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After reading some articles lately on the LD learner and early math, I decided to make some cards to help students develop well connected number paths. This lead to some thinking around setting up a ‘number path placemat’ as well so that students can use a placemat to help illustrate their path to their thinking.

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Number Path Placemat


Number Path Cards


The intent for the cards is that they are laminated, the placemats are to be laminated but with shiny lamination paper so that you can use dry erase markers on it. These are to be used in conjunction with number lines (both horizontal and vertical) and messy math bins.

In class uses so far:

  • Used for manipulative based number talks
  • Helps to bridge gaps for students who are developing an understanding of number symbols (replaces cards in a number deck for fluency games)
  • More or less games to develop magnitude
  • Build connections between representations
  • Connects physical to illustration which helps to give students ways to develop a path to concreteness fade.

Manipulative Based Number Talk




Money Path Cards

I wanted to thank several of my colleagues for the articles and for a great discussion that made me want to figure out how to write down how I was ‘seeing’ for the connections in Kathy Richardson’s conceptual development webs.

Download resources here:

Number Path Cards

Number Path Placemat

Money Path Cards (without pennies)

Articles that inspired:

Evidence-Centred Assesmsent by Kimberly Morrow-Leong (2016)

Three Steps to Mastering Multiplication Facts by Gina Kling and Jennifer M. Bay-Williams (2015)

Thanks for reading!

Kat Hendry





Measurement Activity

This is a task that I recently completed with my grade nines.

Before starting the task we discussed the task as a class, students were invited to ask clarifying questions, and students were given the materials at stations to measure what they needed to so that they could complete the task.

See assignment sheet attached here.Measurement In Class Assignment

Things that went well: Student engagement was high, students were focused. Interested in the task. Students discussed problems that they were having with each other. Not as many students were looking for me to check if they “got it right”.

Things that need improvement: Timing – the whole class needed to be dedicated to the activity. I spent too much time discussing the problems. In hindsight, I needed to let the class spend more time discussing the problems and take myself out of the discussion. In future, I might even record myself to explain the task, then answer questions on a time limit to give myself a time limit and not become the spoiler of great math explorations!

Now that I have photos of the built models that students worked with at stations, I would swap my images in the assignment sheet so that the models are more accurately represented on the assignment itself.

The Net of the Cereal Dispenser:


The Cafe Cereal Dispenser:


Mrs. Hendry’s Model House:

IMG_4067 IMG_4068 IMG_4069 IMG_4070 IMG_4071

Portable Wipe board Activity: Creating an algebraic representation from two points on a line.


In pairs or threes, use the portable wipe boards to demonstrate a graphical method of determining the equation of a line given two points.

On the back of this page confirm this with by writing out an algebraic strategy.

Team A: (1,2),(5,-10)

Team B: (-2,-18),(5,31)

Team C: (4,-12), (-3,2)

Team D: (-2, -10), (4,26)

Team E: (3,-5),(8, 15)

Results and Reflection:

Students all understood how to graph the line based on the two points. That was excellent for what I was looking for as I had not taught how to build the equation of a line from two points at this point in the course. 

Some students demonstrated that they could build the equation of a line without being formally taught. So the question I pose now….. Do I teach them again when I am teaching the rest of the class how to do this formally or do I give them an independent lesson to push their understanding and challenge them? What if their formal algebra suffers because I moved them on too fast? In grade nine math is the conceptual understanding more important? Or the algebra skills?

In my opinion, they are both important but for some students one will outweigh the other.  A few students I have are brilliant but struggle to write evidence down…. they need to see the formal side of algebra so that it can open their level of understanding up and they won’t make order of operations (or inverse order of operations) errors . My focus is on the order of operations and gradually over the program to make this work become formalized so that students will become transitioned into better mathematical writers than when they entered the class.

So to answer my question – what do I do with the students that already built the correct equation of the lines?

Those kids will get accelerated homework for a night after this activity that will teach them how to formalize the process and to check their conceptual understanding, if that homework is completed successfully the student moves on to independent student, challenge problems or activities while his/her peers might have a formal lesson/investigation.

We did repeat a similar activity at the beginning of class the following day to ensure that students understood how to build equations of a line from two points or two characteristics.

Many manufacturers make wipe boards with one side blank and a one by one grid on the other side. You can use dry erase markers on them, making it ideal for quick diagnostics (and you save paper).
I made mine so that I could have a few different styles of grids (one with one quadrant only and then two changing the length and width for the x and y -axis). I used one page of graph paper, one card stock page and two page size amounts of contact paper (adhesive on one side and smooth plastic on the other). I glued the cardstock and the grid paper together before covering each side with contact paper.
For minds on activities, diagnostics or consolidation! They are a fast way to have kids show a variety of representations and levels of understanding within a 10-15 time span of class. You can have students work in collaborative groups or have them work individually then check the work, make a note to see who needs to stay after class for a few minutes for a “mini-lesson”, who needs immediate attention, who needs to work on their academic vocabulary, and who needs to pick up a foundational skill from previous years. These wipe boards, as simple as they are, have been one of the best tools for me to identify when students are struggling (on a daily basis). Of course I think the activities must be meaning full when I use the boards, and I tend to use the boards when I have the students working on collaborative tasks as they promote conversation and accountable talk.

The activity:

A few of the data cards...

Students (in pairs or threes) were given a set of two points (both on one card) on a line, a random slope, a random y-intercept and told they were to confirm or deny if they had the correct characteristics that went with their set of points. If they were not the correct characteristics, students are allowed to “steal” (or trade) their characteristic from another group. Once they had the points, characteristics and built an equation of a line to confirm (or somehow showed evidence) they were to confirm with the instructor.

Work and MaterialsStudents worked very hard during this activity.Working Away


Part 2:
Students confirmed Part 1 by giving the linear equation in slope intercept form. Once they did this, I posed another question.
“What would you have done differently if I had only given your group the set of points and the equation of a line?” “How would you confirm or deny they were a match?”
I walked away from the students – some instantly called me back with a variety of answers, and some spent a few minutes thinking about what tools they would select to solve this new problem.

What if I only gave you these cards....?

Some evidence on the calculator?

The Ask-Auto method of confirmation!


– data cards (file attached)

Game – matching slopes, matching y-intercepts to lines from two points or two characteristics

– graphing calculators (had already taught students how to use the table feature).
– graphing paper (or graphing wipe boards with dry erase markers)

Game – matching equations and characteristics

I tried this matching activity with my grade nine academic math class just a few weeks ago. It was very successful as it allowed me to recognize which students needed a little one on one time to better understand how to rearrange a standard form linear equation to become the slope intercept form.

I gave minimal instructions to the students and told them that each group was going to receive forty cards. There are five linear equations that are represented within the forty cards – it was their job to sort them. First team with correct sets of solutions won a prize!
That meant that there are eight cards relating to each question. Four of those eight were in either standard, slope intercept or some rearrangement of the equation of a line.
It took the students about fifteen minutes to complete the activity. I had a much clearer picture of which students understood all the associated academic vocabulary and in turn who needed some extra help time or mini-lessons.

Some of the cardsCards spread outSome student work

A little more student work…..

The Beginning….

This is the first of what I hope to be many postings regarding education in the field of mathematics and leadership.  I have been working as a teacher for the last six years. I have taught in a few different locations around the world and lately I have become inspired by a few teachers and educational leaders on the international and local scene.

I will be posting ideas for my math classroom and describing how those ideas have gone.  My hope is that others might also submit or post ideas on this blog and be able to further expand our Personal Learning Networks and strive for deeper understanding of our students, how to present our material, how to create student engagement and how to develop higher order thinking skills.

Welcome. Let the Mathematics begin!