratios:

Loads of fascinating discoveries were being made and lots of interesting questions started emerging about how we can or cannot use ratios. Listening into the groups measuring, I thought about what made this activity so high energy and engaging to the children and came up with:

° It is student owned. They weren't given a list of possible body parts to measure and make connections from. They were coming up with their own hypotheses and testing them out.

° It is open-ended inquiry. No set answers, but tonnes to explore and discover.

° Everyone felt successful.  Again, no 'right' or 'wrong' answers. 

° Everyone felt a sense of pride at each ratio discovery they made.

° Easy connections to their own lives.  It is their body, their life.

° Opportunities to think about number relationships in a meaningful and engaging way. 

° Being introduced to a new maths concept (ratios) in a hands on and meaningful way.

° It was collaborative- kids helping each other to measure their body parts, sharing hypotheses, wondering together, discovering together. 

It made me think of how these are some essential elements to making maths learning engaging and exciting for kids.

 

Some of our equal relationship discoveries:
° the length of our foot = the length of our forearm
° from the elbow to the fingertip = top of kneecap to ankle
° length from outstretched arms = height
° tip of nose to chin = height of forehead

Some of our double/half length discoveries:
° height of ear = 2 circumferences of wrist
° circumference of head =2 circumferences of neck

 

The penis to arm ratio length made me giggle (on the inside).  We are just completing a unit of inquiry exploring puberty and human reproduction so it seemed perfectly alright for these boys to use this in their maths learning.....

We shared our discoveries and to reflect, we thought about 'big picture' understandings we gained from this learning experience: 

It's important that children learn that maths is all around them and that it doesn't just exist in worksheets or dreary textbooks.  Maths learning should be exciting, engaging and allow children to have the opportunity to investigate what they are curious about.  This activity certainly ticked those off; the kids loved their maths learning today and many were still buzzing about wonderings or discoveries they had made as they left the room for lunch :)

Tuning into Length

To continue exploring our central idea: 

we are going to explore measuring length as a means of understanding how we use decimals in real life situations. 

To arouse some curiosity and spark some deep thinking towards our unit on measuring length, partners were given the following units of measurement which are all equivalent to 1 metre:

They had several copies of these and discussed different ways they could group them.  

As they sorted into groups, they were encouraged to use the following symbols and note their thinking:

                          

Listening into the discussions, it was interesting to note who knew about the metric and imperial systems and equally, who was able to creatively group them in different ways by making connections.  

It was also really interesting to listen to ways the children were explaining their theories or understandings with their partners as they thought deeper about the units. 

The posters they had made were then shared around in a circle and we discussed what the other groups had thought of that we mightn't have.  This helped the children to broaden their own thinking and understandings. 

Samples:  

To help make our unit into length student-owned, we then thought of one burning question we had from this thinking activity and collated these together that we wanted to discover:

We had some really interesting questions to guide our enquiry into length now. I am also really curious about some of these wonderings too! :)  So we then examined those and created some lines of enquiry that would encompass most of our wonderings:

From this provocation, we were able to create a great maths unit that gives a lot of scope for the children to enquire into what interests them and at their own levels of skills / understandings. 

Tuning into Measuring Length Unit

To help us get tuned into our new unit on measuring length and to help us further explore how mathematical thinking is about creativity, we watched the YouTube version of the book: How big is a foot?

 The story tells of a carpenter needing to build a bed for the Queen,but makes the bed too small because the King's foot is larger than his which he used for the measurements. 

At the part of the story where the apprentice carpenter was sent to jail and was thinking about the problem we discussed what had happened and why.  It helped us to understand the need for accurate and formal units of measurement. Some of us wondered what happened before we had formal units of measurement and we discussed our theories. 

We then thought of creative ways the carpenter could rectify the problem. 

We talked about using other people's creative ideas to help us expand upon them as a creative strategy. To allow for this type of thinking, groups of 4 drew their creative ideas on the same paper so that the group members could be inspired by others. (see below)

We then shared our creative ideas and then as a group, wrote a reflection on what this activity helped us to understand about mathematical thinking in the centre. 

We then reflected together and some of the following wonderings emerged:

° Do all mathematicians believe maths is creativity?

° Why don't maths text books encourage students to think creatively?

° Can you still be successful in maths if you find being creative difficult?

° What do people who are blind do to visualise mathematical thinking?

° What discoveries really needed creativity to be discovered?

Such rich and deep questions and the theories answering them were profound and equally rich.