Category: estimation

How many watermelons can we purchase for RMB59?

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The children have been engaged in various activities related to ‘The Challenge Project’. Different teams will work on specific aspects of the project to help us stay organised. Following on from our inquiry into money, we were now ready to purchase the watermelon. It was time for us to have a small team walk across to the supermarket to buy the watermelon.

The shopping crew updated the others on their trip to the supermarket.

  • Riccardo “We went out of NIS.”
  • Jacob “We crossed the road. We walk over the walkway. Ms. Hannah helped us. The security guards helped us, he stopped the cars and we can go across the road.”
  • Isabella “We got to Suguo and we need to find the watermelon.”
  • Adalyn “We need to check the money. We had 59 RMB.
  • Suzy “We have to test it to see how heavy the watermelon is. Some of the small watermelons were not as heavy as the big ones.”
  • Isabella “We weighed the watermelons so we decide how many we need.”
  • Riccardo “The Suguo people helped us weigh the watermelon and told us how much money is it.”
  • Jacob “We carried it. If it is too heavy we cannot carry it so we need a small one.”
  • Riccardo “We choose 5 first. “
  • Jacob “We first gave them 57, then we gave them another 59. It was less than 59. 2 left.”
  • Adalyn “The two watermelon we add them and we buy them.”
  • Suzy “We went out of Suguo and we cross the road and we go back to NIS. We were safe.”

The experience at the supermarket helped the children experience the process of choosing and purchasing food items. On their trip, they needed to make many decisions and work together as a team to solve the problems they encountered.

Jacob “We are going to the supermarket to buy the watermelon for making the ice pop challenge. 3 minute challenge our buddy can make the watermelon ice-pop. We use 57 RMB to buy the watermelon and we took the middle one and one small one. We chose not heavy one, we choose the smaller one and smaller so we can carry this, used the basket too heavy. Me and Isabella carry it and go to school. We take a long time.”

Many opportunities for mathematical thinking and learning were explored. These authentic learning experiences are great opportunities for children to explore and learn about concepts through real-life experiences.

Our next step would be to carry out the test to find out how many ice pops we can make from one watermelon.

 

YAY! Making the Ice Pops!

 

  • Dahyun “We made the ice cream with the watermelon.”
  • Ciel “We put it in the freezer because then it will freeze.”
  • Evan “Then we took it out because we need to eat it in 3 minutes because we need to have a challenge.”
  • Isabella “It was really hard to take the ice pops out.”
  • Evan “Then we eat it in 3 minutes.”
  • Junsu “Some people don’t eat it in 3 minutes.”
  • Riccardo “It was really icy.”
  • Suzy “But it was yummy.”
  • Evan “It was so cold!”
  • Sea “We eat watermelon like ice pops. We eat it, it’s like cold. I ate it but my teeth was so cold.”
  • Adalyn “We eat watermelon ice-pops, it feels like cold.”
  • Isabella “It was sweet.”
  • Suzy “The ice pop, maybe it was sweeter a little bit more.”
  • Ciel “When Ms. Shemo took one ice pop out, it broke.”
  • Junsu “And watermelon is in the body.”
  • Dahyun “I eat ice cream then my body is so cold.”
  • Evan “I eat the ice cream my teeth feels off.”
  • Isabella “Riccardo finished the ice pop in 3 minutes. And Archie almost finished it.”
  • Sophia “Sea and Jacob finished next.”

The children explained, “It was a fun challenge because it was icy.”

We wonder what our next challenge would be…

What do we know about money?

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We have been planning a small group excursion to the supermarket in front of the school to buy a watermelon. This was the planned next step of our ‘Ice-pop Challenge Project’.

Jacob had learned that the watermelon would cost RMB 59. As a lead into the trip, we asked the children what they already knew about money.

  • Archie “Buying stuff.”
  • Adalyn “Buying food to eat.”
  • Dahyun “Buying Lego and pants.”
  • Riccardo “Where does money come from?”
  • Archie “Everyone has money, but some Indian people do not because the tornado happened and outside they are littering so much. But Japan has money.”
  • Isabella “The money is made of paper.”
  • Jacob “Buying something, when you want to learn something, then you can use the money to buy it. Like cubes.”
  • George “I have money. A little money. My mum gave me money. I use to buy toys.”
  • Sea “I have so many money because I have Korea money. And I put the money in the box and I have Nanjing money too. I think face on the money is different.”
  • Ciel “I have so many so I put in a piggy bank. It is a pig and there is a hole and we put the money, then it will be safe.”
  • Junsu “I have lots of money and I don’t know how much money I get. My dad didn’t tell me. I got the money from dad.”
  • Dahyun “Chinese money is different to Korean and Japanese money.”
  • Euno “I go to Dahyun’s house on Monday and I see Dahyun’s money is many. But I have little money. My grandma gives me money in Korea.”
  • Jacob “My home has lots of money but my mum and dad don’t tell me because then I will tell everybody and its not good. My money is more than other people. Other people want me to give money to him.”
  • Suzy “How do we make money?”
  • Ciel “We can make it with paper.”
  • Sea “I think you need to make with water and paper. If money is like paper.”
  • Jacob “I don’t know where we get money from but I know what is used to make it.”
  • Ciel “We get it from the bank. My mum gets it. They will change the money. There is a little hole and you put it.”
  • Adalyn “Work. My mum and dad work and can get some money.”
  • Sea “Dad is so long time at home and another day short time. He gets money.”
  • Jacob “My mum need to be at home to do our work. Like looking after me.”
  • We keep money is our home.
  • Archie “Give the money to the shop people.”

We decided to empty a wallet to find out how much money the teacher had. As we laid out the different coins and notes, The children began to talk about what they noticed about the money.We placed Base-10 blocks next to the notes and coins to talk about the value and calculate the total.

The children were curious about the different writing, symbols and images on the notes and coins and how they signified currencies from other countries.

  • Ciel “Money is also made of metal.”
  • Archie “The money is on paper and the colour is rainbow.”
  • Sea “Colour is different.”
  • Ciel “Because 20 is smaller than 10. Because then we know they are not the same.”
  • Euno “My money is five money, five 100 money.”
  • Suzy “Maybe we use the paper to cut around. A long paper, not too big and not too small. Suzy When we go to the supermarket we will draw the number then other people can know how many coins does the paper have. My money and daddy need money to buy food, because when we eat all the food then we can’t buy food.”

Jacob decided to calculate to find out how much money was in the wallet. Then, he set aside RMB 59 to buy the watermelon.

Next, a small group of children will visit the supermarket to buy the watermelon. Their research will help them calculate how many watermelons they will need to purchase to make enough ice pops for themselves and their Grade 5 buddies.

The Survey

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We referred to our plan for the trip to the Skyways Kitchen to plan our next steps. The children were eager to invite K2B to join us on the trip to the kitchen. The team created a survey to find out how many children and teachers would like to join K2A on the trip.

Suzy “We can ask them, ‘Do you want to come to the Skyways kitchen to make the PTA but the cupcakes?’” The team wrote their question and possible responses. Then, they went off to K2B to speak to their friends.

Dahyun “I am finding the letter and big letter and I write that. Because then I know letters. Because I sound it out and find the letter, and it helped.”  

Euno “I write the question. I used the alphabet chart to find the letters. I see the alphabet chart and I can write the word.

I sound the letter. It was a little bit hard but then I sound and write and see the alphabet chart and write.”

Euno “I asked ‘Do you want to go to the cafeteria for making the PTA cupcake? And they said ‘yes’. I tell him sign your name on the paper on the ‘YES’.”

Dahyun “Because he want to go to Skyways kitchen and make cupcakes so they say it in the paper. Everybody said yes.”

The surveyors presented the data to the rest of the class explaining their process and what they learned as a result of their research.

Suzy “We are going to K2B and ask them and then I write the names. Everyone wants to go!”

While presenting the information, the class noticed that one child did not want to join the field trip. We wanted to make sure that the team had surveyed all the children. Therefore, we decided to check the responses against the K2B class list. As the names were called we realised that two of the children had not responded to the survey.

The researchers went back to collect the data they needed.

The class was pleased with the results both teachers and 13 of the 14 children wanted to join the field trip.

Having collected the information they need, they are ready for their next step, deciding on the date and booking the school buses for the trip.

How much is a Watermelon?

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Jacob was inspired by our challenge project, particularly the part about making ice pops with watermelon juice. He decided to visit a supermarket to learn more about watermelons. On his return, he shared what he had uncovered.

Jacob used the question starters to help him present his learning to the class.

  • Jacob “Me and my mum is going to the supermarket because we want to look the watermelon is how many money. And how big and how small. I go to Hippo to look how heavy and small. I went yesterday. I take a photo because then we know how heavy. It was 59 RMB.”

Jacob’s presentation made us wonder how many watermelons we might need to make the ice pops. We wanted to make sure we had enough for the project, but we also didn’t want to waste any food. 

  • Suzy “Maybe we can first get one watermelon and then we can test it because then if we didn’t know how many too much or too short.”
  • Evan “We need to ask Ms. Jacqui about the money for the watermelon.”
  • Jacob “We need to listen to other people and look.”
  • Suzy “Say it nice and loud because then other people cannot hear.”
  • Sea “I don’t know if Ms. Jacqui gives the money.”
  • Isabella “We need to tell Ms. Jacqui how many money we need.”
  • Dahyun “We can find the market.”
  • Euno “We don’t tell any people then we don’t have money so we cannot buy the watermelon.”

 

Can we have some money?

A group of children volunteered to take the project plan to Ms. Jacqui to ask her about the money they needed for the project. The children explained that they would need 60 RMB to purchase one watermelon to test the ice pops. Ms. Jacqui was excited to hear all about their plans and invited the children to think about the different steps they needed to take to plan a safe field trip across the road.   

They needed permission slips, money to purchase the watermelon and teachers to accompany them on the trip.   

 

Do we have enough ice-pop moulds?

Teacher “What about the moulds for the ice pops do we have enough for everyone?”

Isabella recalled using the ice pop moulds when she was in K1 and decided to reach out to Ms. Hannah to see if she could find them in the Early Years kitchen. Mohammed and Adalyn wanted to help Isabella with the task.

The team looked in all the cupboards to look for the ice pop moulds but couldn’t find them. After a lot of searching, they found two sets of 6 ice pop moulds in the Early Years pantry.  

The children decided that they needed 16 moulds for the children and the teachers in K2A. But they only had 12! They used what they knew about numbers and calculations to help them solve the problem.

They decided that they need to buy 6 more moulds to have enough for everyone in K2A.

The Chocolate Milk Project: Calculating Volume

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The children are deeply engaged in their inquiry, solving problems and organising themselves to help plan the field trip to the Skyways kitchen. One of the suggestions they had was to make chocolate milk at the Skyways kitchen. We decided that this would be a good opportunity for the children to solve a real-life problem using their understanding of number and calculations. 

How many milk cartons do we need to make chocolate milk for all the children and teachers in K2?

We began by estimating how much milk they thought they would need.

  • Evan “I think 2 boxes of milk because we can drink with 2 classes, because one class can drink one milk.”
  • Adalyn “We don’t know how much one box of milk has.”
  • Ciel “I think it has 20 or 25.”
  • Jacob “I think 25 meters. We can measure it. With a ruler.”

Estimating how many cups of milk are in one carton.

The mathematicians drew to share their ideas, the estimates ranged from 10-20 cups in each milk carton.

We noticed that the children were referring to the ‘units’ (millilitres) of measurement when talking about volume. Riccardo had also suggested using a measuring cup with numbers on the side to measure the milk. Their explanations and suggestions communicated their working theory that, ‘we can use a ruler and measuring tools to measure accurately’.  Having noticed this interest in using standard units, we decided to draw their attention to the 1L displayed on the milk carton.

But how much is a litre (1L)?    

As the children are familiar with the use of the Base 10 system to represent numbers and number relationships, we used the blocks to draw a parallel to the ‘volume’ discussing the value of one, ten, one hundred and one thousand.

The mathematicians concluded that the milk carton had 1000ml, or one litre (L) or 2 of the 500ml jugs of milk.

We decided to check if Jacob’s estimate that a cup of milk was of 25ml was correct. We poured out one cup of milk from the carton and used the measuring jug to measure it. We learned that there was 150ml of milk in one cup. We used Base10 blocks to show the number.

How would we know how many cups of milk were in each milk carton?

The mathematicians used words, images and numbers to make their thinking visible. As they documented their ideas, we noticed that they were calculating the quantity in millilitres and cups. Therefore, we continued to use the Base-10 blocks to help them calculate, solve and explain their math problem.

We noticed that each child processed the problem and documented their strategies differently. They shared and listened to each other’s strategies and thinking and helped each other with the calculations.

Together, they learned that a carton of milk had about 6 cups of milk.

The team presented their process and learning to the class.

  • Ciel “We measured what milk is inside.”
  • Evan “We measured about 100 of milk.”
  • Jacob “One box has equals 6 cups of milk. Because we already measured it. One cup has 150 %.”
  • Evan “2 cups have 300 ml.”
  • Adalyn “4 have 600ml because 300+300=600”
  • Evan “6 cups have 900 because we think it.
  • Adalyn “Because 600+300=900ml and 100 left over.”
  • Evan “Yes, because 900+100=1000.”

We look forward to our next steps as we plan our trip to the Skyways kitchen. 

A plan to make Chocolate Milk!

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We decided to revisit our first ideas about the wasted milk. The children recalled Mr. Patrick’s suggestion to make chocolate milk when they visit the kitchen.

  • Adalyn “We can use the milk to make chocolate milk.”
  • Riccardo “But we don’t know how to.”
  • Suzy “I know, Mr. Patrick knows. We can ask him.”
  • Jacob “K2A and K2B are going to drink the chocolate milk.”
  • Riccardo “We need chocolate to make the chocolate milk but we don’t have it. Maybe we can go to the cafe to buy some chocolate.”
  • Jacob “We can buy the chocolate from the cafeteria where we get lunch.”
  • Suzy “We can go to buy the chocolate from the chocolate shop.”
  • Jacob “We can collect milk from K2A, K2B and K1 when we have lunch in the kitchen. We can ask them for the milk that is not used.” 

Teacher “How much milk do we need?”

  • Jacob “We can measure the milk with a ruler.”
  • Riccardo “We can measure it with the ruler plate, the plate with numbers.”

The children’s conversation revealed their understanding that we use tools to measure accurately. They suggested using a measuring cup to find out how much milk we need to collect for both classes to have a cup of chocolate milk.

Which one does not belong? Bicycles

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Which one does not belong? Why?

The children were encouraged to look carefully at the four different quadrants with bicycles. They had to decide if A, B, C or D did not belong and explain why. A group of children focused on the positioning of the different bicycles explaining that some were parked in the shape of an X and others in rectangles. Ciel noticed that some bicycles were smaller than others. Isabella and Suzy decided to count the number of bicycles to decide which section did not belong. We moved to count the number of wheels in each section. Then we counted how many purple or yellow bikes each section had.

The children use their knowledge of doubling to find the total, explaining that 4 + 4 was 8, 5 + 5 was 10, 8 + 8 was 16 and 10 + 10 was 20.

The ‘which one but doesn’t belong’ activities help the children look carefully at the clues provided to make decisions. It encourages them to think about what they know about numbers, patterns, shapes and data, and to explore connections to make decisions. These mathematical conversations help the children estimate, notice and analyse information to develop their mathematical identities. 

The Trolley Project – Parts and Instructions

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Over the last few days, the team of assemblers have continued to work on the trolley. They felt it was very challenging to put the parts together. They gathered to discuss the problem before they began their task.

They began by looking carefully at all the different parts of the trolley.

  • Isabella “We have the small parts such as screws and wheels.”
  • Adalyn “We have the nuts.”

  • Jacob “We have the holders for holding the sticks.”
  • Isabella “We have the tools for assembling the trolley.”
  • Evan “We have the words.”
  • Adalyn “那个叫说明书。”（that’s called the instruction) A picture of the trolley.”
  • Jacob “The big parts of the trolley, like the baskets and sticks to connect them.”

Now that we have all the different parts of the trolley and the tools to assemble it, where do we start?Adalyn suggested that they read the instructions carefully. Isabella emphasised the importance of the pictures in the instructions. However, as they tried to assemble it, Evan could see that it was very wobbly. Isabella suggested taking the wheels off. Jacob agreed, explaining that this could come right at the end.

  • Isabella “There are some numbers that show us the steps.”
  • Jacob “Some parts such as the long sticks are too hard for us to insert”
  • Evan “We don’t have enough muscle.”
  • Jacob “We need an adult to help.”
  • Isabella disagreed and said, “We children can work together”.

The team continued their work together, assembling and dismantling parts of the trolley as they tried to complete the task. During the week, a clean-up in the Early Years centre posed a new problem!  

One morning, when the team went back to continue with their project, they found some of the parts were missing. How can we assemble the trolly without the parts?

Yet again, the team sat down together to work out which parts were missing. And how they might solve the problem. Isabella suggested that they look at the paper instructions to figure it out.

The instructions provided information on all the different parts that were required to assemble the trolley. They needed screws, nuts, black rings on the wheels, hooks and the holders. Together the team tried to calculate how many of each they needed in total. The problem invited the children to use their understanding of calculations to find the number of missing parts.

  • The nuts: Adalyn “We need 12 in total and we used 4, so 8 of them are missing.”
  • Hooks: Jacob “We had two before and now we only have one.”
  • The holders for the screws: Evan “There are 6 in total on the instructions, but there are three levels in the instructions, and we only need 2 levels for our trolley so we need two more.”

They continued to work on creating a list of items they needed. Then, the team plan their next steps to solve the problem. 

Jacob suggested asking the facilities department for the missing parts because they have the staff who come and fix items that are broken in the classroom. Isabella suggested reaching out to Mr. Matt as he helped fix the table. Jacob recalled Mr. Arek helping to fix ‘The Nest’ in the playground. Adalyn thought Ms. Jo might be able to help as well as she has lots of different materials for making things.

  • Adalyn “If none of the people that we mentioned above has the parts we need, we can buy another set of the small losing parts we need.”
  • Jacob disagreed, “if we buy only a set of the small parts, the other trolley is going to miss some parts.”
  • Evan disagreed with Jacob, “I think the shop must have some extra small parts.”

Everyone agreed with Evan’s suggestion, and they decided to ask the school purchasing office to help them source the missing parts. To do this they decided they had to:

  • take a photo of the parts they need
  • make a list of the parts that need to be purchased
  • measure the size of the different parts to give accurate information.

They worked together to gather all this information to take to the school’s purchasing officer. We look forward to their next steps as they solve the problem of ordering and purchasing the missing pieces in the trolley.

 

How tall is the Tower?

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The tower in the block play area cannot be missed!!

It has been standing tall for a few weeks, with only its steeple toppling over on a few occasions when children pass by or try to adjust the blocks that support its design. We noticed the children adjusting the columns, replacing and testing out different shapes to see which ones offer better support. Through trial and error, the engineers developed and tested theories about balance, shapes and design.  

They were now more intentional when choosing the shapes for different sections of the tower. For instance, they realised that using broader, flatter shapes horizontally provided more foundational support and that they could make the steeple taller by using cylinders with a greater diameter at the bottom. Throughout the process of experimentation, the engineers discussed and negotiated ideas, looking for ways to work collectively to reach their goal, of building the tallest tower.  

Through inquiry, we explored different ways to measure the height of the building. At first, the children used non-standard units to measure the tower.

Then, a team uncovered the use of standard units and decided to measure the tower using a ‘flexible, long ruler’, a measuring tape.

The children shared estimations of the height of the tower.

Then, we used the measuring tape to measure the tower accurately. The children were excited to learn that the tower was 190 centimetres tall!

During outdoor playtime, a group of children met Mr. Lee and explained that they had built a tower that was taller than him. Mr. Lee decided to check if this was true. As he stood next to the tower he asked, “How tall am I?”  

 

Tools for Measurement

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Over the last few days, we have noticed the children showing an interest in exploring the concept of ‘measurement’ through their play and engagement. 

How might we measure accurately?

During choice time, Jacob went over to the tower with a building log and began to measure its height. He said it was 9 or 12 logs high. As we watched him measure, we noticed that the block overlapped as he placed it from point to point making his measurement change.

He was invited to place the logs horizontally across the floor to see the length of 9 logs. While placing the blocks, he was encouraged to think about the reason for choosing logs of similar size.

Isabella, Adalyn and George were curious about a piece of documentation on the wall from the previous year that recorded the children’s height.

  • Isabella “We are measuring Adalyn’s and my height and George’s height. That day I was the same height as George but now I think I am higher than that.”
  • Adalyn “Good sleeping and good eating makes you tall. At home I am 1,2,2 (1 米23 ) tall. Because you wear shoes you are taller so you shoes off. I have this at home and my sister is. 1 米5几 。
  • Isabella “I am 112 tall.”

Isabella and Adalyn were also curious about the sand timers and wondered what they could do in a short time.

We decided to provoke the children’s thinking about ‘measurement’ by presenting the photographs and videos back to them. The children were excited to share their ideas about the measuring tools.

The first reference they made was to the ruler in the classroom. They explained the significance of the ‘numbers’ when measuring. We documented the children’s ideas on chart paper which we will use as a collection of reference points.

Over the next few weeks, we will look for opportunities to test some of the theories the children have about ‘measurement’ and measuring tools. We wonder how they might use different tools to share their observations which in turn helps them understand how tools could be used to measure the attributes of objects and events. 

Big Ideas-

– standard units allow us to have a common language to identify, compare, order and sequence

– we use tools to measure the attributes of objects and events

– estimation allows us to measure with different levels of accuracy.

Taller than a Teacher!

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Over several days, Evan and a team of engineers have been building a structure in the block play area. The team worked hard to find solutions for the steeple as it kept falling over. Through trial and error, they explored different ways to make the structure taller. One afternoon, Evan was excited to learn that the block tower was taller than him. He wondered if it was taller than Adalyn (as she was taller than him). As Adalyn stood next to the tower, Evan could see that it was taller than her. 

Adeline and Evan wondered if the tower was taller than the teachers. First, Ms. Sophia stood next to the tower. She was taller than the tower. Ms. Shemo and Ms. Sophia were both taller than the tower!

 

The engineers went back to work. The tower was now taller than them making it harder for them to place the blocks. George looked around the classroom. He was excited to share his solution, “I know, we can get a chair to stand on then we will be able to reach that high.” (in Mandarin) The team carefully positioned the chairs, so they reach beyond the highest block on the structure allowing them to reposition and test their new ideas.

As they stacked the new blocks, the steeple on the tower collapsed. They persevered, trying many different positions and shapes, but parts of the tower continued to fall. Evan looked around for new shapes that could be used in the structure and noticed a block they had not used before. He had a new idea that he wanted the team to test, “We can add more flat pieces on the joint part and the building can be more stable and will not be that easy to fall.” (in Mandarin)

Isabella “I found more of this kind of green wooden pieces and I’m going to add them at the joint part of the block sticks.” (in Mandarin) 

Evan “We need to top the stick on the middle part of the two underneath. Because it will help the one on the top to stay more stable.” (in Mandarin)

They used all the green blocks that were available on the shelf. But there weren’t enough. As Isabella observed the structure, she realised the significance of the flatter, wider shapes that made the building more stable. The flat shapes held more blocks which in turn allowed them to go higher. She looked around for blocks that had similar characteristics and paused at the wooden cookies. She decided to test her theory.

Even though the building collapsed many times, Evan didn’t give up. He continued stacking the blocks, learning through trial and error that being more intentional about the placement of the blocks resulted in greater success. After many attempts, his tower was done.

He was ready to invite Ms. Shemo to stand next to the building. The team were excited to see that the building was as tall as Ms. Shemo!

As Ms. Shemo looked at the building she invited the children to think about the concept of measurement, “How can we measure the height of the building?”

Ms. Shemo was worried about the building collapsing before the children could have an opportunity to explore tools that help us measure. Therefore, she suggested recording the height of the building on the wall next to the structure. Isabella helped Ms. Shemo find a solution to gauge the approximate height. They used a coloured sticker to mark the position. 

The team continued to work on their tower, testing theories and ideas to make the tower even taller. After several days, they were ready to test the height to see if it was taller than Ms. Shemo.

They called Ms. Shemo to stand next to the building. The children cheered with excitement as it was much taller than her!

Evan quickly remembered what they had done the previous day, and brought a flat, long beam to help Ms. Shemo find the correct level for the new sticker. 

Ms. Shemo invited the children to reflect on the question she had about the measurement of the structure. “How can we measure the height of the building?”

We decided to share a photograph from the previous year which focused on the concept of ‘measurement’ to guide the children’s thinking.

The children quickly tapped into their memories from the previous year, recalling how they had explored height by creating a ruler.

  • Adalyn “He was seeing who is taller.”
  • Isabella “He is using his hand.”
  • Ethan “Edward is stretching his hand to his head.”
  • Suzy “I see some numbers.”
  • Evan “I see some colouring.”
  • Isabella “I see some drawing.”
  • Suzy “The numbers is for knowing who is bigger.”
  • Jacob “Finn is 33 tall.”
  • Evan “I think Edward is 20.”

As Suzy demonstrated how to read the measurement, Isabella reminded her that she needed to place her hand ‘straight’ (not at an angle) and read the number across.

  • Suzy “How can we know that because we can see a number over here.”

As we looked at the photograph of the tower, we invited the children to think about their wondering, “How tall is the tower?”

  • Suzy “I think the building is 56.”
  • Isabella “I think it is 57.”
  • “That ruler on the wall is 66” explained Jacob, recalling the highest number on the ruler they had created the previous year.  
  • Isabella “100 is too many!”

As the children shouted out their estimates, we recorded them on a table.

We look forward to seeing how the children will use their prior knowledge about measurement to find out the height of the new tower.

All Kinds of Boots

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What do you notice? What do you wonder?

We documented the children’s observations and questions.

See

  • Morning “Some shoes are small and some shoes are big.”
  • Motong “There are many different colour shoes and some are tall and some are short. I see 10 pairs of shoes.”
  • Wyatt “Many colours on the shoes.”
  • Oliver “Some shoes are fat and some shoes thin.”
  • Jeongyoon “There are 20 shoes.”
  • Eli “Some boots are for rain and some boots are for walking and some are for winter.”
  • Oxford “One is green. Some are made out of feathers and some are not. Some boots are in the ice. Some boots have no stickers in the front.”
  • Beomjun “3 little shoes and big shoes is 3.”
  • Eunbyul “Big, medium and small boots.

Questions

  • Jeongyoon “Whare there have the shoes and the boots?”
  • Wyatt “Why has many coloured boots and shoes?”
  • Motong “Why are there black shoes?”
  • Oliver “I know that the boots are used for walking or snowing for but what else are they for?”
  • Eli “Why do some have a name on the front and some don’t?”
  • Oxford “Why do we need the stickers?”

We counted our shoes to see how many pairs we had all together.

We had 11 pairs!

Task:

– Create your own 2’s collection using objects in the classroom.

– Count in 2’s using your objects.

Challenge: Use collections to share more ways to skip count!

The children develop an understanding:

– that the operations of addition and subtraction are related to each other and are used to process information to solve problems

– of how number operations can be modeled in a variety of ways

– that there are many mental methods that can be applied for exact and approximate computations

The Shape Test

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A paper cube that Oliver made after the paper experiment led to a discussion about 3-dimensional shapes.

The team wondered about the strength of paper shapes and decided to test their theories.

The team wondered:

  • if some paper shapes were stronger than others.
  • which shapes they could make to test their theories.

The team recalled a previous learning experience of going on a shape hunt and decided to refer back to the activity to choose the 3-dimensional shapes they wanted to make and test. When choosing the shapes Oliver stated, “Sphere is impossible for me cause how can you fold the paper round. I want to make a cylinder!”

Eli pointed at the pentagonal prism, “I want to make that one.”

Having thought about their options for paper, they decided to choose card stock instead of paper for their test as they believed it would be stronger than the A4 paper.

Oliver made his first paper cylinder by rolling up the paper and fastening it with tape. However, he quickly noticed that the edges weren’t flat and realised that this would impact the test. He decided to make a second cylinder, taking care to keep the edges of the shape levelled. During testing, Oliver discovered that the top and bottom edges of his first cylinder were not stable enough, so he decided to make a new cylinder.

 

Having looked at the pentagonal shape, Eli realised that to fold a pentagon, he needed to divide the paper into five equal parts. Eli initially used a ruler to draw lines but found that the width of one ruler was too narrow, which resulted in a lot of extra space at one end.

Then, decided to use the width of two rulers, but each section was too wide and there wasn’t enough space on the card for 5 equal sections.

Eli shared this challenge with the teacher, explaining that he wanted to divide the long edge of the paper into five equal parts.

Having heard Eli’s challenge, the teacher decided to bring Eli’s attention to the concept of measurement to think about what he already knows about the function of hash marks and numbers on a measuring tool.

Ms. Eileen “How long is that edge? How did you measure it?”

  • Eli thought about this and then pointed to the ruler and said, “Use ruler.”

Eli used the ruler to solve his measurement challenge, learning that the length of the paper was about 30 centimetres.

Ms. Eileen “How can we divide 30 into 5 equal parts?”

Eli found the unit cubes and counted out 30 unit cubes to represent the 30cms. Then, he divided them into 5 equal parts, with each part being 6cm.

Finally, Eli drew out the lines and folded his paper pentagonal shape for the test. The researchers were now ready to test their shapes!

The team decided to choose books that were of a similar size for their test. As they placed one book at a time on the shapes, they began to see that although the shapes were made with paper, they were extremely strong.

The team had enough books to reach a total of 19 books for each shape. Then, they ran out of books!

As they didn’t have enough of the same books in the classroom to support the progression of the experiment, they decided to test their shapes in the library.

The team’s paper and shape experiments have allowed them to think about the function of shapes and materials in design and engineering and the impact of forces like compression and tension that act on structures. Through their experimentation, they continue to explore how the design can impact the strength and stability of structures.

 

 

 

How to make Banana Cookies!

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One child was excited about bringing his Nana to school one morning. She lives in Australia but visited him during the Chinese New Year holiday. Over the holidays he planned an activity that he could do with Nana in school. They decided to show the children how to make banana cookies.

He bought the ingredients with Nana and then tested his recipe at home. Then, he made a video to share his process with his friends. When school reopened after the holidays, the child invited Nana and his Aunty to school as they were the cookie experts.

Next, we had to work out how many cookies we needed.

  • Motong “We counted how many cookies we need to make.”

  • Jeongyoon “We needed 29 because 4+5=9 and 1+1=2 so we need 29. 15+15=30 so 15+14=29.”

Through their conversations, we noticed that the children were thinking about the operations of addition and subtraction and how they are related to each other.

  • Liz “We made banana cookies.”
  • Motong “We make cookies and Eli’s Nana helped us to make.”

  • Eli “We are putting coconut oil in the bowl and it is good for the cookies because it’s very yummy.”
  • Lydia “We mix the things to make the banana cookie.”
  • Oliver “The cookie was almost finished so I put one little drop of the dough on the paper and then I put it in the oven.”
  • Motong “We put the banana cookies in the oven because it will change the cookies when it is hot.”
  • Oliver “It turns browner.”

The children were exploring the impact of temperature and how it could change textures and substances.

  • Wyatt “We made cookies to take to K2B and ate it.”
  • Motong “We draw how we make the banana cookies.”
  • Eli “We used numbers and words.”
  • Motong “We used spaces (lines and squares) because we know that is 1 thing.”

We observed the children using several ideas to share their ideas on paper. They used a combination of drawing and writing to narrate and tell about the events in the order in which they occurred.

We paused to talk about the K2 writers’ drawings. The children noted that some writers used numbers to show the steps needed to complete a task while others used spaces or drew around a picture to share the same idea (procedures/steps). Some writers used arrows to show ‘the next steps’ in the process. The children noted that including labels with the drawings helps others ‘read’ the information.

Some children used sentences to share their ideas and others used lots of details in their drawings, all important crafts that good writers use to share messages and information with others.

 

Can you make a paper airplane?

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The children continued to make paper airplanes using recycled paper. They were experimenting with new designs and different sizes of paper.  

Morning “I am making paper airplanes. Lydia taught me how to make paper airplanes.”

Oliver wanted to measure how far his paper airplane went in the classroom. He used a measuring tape with numbers to check how far it had gone.

  • Eli “He is measuring how far we threw the airplane.”

We posted the documentation about the paper airplanes in the corridor.

  • Howie “We are looking at paper airplanes because we can remember how much time to take to make the paper aeroplane.”
  • Liz “We tell people to make the paper airplane.”
  • Eli “Get a paper from the classroom and they can take and then they can make airplanes. We can come and make some too.”
  • Eunbyul “It’s airplane too far and write your name and what number to see how far the paper airplane went.”

  • Oxford “I am flying the plane.”
  • Eunbyul “We see who is no far and who is too far.”

  • Jeongyoon “Standing the line.”
  • Eunbyul “We have to stand on zero. Zero first and flying paper airplane.”

  • Oxford “I draw the numbers, 100, 200, 300, 400… Everybody can know where is the 300.”

  • Eli “Pin the paper plane on the wall because if we don’t pin it no one will know we made a airplane.”
  • Eunbyul “I made one paper airplane and faster and very far. 300cms.”

The children use what they know about number and measurement to record how far their paper airplanes flew. They are learning that standard units allow us to have a common language to identify, compare, order and sequence objects.

The Paper Airplanes

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Noticing the children’s interest in making paper airplanes, Ms. Eileen decided to introduce the children to a new design.

The children followed the instructions to make the paper airplane.

  • Eli “I want to throw it outside because outside will have wind so it will fly fast and high.”
  • Howie “I think the airplane the airplane can fly really high and really fast because the wind is really strong and it will go fast. We can feel it when the wind is cold you know what is the wind.”

We looked at a photograph of the playground to help us decide where we might fly the planes from. What would we need to consider?

  • Liz “I think airplanes go to water is broken. Airplane is paper, paper in water is wet and broken.”
  • Oliver “I think the airplane might go round and round all the time I think. Because the wind is going left then the airplane will go left and if the wind is going right then the airplane will go right.”
  • Wyatt “Outside is airplane is go out of school and people can’t go outside of school and then you make it again.”
  • Morning “The airplane will go to the tree and the people cannot play with it.”
  • Eli “It can go over the fence because if you throw on the mountain then it will go over the fence and no one will get it and it might go into the building and there might be sharp things and then it will get a hole in it.”
  • Motong “We can send it from the slide. We can stand on the yellow wall because the airplane will fly very far.”
  • Jeongyoon “If we fly it from the roof, then we can’t get it.”
  • Lydia “I think this flying to outside you can’t take it (the airplane).”
  • Eunbyul “If it goes to a very tall tree then I will not catch the airplane.”
  • Howie “Then, we can climb the tree.”
  • Oliver “The sticks are not very strong.”

How can we find out which airplane has gone the furthest?

  • Oliver “I think if the airplane looks the best then it goes the furthest. And my airplane looks the best.
  • Eunbyul “Throw it and it will go up and down.”

When you run a race, can you start from different places?

  • Eli “No, we have to stay together.
  • Howie “Some people together in the back, the first people will get number 1. The people in the back will be number 2.”

The children explained that they had to fly the paper airplanes from the same location for it to be fair. The children discussed the different options. The children were excited to see many planes flying high above the playground. Perhaps our planes would fly high too!

Many of the children suggested flying the plane from a height as it would help the plane go further. They agreed that the best spot would be the top of the short wall.

We decided to go out and try this out. The paper panes took off from the wall. We watched them scatter around the playground. 

How would we know which plane went the furthest?

Howie suggested that we use a tape to measure the distance. Ms. Shemo did not have such a long tape but had some string instead. We measured and cut out the string to mark the distance.

When we went back to class with the string, we had them in bundles on the floor. Many children believed Eli’s plane flew the furthest because his bundle of string was ‘higher’. We recorded everyone’s best guess using tally marks.

But how would we know for sure? How do we measure things in real life?

Eli suggested using the ruler. But the ruler was short, and it would take a long time to measure them.

Liz suggested measuring them using the white PVC pipes. We brought one over and kept it next to the ruler. It was longer. We noticed the numbers on the ruler and decided to add them to make our ruler with the pipe. But, there were too many numbers to write.

After some thought, we decided to count in 5’s and record them on the pipe. The children helped identify the numbers from 0-100.

Then, we began to measure the twine. We recorded the distance each paper airplane flew. Finally, we had the data we needed. Eli’s paper airplane flew the furthest!

Throughout this experience, the children shared their theories about paper airplanes, and considered the properties of paper. They considered the concepts of speed, height, distance and variables that may affect the flight of the paper airplane. They explored measurement, data handling and number, to find out who’s paper airplane flew the furthest.

Math Talk – Gathering Data

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We gathered to solve a Maths problem. We are learning how to collect information by organising objects in different ways.

  • Eli “We are looking how much bugs and insects. And we counted how much is the same and how much different insects.”
  • Oliver “You have to look at the board and see the board and count. Its because if you do nothing there is zero insects.”

  • Jeongyoon “Drawing bugs.”
  • Eli “I have to think and look at the picture and look at how much insects there are.”

  • Eunbyul “Sharing ladybugs and drawing on the whiteboard.”
  • Motong “This is a garden. Everybody draw.”
  • Wyatt “It’s drawing pictures.”

Next, we used colour blocks to explore data collecting.

  • Howie “These are colour blocks. To use same colour blocks to build together. Counting blocks.”
  • Wyatt “Its writing on the paper. Putting blocks on the paper and then draw.”

  • Oxford “I am putting blocks on the paper then we can do drawing.”
  • Motong “I had orange the most, 4. I had only 1 dark green and purple and yellow and red.”
  • Eli “I had green, 8, the most but the green when I put it in the bowl I found lots of green like 8.”
  • Morning “I had blue the most. 7.”
  • Liz “I had 3 blue, I have green is 9 the most. I have 2 red and 2 orange.”
  • Oliver “I have the most is yellow, 4.”
  • Eunbyul “Is from 1 is green.”
  • Howie “I have drawing one white block.”
  • Jeongyoon “I have a green 7, the most.”

The children used colours and numbers to document their information. We noticed that they used comparative language (most, little, lots) to explain their data.

Next, we decided to organise our blocks in columns. This helped us see the different colours and quantities. 

Then, we documented what we saw on paper, creating column graphs to record the data. We noticed how the children represented one real object with one picture/coloured square.

Organising the Shed: Sorting and Data Collection  

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A team of children went to the shed to begin sorting the toys. They placed tubs for the sand toys, put the kitchen and cooking items on one rack and all the trucks and diggers on the shelves.

Next, Doho and Sean went to look for Mr. Jamie, to ask him if he could help the team mount the hooks on the pegboards.

Sean and Doho explained the problems they had, and then they went out to the shed with Mr. Jamie. Together, they were able to problem-solve and make a plan to mount the hooks.

A team of K2 mathematicians went to the shed to gather more information to plan the next step of the project. We needed to find out how many hooks, tubs and racks we will need to sort and organise the different toys in the shed.

 

The team began to think about the different ways we can record data. We decided to divide the paper into four to record the number of kitchen items wheelbarrows trucks and sand toys.

Then, the data collectors used pictures, words and numbers to record their information. 

We observed the children:

·     gathering, recording and organizing information

·     listening actively and respectfully to others’ ideas and listening to information

·     using mark-marking to convey meaning

·     taking responsibility with tasks

·     using strategies to problem-solve

The Early Years Florists

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A group of children worked with Ms. Hannah to create a flower arrangement for each class in the Early Years. This is an ongoing project that different groups of children work on every few weeks.

This time, the florists worked on creating a Chinese style flower arrangement with the focus of balance. Joon and Mason were our K2A florists for the week.

The florists had several pointy stands to use with their flower arrangement.

They decided who will use the different stands by pulling paper that were of different lengths.

Ms. Hannah showed the children how to place the flowers on the pointy stand.

Then, the florists had to choose one flower and put it on their stand. Thy had to consider balance, the length of the stems and how the flowers were going to be arranged.

When they placed the second flower, they needed to work out how they can balance both flowers. Then, the florists included the leaves. The florists had to take turns and collaborate, using their skills of observing, thinking and decision making to complete the arrangement beautifully.

The young florists stood back to decide if their arrangements were done well. Finally, they had to agree on which flower arrangements will be presented to the campfires and which ones will remain in the Atelier.

Joon and Mason proudly shared their arrangement with their classmates and placed it next to the class journal to welcome everyone to K2A!

Measuring with Unit Cubes

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We reviewed the measurement activities we did previously. We discussed the language used to describe length, height and different measures.

Then, the children were presented with the image of the spoons.  

Image: Math at Home

What do you notice about the spoons?

How are they the same or different?

The children noticed that:

  • two spoons had holes at the end (3,8)
  • one was like a toothbrush (1)
  • one had a pattern on the handle (8)
  • one was like a toy car (9)
  • some were longer and others were shorter, they had different lengths!

 

How can we tell how long they are?

What can we use to measure them?

What do we need to remember when we measure objects?

Patrick explained that the spoons should be lined up at the same level to measure them properly. We can also use a ruler to measure the length of the spoons.

Kenan helped Patrick arrange the spoons so that we can measure the length of the spoons accurately. We noticed that the spoons were different lengths, that they were made with different materials and were used for different purposes.

The children were introduced to a Seesaw activity. Then they went on a measurement hunt.

They used the cubes to measure the different items in the classroom to find objects that were approximately (about) 5, 10 and 15 unit cubes long/tall. They documented their research on Seesaw.

Learning Outcomes: Measurement

  • standard units allow us to have a common language to identify, compare, order and sequence objects
  • we use tools to measure the attributes of objects and events
  • estimation allows us to measure with different levels of accuracy

Measurement – Weight (mass)

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The children have been growing and caring for plants. They have been measuring the growth each day, and documenting their learning in their journals.

We decided to introduce the children to vocabulary they can use to describe and compare ‘growth‘ and ‘change‘.  

The children have been identifying, comparing and describing attributes of real objects and situations using quantities, height and length.  

 

The young mathematicians gathered to talk about a new measuring tool in the classroom. We know that mathematicians make predictions, estimate, gather data and improve their work to understand and solve problems.

 

Ms. Shemo showed the children a number of different items and a weighing scale with weights.

The mathematicians observed carefully and used their prior knowledge of measurement to make predictions about the weight of the objects. Vocabulary to describe weight was discussed with the mathematicians as they made choices about their observations (voting by standing/sitting).

Then, we compared the weight of the different objects to check if our predictions were correct.

We used pictures and words to describe what we observed.

We know that mathematicians consider problems carefully and then make decisions based on the information and the data they have gathered. The young mathematicians did not touch the different containers of liquid and therefore had to make a reasonable judgement based on what they could observe. They could see right away that knowing how much liquid is in the containers (capacity) allowed them to make a more informed decision.

We tested our new ideas using stones of various sides. We held the weights in our hands and considered what the numbers of the little weights meant. We will continue to explore the concepts weight (mass), length, height, quantity and capacity (volume) in the coming weeks.  

Counting Squares

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The students were presented with a picture that had a heap of red and yellow Unit Tiles.

What do you wonder?

  • Tracey “Why does red and yellow? Why are they not rectangles?”
  • Patrick “Who takes yellow and red to mix it.”
  • Kenan “Why yellow and red is putting in?”
  • Mason “What does it mean?”
  • Olivia “Why don’t they have blue and green?”

 Estimate how many squares are in the pile?  

Next, the children estimated how many Unit Tiles there were in the pile. They noted this down.

How many red?

How many yellow?

How many Unit tiles we used to make the pattern?

Then, we watched a video that gave the children more clues. The video stops midway, showing an incomplete pattern. The children used pictures to draw and share the complete pattern, and to find out how many tiles were used in all.

Finally, they were able to record how many red and yellow tiles were used to make the pattern.

Through this task the children were able to:

-estimate

-share their thinking

-document ideas using drawings and numbers

-problem-solve

-work in collaborative groups

 

Dot Talks

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We have been estimating and subitising groups of objects to help us learn more about number and calculation. Subitising is the ability to look at a small number of objects and instantly recognise how many objects there are, without needing to count. We frequently subitise, estimate and calculate to make decisions and complete tasks, therefore, this is a valuable skill that helps us in our everyday life experiences.

To help us practice this skill, we used a short routine called ‘Dot Talks’.

First, the children were shown a card with a number of dots.

The following questions guide their thinking and problem-solving:

  • How many dots are there?
  • How do you know?
  • How did you count the dots?

Then, they used their whiteboards to document their thinking.

Next, they transferred their thinking onto paper and used coloured pencils to show how they have grouped their dots to make it easier to count.

While documenting the different ways we counted the dots, the children had opportunities to build number sense, articulate their thinking, and appreciate different perspectives.

We created a chart showing all the different ways we counted the dots.

We are learning that number operations can be modelled in a variety of ways.

Other Examples

 

What does it mean to estimate?

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The students were presented with a math task to explore estimation. Estimating means roughly calculating or judging a number or value.

‘Estimation skills provide students with an ability that instils confidence with number. Everyday life requires estimations and approximations such as rounding to the nearest ten, hundred or thousand (Booker, Bond, Sparrow & Swan, 2010).’

A row of dice was placed at the edge of the green rectangle. First, we counted to find out how many we needed on one side of the shape. Then, a question was presented.

How many dice will we need if we were going right around the edge of the rectangle?

The children used their whiteboards to write their estimates (best guess). Then, we recorded these estimates on the board.

Next, we added a few more around the perimeter of the shape.

The children could change their estimate based on the new information presented. Finally, we placed the dice around the edge of the rectangle to check our estimations.

We needed 22 dice to go around the rectangle!

We had a smaller rectangle and so we tried to find out how many dice would go around the edge of the smaller rectangle.

We used an empty number line to find out the estimate that was the closest to the actual number. 

Snack Plate – Math Talk

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The children were presented with a photograph of 4 snack plates. The different plates had servings of carrots and celery with hummus.

The children were invited to share their observations.

  • What do you notice?
  • What do you wonder?

We used numbers, symbols, words and sentences to record their ideas.

We wrote equations to show the combinations of carrots and celery.

The children were invited to use coloured tiles to recreate the different combinations. 

They worked in 4 teams to share their thinking and problem-solving.

We used coloured tiles to find the different combinations of 7.

We observed the children using number names to share their observations. Many of the students explained their thinking using addition sentences, counting groups/sets of objects to find the total.

 While working together or alongside others, the children found ways to bring their ideas to the group.

Conceptual Understandings:

Number Sense

  • number operations can be modeled in a variety of ways

Approaches to Learning (ATL’s) 

  • observe carefully
  • notice relationships and patterns
  • present information in a variety of modalities
  • listen actively and respectfully to others’ ideas and listen to information
  • participate in conversations

Equivalent Fractions

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We continue to use a range of material to make sense of fractions. We wonder how we might: 

  • compare and order 1/2, 1/4, 1/3 and 1/10  of shapes and sets using concrete materials
  • model equivalent proper fractions 1/2, 1/4, 1/3 and 1/10

We watched the BrainPop video on Equivalent Fractions.

Then, we used manipulatives to model fractions, looking for was to create 1/2, 1/4, 1/3 and 1/10  of shapes. 

 

Design Challenge – Obstacles and Prototypes

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If you could design any structure in the world, what would it be?

The students began to create their design plans, labelling and providing important information about the ‘purpose’ of their structure.

Challenges and Obstacles:

The students shared their first plans with a learning buddy. They interviewed each other, asking challenging and thought-provoking questions about the design, materials and its purpose.

Then, they were encouraged to think about the ‘challenges’ or obstacles they foresee in their own design. They identified this using a red sticker. The students presented their challenges to the class.

Their next step would be to create a prototype of their design. They would need to apply the knowledge they have about materials, and use the skills they have gained through the different design challenges they have experienced during the unit, to complete the task.

Conceptual Understandings:

– we solve problems during the creative process by thinking critically and imaginatively

– designs grow out of natural curiosity 

Fractions and Measurement

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We began by brainstorming ‘What we already know about ‘fractions‘.

Then, we watched a video on BrainPopJr. to learn more about fractions. 

We noticed that a fraction tells you the number of parts out of a whole.

The students drew pictures to recognise 1⁄4, 1⁄3 and 1⁄2 of shapes.

Then, they worked in teams to create equal sets of objects with a focus on fractions. ​

Our next inquiry was into ‘measurement‘.

How might we measure different objects?

We have watched different videos to learn about length, mass and volume. We explored the connection it has to the Base 10 system.

Length and Height

MASS

VOLUME

We wondered how we can use the language of fractions to share our measurements.

We are working independently and in teams to solve problems and learn mathematical concepts.

Big Ideas:

Number Sense

  • that fractions are ways of representing whole-part relationships

Measurement

  • that objects and events have attributes that can be measured using appropriate tools
  • that relationships exist between standard units that measure the same attributes
  • that estimation allows us to predict and check our measurements

Lots of Pieces – Number Problem

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We’ve been trying to organize our stuff. Brian has a lot of puzzles!


What do you notice and wonder?

  • “I notice that there are hundreds of pieces in the picture.”
  • “Does Brian like puzzles?”
  • “If there are 13 puzzles, how much money did they cost?”
  • “How old is Brian?​”
  • “There are numbers on the puzzles so you can see how many pieces there are.”

How many puzzle pieces do I have all together? Just take a guess!

Now, do the math to find an exact answer.


What are some strategies or different ways to add this up, to make it easier to find the total?

Data-handling

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We are learning that information can be expressed as organised and structured data.

To help us explore this further, we looked for objects and collections that we can organise and categorise.

collections 

 

Then, we recorded our data on a table and created bar graphs to show our information.

table 

graph 

Next, we generated questions about the graph that we can ask others. We know that reflecting on our learning can help us become confident mathematicians.

questions

We used two sentence starts to help us reflect on our data collection inquiry.

  • Something that I am proud of…
  • Something I found challenging…

reflections 

The Role of Estimation in Measurement

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Why do we estimate?

Our story begins with a group of students creating a structure using wooden blocks.

  • “That is so tall!” shouted one.
  • “I think it is taller than the teachers!”, said another.

  • Lawrence “I think Ms. Shemo is 153cms tall.”
  • Teacher “How would you know that?”

Lawrence explains that it is approximately 100cms from the floor to his shoulder. He added another half (50cms) and estimates that Ms. Shemo is approximately 153cms tall.

What do we know about measurement? When do we measure?

The students began to share their ideas.

The students were invited to estimate how tall the teachers are, “But what about how tall we are?” “And what about objects in the classroom?”

They created a table to record their data. They first estimated the height of the different objects. Then, they used measuring tools to check the actual measurement.

The next day, the students were presented with a photograph of Mr. O. How tall is Mr. O?

 

The students shared their estimates.

The students were presented with a second picture of Mr. O, this time Ms. Delia is standing next to him. Would the children change their estimates based on the new information?

The students shared their final estimates. They explained their thinking and strategies with each other. We wonder how we might measure Mr. O…

The students had created a structure using blocks. Was the tower taller than Mr. O?

How tall is the tower?

The students measured the tower. It was One hundred and seventy seven centimetres! 

Lawrence “But there are different ways to say one hundred and seventy centimetres!” 

The students explained their thinking.

We wonder if Mr. O is taller than our tower!

Our journey continues…

How are YOU a Mathematician?

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The students thought about the different ways they solve problems and the strategies they use as mathematicians. First, they wrote their ideas on post-it notes. Then, they shared their thinking with each other. We documented these ideas on chart paper. 

We are mathematicians because we are:

  • solving problems
  • thinking
  • calculating
  • using manipulatives
  • using strategies
  • estimating
  • questioning
  • playing games
  • looking for different ways to solve problems

We know that information can be expressed as organised and structured data. We were mathematicians when we used a table to gather and record data.

Then, we used our knowledge of number to help us discuss an image. The following questions helped the students notice and share their ideas.

How Many?

  • What do you see that you can count?
  • Can you count in different ways?
  • Does the placement of the objects give you ideas?
  • What groups do you notice?
  • What equations could you write to describe how many?

Each student documented their own thinking. Then, they presented their strategies, questions and ‘ways of seeing’ the image with the class. These ideas were documented on chart paper. Through this provocation, we could see how mathematicians see things and express ideas in multiple ways.  

Same & Different

We looked at two pictures. We wondered what was the same and different between the two pictures. The students used different strategies to share their thinking. Then they presented their thinking to the class.

How are pictures A and B mathematically the same, and how are they different?

● A and B are the same because …

● A and B are different because …

We are learning to:

  • consider different perspectives
  • notice and share patterns and connections
  • make thinking visible 
  • share ideas and thinking through discussion 
  • present ideas to others

5 Moves to 100! – Math Games

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The students continued to strengthen their understanding of place value and addition through the game ‘5 Moves to 100’.

They were encouraged to discuss their thinking and strategies used while playing the game.

Students could make the game more challenging if they wished.

As always, we are reminded that playing collaborative games helps students build a positive classroom culture that celebrates relationships through connection.

The Scale

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Why do we need a scale?

The students concluded that a scale is needed as it is not possible to use actual measurements to draw objects on the chart paper map. All measurements would be rounded to the nearest 10 to make it easier to work out the measurement of the different objects. 

Why should all the groups use the same scale?

The students have been discussing and deciding on the scale that should be used in the final map. They agreed that everyone should use one scale as then the objects drawn would be measured using the same scale. To demonstrate this idea, we used two different scales to draw the height of ‘HANNAH’. The students could see that using two different scales resulted in two different heights of the same object. 

Next, we decided on the different colours we would all use for the different objects in the garden. We reviewed what we had done so far and what our next steps would be. 

The students finally agreed on the scale 5cms = 100cms. They worked out the different measurements using the scale. 

The students then began to round all their measurements to the nearest 10. Then they worked in their teams to draw and create all the objects needed for the final map. 

Exploring Fractions

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We began by brainstorming ‘What we know about fractions‘.

Then, we watched a video on BrainPopJr. to learn more about fractions. We noticed that a fraction tells you the number of parts out of a whole.

The students drew pictures to recognise 1⁄4, 1⁄3 and 1⁄2 of shapes and sets.​

Next, we created sets to show 1⁄4, 1⁄3 and 1⁄2. Then we explored fractions on a number line.

We compared and ordered 1⁄4, 1⁄3 and 1⁄2 using concrete materials.

TASK: Order the fractions (chocolate) from the biggest to the smallest.

Then, we wondered what we know about equivalent fractions. 

We watched another video on BrainPopJr. to learn more. 

We modelled equivalent fractions of 1⁄4, 1⁄3 and 1⁄2 using concrete materials. We noticed that we can make equivalent fractions by multiplying or dividing both top and bottom numbers by the same amount. 

We completed two activities on Seesaw to help us explore this concept further.

Through our work on the Community Garden Plot Project, we have had to divide, multiply, explore fractions and calculate to find and record measurements. 

Creating a Floor Plan

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The students have been drawing, recording measurements and talking to each other about the different ways they might complete their final map of the ‘Community Garden Plots‘. To help us visualise other ways of documenting measurements, we created a floor plan of the classroom. This time, instead of drawing directly on paper, we wrote our measurements on post-it notes. 

First, we measured the length and width of the classroom. The students decided that the meter stick would be the most appropriate tool for this purpose.

Next, we thought about the measurements 790 cms X 947 cms. We used what we know about rounding to make the task easier. Our new measurement was 800 cms X 950 cms. The students realised that we cannot draw this on paper. We needed to think about a scale. They suggested we use the scale 1cm=10 cms. We used this information to draw the classroom floor plan.   

Then, each student measured different pieces of furniture that were in the classroom. Again, they rounded to the nearest 10 and wrote down their new measurements.

Finally, they drew a picture of their object to include on the floor plan. We used blu tak to position the objects as they could be moved around easily.

We wonder how this experience might influence the way the students create the map of the garden plots. How might rounding, scale and shape, influence the layout of the final map?

The Project Plan

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The students were working in groups to create a project plan to help them design a map of the Community Garden Plots. They went out to the garden plots to document their thinking and inquiry. 

They discussed their ideas, deciding how they want to work as a group to create the map. Some initial wonderings:

  • What will we include?
  • How will we measure around the pots?
  • When were the garden plots created?
  • How will we measure the plots inside the greenhouse?
  • What should we include in a map key?
  • What might the scale be?
  • How long is the whole community garden plot area?
  • How is the recycle bin used?

We used flags to demarcate the different areas each group will measure. 

The teams decided on the different materials and tools they will need to complete this task. 

The Project Plans 

Through this project the students have opportunities to develop a deeper understanding of mathematical concepts. They will explore how:

  • objects and events have attributes that can be measured using appropriate tools

  • estimation allows us to predict and check our measurements

  • position can be represented by coordinates on a grid

Approaches to Learning:

Communication Skills/ Research Skills:

  • Ask relevant questions that can be researched
  • Make a plan for finding information
  • Gather information
  • Use senses to find and notice details
  • Record observations by drawing, note taking, charting, tallying, writing
  • Sort and categorize information
  • Present information in different ways

Social/ Self-management Skills:

  • Plan tasks and set goals
  • Use time effectively
  • Be organized
  • Cooperate

Thinking Skills:

  • Observe carefully in order to recognize problems
  • Make “thinking visible”
  • Make connections
  • Reflect on learning by asking questions

Area and Perimeter

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We have been measuring the length of different objects around us. We know that objects have attributes that can be measured using appropriate tools.

First we watched the BrainPop Movie to learn more about Area and Perimeter. 

Calculating Perimeter 

Square Units

Calculating Area

Calculating Area in Meters 

The students were presented with two tasks to help them explore Area and Perimeter. 

TASK 1:

TASK 2:

Storytellers in the Community

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We have been creating stories that we want to share with our community. These stories are significant as they have a message or an important idea to communicate to the reader.

The students used a story planner to help them decide on the important elements of their story.

Then, they wrote their stories and shared them with the class. After making changes and editing their writing, they were ready publish their work. Many of the students decided to create their own short stories. These stories will be included in a Grade 2A Memory Book.

The class had discussed the idea of creating a collaborative piece of art or artifact, that communicates our stories and culture to the community. We had a large piece of canvas in the classroom. We wondered how we could use this piece of canvas to create an artifact.

  • How big should it be?
  • How would we draw on it?
  • Where will we display the mural?

We made a plan. The students shared their ideas and perspectives. What if each student drew a picture from their story, on the canvas? We would have 16 stories!

The students wondered how big each section would need to be. One student measured the width of the canvas and shared his suggestion for dividing the canvas.

The students agreed that each section would be 35cms. wide. But what about the length?

The students began to suggest different lengths. 45cms in length? 50cms. in length? We created a chart to document the data as the students voted for their choice. 

Then, we drew two of the most popular measurements on paper.

Next, the students voted to decide on the best length.

An agreement was reached. Each section of the canvas would be 35cms. X 55cms.

We will have 16 sections and 16 images that share what we value as a community.

We are finally ready to divide our canvas and begin to draw our stories to create the mural.

We have a plan to guide us as we create together.

The students used Book Creator to publish their short stories. These stories will be included in a Grade 2A Memory Book.

Here are a few published books:

Each student painted an image on a mural that represented their individual story. The students enjoyed this collaborative project that tells a story about the culture and values we share as a community.

Our Learning Story continues…

Line Plots

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Displaying Data on Line Plots

We had a tub of sticky worms. We wanted to collect data on the length of the different worms.

First, we created a line plot to display the measurement data. We recorded the title on the line plot and wrote centimetres below the empty number line. The students began by measuring the length of the worms. The longest worm we had was 20 cms. and the shortest was 4 cms.

Next, we wrote the numbers 4 to 20 on our empty number line. We were ready to collect the data. Each ‘X’ represented 1 worm.

Making Line Plots from Measured Data:

Then, the students worked in 5 groups to generate a set of data by measuring strips of paper and then displaying their data on line plots.

They worked in teams to measure the strips, sort the information and document their findings on a line plot. Each group created a line plot to document their data. We compared the line plots of each group and discussed the data we had gathered.

Through these inquiries, the students developed the following Approaches to Learning.

Students worked in mixed groups to answer the questions posed by each research group. 

Line Plots


Line Plot Activity PDF

Measurement – Length, Width, Height

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What do you know about Measurement?

We began by brainstorming and documenting our thoughts on chart paper. 

Vocabulary

Next, we used Cuisenaire Rods to explore measurement. The students had to solve a riddle to find the missing rod. They had to use the ruler to measure accurately in centimetres.    

Cuisenaire MATHS Activity

Then, we discussed a Maths Problem. We talked about the different strategies we can use to solve the problem. We recorded our thinking on chart paper and in our Maths journals. 

One student wanted to know how many metres Jimmy would travel all together, if he rolled 10 times.

The students documented their own thinking and strategies in their Maths Journals. 

We all wanted to know what 15 metres looked like. How far was that? 

We went outdoors to measure 15 metres. The students helped record the distance using a metre stick. 

Then, we ran the distance to see how far Jimmy rolled the first, second and third time. 

Next, the students went on a scavenger hunt. They were tasked with finding objects in the classroom that were a specific measurement. They began by measuring the length of their Maths journal.

Through these experiences the students were able to:

Thinking Skills:

Analysing

  • Observe carefully in order to recognize problems and find solutions
  • Practise “visible thinking” strategies and techniques.

Research Skills:

Formulating and planning

  • Ask or design relevant questions of interest that can be researched.
  • Outline a plan for finding necessary information.

Data gathering and recording

  • Gather information from a variety of primary and secondary sources.
  • Record observations by drawing, note taking, annotating images.

Evaluating and communicating

  • Present information in a variety of formats and platforms.

Communication Skills:

Listening:

  • Listen to, and follow the information and directions of others.
  • Listen actively to other perspectives and ideas.
  • Ask for clarifications.

Interpreting: Interpret visual and oral communication.

Speaking: Speak and express ideas clearly and logically in small and large groups.

Writing:

  • Record information and observations by hand and through digital technologies.
  • Organize information logically.
  • Understand and use mathematical notation and other symbols.

Self-management Skills:

  • Use time effectively and appropriately.
  • Keep an organized and logical system to document learning.
  • Use technology effectively and productively. 

Counting Collections

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We began by looking for patterns in numbers. We skip counted in 2’s, 5’s, 10’s, 3’s and 4’s starting from 0.

  • What do we notice?
  • How might we use what we know about skip counting, in other situations?

TASK!

What do we have a lot of in the classroom? Come up with a way to count your whole collection. You will have to be organised and think about how you can keep track. You might need to create sets or use containers.

  • Once you know how many in your set, take a of it.
  • Use the tool and explain your strategy in your Maths Journal.
  • Complete Page 2 on the activity template.
  • Use the tool to show how you worked out the total and prove that your answer is right.

 

Sorting, documenting and explaining our strategies! 

Rounding

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We began by guessing how many dice were in the glass jar. First, everyone estimated how may were in the jar. Then, we counted to check how many dice were actually in the jar. There were 55 dice in the jar!

Next, we discussed how we might round that number to complete the sentence ‘There are about ____ dice in the jar‘.

Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use.

We all agreed on the answer. 

There are about 60 dice in the glass jar!

We practiced rounding numbers together. Would we round up or down? 

The students completed the activities independently using their understanding of rounding. 

Next, we played a game. The students had to walk around the class and answer 28 questions posted around the classroom. They needed to round to the nearest TEN and nearest HUNDRED.

The Card House

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What did you notice?  What do you wonder?

  • Carlotta “I wonder how the cards come out of the bag in triangles.”
  • Dohoon “How many cards did they use? How many are odd numbers? How many shape cards?”
  • Eunseong “How tall is it?”
  • Sam “How many cards? How many triangles?”
  • Chanwoong “How did they stick the cards together? Which one is the joker card? Can this be a village?”
  • Hannah “What is it? What are they making?”
  • Seungje “Where did he buy the cards?”
  • Ryder “How many triangle cards? If there are more cards, how many more buildings could he make? Is there a triangle cards that are 4,4,4 and 2,2,2? Is there so much cards, can they make a whole country?”
  • Kavel “How did they make the video so fast?”
  • Sky “How do they stick one card and one card to a triangle? If they have more cards, can they build a tower?”
  • Jiwan “How many cards all together?”

How many cards? How many card triangles?

We watched the video to help us solve the problem. 

We documented our thinking and strategies in our Maths Journals.

Together, we worked out how many cards were used to create the ‘Card House’.

Then, we counted the number of triangles used to create the ‘Card House’.

We realised that counting in 3’s was a great strategy to use!!

Maths Provocation: Jimmy’s Ramp

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Jimmy set up a ramp for his toy cars. He and his brother Joe each sent one car down the ramp. 

We gathered to think about the provocation. Here are some of our initial wonderings.

I wonder…

  • … whose car is faster.
  • … whose car goes straight
  • … if the car falls down
  • … how the ramp is made
  • … if the cars fall down from the side of the ramp
  • … what Jimmy used for the ramp
  • … who pushed it down first
  • … whose car is slower

Joe’s car rolled 15 centimetres farther than Jimmy’s.

1) If Joe’s car rolled 27 centimetres (cms), how far did Jimmy’s car roll?

How could you get started?

2) Does this problem make you think about addition or subtraction?

3) Whose car rolled farther? Draw a number line to model the problem.

4) Follow Up:

Make your own ramp with books, cardboard, or other materials you find. Roll 6 different objects down the ramp and measure how far they go.

5) Record your data on a table.

6) Make up your own story problem with the results.

We began to construct some questions that we might want to ask about the data in our table. 

Mr. Matt worked with the students to help them create questions using ‘Question Words’. 

Sample Student Questions:

we wonder what YOUR ramps might look like…

Place Value Structure

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The students were invited to create a single structure using Place Value Blocks, using 25 pieces in total. Then, they had to provide the total value of the structure.

Instructions:

  1. Build a structure with 25 base ten blocks
  2. Take a photograph
  3. Use labels to show the value of your structure
  4. Complete the ‘Title’ of your post “My Base 10 Block Structure is worth _____ = ___ hundreds,___ tens, ___ones.”

This task involved discussions about number, trading, grouping and decomposing.

Student Responses:

What might your Base 10 Block structure look like?

What is the value of YOUR structure? 

The Block Tower Challenge!

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We were excited to take on a Design challenge!

We used pictures, words and numbers to express our ideas and thinking visually. We used mathematical language to explain our thinking to our friends.

We documented out thinking in our Maths Journals.

We worked in teams to create our own Maths Tower Challenge!

Here are some of our challenges for YOU! 

During this task, we had opportunities to:

  • understand questions
  • use mathematical skills, knowledge and understanding
  • solve problems independently
  • use appropriate mathematical language
  • share thinking clearly in words, symbols, numbers, pictures
  • identify the key information to solve a problem
  • choose and use appropriate problem-solving strategies
  • explain a process – how the problem was solved

Measurement – Size, Height & Length

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Online Learning

Focus: Thinking Skills, Research Skills, Communication Skills

We have been exploring objects around us, and finding ways in which we can identify, compare and describe their attributes. Here are a few different collections that have been organised by different attributes.

What do you notice? What do you wonder?

You might want to explore your own environment to find objects that you can compare, sort and organise in different ways. 

🌻 Through this invitation, the children have opportunities to identify, compare and describe attributes of real objects.

Balancing

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Online Learning

Focus: Thinking Skills, Research Skills, Self-management Skills

How heavy is the 🍎 apple?

  • How can we find out?
  • Can we use other materials and objects to weight the apple?  

Let’s read the story ‘BALANCING ACT’ by Ellen Stoll Walsh to explore weight and balance.

In this story, two mice 🐁🐁 make a teeter-totter. They play on their teeter-totter, balancing each other out until their friends come along to join their play. They think of different ways to include their friends, which leads to solving problems with weight and balance.

How might we make our own balancing scale?

Here is one way to create your own balancing scale. You might have other ideas to create your own scale! Follow the instructions in the video to make a balancing scale. 

Materials Needed:

  • 2 cups/small containers
  • 1 clothes hanger
  • A sharp object (to make the holes)
  • 4 pieces of twine about 60cms in length 

Steps:

  1. You may need an adults help to use a sharp object, or a hole punch to make holes in 2 small containers as shown in the instructional video. 
  2. Cut 4 pieces of twine about 60cms in length. The twine needs to be thick and strong enough to make the balance scale more durable.
  3. Tie the ends of the twine through the holes in the containers to the ends of the clothes hanger as shown in the instructional video.
  • What weighs the same?
  • How heavy or light are different objects or substances?
  • How might we weigh different materials and substances such as liquids and solids? 

Light and Heavy What things are light? What things are heavy? Let’s explore the concept of weight through this non-fiction picture book. In Light and Heavy, a girl investigates what she can and cannot lift.

Through this invitation, the children can investigate how objects have attributes which can be measured using non-standard units, which can then be used to sort and compare. 

Beans in a Pod

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Online Learning

Focus: Thinking Skills, Communication Skills
Mathematics: Estimation, Number

Numbers are a naming system, numbers can be used in many ways for different purposes in the real world. This invitation encourages estimation, problem-solving and discussion.

  • What do you wonder?
  • Estimate how many beans are in each pod.
  • How many beans would there be altogether? How do you know?
  • What do you wonder?
  • Estimate how many beans are in each pod.
  • How many beans would there be altogether? How do you know?

Through this provocation we can:

  • explore number names
  • explore quantities
  • estimate
  • understand the terms more, less same as
  • problem-solve
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