Combining Two of My Favourite Things: Building Thinking Classrooms and Set of Problem Solving Questions as Homework

A few years ago I read about the research of Peter Liljedahl, a professor at the Faculty of Education at Simon Fraser University in Canada. His Building Thinking Classrooms has been something that I have been exploring in my own classroom for about two years. I love the idea that "The person thinking is the …

For the Love of Ratios

I love teaching ratios. I begin with an image like the one below and use the "Stand and Talk" routine by Sara Van Der Werf. I ask the students "What do you Notice? What do you Wonder?" Students always impress me with their thoughts and ideas and after writing down their ideas, we look at …

Algebra: An Introduction through Patterns

Exploring patterns is a huge part of being a mathematician. Students are introduced to new concepts by investigating patterns and determining generalisations. Patterns can introduce students to the concept of variables and algebraic notation In grade 6, we introduce the concept of algebra through a unit called 'Puzzles and Balances'. We begin the unit with …

Brain Boosters

Brain Boosters is my term for starters at the beginning of the class. I tell my students that we are massaging their brain and preparing for the learning ahead. We normally spend 5-10 minutes on our Brain Boosters although there are classes where they take a bit longer. Brain Booster Idea 1: Numeracy Puzzles. I …

An Introduction to Exponents

Using different forms of mathematics notation can be challenging for students. In grade 6, we introduce students to exponential form. In order to give context for the students I begin by setting my students a challenge: How many times is it possible to fold a piece of paper? I love watching my students' focus as …

Mean, Median and Mode

Teaching middle school, most of my students entering my classroom having experienced find the mean, median and mode of data. During our unit "How Mathematician's Investigate", we explore these concepts more deeply. Most students' initial response is that they know everything about mean, median and mode. However, upon further questioning and reasoning, it is clear …

Using Colours and Visuals to Determine Algebraic Generalisations

I will write a post later about how I introduce my students to algebra, but at the moment I am planning the first unit of the year for my seventh graders. They have already had an introduction to algebra, but I like to revisit the idea of using visuals and colours in order to understand …

Quiet Thinking Time

I am a huge advocate for quiet thinking time in the classroom. I love collaboration, but argue that quiet time where students can think about their own learning is just as powerful. Susan Cain is a huge advocate for introverts. I have read both her book Quiet as well as her book Quiet Power: The …

Engaging with Circles

My students have been learning about circles - what makes a circle unique when comparing it to other shapes? They have been learning at their own pace while engaging in Geogebra activities and investigating the circumference and area of a circle. Cheeseballs After a week of independent learning and helping small groups of students with …

Connections between Writing and Mathematics

Teachers at my school's elementary campus have been working with Matt Glover on professional development involving children's writing. We were fortunate to have him join us in the middle school for a short session this week. During his discussions with us, I was constantly reflecting on how much the development as a writer is so …

A Learner’s Mathematics Toolkit

What is a mathematics toolkit? In our middle school, each student has a toolkit for mathematics class. It is a basic A5 scribbler (small notebook) and it serves as a reference, teaches reflection skills and calms anxiety during an assessment. What do we include in it? As a class, we, the teacher and students, decide …

Integer Adventure Continues

Although my students made so many connections to adding and subtracting integers with the balloon game, I like to give them different approaches to facilitate learning. Algebra Tiles I love mathematical manipulatives. My favourites are dice, my red/yellow and tokens (which I use for everything), but algebra tiles are right up there on my list …

Using Games to ‘Practice’

I put practice in quotes, because I really think it is more about consolidating understanding, which I suppose is what we mean by practice. Mark Chubb wrote a great article about the role of practice in mathematics class. For me, the word practice brings up ideas of completing 20 similar questions in a mathematics textbook …

Integer Adventures

This year, I used NRICH's 'Up, Down, Fly Around' Balloon game to introduce addition and subtraction of integers. I met Fran and Charlie from NRICH during a mathematics conference in Vienna last year and they are as lovely as their problems are rich. Since every class is different, I gave the game my own unique …

Integers and language

I was chatting with my friend Michelle about learning mathematics. Integers came up and the discussion led to the use of language when introducing a new mathematical concept to someone. The difficulty we were discussing was in relation to integers; why do educators sometimes use the terms 'minus 3' when referring to -3? When students …

Mixed Numbers – why do they exist?

We recently had Monica Neagoy visit our school to do workshops with our junior and middle school teachers. During the PD session, the conversation turned to mixed numbers and the fact that they tend to only exist in English speaking countries. I teach with a colleague from Italy and have had discussions about different mathematical …

The Start of Integers

Here is a problem I use to introduce integers. I never tell my students what we are learning, I just give them the problem and see what they can find. (we sing itsy, bitsy spider first) If a spider climbs 3 metres up a waterspout during the day, then slides back down 2 metres every …

Multiplying Fractions

My journey of fractions continues. This post is focusing on multiplication of fractions, again using students previous understanding of whole numbers. Whole number by a whole number I love the area model for multiplication. We start with a simple problem such as (2)(3) Whole number by a fraction I have been using Alice in Wonderland …

Dividing Fractions

When I did my Masters of Education, I wrote a paper on fractions and explored the research surrounding the challenges that students have with fractions. Since that time, I have grown in my own understanding of how best to guide students in their understanding of fractions. To start, I am going to focus on division …

The Starting Line

This is my attempt at sharing ideas of teaching mathematics conceptually, building on student's previous understandings. My focus is on proof and reasoning and my students know that my favourite question to ask them is "WHY"? I have been teaching mathematics for a long time. Some of my ideas I have been using, and tweaking, …