Math Talk – Tens & Ones

What do you see?

What do you know?

When we look for patterns, we notice what changes and what stays the same from one picture to the next.

Drawing or building the pattern helps us think about what comes next!

The children used mathematical vocabulary to share their observations about the image.

We documented these ideas using symbols, words and numbers.

Then, we played a game of ‘Trash and Treasure’.

This game helps the children learn about place value and how to use the Base10 Blocks to find the biggest and smallest numbers.

The Paper Airplanes

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.

Exploring Numbers

What do you know about the number 3?

The children shared what they noticed about the shape of the Numicon shape.

It looked like a heart, a boot, a letter ‘V’ and it has 3 holes.

What numbers do you see in this shape?

If we wanted to ‘make’ this number, what are the different ways we might try to make it?

  • Oxford shared the first suggestion “2 and 1.”

He was invited to share his suggestion using numbers and symbols. The children began to share other ways to show 3.

Next, we looked for ways to show 5.  

What do you know about the number 12?

Oliver “It has a 1 and a 2.”

Eli “On the bus. So we know where it is going.”

Liz “The clock has 12.”

We used the Cuisenaire Rods and Numicon Shapes to find different combinations that total 12.

Then, the children worked in groups to find combinations that total 15,16 and 20. We noticed how they used their thinking skills to calculate.

They used manipulatives to create models. They used numbers and symbols to share representations of their understandings.

Throughout the task the children worked together in small groups, sharing ideas and taking turns to document their learning.  

Readers, Writers and Mathematicians

At the beginning of the school year, the children wrote the morning message. They used what they knew about letters and sounds to spell the words.

The Morning Message often includes a question or a wondering that leads to discussions, literacy or mathematical activities. While reading the message we identify letters of the alphabet and familiar High Frequency words. The children are encouraged to notice important reminders as writers; spaces between words, capital letters to start a sentence and punctuation at the end of a sentence.

Groups of children often meet with a teacher to work on key literacy skills. These are dedicated times when the children explore books to learn the different skills and strategies that readers and writers use to communicate effectively.

Activities that follow reading experiences usually involve reflecting on reading and using drawing, writing and spoken words to express an idea. The children might share an important part of the story, talk about the characters and settings, or discuss the different ideas presented in fiction and non-fiction texts.

It is important to remember that each child is an individual who works on specific skills while reading independently or collaboratively.

With prompting and support the children:

  • ask and answer questions about key details in a text
  • retell familiar stories, including key details
  • identify characters, settings, and major events in a story
  • ask and answer questions about unknown words in a text.

Geometry: Odd Shape Out

Which One Doesn’t Belong?

We invited the children to look at a set of four pictures. They had to decide which one didn’t belong with the other three and use math words to describe their thinking. There are many ways to think about each one!

We noted their reasons why each of the pictures might not belong with the other three.

A does not belong!

  • Jeongyoon “This one has no corners and the other ones have corners.”
  • Howie “This does not have straight lines.”
  • Eunbyul “Circle is line is 1 and two yellow has 4 lines, and C has 5 square and D has 3 lines.”
  • Eileen “The circle does not have any angles, the square, cube and triangle have angles.”

B does not belong!

  • Liz “B the sides are longer.

C does not belong!

  • Wyatt “This one has a lot of sides and the other ones didn’t have lots of sides.” (in Mandarin)

D does not belong!

  • Lydia “D, this is blue and the other is yellow.”
  • Morning “This is blue and the other one D has 3 corners and the other has 8 corners and 4 corners or round. The only one that has 3 corners. s are yellow.”
  • Eli “The triangle but it has 3 corners and all the others have round or 4 or 8.”
  • Oxford “This has 3 lines and C has 4 lines and A has 1 line and B has 4 lines.
  • Oliver “Does not belong its because the one that has 3 corners is blue and blue is not wood.”
  • Motong “This one is blue and the other ones are yellow.”

We noticed that the children used describing words to classify the shapes. They used the words corners and sides to express their ideas.

Oliver explained that the shape in ‘C’ does not belong because it’s a cube, a 3D shape.

Teacher: But what makes it a 3D shape? What does that mean?  We look forward to exploring this further.

Math Talk – Gathering Data

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.

A Math Story – The Sleepover!

We read the story ‘The Sleepover’ by Catherine Twomey Fosnot. In this Maths story, a little girl invites her friends to stay over. Aunt Kate babysits the children and prepares snacks and juice for them. However, the children keep moving between the beds and trick Aunt Kate.

 

 

As we read the story, the children noticed the different combinations to make 8 and used their mathematical knowledge to express their thinking.

They recorded their thinking on paper. We used counters to help us problem solve.

We are learning that:

  • Math is in our world!
  • Number operations can be modelled in a variety of ways.
  • We can use pictures, numbers and symbols to share our thinking and problem-solving.
  • We can tell stories using numbers.

Math Talks

Maths Talk is a collaborative process where children’s thinking, ideas and strategies are discussed, shared and or exchanged. The routine reveals children’s understanding and misunderstandings and encourages dialogue about mathematical concepts.

Which One Doesn’t Belong?

Dots in Two Colours

The children were invited to look at the set of four pictures and decide which one doesn’t belong with the other three.

They were encouraged to share their thinking using math words. There are many ways to think about each one!

We noticed that the children tapped into their prior knowledge about quantity and colour to explain their reasoning.

 

 

The Number 5!

What do you notice?

What do you wonder?

How many different ways can you show this number?

The children were invited to use manipulatives, numbers and words to share their thinking. We wonder how we might apply what we know about the number 5 to explore bigger numbers!

We wonder how number operations can be modelled in a variety of ways.

 

Approaches to Learning (ATL’s) 

  • observe carefully
  • analyse and interpret information
  • notice relationships and patterns
  • listen actively and respectfully to others’ ideas and listen to information
  • express oneself using words and sentences
  • understand symbols

100 Hungry Ants

We have been using Place Value Blocks to model numbers and show our thinking.

We read the story ‘One Hundred Ants‘ by Elinor J. Pinczes, illustrated by Bonnie Mackain. 

The story begins with a group of hungry ants that decide to march off single file to a picnic. However, along the way, they realise they are moving too slow and begin to divide themselves in different ways to help them get to the picnic site quickly.

As we read the story, the children worked in pairs to document their thinking using Base 10 Blocks, pictures, words and numbers.

They first went in one line of 100.

2 lines of 50.

4 lines of 25.

5 lines of 20.

And 10 lines of 10.

Next, the students retold the story in their own words, using the images they created to document their thinking.  

Through this activity we:

  • explored how the base 10 values system is used to represent numbers and number relationships
  • used the operations of addition to solve problems

Same and Different: Frogs on a Log

  1. What is mathematically the same about pictures A and B, and what is different?
    • A and B are the same because …
    • A and B are different because …
  2. Make a third picture of some frogs. Explain how your picture is the same as pictures A and B, and how it is different.

Responses

Math Talks – Dominoes

  • What do you notice?
  • What do you wonder?
  • What comes next? 

Show or tell what the next few pictures look like. Describe how you know.

  

Laundry Fun

The children have been dipping into their extra clothing bag to change into clean and dry clothes when needed. Frequently, the children comment on the number of clothing in their bags. We decided to offer the children a data gathering experience to help them use number and data collection for a real purpose.

We began by presenting the children with this image and prompt:

What do you notice?

We encouraged the them to think about the way the clothing was sorted.

The children noticed that:

  • the labels and pictures to help us know what the items are.
  • the clothing was organised in rows and columns.
  • there were 15 items in total.

How might you use pictures, numbers, or words to show what is happening?

The children began to make their thinking visible on paper.

They gathered the clothing in their extra clothing bags, sorting and organising them to make it easy to count and document their observations.

Then, they used a graph paper to show the number of different items in the bag. Through this experience the children were able to collect information to make decisions.

The next time your family does laundry, you can sort the clothes into categories by type. Some possible prompts could be…

  • How many categories are there? Which category has the most?
  • Which has the fewest?
  • Is it different for each person in your home?

The Cake Problem

K2B made two cakes. They asked if we can help with the frosting and cutting. We agreed.

The mathematicians thought about the problem. We had 2 cakes. We needed 16 pieces from each cake. The pieces must be the same size. First, we talked about the shape of the cake.

  • Patrick “The cake is a rectangle. Two sides are the same length, two sides shorter and two sides longer.”
  • Eunice “We draw rectangles because we have to think about how to cut it.”

  • Euijin “We draw 16 pieces.”
  • Kenan “We need to draw the 16 people. We have to make two 16’s.
  • Joon “It is 16 pieces.”

  • Patrick “We are erasing and fixing the pieces to make it right. When you don’t get it correct, you need to erase and try again.”
  • Noah “We are sharing our drawings.”

  • Doho “We draw and we show them.”
  • Sean “We can cut the cake 2 ways.”
  • Doho “We cut the cake.”

  • Eunice “We put the cream.”
  • Patrick “The cake looks like pancakes or cheesecake.”
  • Euijin “The cream cheese.”
  • Eunice “It’s almond cream.”
  • Patrick “It is sugar cream.”
  • Allen “I think this cream is white chocolate.”
  • Doho “Very YUM!”

 Student Learning Outcomes: Number Sense

– fractions are ways of representing whole-part relationships

How many triangles can you find?

A shape puzzle was presented to the class during Morning Meeting.

The mathematicians were invited to find as many triangles within the shape puzzle. First, we used card to draw and cut out the triangle puzzle.

Then, the mathematicians played with the pieces to find as many triangular shapes as they can. Manipulating the different pieces allowed them to think of a range of combinations.

Then, we used the image to draw out the different triangles.

The mathematicians found 17 triangles!

We wonder how many YOU can find!

Approaches to Learning (ATL’s) 

  • observe carefully
  • record observations—drawing
  • make thinking visible

Measuring with Unit Cubes

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

Splat!

What is SPLAT?

The ‘SPLAT’ math activity is a great way to talk about number. Essentially, a set of dots are shown using manipulatives or a screen. A “splat” or blob covers some of the dots. Then question is:

“How many dots have been covered by the splat?”

The mathematicians used what they know about number relationships to solve the problem. Exploring some of the thinking and reasoning led to creating equations. Finally, the children created their own class ‘SPLAT’ book.

Base 10 Value System

In Kindergarten, we have been exploring numbers in different ways through games and explorations at different centers. We offered the children a provocation to start a conversation about number.

How can we show 16?

Some of the children put their ideas down on the whiteboard. We discussed the ideas and pictures they shared.

Then, we introduced the children to a place value mat. The base 10 value system is used to represent numbers and number relationships.

As we rolled the dice, we began to count and add ones onto the mat. When we reached 10 ones (or units), we regrouped them to make a ten! We continued with the game as we practiced grouping the ones to make tens.

We will continue to use the base 10 value system to represent numbers and explore number relationships.

Counting Squares

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

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?

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

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

Lots of Pieces – Number Problem

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?

Math Talk – Graphs

We have been counting collections and exploring different ways we can collect and share data. Ms. Delia shared 4 different images with the students to help them think about other ways we might share the data we gather through our projects.

Teacher “What do you notice?”

Graph 1

  • Hyun Seo “That tells me that the favourite ice cream shows that it is about the favourite ice-cream.”
  • Ethan “That one is left to right, the other one is the bottom to top.” (referring to the vertical vs horizontal graphs)

The students talked about the horizontal and vertical bar graph.

  • Grace “The difference is that there 1-10 and this other one has it to 100.”
  • Yuchan “There is a very small line at the bottom. Because then the small line is 25, to 50 to 100.”
  • Yuki “Here there have a colour, change colour can see clearly so other colours can see well.”
  • Fedo “If you turn it the other way it will be like the other bar graph.”

They explained that the length of the bar shows the data.

Graph 2

  • Hayoon “I see two circles. In the middle, like the Olympic. This one in the middle is the same. The same thing the whale and fish have.”
  • Seungbin “I don’t see numbers in it.”
  • Ella “Data is like, we ask people and research and then we make data with like how many people like ice cream and they are using research skills. Like we have to research about the whale and the fish and find what we have in common.”

Teacher “When can we use this diagram?”

  • Ethan “When they are the same or not the same. Like a wolf and a dog.”
  • Alejandra “And the things about the same are in the middle.”
  • Lawrence “What is that graph?”

We named the diagram ‘Venn Diagram’.

Graph 3

  • Fedo “All of them equals 2. So it means they ate 2.”
  • Yuchan “Each mango is 2, so if it is 3 mangoes it means 6 mangoes.”

Teacher “This is why we call it a picture graph.”

  • Lawrence “The picture shows the tally graph.”
  • Alejandra “10.”
  • Ethan and Hayoon “I think it’s 20 apples.”
  • Ethan “I like because it shows pictures. If someone does not know the spelling, then you can use pictures.”

Graph 4

  • Grace “It looks like mountains, and it shows numbers.”
  • Diego “I think this looks the like the bar graph, you use the line and the dots.”
  • Gihyeon “I notice it looks like a W.”
  • Ella “Because here its 50. So when you go down you can see how many bikes were sold. In January 50 bikes were sold and in February 30 bikes were sold.”
  • Yuchan “I notice that its like a news graph. Like weather. Like how sunny or cloudy.”
  • Seungbin “I saw in a book and it shows how the earthquake happens. Like in other countries how much it happens.”
  • Lawrence “It shows like If you don’t put the line.”
  • Seungbin “It is shows a little bit and then it keeps going and then in the last it shows going high.”

Next, the students were given different scenarios. They had to work in teams to decide which graph would be the ‘best’ choice to share the data.

Patterns

We began by discussing and sharing what we already know about patterns. The students noted their ideas on large chart paper.

  • Ethan “You can repeat something or add more.”
  • Seoyeon and Ella “pattens can be shapes. Patterns have to repeat all the time.”
  • “Patterns can be numbers.”
  • Agata “Patterns can be long or short.”
  • Seoyeon “Patterns can be colours.”

Questions: 

  • Agata “Can patterns be built with people?”

Next, the students were presented with a series of images. They documented the image and their ideas using pictures, numbers and words.

I can see…

  • “…strawberries and blueberries.” – Grace
  • “…one strawberry changed to a blueberry.” – Ethan
  • “…strawberry -1 each and blueberry +1 each.” – Seungbin
  • “…the number of the strawberry is getting smaller and replacing it with a blueberry.” – Ella
  • “…I see the picture going down is the blueberry is more more.” – Lawrence

How can you show these patterns using numbers?

What would the next 3 pictures in the sequence look like?

Then, they decided on how they would continue the pattern. They justified their ideas to the group.

Finally, the students created their own pattern using manipulatives, symbols and numbers, demonstrating how patterns can be represented in a variety of ways.

Our exploration on patterns continues…

The Ramp

We gathered to think about a MATH provocation.

  • How might we solve this problem?
  • What strategies can we use?
  • What tools would we need?
  • What would be the first step?
  • How can we use pictures, numbers or models to solve math problems?

We worked through the task together and recorded our thinking in our Math Journals.

We thought about the different tools we would need to solve our problem. The students discussed their thinking and worked through their task using math vocabulary related to number, measurement and data-handling.

Next, they worked on creating and testing their own ramp. They needed to work in teams, solving problems and negotiating ideas.

The students thought about the materials they would need, the height and placement of the ramps as well as the objects they would test.

Then, they recorded their data on a table and discussed and shared a question they could ask about the data they collected.

Through this experience the students had opportunities to:

  • conduct research
  • work as a team
  • think
  • cooperate
  • listen
  • persevere
  • problem solve
  • have fun and celebrate learning together!

How are YOU a Mathematician?

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

Creating Sets and Groups

We have been exploring multiplication and division in Second Grade. The students began with a warm up activity to discuss what they noticed and wondered about this image.

The students used whiteboards to document and share their thinking.

We watched a short video on Multiplication as groups of objects to help us create sets and groups using materials in the classroom.

The students worked together in teams to create different sets of 2’s, 3’s, 4’s 5’s and 10’s.

They included multiplication equations to explain their groupings. 

Our research with number helped us complete a multiplication chart.

Multiplication

What do you notice?

What do you wonder?

 

The students shared their ideas about the images. 

We concluded that 8 is an even number, because 8 counters can be placed in sets of 2 with no leftover counters.

Next, we discussed the following images. What can we count? How might we count?

We documented our thinking.

 

Key ideas:

  • exploring the concept of odd and even numbers
  • examining equal groups related to repeated-addition equations (e.g., 5 + 5 + 5 = 15)
  • visualizing equal groups with arrays and area models

Unit Vocabulary

Then, we used manipulatives to create our own arrays. 

Making Arrays

  • Make arrays with square tiles and record the repeated-addition and multiplication equations.

12

 

 

16

 

18

21

24

30

 

 

Same & Different: Rainbow Arrays

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

The students shared their thinking and reasoning. 

Finally, we shared our ideas about the following picture. 

Spring Garden

  • Show what is happening using pictures, models, or numbers.
  • What do you notice? What do you wonder?
  • What math questions can you ask about this situation?

Click on image to play an Online Game

 

Oggie Doggie Tags for the Circus

We have been learning the words to our songs, practicing the actions and creating make up and costume designs.

Grade 2 will play the ‘Oggie Doggies’ in the show. We had to create dog tags for the characters. We decided to use wood cookies for this purpose. We had to decide on the ribbon we will need for the tags. The students began to suggest different colours for the ribbons. There were clearly too many choices as Ms. Heidi said we could only have 5 choices. We had a problem. Which 5 should we choose?

First, we listed all the colours the students suggested. We had 9 choices. How should we organize this information?

The students suggested we create a chart and record the data on it.

(Information can be expressed as organised and structured data)

We had a clear first, second and third choice. However, three colours were competing for the 4th and 5th choice. The students suggested that they take a second vote to find the fourth and fifth colour. We recorded this data on a second table.

Now, there was a clear choice for the remaining two colours.

We finally had our 5 choices for the ribbons. Next, we voted a third time to find out the quantity of each colour we had to purchase. We created a third table to record this information.

Then, we created a column graph to record the data. We decided that each square would represent 2 people as there wasn’t enough space for the highest number.

We gave Ms. Heidi the information she needs, the chosen colours and the quantity of each colour.

When the wood cookies arrived, the students used a wood-burning tool to write their names on the wood cookie.

Then, they used acrylic paints to paint their wood cookies.

Finally, the DOG TAGS are ready for the SHOW!

Research Skills:

  • ask relevant questions that can be researched
  • make a plan for finding information
  • gather information
  • record observations by charting, tallying, writing

Measurement – Length, Width, Height

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. 

Patterns with Cubes

What do we know about patterns?

We are exploring patterns by discussing, extending and thinking about growing patterns.

What do you notice? What do you wonder?

The students help extend the pattern to show what the next few pictures might look like. 

They justify their answers by using manipulatives, drawings and oral language to express their thinking.

We documented our thinking on chart paper.

This led to a conversation about odd and even numbers. We wonder where this learning might take us next…

Problem Solving Strategies

We have been talking about problem-solving strategies that we can use to solve word problems. 

* Read the problem 2 or more times.

* Underline the facts. {numbers, key actions, vocabulary}

* Circle the question.

* Model a problem. {counters, base-ten blocks}

* Act out the problem. {Students act out, use technology} (Acting out 5+3=)

* Create drawings or diagrams.

* Retell or use graphic organizers. (Beginning, Middle and End)

* Solve the problem.  {Draw a picture.}  

* Write the answer. {Number sentence + Sentence.}

We continue to use different strategies to show our thinking and problem-solving.

Problem Solving Strategies

Rounding

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

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 Talks – Cards

  • 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?

First, the students noted down observations and ideas in their Maths Journals. They were encouraged to use pictures, words and numbers. Next, they presented their thinking and reasoning to the class.

Finally, the students documented 3 or more explanations provided by others, in their Maths journals.

Maths Provocation: Jimmy’s Ramp

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…

Creating Patterns

We invited the students to share their initial understandings/ ideas about ‘PATTERNS‘. Their documentation included examples of repeating patterns. 

Then, we posed the following pattern talk by @MLCmath

The students began to share what they observed and what they thought. 

Next, the students created their own patterns. Here are a few examples…

Next, we watched a video on BrainPOP Jr. on Patterns

We wondered what patterns we can see around us. Perhaps we can create our own patterns! 

THE TASK

Here are some of the patterns we observed in our environment and others we created with materials we have around us. 

What patterns do YOU see around you? 

The Block Tower Challenge!

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

Same & Different

Look at the two pictures. What do you notice?

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 …

First, the students engaged in a discussion technique ‘think-pair-share’, which is used to help students form individual ideas, discuss and share with the others in a group.

Then, we documented ideas presented by the students.

The students needed to:

  • consider ideas from multiple perspectives
  • speak and express ideas clearly and logically
  • listen actively to other perspectives and ideas
  • ask for clarification

What are YOUR thoughts?

Are ‘A’ and ‘B’ the same or are they different?