Tuning into Measuring Mass

          


To we began exploring our new unit:

Central Idea: Converting units and using decimals helps us make sense of the measurement of mass.

Lines of Inquiry:

° FUNCTION: Strategies we can use when measuring mass

° FUNCTION: How we can convert units of mass

° FUNCTION / CAUSATION: How we use decimals with mass and why

° CONNECTION: How we use the measurement of mass in our daily lives



To begin tuning into the concept of mass, as the children entered, they saw the following on our board:

As we were going to begin exploring how to convert grams into kilograms and vice versa, I thought it was important that they gain a sense of what 1 kilogram actually feels like.  

Using their arms like a balance scale, they hefted their school bag and compared its mass with the 1 kg weight in their other hand.

They were then asked to estimate what they thought the mass of their bag was.

As well as helping them sense a kilogram, it was also an interesting one-on-one pre-assessment as I listened to the thinking of each learner. 

Some of the thoughts shared were:

° I can feel my bag is a lot heavier than 1 kilogram.

° I think my bag is just a tiny bit lighter than 1 kilogram so I estimate it is 3/4 of a kilogram.

° I feel my bag is more than double the kilogram.

° Wow! Is this really a kilogram? It's really heavy!!

° I think my bag is about half of the kilogram. 

° Olivia said her bag was about 1 kilogram. Can I now heft her bag with mine to see if my estimate is close?

° Could I put my bag on a scale to see if my estimate was close?

° What has Louisa got in her bag? Her bag is more than double mine!

° I think its somewhere between 1 and 2 kilograms.

° I would say its less than 1 kilogram, but I'm not sure by how much.

° So my mum weighs about 70 of these weights?!?

° What do you call the things that are less than a kilogram?

As you can see, there were lots of diverse thoughts taking place. It was interesting for me to hear their reasoning skills, who was thinking of fractions, who was comparing by doubling etc. 

After each had hefted, I then asked them to show on the number line where their estimate belonged.

This also become a key informal assessment as each child shared where they would place it and what their estimate was.

I was thinking about:

° Who is using simpler masses such as 1 kg and who was confident in taking their thinking to masses such as 0. 75 kg or 1 . 25 kg etc?

° When they gave their mass estimate, I asked if they could express it in different ways?  Some could express it in grams, some could express using fractions and some could only express it one way. 

° Who was noticing the other masses already recorded on the number line and used that to determine their own estimates?

I felt I was able to gain a sense of where each child was at with their experiences and / or understanding of measuring mass and using decimals.

When everyone had hefted their bags, we then looked at the number line of estimates and I asked what does this make us wonder?

° How could we check if our estimates were close?

° Is hefting really a useful way to measure the mass of objects?

° How could we add all the decimals?

° What's the difference between the heaviest and the lightest?

Table partners then discussed these questions posed sharing their ideas and strategies.

As the purpose behind this was to tune us into what a kilogram feels like and also to gain an informal glimpse of where each learner was at with mass, we didn't go into this further. 

Sometimes, I think it is good to keep us wondering about certain things that we can come back to later.

I suggested that we use our number line as part of home learning next week, so during our day, if you have a mathematical question you think we should try to solve, jot it down on a sticky note and place it beside the number line. 

At the end of the day, decided upon four questions to solve for home learning in addition to a suggestion that we convert the kilograms to grams.

So, this is what our home learning looks like:

We will come back to the strategies they created to measure the exact mass of their bags later in the week after we have gained a deeper understanding of converting grams and kilograms.

What we did do after this, was we explored how to convert kilograms into grams and vice versa and then used this understanding to apply with our 'Travelling into Space' investigation: 

Link to 'Travelling into Space'

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

Wet Weather Recess Symmetry

Wet weather recess times can be a great opportunity for children to play and explore mathematical concepts. 

One of the options children have been choosing to do is to create half or a quarter of a symmetrical shape / pattern. Then, they give it to a classmate to see if they can continue making the shape symmetrically.





Here is a design a student created and gave to a classmate:

   








Identifying the two lines of symmetry, the classmate was then able to complete the shape:

 

Another example:

.....and what their classmate created:

Those choosing to do this during their wet weather indoor recess times have really been enjoying trying to create challenging shapes:

Student Agency Classroom Strategy

Student agency is being given more thought and focus in the new PYP changes. Student agency refers to giving children a level of control, choice, autonomy and power of their learning.

We all know that when children are given choice in what and how they learn, the learning engagement rises significantly.


This was our last week before the Christmas holidays and I wanted to experiment with a different way of offering stronger student agency for maths.

The children were given the table (below) of learning experiences on a Google doc.

The learning experiences were divided into three columns. The first column were to be carried out individually (to ensure each child had some personal thinking time), the middle column needed to be done with a partner (to ensure different strategies were being explored through sharing) and the third column they could choose to do alone, with a partner or as a trio. 

To help broaden who they were learning with, they could only do a learning experience with a certain classmate once. I had been noticing lately that some children were consistently choosing the same partners to learn with so I wanted to help them see the benefits of broadening their learning partner choices.

The top three learning experiences were mandatory and they knew those three needed to be completed by the end of the week. These were chosen as informal formative assessments where I was able to observe who might need additional help in our future ratios and probability units and what sort of help would be needed.

Provided those three were completed by the end of the week, the children were able to choose any of the other learning experiences. There was no expectation to complete any others. This allowed them to put as much or as little time needed. 

Christmas Maths

Individually	With a Partner (Choose a different partner for each activity)	Choice: Individually or with a partner (Choose a different partner for each activity)
Baking Christmas Biscuits Materials Needed: ° Doc (link above)	Elves' Uniforms - Possible Combinations Materials Needed: ° Doc (link above) ° whiteboard for creating strategies	Christmas Word Problems   Materials Needed: ° Doc (link above) ° whiteboard for creating strategies
Santa’s Workshop Map Materials Needed: ° Doc (link above) ° Map ° ruler	Christmas Trees- fractions / decimals Materials Needed: ° Doc (link above) ° square centimetre paper	Wrapping Christmas Presents Materials Needed: ° Doc (link above) ° boxes ° ruler
12 Days of Christmas Materials Needed: ° Doc (link above) ° Whiteboard	Design a Christmas tree ornament out of triangles and rectangles. Eg angels, stars, etc Then create a strategy to measure its surface area	What is the surface area of the Christmas star? Materials Needed: ° Christmas star
Estimate the number of Christmas baubles in the box on the laptop trolley. Rules: You cannot pick up the box. Write your estimation on a sticky note and place it with your name in front of the box.		Four Christmas Maths- Challenging Materials Needed: ° Doc (link above)

Google Doc Link to the Table (above)




Estimating: How many Christmas baubles link




N.B Doing this again, I will offer two or three levels of word problems to help cater to different learning needs like normally is offered in our class. (I was pretty rushed Sunday night creating all this, so I really need to put some more time into creating different levelled options for the mandatory learning experiences)

The week of learning was incredibly successful. There was always high levels of engagement and there was genuine excitement when they knew maths was the next learning we would be doing. Children were opting to do these learning experiences when they extra time to choose what learning they did. Some children were spending an impressive amount of time trying to create strategies and they were developing their own hyptheseses to prove or disprove. (The probability elves combination saw some students displaying strong perseverance and amazing mathematical trail and error skills to try and create a strategy)

There were some conceptual understandings or skills that some children might need to learn to do some of their learning experiences, so I suggested that we have 10-15 mini-inquiries that the children could sign up for each day over the week. There was a request to learn how to measure the area of a triangle in an easier way, so that was offered on the board and some children chose to sign up for that mini-inquiry with me on one of the days during the week. Not all children ended up signing up for it and that was alright. Those mini-inquiries were a great way to create and test hypotheses they formed. Some samples from that mini-inquiry small group:

Wonderfully, a student offered to run their own mini-inquiry. They had become really curious about the most effective strategy to solve the '12 Days of Christmas' problem. Four children signed up and they independently ran their own mini-inquiry where they shared the strategies they had used and then they tried to determine which were the most effective strategies. The group didn't need me to ran this and observing, it was fabulous to hear of some of the connections and patterns they had discovered whilst trying to solve it. Some samples:

By creating this tallying strategy, this learner was able to see a pattern that the day determined how many more gifts were given. They continued to test their hypothesis and proved it was true.

Another small group had been completely engaged and curious to find an effective strategy or pattern with the probability combinations elves' uniforms problem. They had spent over an hour creating multiply hypotheses and testing them out. They offered a mini-inquiry which a few classmates also signed up for where they shared discoveries and wonderings they still had:

I was curious to find out why there was such a positive buzz towards their learning and so in class and group discussions, I heard the following reflective feedback:

° They loved having choices- both what to do and who to do it with

° They liked how there was a range of active learning experiences and others that required sitting down. One student shared how they felt they could learn according to their mood- if they were in a high energy mood they could do the more active activities.

° They liked the sense of accomplishment and responsibility in having the three mandatory activities to complete (Some shared a sense of pride when they had completed those three)

° They liked how there was a mixture of different mathematical thinking- measuring area, ratios, fractions etc

° They liked the flexibility of learning where they wanted to and with whom.

° Some shared how they liked being 'forced' to learn with a different classmate each time as they thought it helped everyone to feel more included (interesting!)

° They also liked how they felt like communityof mathematicians by sharing strategies they had created / used when others might be stuck with ideas.

° They loved the theme of Christmas. There were suggestions that we should try to always do a week like this when other holidays arise such as Valentine's, Easter, student birthdays etc.

Thinking about their reflective feedback, I plan to set up learning experiences more often like this for the rest of the year. There is a lot of research for the benefits of student agency and I think when we can create and experiment with different approaches to honouring this in our classrooms, we can help raise the engagement of curiosity in our learners.

I loved their idea of creating their own mini-inquiries for classmates to sign up to participate in and definitely want to explore that strategy a lot more after the holidays.