Teach Math with Spiralled 3-Act Tasks – a full course

This semester was my first go at spiralling a course through problems instead of units. Traditionally we teachers follow the chapters and sections from the textbook. Well why not? It’s all laid out and organized nicely….most times in 1 day chunks….no planning needed, am I right???

How exciting is it though? How much do students really need to think? Are they really solving problems and learning mathematics.

After reading about spiralling from Alex Overwijk and bouncing ideas back and forth with Kyle Pearce we decided to give spiralling 1P math with 3 act tasks a try.

Each day or two I would  introduce to a new 3-act math problem (read Teaching with 3-Act Tasks) to solve with students. We would use that to stimulate wonderings and finally narrow down to a particular goals I wanted to cover.  Each of these lessons is taught with a 4 part math lesson (From Kyle Pearce) which always has students working on solving problems on their own FIRST, and then we step in and teach skills (“math teachery” way) after.

We did not teach within units. We mixed up our 3-Act tasks and problems throughout the semester.

I kept a list of all lessons, and order I used, along with any resources like blog posts, video files, handouts, etc. I wanted to share that list below.

Spreadsheet design was by Kyle

The spreadsheet shows for each day,

  • the strand we covered,
  • the learning goal (LG – for my assessment sheet),
  • the topic, notes for planning,
  • the inquiry lesson portion (3-Act math problem(s))
  • connections to other strands (a place for me to remind myself to tie this piece to other strands)
  • the consolidation/practice resources/links
  • other resources like blog posts, handouts, links, tweets, etc.

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You may notice the bright pink row. These are our assessment/mastery days. We had one whole class each week for this.

The first half of an assessment/mastery day class was handing back of past paper assessments that look like:


Each one consisted of 4 questions that covered the learning outcomes of the last week or so.  I wrote feedback for any question that weren’t completed perfectly. They were to read the feedback and re-do those questions.

I let them know that everything counts…..I consider all our conversations, my observations and anything they hand in for their grade.

Also during the first half of class students worked towards upgrading their skills. They access their customized spreadsheet which shows their achievement on each of the learning goals. They choose a learning goal to upgrade. Based on their prior achievement they are given another task to try. After I assess this new task I go and change the mark for that learning goal.

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Both Kyle and I have written posts on this sheet a few times. (here, here, and here). An idea we extended from Alice Keeler.

We spend a good chunk of time working at getting better on our skills always promoting growth!

The last half of the class we do this week’s paper assessment (that looks like the one above). I mark it and give it back so that next Tuesday we can do that all over again.

Here are some benefits I have noticed from both spiralling and teaching through problem solving:

  • Almost no need to review at the end of the year. We reviewed all through.
  • Students see how math connects together. (Proportional reasoning shouldn’t stand as a lone unit when you have linear relations and algebra to teach too!).
  • Students were more confident in math than I’ve ever seen them. (And for 1P’s too!). When teaching in units, students know that whatever problem we will solve today HAS to do with what we learned yesterday. When we teach through spiralling students are always wondering what math they can use to solve the problem at hand. My students became great at risk taking! They would try! How many times has it been where we give a new problem to our students they complain that you haven’t shown them how to do this. My students were given new problems everyday and they became great a trying strategies. Whiteboards help immensely with this too!
  • A time saver! You may think that I would run out of time teaching this way…..I couldn’t possibly teach through problem solving and still cover everything, let alone booking a whole day dedicated to growth EACH WEEK! We had lots of time. Since each lesson tied multiple expectations and learning goals together, we could cover more in one lesson than we could in two lessons the old way. The growth/upgrades each week allowed students to practice skills from all over the course. Around mid-term time I gave my students an old final exam to see how they would do, and they did great!!! I was amazed. We still had half a semester to go!

Since we are coming close to the end I wanted to share my experience! Feel free to check out my daily plan from grade 9 applied

As always, if you have any recommendations or feedback for me I would love to hear about it!



Hidden Beads!

I’ve had an amazing teacher candidate (@misschacon_7) paired with me for the last two weeks. Every day she comes excited to try and learn new things. Today she came in with a great lesson for solving multi-step equations. Here is her activity:

She paired up students by randomly assigning them a playing card……each person was to find their match. Each pair went to one of our vertical writing surfaces (blackboards and whiteboards) where she asked students to solve a series of problems like….

How many marbles in each bag?

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She then gave them all sets of cups and beads.


Player 1 is to create an equation by hiding the same number of beads in the cups. They also have to ensure each side (whiteboards) must balance (have the same number of beads total).

Player 2 is to “figure out” how many beads are in each cup.

After player 2 has determined how many, they switch roles and start again.

Here is a round:

Player 1 sets up this up (she decided to put cups inside cups so we couldn’t see how many beads)


Player 2 starts on it….



and she ended up with….



and the answer??


Lots of great thinking going on here…..especially for the creator of the equation. Here is a group who realized there was a problem…



While player 2 was solving, she realized that she was getting a negative answer for the number of beads. Weird!!! So we asked player 1 if she made sure they boards were balanced to begin with……ooops they weren’t. So they couldn’t have been equal to start with! Let’s re-do.




Miss Chacon worked the room awesomely….visiting each group and asking probing insightful questions! My students were sad to see her go….today was her last day. We’ll miss you Miss Chacon!

Speedy Squares

Last week I attended the annual OAME (Ontario Association of Mathematics Educators) in Toronto. It was so great to finally meet some of the people I’ve been tweeting with.

I was pumped to attend Mary Bourassa’s double session on great classroom activities. One of the activities that I’ve seen on her blog, but not used in my own classroom was Speedy Squares. So when I had an opportunity to try it, I jumped on it!

There is something special about doing the lessons yourself while learning about a lesson at a conference.

Read about the lesson:

You can read about the lesson on her blog here part 1 and here part 2.

The big question: We want to determine how long it will take to build a 26 x 26 square out of link cubes.

More Curious

While actively building the squares I had a great idea to make the introduction to the activity a little more curious! So when I got back to my classroom I broke out the cubes and created this….

Maybe before the time trials of building the squares, we can dive into generating questions and wonderings first.

  • What is he making?
  • How many squares will he use?
  • How long will it take?

Now that we have generated questions….we can then move onto Mary’s awesome two day lesson.

Once students have got an answer to how long they would take to build the 26 x 26 square, you could show the video of me building it!

I’m really interested to see if elementary teachers can use this in their classes and what they come up with!

Trashketball – A Spiralled Lesson!

This was our multi-day, curriculum-spiralled, activity this week!

Day 1 – Filling the Bin!!

Let’s get curious!!…..I showed this video from Andrew Stadel, and took questions & wonderings:

We settled, (I chose) on the question on how many paper balls would fill a bin! They made predictions, too high, too low and right on!

They made paper balls and found their diameter. We agreed that each ball could be different so we recorded everyone’s diameter and averaged them to give the “average ball size”


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