Building a Mathematical Learning Community

Grade 6

Table of Contents

2. Introduction

3. Overview

• Lesson #1 - Self Awareness & Self Identity

• Lesson #2 - Identifying & Managing Emotions

1. Slide Deck Purpose

• Lesson #5 - Maintaining Positive Motivation & Perseverance

• Lesson #3 - Identifying & Managing Emotions

• Lesson #4 - Maintaining Positive Motivation & Perseverance

• Lesson #6 - Building Relationships & Communication

4. Building Community Lessons

• Lesson #8 - Think Critically & Creatively

• Lesson #7 - Building Relationships & Communication

• Lesson #9 - Self Awareness & Self Identity

Slide Deck Purpose

This slidedeck is intended to walk you through building a math community.

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The anchor charts you build during these few weeks should be addressed and referred to on a regular basis.

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The Minds On and Consolidation activities were designed for you to easily adapt the topic and use them throughout the year, not only in math but in all subject areas.

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Fostering Overall Well-Being

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“There is strong evidence that developing social-emotional learning skills at school contributes to all students’ overall health and well-being and to successful academic performance. It also supports positive mental health, as well as students’ ability to learn, build resilience, and thrive”

The Ontario Curriculum, Grades 1-8: Mathematics, 2020

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Social Emotional Learning (SEL) is one component of supporting well-being. It is important that we continue to develop positive relationships with peers and caring adults throughout the year.

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The five SEL skills that we will be focusing on during the first few weeks, and that will continue through the year are:

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• Self Awareness & Self Identity
• Identifying & Managing Emotions
• Maintaining Positive Motivation & Perseverance
• Building Relationships & Communication
• Think Critically & Creatively

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*For more information & suggested tasks Click HERE

Introduction

Part 1

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Equity, Diversity, & Inclusion

WRDSB educators can build equitable, inclusive, and anti-oppressive learning communities within the framework of Culturally Responsive & Relevant Pedagogy (CRRP). For more information see the WRDSB’s Comprehensive Approach to Mathematics.

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“Culturally responsive and relevant pedagogy (CRRP) reflects and affirms students’ cultural and social identities, languages, and family structures. It involves careful acknowledgement, respect, and understanding of the similarities and differences among students, and between students and teachers, in order to respond effectively to student thinking and promote student learning.”

The Ontario Curriculum, Culturally Responsive & Relevant Pedagogy (CRRP)

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“In mathematics spaces using CRRP, students are engaged in shaping much of the learning so that students have mathematical agency and feel invested in the outcomes”

The Ontario Curriculum, Grades 1-8: Mathematics, 2020

Ontario Math Curriculum

Introduction

Part 2

Overview - Week 1

Overview - Week 2

Self Awareness & Self Identity

Day 1

Self Awareness & Self Identity

• Identify how their strengths as learners, and their interest in mathematics, help them develop confidence and a positive identity as a math learner.

B1 Number Sense

• Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.

Social Emotional Learning Focus:

Essential Key Mathematics Concepts Focus:

Curriculum Connections

Preparation & Materials:

• Preview lesson and click through any animations
• Student Mat (Concept Circles, 1 per student, 3 versions to offer choice & differentiate)
• Collect
• Chart Paper & Markers (to build a “What is math?” anchor chart)

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Instructions:

• Introduction:
• Whole class brainstorm “What is math?” to build an anchor chart or build a digital version using a tool like Canva. Post it so students can reflect on it today and over the next few weeks.
• Minds On:
• Which One Doesn’t Belong routine, Numbers 17 Prompt students to give reasons why each number doesn’t belong to the set. Record all responses so students see that all student thinking is valued.
• Action:
• Concept circle routine with different representations of numbers. If concept circles are new to you, see page 190 in Teaching Math with Meaning by Cathy Marks Krpan or watch this video.
• Consolidation:
• Gallery walk routine of students’ concept circles. As they observe others’ circles, ask them to look for a representation that many people used and a representation that they found interesting.
• Reflection:
• Students add a dot (with a marker or sticker) to an area of math that they feel a connection to (something they enjoy, something they use etc.). Or you could poll that class and have students raise their hands for their area of math.

Teacher Instructions

Student Mat

Student Mat

Student Mat

What is Math?

Create an anchor chart on paper or using a digital tool

Introduction

Source: talkingmathwithkids.com

Which one doesn’t belong?

Can you find reasons why each number doesn’t belong?

A

C

D

B

Minds On

Concept Circles

How can we represent the number in different ways?

48

12 × 4

96 ÷ 2

How can you decompose the number?

How can you represent it using manipulatives or drawings?

What expressions can you make to equal the number?

How else can you represent the number?

Source: Teaching Math with Meaning by Cathy Marks Krpan

Action

Concept Circles

Your turn: choose a number between 1000 and 100 000. Choose a concept circle template. Write your number in the centre and represent it differently in each section.

Ideas…

• Decompose the number
• Represent it with a drawing
• Create expressions that are equal to your number

+ − × ÷

Source: Teaching Math with Meaning by Cathy Marks Krpan

Action

Gallery Walk

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Display your completed concept circle

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As you walk around to observe everyone’s work…

• look for a representation that many people used
• look for a representation that is interesting

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Remember:

• Pause to observe each circle for about 10 seconds
• Walk silently - save your comments for our whole class discussion

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Consolidation

Gallery Walk Discussion

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Return to your seat

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Raise your hand to share…

• a representation that many people used
• a representation that is interesting

Consolidation

What is math?

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Where is the math in your concept circles?

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Let’s look at our “What is math?” anchor chart again…

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Do we need to add anything?

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What type of math do you connect with the most? Put a dot next to it on the anchor chart.

Reflection

Identifying & Managing Emotions

(Recognizing Sources of Stress and Coping with Challenges)

Day 2

Identifying & Managing Emotions

• Students can express and manage their feelings, and show an understanding of the feelings of others, as they engage positively in mathematics activities.
• Student can work through challenging math problems, understanding that their resourcefulness in using various strategies to respond to stress is helping them build personal resilience.

Social Emotional Learning Focus:

C1 Patterns and Relationships

• Identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts.

Essential Key Mathematics Concepts Focus:

Curriculum Connections

Preparation & Materials:

• Preview lesson and click through any animations
• Collect
• Chart Paper & Markers (to build anchor charts for Independent Work and a “Feelings chart”)
• Cuisenaire (Relational) Rods
• Graph Paper or Grid Whiteboards & Markers

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Instructions:

• Introduction:
• Create a poster for Independent Work with the class.
• Minds On:
• Which One Doesn’t Belong routine, Photos 5. Prompt students to give reasons why each image doesn’t belong to the set. Record all responses so students see that all student thinking is valued.
• Action:
• Rod Trains from youcubed.org. Students work independently. Introduce the grid and explain that their task is to make the longest path across the grid while following the rules. Pause while students are working and ask people to share hints with others. If time, extend the task to grids of other sizes.
• Consolidation:
• Debrief strategies to make the path longer. What advice would you give someone working on this task?
• Reflection:
• Create feelings chart with 3 columns for low mood, regulated or calm mood, and heightened mood. Ask students to name some emotions in each category. You could use lesson 1 from Zones of Regulation.
• Here’s a “feelings wheel” that may be helpful to generate ideas.

Teacher Instructions

Create an anchor chart on paper or using a digital tool

Independent Work

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What does independent work mean?

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What does it look like? Sound like? Feel like?

Introduction

Source: talkingmathwithkids.com

Which one doesn’t belong?

Can you find reasons why each set doesn’t belong?

A

C

D

B

Minds On

Rod Trains

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You have rods of unit �lengths from 1 to 10.

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How many different rod trains can be made from any length of rod?

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For example, you can �make these 4 trains �for the 3-rod.

Source: youcubed.org

Action

Rod Trains

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What strategies did you use?

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How did you know when you had found all possible trains for a unit rod?

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What would have been helpful as you were working?

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What strategies did not work?

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How did you record your work?

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How did you feel as you were working on this task?

Source: youcubed.org

Consolidation

Feelings Chart

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We all experience a variety of feelings throughout the day.

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Where would you put the following feelings?

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Add your own feelings to the list.

tired

cheerful

frustrated

angry

thoughtful

optimistic

bored

lonely

proud

discouraged

Create an anchor chart on paper or using a digital tool

Reflection

Identifying & Managing Emotions

(Recognizing Sources of Stress and Coping with Challenges)

Day 3

Identifying & Managing Emotions

• Students can express and manage their feelings, and show an understanding of the feelings of others, as they engage positively in mathematics activities.
• Student can work through challenging math problems, understanding that their resourcefulness in using various strategies to respond to stress is helping them build personal resilience.

Social Emotional Learning Focus:

C1 Patterns and Relationships

• Identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts.

Essential Key Mathematics Concepts Focus:

Curriculum Connections

Preparation & Materials:

• Preview lesson and click through any animations
• Print
• Dice Train Student Page (for groups to use as a reference)
• Collect
• Lots of dice (at least 4 per group of students)

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Instructions:

• Introduction:
• Video Believe in Yourself from youcubed.org.
• Minds On:
• Number talk routine: How many dots? Prompt students to describe how they saw/grouped the dots and how they determined how many there were.
• Action:
• Dice train from NRICH. Students will work in partners or small groups to build as many dice trains as possible with 4 (or more) dice. Go through the slides explaining the rules. Print out the rule paper for groups to have copies.
• Consolidation:
• Debrief the number of trains they could make, the strategies they used, and how they kept track of their work.
• Reflection:
• Add situations to yesterday’s feelings chart. Ask students to reflect on today’s math class and identify situations that evoke different feelings, as well as other situations they experience at school. Add those situations to the chart. It is important to accept and validate that different people will have different feelings in the same situation or on different days. Just notice how we can link some situations to some feelings. You could use lesson 7 from Zones of Regulation.

Teacher Instructions

Dice Train

Source: NRICH

RULES

1. Faces that touch each other have the same number.

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• The number on the top of the funnel must equal the total of the numbers showing on top of the remaining dice (carriages).

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• Always use four or more dice so you have at least two 'carriage numbers' to add up.

Obeying all the rules, how many solutions are possible?

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You can make models with 4 dice or you could make it longer. Each train must have the funnel on top of the front dice.

Funnel

Carriage

Student Page

Play the video Believe in Yourself

Believing in ourselves is very important for our brain to grow.

Think of a time when you believed in yourself. What was the activity?

Was there a time when you surprised yourself with what you could do?

Introduction

How many dots?

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How do you see them grouped?

How did you find the total number of dots?

Source: ntimages.weebly.com

Minds On

How many dots?

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How do you see them grouped?

How did you find the total number of dots?

Source: ntimages.weebly.com

Minds On

How many dots?

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How do you see them grouped?

How did you find the total number of dots?

Source: ntimages.weebly.com

Minds On

Dice Train

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This dice model represents an old �blue steam train with a white funnel�on the engine at the front.

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The dice that make up the train �are joined using three rules:

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• Faces that touch each other have the same number.
• Underneath the white dice is a 3 touching a 3 on the blue dice.
• The blue dice has a 6 on the face that touches the 6 on the middle blue dice.
• The middle blue dice has a 1 that touches the 1 on the last dice.

Source: NRICH

Funnel

Carriage

Action

Dice Train

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This dice model represents an old �blue steam train with a white funnel�on the engine at the front.

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The dice that make up the train �are joined using three rules:

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• Faces that touch each other have the same number.

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• The number on the top of the funnel must equal the total of the numbers showing on top of the remaining dice (carriages) that can be seen.
• The 4 on top of the funnel equals the two 2's on top of the blue carriages.

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RULE 3: Always use four or more dice - so you have at least two 'carriage numbers' to add up.

Source: NRICH

Funnel

Carriage

Action

Dice Train

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This dice model represents an old �blue steam train with a white funnel�on the engine at the front.

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The dice that make up the train �are joined using three rules:

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• Faces that touch each other have the same number.

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• The number on the top of the funnel must equal the total of the numbers showing on top of the remaining dice (carriages).

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• Always use four or more dice so you have at least two 'carriage numbers' to add up.

Source: NRICH

Funnel

Carriage

Action

Dice Train

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Obeying all the rules, how many solutions are possible?

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You can make models with 4 dice or you could make it longer. Each train must have the funnel on top of the front dice.

Source: NRICH

• Faces that touch each other have the same number.

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• The number on the top of the funnel must equal the total of the numbers showing on top of the remaining dice (carriages).

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• Always use four or more dice so you have at least two 'carriage numbers' to add up.

Funnel

Carriage

Action

Dice Train

How many trains were you able to make with 4 dice?

What strategies did you use to build the trains?

How did you keep track of your work?

Could you make a different number of trains when you used 5 or more dice?

Consolidation

Feelings Chart

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We all experience a variety of feelings throughout the day.

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Are there more feelings we should add to the chart?

Let’s think about situations that you might experience at school.

• As you were working on math today, what feelings did you experience? Let’s add “working on math” and “working with partner(s)” to the chart. What column(s) should we put those situations in? Describe why it belongs in that column.
• What other situations do you experience at school? Let’s add a few more situations to the chart.

Reflection

Maintaining Positive Motivation & Perseverance

Day 4

Maintaining Positive Motivation & Perseverance

• Students recognize that testing out different approaches to problems and learning from mistakes is an important part of the learning process, and is aided by a sense of optimism and hope.

B1 Number Sense

• Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.

B2 Operations

• Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.

Social Emotional Learning Focus:

Essential Key Mathematics Concepts Focus:

Curriculum Connections

Preparation & Materials:

• Preview lesson and click through any animations
• Print
• Student Page (1 per pair)
• Collect
• Chart Paper & Markers (for the Helpful and Unhelpful Thoughts anchor chart)
• Paper or Whiteboards & Markers

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Instructions:

• Introduction:
• Brainstorm helpful and unhelpful thoughts for persevering with a challenging task at school. Create an anchor chart with your lists. Source: School Mental Health Ontario.
• Minds On:
• Number talk routine: Doubling and Halving. Source: Number Talks by Sherry Parrish, page 278. These number strings encourage students to notice the commutative property in multiplication and that when one factor is doubled and the other is halved, the product stays the same.
• Action:
• The Marching Band problem. Students work with a partner to figure out how many students are in the band. This problem highlights multiples of 7 and which numbers have 2, 3, 4, 5, or 6 as factors. Encourage students to keep track of everything they try on paper or a whiteboard.
• Consolidation:
• Pose the discussion questions.
• Reflection:
• Encourage students to notice unhelpful thoughts and start to replace them with helpful thoughts.

Teacher Instructions

The Marching Band Problem

A marching band wants to line up for their performance.

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They tried and tried to figure out how many lines will make everything even.

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• When they line up in twos there is 1 left over.
• When they line up in threes there are 2 left over.
• When they line up in fours there are 3 left over.
• When they line up in fives there are 4 left over.
• When they line up in sixes there are 5 left over.
• When they line up in sevens there are no students left over.

How many students are there?

Record Your Thinking Here;

Student Page

Source: School Mental Health Ontario

Introduction

Helpful and Unhelpful Thoughts

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When you are working on a challenging task, what thoughts help you to continue to persevere?

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What thoughts are unhelpful and lead to giving up?

Create an anchor chart on paper or using a digital tool

Introduction

Number Talk

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1 × 16

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Source: Number Talks by Sherry Parrish

2 × 8

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4 × 4

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8 × 2

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16 × 1

How did you determine the products?

What do you notice about the numbers?

Minds On

Number Talk

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1 × 24

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Source: Number Talks by Sherry Parrish

2 × 12

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4 × 6

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8 × 3

How did you determine the products?

What do you notice about the numbers?

Minds On

The Marching Band Problem

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A marching band wants to line up for their performance.

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They tried and tried to figure out how many lines will make everything even.

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• When they line up in twos there is 1 left over.
• When they line up in threes there are 2 left over.
• When they line up in fours there are 3 left over.
• When they line up in fives there are 4 left over.
• When they line up in sixes there are 5 left over.
• When they line up in sevens there are no students left over.

How many students are there?

Action

The Marching Band Problem

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How many students are there?

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How did you solve this problem?

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What tips would you give someone who had to figure out the number of students in the band?

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How did you organize your work?

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What does this problem tell you about the number 119?

Consolidation

Replacing Unhelpful Thoughts

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Did you notice any unhelpful thoughts as you were working?

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When you notice unhelpful thoughts, try replacing it with a helpful thought from our poster.

Reflection

Maintaining Positive Motivation & Perseverance

Day 5

Maintaining Positive Motivation & Perseverance

• Students recognize that testing out different approaches to problems and learning from mistakes is an important part of the learning process, and is aided by a sense of optimism and hope.

C1 Patterns and Relationships

• Identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts.

Social Emotional Learning Focus:

Essential Key Mathematics Concepts Focus:

Curriculum Connections

Preparation & Materials:

• Preview lesson and click through any animations
• Print
• Print or Draw an Anchor Chart of the Stages in a Learning Pit
• Collect
• Decks of cards (each group of 2-4 students will need 1 suit from the deck, so one deck of cards is enough for 4 groups)

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Instructions:

• Introduction:
• Play the video to introduce a Learning Pit by James Nottingham.
• Minds On:
• Tell the class you will be doing a task that may put them in a learning pit. They need to notice how they feel as they work today. Place students in groups of 4.
• Action:
• Ace 2 3 Card Challenge. Students work in groups of 2 to 4 to arrange their cards so that they can deal them in order from A to King. The challenge? Deal one card, then put the next card on the bottom of the deck and repeat - one deal and one to the bottom until they have dealt all of the cards.
• Consolidation:
• Ask students to share how they felt at different stages in the learning pit. Record all answers to show that different people will respond differently to challenges.
• Reflection:
• Look at the list of helpful and unhelpful thoughts from yesterday. Encourage students to identify helpful thoughts that they could use when they find a task to be challenging.

Teacher Instructions

Play the introductory video for The Learning Pit

What was one thing that you want to remember about

“The Learning PIt”

Turn to a partner and share your thoughts.

Be ready to share one thing with the class.

Introduction

Learning Pit: Let’s Make Squares

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While you are working today, pause every minute or so to notice your progress on the task and how you are feeling.

Minds On

Ace - 2 - 3 Challenge

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Watch this video to see your goal today.

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Action

Ace - 2 - 3 Challenge

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How do you need to organize your cards?

Every other card goes to the bottom of the deck.

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Action

Learning Pit: Ace-2-3 Challenge

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How did you feel at the beginning of the task? Let’s add those feelings to our learning pit poster.

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Consolidation

Learning Pit: Ace-2-3 Challenge

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How did it feel at the bottom of the pit?

Consolidation

Learning Pit: Ace-2-3 Challenge

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How did it feel as you were climbing out of the pit?

Consolidation

Learning Pit: Ace-2-3 Challenge

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What did you learn as you worked through the problem? How did it feel at the end?

Consolidation

Helpful Thoughts

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Read over the list of Helpful Thoughts that we made yesterday.

Did you think or say any of them as you were working today?

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Which one(s) might be helpful to you the next time you are doing a challenging task?

Reflection

Building Relationships & Communication

Day 6

Building Relationships & Communication

• Students can work collaboratively on math problems – expressing their thinking, listening to the thinking of others, and practicing inclusivity – and in that way foster healthy relationships.

B2 Operations

• Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.

C1 Patterns and Relationships

• Identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts.

Social Emotional Learning Focus:

Essential Key Mathematics Concepts Focus:

Curriculum Connections

Preparation & Materials:

• Preview lesson and click through any animations
• Collect
• Chart Paper & Markers (to build the anchor chart for Collaboration)
• Paper or Whiteboards & Markers
• Money Manipulatives (e.g., nickels, dimes, quarters may be helpful for some groups)

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Instructions:

• Introduction:
• Create a poster for Collaboration with the class.
• Minds On:
• Number talk routine: Breaking factors into smaller factors from Number Talks by Sherry Parrish, page 283. These number strings encourage students to apply the associative property with 1 x 2 digit multiplication. Modelling the final expression in each string using an array may help students recognize that as a model they can use for the activity.
• Action:
• Watch the video poem by Shel Silverstein. Nickels, Dimes, and Quarters from Peter Liljedahl’s Building Thinking Classrooms in Mathematics, page 143. Students work with a partner or group of 3 to determine how many different ways there are to make a dollar with nickels, dimes, and quarters.
• Consolidation:
• Ask students to share the strategies they used and how they kept track of their solutions.
• Reflection:
• Review the Collaboration poster you made at the beginning of today’s lesson and reflect on how they worked during the activity.

Teacher Instructions

Create an anchor chart on paper or using a digital tool

Collaboration

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What does collaboration mean?

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What does it look like? Sound like? Feel like?

Introduction

Number Talk

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Source: Number Talks by Sherry Parrish

2 × 3 × 8

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4 × 2 × 6

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6 × 8

How did you determine the products?

What do you notice about the numbers?

Minds On

Number Talk

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Source: Number Talks by Sherry Parrish

4 × 3 × 4

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2 × 2 × 12

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8 × 3 × 2

How did you determine the products?

What do you notice about the numbers?

2 × 2 × 3 × 4

12 × 4

Minds On

Nickels, Dimes, and Quarters

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Source: Building Thinking Classrooms in Mathematics by Peter Liljedahl

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How many nickels do you need to make a dollar?

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How many dimes do you need to make a dollar?

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How many different ways are there to make a dollar using only nickels, dimes, and quarters?

How many quarters do you need to make a dollar?

Action

Nickels, Dimes, and Quarters

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How many different ways did you find? Do you have all of them? How do you know?

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What information was important to find different ways to make a dollar? How are the coins related to each other?

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How did you keep track of your work?

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What tips would you give someone who had to solve this problem?

Consolidation

Collaboration

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How did you collaborate today? Which skills did you use?

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What did you appreciate about your partner today?

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Is there anything we should add to the poster?

Reflection

Building Relationships & Communication

Day 7

Building Relationships & Communication

• Students can work collaboratively on math problems – expressing their thinking, listening to the thinking of others, and practising inclusivity – and in that way foster healthy relationships.

B2 Operations

• Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.

Social Emotional Learning Focus:

Essential Key Mathematics Concepts Focus:

Curriculum Connections

Preparation & Materials:

• Preview lesson and click through any animations
• Print
• Student Page (1 per group/pair)
• Collect
• The Collaboration poster you made yesterday
• Paper or Whiteboards & Markers

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Instructions:

• Introduction:
• Add sentence starters to the collaboration poster.
• Minds On:
• Would you rather math routine: Lemonade. Put students in their groups before starting the Minds On task. As a group, students need to communicate their preference and reasoning and listen to the other members to come to an agreement about which option they want.
• Action:
• Four Numbers from Peter Liljedahl’s Building Thinking Classrooms in Mathematics, page 81. Students work with the same partner or group of 3. They choose four numbers from 1 to 9 at random and use those numbers and any operations to make the values 1 to 30. Have them work on paper or whiteboards.
• Consolidation:
• Ask students to share how they collaborated and how their understanding changed by seeing what others were doing.
• Reflection:
• Review the Collaboration sentence starters from the beginning of today’s lesson and reflect on how they worked during the activity.

Teacher Instructions

Four Numbers

With your partner or group of 3, select four random numbers from 1 to 9.

Use ONLY these numbers and any operations to make the values from 1 to 30.

You do not need to use all 4 numbers in each equation, and you can use the same number more than once.

Source: Building Thinking Classrooms in Mathematics by Peter Liljedahl

Student Page

Collaboration

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Let’s look at the collaboration poster we made yesterday.

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Today we’re going to add some sentence starters so we can help each other work together effectively.

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When collaboration is working well, what are some things we might hear people say? What do we say to keep it looking, sounding, and feeling good?

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When collaboration is starting to break down, what might we notice? What can we say to help people work together and focus on the task?

Introduction

Discuss with your partner or group of 3. �Share your reasoning and pick ONE of the options.

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What reason was most important to you?

Would you rather have Option A or Option B?

Option A

A pitcher of 2 liters of orange juice

Option B

4 juice boxes with 250 mL of orange juice in each

Minds On

Four Numbers

With your partner or group of 3, select four random numbers from 1 to 9. Use whiteboards or scrap paper to work your thinking. Collaborate the answer on one piece of paper.

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You might come up with multiple answers. You will need to communicate and compromise on what equations you will put on your sheet.

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Use ONLY these numbers and any operations to make the values from 1 to 30.

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You do not need to use all 4 numbers in each equation, and you can use the same number more than once.

Source: Building Thinking Classrooms in Mathematics by Peter Liljedahl

Action

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1. How did you share your work with others?

2. How did someone else’s ideas or answers inspire your work?

3. I am a Mathematician!

Now We are going to do a 3 Finger Self Reflection.

Close your hand. As I talk, raise one more finger when you have thought about that question or idea.

Four Numbers Debrief

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Class Discussion:

What values were you able to get? Were there numbers that were harder to get? Why?

Consolidation

Collaboration Sentence Starters

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What sentence starters did you find helpful when collaborating with your partner(s)?

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What communication was NOT helpful? Why not?

Reflection

Think Critically & Creatively

Day 8

Think Critically & Creatively

• Students are able to approach problems from different perspectives and connect real life contexts to their mathematical understandings to help them make informed judgements/decisions.

B2 Operations

• Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.

C1 Patterns and Relationships

• Identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts.

Social Emotional Learning Focus:

Essential Key Mathematics Concepts Focus:

Curriculum Connections

Preparation & Materials:

• Preview lesson and click through any animations
• Print
• Optional: Grids for Frogs (to help students track where they are)
• Collect
• Manipulatives that students can use as frogs (2-colour counters or cubes)
• Optional: Post the link to the online version of Frogs to your digital classroom

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Instructions:

• Introduction:
• Mill to Music- Play music- when the music stops have them find the closest partner. Ask a question and have them respond. Then play the music and repeat until all questions are asked. What does it mean to take risks in math class? Discuss why some risks are good (essential, even!) and how and when taking a risk would be bad.
• Minds On:
• Estimation routine: day 17 staples in a box. Ask students to estimate how many staples are in the box. What information do they have? What do they need to guess or infer? What number is definitely too low? What number is definitely too high? Can they agree on a number (or a range) as a class? Reveal the number to see if your estimate was close.
• Action:
• Frogs from NRICH. Students can work alone or with a partner. The goal is to swap the positions of the red and blue frogs in the fewest moves possible. It is important to track each move that a frog makes for students who are using manipulatives. Option: post the online version to your digital classroom.
• Consolidation:
• Ask students to share their answers and how they took risks today.
• Reflection:
• Make a poster with a risk-taking continuum. What types of risks are good? What type of risks are bad?

Teacher Instructions

Once you have a partner label yourself A and B

Walk around the classroom as the music plays. When the music stops find a partner closest to you and wait for the question.

1. Partner A goes first. Partner B listens.

What does it mean to take risks in math class?

Risk Taking in Math Class- Mill to Music

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Thank your partner. Play music. When music stops find a new partner.

3. Decide with your partner who goes first.

When would it be a bad time to take a risk? Why or how would it be bad?

Thank your partner. Play music. When music stops find a new partner.

Introduction

How many total staples come in the box?

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Estimate how many staples are in the box.

What information do we have?

What number is definitely too low? What number is definitely too high?

What range can we agree as a class?

Reveal Answer

Minds On

Frogs

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There are 2 brown frogs and 2 green frogs sitting on lily pads, with one space between the groups.

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You have to swap the green frogs with the brown frogs, BUT there are some rules:

• A frog can only move one square at a time.
• A frog can jump over just one frog of a different colour (at a time).
• All frogs can only move forwards from the direction they start in.

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What is the smallest number of moves it takes to swap them over?

Source: NRICH

Action

Frogs

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Try it with 3, 4, or 5 frogs on each side.

What is the smallest number of moves it takes to swap them over?

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• A frog can only move one square at a time.
• A frog can jump over just one frog of a different colour (at a time).
• All frogs can only move forwards from the direction they start in.

Source: NRICH

Action

Frogs

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What helped you work on this challenge? What tip or strategy would you give to someone starting this task?

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How did you take risks today? �How were the risks helpful to your learning?

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What would have happened if you hadn’t taken �any risks at all?

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Did you take any risks that you think were bad risks? If so, how were they bad?

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Consolidation

Create an anchor chart on paper or using a digital tool

Risk Taking in Math Class

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Record examples of bad risks and good risks under the two ends of the continuum.

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Are there risks that belong in the middle? Discuss.

Source: Building Thinking Classrooms in Mathematics by Peter Liljedahl

Reflection

Day 9

Self Awareness & Self Identity

Self Awareness & Self Identity

• Identify how their strengths as learners, and their interest in mathematics, help them develop confidence and a positive identity as a math learner.

C1 Patterns and Relationships

• Identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts.

Social Emotional Learning Focus:

Essential Key Mathematics Concepts Focus:

Curriculum Connections

Preparation & Materials:

• Preview lesson and click through any animations
• Print
• Student Page - New WODB (1 per student)
• Collect
• What is Math? (poster from the first day of school)
• Paper or Whiteboards & Markers

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Instructions:

• Introduction:
• Video: Speed is Not Important from youcubed.org
• Minds On:
• Math Connections routine: instead of asking students which one doesn’t belong in a set, introduce you are looking for a tie for two - something that 2 of the items have in common. Then look for a thread for three - something 3 of the items have in common. Finally, what unites all for items?
• Action:
• Our Connections: in groups of 4, students will ask each other questions to find something that 2 people have in common, something that 3 people have in common, and something that all 4 of them share, as well as something unique about each person. Physical characteristics are NOT allowed.
• Consolidation:
• Gallery walk to see the different connections people have.
• Reflection:
• Look back at the What is Math? Poster you made on the first day of school. Ask each student to reflect on a way in which they are a mathematician.

Teacher Instructions

Talk to each other to find something that is unique about each person.

Write it with the person’s name in the grid.

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Find a tie for two people, a thread for three people, and a fit for

four people and write them beside the grid.

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Do NOT include physical characteristics (hair colour, height etc.)

Student Page

Watch the video Speed is not important

Discuss with a partner the idea that math is NOT about speed.

What is important in math is to think carefully, deeply, and make connections.

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Introduction

Math Connections�(the opposite of Which One Doesn’t Belong)

Sources: Presentation by Lido Valencia at OMCA, February 2025

Article: Putting the Belonging Back Into Which One Doesn’t Belong? By Delise Andrews & Karla Bandemer

Minds On

Math Connections�(the opposite of Which One Doesn’t Belong)

A

C

D

B

Source: Presentation by Lido Valencia at OMCA, February 2025

Minds On

Our Connections

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In your group of 4, draw a grid and write your names in it. Talk to each other to find something that is unique about each person. Write it with the person’s name in the grid.

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Find a tie for two people, a thread for three people, and a fit for four people and write them beside the grid.

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Do NOT include physical characteristics (hair colour, height etc.)

A

C

D

B

Action

Gallery Walk

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Display your connections

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As you walk around to observe everyone’s work…

• look for something that links many people
• look for a connection that is unusual or interesting

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Remember:

• Pause to observe each group’s connections
• Walk silently - save your comments for our whole class discussion

Consolidation

Gallery Walk Discussion

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Return to your seat

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Raise your hand to share…

• something that links many people
• a connection that is unusual or interesting

Consolidation

I Am a Mathematician

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Review the poster “What is math?” from the first day of school.

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Has your opinion about math changed over the past 2 weeks? Are there examples to add to the poster?

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Take a moment to think about the ways that YOU use math: You ARE a mathematician!

Reflection