## 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.

## Mouse Count

We read the picture book 🐁  Mouse Count by Ellen Stoll Walsh. This is a wonderful picture book that encourages conversations about number, quantity and addition.

After reading the story, we watched a short video that encouraged the children to think about the multiple combinations that make 10.

We wonder how many different ways 10 mice can be arranged with some in the jar and some in the grass.

Through play and dialogue, we looked a few different combinations using stones to represent mice.

Then, the children were invited to make their own number book.

One student decided to tell his own number story using the different loose parts in the campfire.

We are learning to create number stories by modelling joining and separating concrete objects. We can use language to describe changes to a collection as objects are added or taken away.

The children documented their thinking on paper using pictures, numbers and symbols. These pages will be collated to create a number book.

As authors and illustrators, their next task was to decide what the cover of the book should look like.

They had to think of a ‘title’ that gives the reader an idea of what the book might be about.

Finally, the children included a picture on the front cover along with the authors name.

## 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

## Equivalent Fractions

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.

## Fractions and Measurement

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

## Area and Perimeter

How can we measure the perimeter of different objects? What is area?

We know that objects have attributes that can be measured using appropriate tools.

Then, we used Lego to explore this further, sharing different examples of how perimeter and area can be calculated.

Next, we used virtual colour tiles to calculate the area of a shape.

## Creating Structures with Shapes

The students were invited to recreate a structure using shapes.

1. Choose a structure that you would like to recreate with shapes. Recreate it

Three Options:

• Option 2: Use paper shapes to create a collage

• Option 3: Use play dough or clay

• 2. Create a table showing all the different shapes you have used.

Student Responses

Through this experience, students were learning that:

• information can be expressed as organised and structured data
• geometric shapes and associated vocabulary are useful for representing and describing objects in real-world situations
• specific vocabulary can be used to describe an objects position in space
• shapes can be transformed in different ways

## 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?

## Double and Half

What is double, what is half?

We began by brainstorming what we already know about double and half.

Then, the students looked for examples of double and half in their environment.

Big Ideas:

• fractions are ways of representing whole-part relationships
• number operations can be modeled in a variety of ways

Thinking Skills, Communication Skills:

• share strategies and ideas
• understand and use mathematical notation and other symbols

## Regrouping and Decomposing

We have been exploring different ways we can make numbers.

Regrouping in math is when you make groups of ten when performing operations.

To decompose (break apart) in math is to break down numbers into parts.

We used these strategies to help us solve addition and subtraction equations.

Conceptual Understandings:
· the operations of addition and subtraction are used to process information to solve problems
· that number operations can be modeled in a variety of ways

## 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.

## Data-handling

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

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.

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

## Word Problems

We have been talking about the different strategies we can use to solve word problems. We have been modelling, drawing, acting and using numbers, symbols words to solve these problems. We will continue to use these strategies to explain our thinking and problem-solving.

The Word Problem

The Word Problem

## The Role of Estimation in Measurement

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…

## 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

# 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.

## Number Sense – Math Games

Our Math focus this week was on building our number sense through games, discussion and problem-solving. Students were encouraged to interact with each other during the online sessions to help build a sense of community.

Math Vocabulary

We began by talking about ODD and EVEN numbers. We used manipulatives, pictures, and numbers to share our ideas.

Students:

• “odd and even numbers can be divided by two and each person gets the same
• if I had three sweets and I shared it with a friend then it won’t be equal
• 15 is an odd number because one person has 7 and the other has 8
• ODD numbers are like 1,3,5,7,9 and EVEN numbers are 2,4,6,8,10”

Next, we played ‘Reach the Beach’!

The focus of the game was to identify odd and even numbers. The students were able to make the game as challenging as they wanted to by adding more dice, or multiplying the digits instead of adding them.

The next game we played was ‘Trash and Treasure’. This game develops an understanding of how the position of a digit within a number determines its value.

The students were then invited to create and play their own games. This provoked their thinking and developed their self-management skills. Students were able to stretch their thinking by making the games more challenging. Taking responsibility for completing tasks and being open-minded while playing team games was also fostered through these activities.

Odd and Even

Trash and Treasure

Conceptual Understandings:

Number Sense:

• the base 10 value system – the position of a digit within a number determines its value
• the operations of addition and multiplication

## Exploring Numbers

Next, we used manipulatives to show the number 15 in different ways. The students suggested different equations and we documented these ideas using counters and number sentences. Next we showed our thinking using an empty number line.

The students were invited to ‘show’ numbers in different ways through a video provocation.

They could use materials/objects (blocks, stones, chopsticks) to share their ideas. They could use numbers and symbols to explain their thinking.

They went on to create and show the number ‘21‘.

They were challenged to write a story problem to go with one of the ways they showed 21.

Through this activity the students explored numbers, using manipulatives, to compare and model numbers in a variety of ways.

## The Scale

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.

## The Case of the Gummy Bears

Elena gifted Ms. Shemo a pack of Gummy Bears because Ms. Shemo likes to eat them. However, there were too many Gummy Bears for one person!!

Ms. Shemo said we can share the bears if we can estimate, measure and use what we have learned in Math to solve the problems she provided. The students agreed.

First, we estimated how heavy the packet of Gummy Bears were. Each student shared their best guess.

We needed to compare the weight of another object to see if we can improve on our estimation.

We weighed a pencil. It was 4 grams. The students held the two objects in their hands to compare the weight of each object.

Then, they decided to change their initial estimate (blue) and shared a new estimate (red).

Then, we weighed 1 bear.

It was 2 grams, 3 bears were 7 grams and 5 bears were 10 grams.

Next, we weighed ALL the bears in the packet. They weighed 200 grams!!! Steve had the closest estimate (150g)

We wondered how many bears were in the pack.

We estimated how many bears there might be. The students agreed that if 1 bear was 2grams, then 200grams would be 100 bears.

If this was so, the students decided that they will share the bears equally:

• each student (17) will get 5 bears
• each teacher (3) will get 5 bears​

Unfortunately, there were ONLY 90 bears!

We had to rethink our plan.

After much discussion and problem-solving (+, x, ÷), the students agreed on the following:

• each student will get 4 bears
• Mr. Mike, Mr. Matt, Ms. Shemo, Ms. Jennie and Ms. Cindy (as she helped us with the memory book) will get 4 bears each
• Mr. Snyder will get 2 bears

The students were happy to chew on their yummy treat after all the thinking and problem-solving they had done!

## Exploring Fractions

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 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

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

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

## The Community Garden Plot Project

24 March 2021

We have been using manipulatives to explore measurement. We have been measuring the Perimeter and Area of different shapes.

Mr. Danny, the Activities Director needed some help. He asked the students if they could create a map of the ‘Community Garden Plots‘.

We began by brainstorming what we already know about maps. We documented our thinking and ideas on chart paper.

Next, we thought about the map of the ‘Community Garden’.

• What should it include?
• What would we NEED to create the map?

The students wrote down their ideas. They shared their ideas with each other.

A plan was beginning to unfold.

Then, we went to the garden to take a closer look at the garden plots.

• What else do we need to think about?
• What steps do we need to take to complete the task?

The students continued to document their ideas on paper. They discussed their ideas with each other.

What skills would we need to complete the task? The students shared their thinking.

(Developing the Approaches to Learning​)

• Kavel “You have to manage yourself. I think we should use thinking skills because we need to think how we need to measure the right proper way. We need to put the tool on the ‘0’ or it will be the wrong measurement.”
• Carlotta “You use thinking skills, to think about how you are going to measure things. You also need to use your social skills because you are already measuring one thing then you got to tell other people that they should not measure again.”
• Chanwoong “We use communication skills because we all have different ideas so we have to communicate ourselves. We also need research skills because we have to ask questions about it and we have to gather and research the information on the garden.”
• Reg: “You have to use your communication skills when you have already done a task you have tell others you have already done it. We also have to use Math skills because when we make the plot when we make the area around the garden plots, the perimeter, so we know the area of the plots. It will help us when we make the map. Like 1 meter of it can be like 30 or 20 cms.”
• Hannah “You will need to use your mathematical skills, to write down the things like ideas and then count because we need to count how many plots.”
• Sky “We need to count, because we need to know how many of the trees, pots and plots we need to draw on the paper. We need thinking skills because if we don’t think and we just say its like 2 cms (estimate) then we will get the wrong answer. If you measure it correctly then you will get the right answer. We need to be mathematicians because we need to add all the meters and cms. together. If you don’t you will have the wrong answer. ”
• Stella “We need Math skills, because you need to make a map you still need to think of math.
• Changhyeong “We need thinking skills because we need many ways to measure the ground.”

24 March 2021

Over the last few weeks, the students have been collaborating in their groups to plan how they will create the map of the ‘Community Garden’ at NIS.

We created a table to list the materials we will need to complete the task. Students populated the table based on the needs of their individual group.

Next, we sourced the materials from the resource room.

Then, we went out with our tools and resources to begin measuring. The students had to decide how they will manage their task and document their learning. Through this experience, the students have many opportunities to use the skills and knowledge, for an authentic purpose.

We wonder what our next steps would be….

## Area and Perimeter

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

Calculating Perimeter

Square Units

Calculating Area

Calculating Area in Meters

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

## 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?

Click on image to play an Online Game

## Storytellers in the Community

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…

## 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

## Line Plots

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

## Doubles and Halves

What is double, what is half?

The students went on a number exploration to create examples of doubles and halves.

1. Find examples of double and half in the classroom.
2. Take a picture of your example.
3. Post 10 examples of double and half on Seesaw. 1 example on each page.
4. Use pictures (draw), numbers and words to justify your image.

They used their iPads to collect evidence. They took photographs, made notes and shared their examples.

We watched a BrainPop video on Doubles

The students explore how halving is the inverse of doubling. The students continue to document and practice their doubles and near doubles facts. They are encouraged to apply these understandings when solving Maths problems.

Thinking Skills, Communication Skills

• share strategies and ideas
• listen to instructions
• understand and use mathematical notation and other symbols

Self-management Skills:

• manage time and tasks effectively

## 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…

## Telling Time

What do you know about time?

The students shared their thinking. We documented what we already know on chart paper.

Vocabulary

This is our schedule for Tuesday. The schedule helps us plan, guides our daily activities and reminds us of what is happening throughout the day.

We are learning to:

• read the time to five minutes on a digital and analogue clock
• name the days of the week, months and seasons in order
• use a calendar to determine dates
• solve real life problems involving time

How does time impact the decisions you make? We wonder…

## 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

## Counting Collections

We began by looking for patterns in numbers. We skip counted in 2’s, 5s, 10s, 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?

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

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.

## Fact Families

We gathered to discuss what we know about a fact family. We defined it as a group of math facts or equations created using the same set of numbers. We noticed the relationships between the three numbers involved in the fact family, and how the operations of addition and subtraction are related to each other. We thought about how we could use this strategy to process information to solve problems.

## Number Sense

We have been developing our Number Sense by solving Mathematical problems. The students were encouraged to use Base 10 Blocks and numbers to show their reasoning/thinking.

Oscar used 7 base-ten blocks to create a number. What are some different numbers he may have created? ​

Peter and Sarah were using place value materials to model numbers. Peter used 3 hundreds, 2 tens, and 4 ones. Sara used 2 hundreds, 12 tens, and 4 ones. Did Peter and Sarah show the same number?

Are 7 hundreds, 3 tens, and 5 ones the same as 5 hundreds, 3 tens, and 7 ones? How do you know?

Here are a few more Maths Problems:

## 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.

## 100 Hungry Ants…

We have been using Place Value Blocks to model numbers, solve problems and express our thinking.

We have been using manipulatives and drawings to explain our strategies for decomposing and regrouping.

We wondered how we might express our ideas, create and share stories about number.

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, we documented our thinking using Base 10 Blocks, pictures, words and numbers.

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

Here are a few stories…

## 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?

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

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

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.”

Student Responses:

What might your Base 10 Block structure look like?

What is the value of YOUR structure?

## Pattern Block Designs

The students were invited to use Pattern Blocks to create designs. Each pattern block shape had a value. The complete design needed to have a total value of 24, 40 and 60.

Next, the students completed a bar graph using the information in their Pattern Block design. Finally they wrote a number sentence that reflected the data they collected in their graph.

Instructions:

1. Use Pattern Blocks to create 3 shape designs that have a value 24, 40 and 60.
2. Take a picture of your designs.
4. Complete the graph to show how many shapes you used in your design.
5. Write a number sentence that reflects the data collected in the graph.

Creating the designs involved a lot of problem-solving, thinking, calculations and conversations. Here are some Student Responses:

What designs might YOU create?

What is the SUM of YOUR design?

## The Value of a Number

We have been exploring how the position of a digit within a number determines its value. The following task encouraged the students to find different ways to ‘SHOW’ numbers.

We began by rolling three dice to find the 3 digit number that will be represented in different ways.

Here are some examples of student work:

Next, we wondered if there were different ways to ‘SHOW’ a number.

Could we show 253 in a different way by changing the tens?

What if it had 2 hundreds and 4 tens? How many ones would you need to have so it is still 253?

How might we decompose the following numbers into hundreds, tens, and ones and then find a different way to show each one by changing the hundreds or tens digit?

G2 Number Vocabulary Cards

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