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Number Talks

From Patterning to Algebra

From Patterning to Algebra

From Patterning to Algebra: Unit Expectations

Here are the Curriculum and Connections expectations for this unit.

Grade 8 Patterning and Algebra

(1) Number Talks and Chronological Photo Gallery

This is a gallery of everything we've studied during this unit, in the order we've studied it. Hopefully, this will show how the four different types of activities we do in class are tied together (number talks; strategy walls and math journals; 3-act math and inquiry problems; and exit tickets).

When I do a 3-act math problem or an exit ticket, I am usually aiming for a conceptual understanding of the problem. I often find that this needs to be supported by a series of number talks, which help teach the skills underlying the concepts.

(2) Strategy Walls and Math Journals

[Watch this space for updates.]

(3) 3-Act Math / Inquiry Problems

  • The Coke Problem

[Watch this space for updates.]

  • The Pizza Problem

This problem was complex enough for its own post.

(4) Exit Tickets

  • The Hexagonal Prism Tank Problem

The purpose of this problem is to help students understand the relationship between the area of a base of an object and its volume.

Download as PDF (printable): 2016-05-10-from-patterning-to-algebra-gss-filling-hexagonal-prism

Download for Word (editable): 2016-05-10-from-patterning-to-algebra-gss-filling-hexagonal-prism

2016-05-10-from-patterning-to-algebra-gss-filling-hexagonal-prism

Dot Talks: Starting Number Talks

Dot Talks: Starting Number Talks

Making Number Talks Matter

We just started number talks in our grade 8 math classroom back in January. I started preparing the idea after a workshop where I was given the book, "Making Number Talks Matter" (not an affiliate link). I tried it because it's always fun to try teaching in new ways, but I have found an interesting shift in student work since we have started doing math this way.

Subtraction Number Talks

It took us about 3 weeks of daily, 20-minute number talks to develop the strategies in this gallery. Once students had developed their subtraction abilities sufficiently, I gave them names for the different strategies, and then the students chose which problem best represented each strategy.

Changing Methodology

Up to now, I have always spent a lot of time and energy agonizing over precisely which strategies students are ready for, and which ones I should teach, in specifically which order. Since starting number talks, I've been forced to change. I still have an idea of which strategies I want students to develop, but with Number Talks, it is no longer possible to directly teach specific strategies. Rather, I have to develop a series of good questions that will point the class in the direction of developing efficient strategies.

This is simultaneously more and less challenging that planning which strategies to teach.

  • Number Talks are less challenging, because I don't have to worry that a lesson will fall completely flat. If I make a problem too easy, I can always work another problem into the same number talk. If it's too challenging, we can still have a good discussion, and we can hit the same concept using a different question the next day. At the same time;
  • Number Talks are more challenging, because I have to force myself not to give away the answer. The pleasure of doing mathematics is in the discovery, and as a teacher, it is very difficult not to chime in with my own ideas. It can also be challenging to try to invent questions that will encourage students to develop strategies that are more efficient than what they currently have.

Follow-Up: A Month of Number Talks

Here is a gallery of some of the other Number Talks we have done since. Some of the questions are here twice I teach two classes of grade 8 math. While I was doing these number talks, we started off with a unit on "Fractions" (where the goal was to understand that percentages, fractions and decimal numbers are three ways of representing the same quantity) and moved into a unit on "Patterning to Algebra" (where the goal was to understand that tables of values, graphs and equations are three ways of representing the same pattern). That shift is reflected somewhat in the series of Number Talks.