Grade 8 French as a Second Language (FSL) Long-Range Plans

Grade 8 French as a Second Language (FSL) Long-Range Plans

This is my latest attempt at organizing the grade 8 Ontario FSL curriculum's expectations into units that make sense. I try to develop my long-range plans into a one-page, "year-at-a-glance" type of document. I more or less succeeded in this case, since the resulting documents are ledger-sized. I'm a big fan of the following quote when it comes to long-range plans.

No battle plan survives contact with the enemy. - Helmuth von Moltke the Elder

That sort of summarizes how I expect these long-range plans to work this year. These documents are both very much works-in-progress, and have likely changed repeatedly by the time you read this. Feel free to modify them to your needs, and let me know if you have any suggestions or if you see any glaring omissions.

Grouping the Ontario Grade 8 French as a Second Language Expectations

The first thing I did was to try to find the expectations that looked similar between the four strands (reading, writing, speaking and listening). Most of the expectations aligned nicely, but some didn't match up.

Next, I tried to find a theme that bound the whole set of expectations together. In this case, I called the units "Fiction: Analyzing Narrative Text Patterns", "Media Texts: Evaluating Texts", "Non-Fiction: Summarizing Important Ideas While Reading", and "Poetry and Song: Making Connections".

Finally, as I go through the process of teaching these units, I will have a chance to readjust the titles, and to see if any of the expectations should be moved around.

Download for Excel (modifiable): 2016-06-30 Grade 8 FSL Curriculum Expectations Grouping Download as PDF (ready for print): 2016-06-30 Grade 8 FSL Curriculum Expectations Grouping

Or just click on the following image to enlarge (though the quality is vastly better in the above two files).2016-06-30 Grade 8 FSL Curriculum Expectations Grouping

Ontario Grade 8 FSL Year-at-a-Glance

Here is my formalized version of the grouped expectations. I've broken them down into the following periods and units.

  • September - November: "Fiction : Analyzing Narrative Text Pattern"
  • December - January: "Evaluating Texts"
  • February - March: "Summarizing Important Ideas While Reading"
  • April – June: "Making Connections"
  • Full Year: "Synthesizing and Making Inferences"

Each unit hits on group expectations for each of the four strands, in the order I'll be doing them: (C) Reading, (D), Writing, (B) Speaking, and (A) Listening. On top of that, I've added « Les études grammatiques » ("Grammar Talks"), which are analogous to Number Talks in the sense that I'm planning on putting problems on the board and have students analyze possible solutions.

Download for Word (modifiable): 2016-06-30 Grade 8 FSL Year at a Glance Download as PDF (ready for print): 2016-06-30 Grade 8 FSL Year at a Glance

Or just click on the following image to enlarge (though the quality is vastly better in the above two files).

2016-06-30 Grade 8 FSL Year at a Glance

Planning a Flexible Framework for Intermediate Mathematics

Planning a Flexible Framework for Intermediate Mathematics

This is an overview of what we will be discussing during our curriculum framework professional development session on August 25th. We will be at the DDSB Education Centre, room 2015 from 8:30 AM to about 2:00 PM. I hope you will all be finished your initial planning before 2:00 PM, but I put some extra time as padding, to avoid cutting short any great discussions.

Why I Enjoy Math

This is one of the recent math problems that I've enjoyed solving. Fill in 4 cells to give products shown in each row/column, sum of 4 cells must be 80.

There are two main experiences that I can point to that really drove me to want to teach mathematics. The first was my grade 12 calculus course. What I enjoyed the most about that class was when we were given time to work on tough problems. I was lucky enough to be in a class where most (if not all) of the students really wanted to be there, and really wanted to learn. The teacher didn't pull any punches, and gave us really tough problems to work on. I remember working on those problems both individually and with other students for hours. The sheer difficulty of the problems made them intensely satisfying to solve.

The second really positive experience I had was one of my university math courses about the process of problem-solving. The course was entirely based on the book, "Thinking Mathematically", by Mason, Burton and Stacey. In that book, I found that the authors had summed up the essence of what is satisfying about mathematics: solving intricate and difficult puzzles by finding the simple logic that underlies them. The book showed where the art and the science of mathematics meet. (It sometimes feels like many of the new ideas of how to engage students in math are pulled from this book. The problems are simple enough that they can be understood and attempted by grade 7 students, but are complex enough that they can lead to university-level solutions.)

So, I do math because I enjoy solving intricate puzzles, and I find it extremely satisfying when seemingly impossible problems can be solved simply by looking at them in the right way. And the reason why I teach math is that I enjoy seeing students get the same satisfaction out of these puzzles.

The Perfect Lesson Plan: a Hypothesis

Unfortunately, there is a disconnect between the way I enjoy learning mathematics and the way that I felt I was expected to teach mathematics. I get excited about learning math when I'm faced with a challenging problem that I can generate good hypotheses for, but that takes a while to figure out the underlying structure. I enjoy teaching math when I see my students going through the same process: they have a tough problem that is easy to understand, but which is tough to solve. Take, for example, the first problem in "Thinking Mathematically".

Warehouse

This problem is simple enough that students can understand the question easily, but complex enough that it takes some time to figure out. That's precisely what makes it so enjoyable to work on. But when you go in to the Ontario Math Curriculum (Grade 8 Number Sense is on page 111), it's not immediately clear whether this question really teaches kids to "solve problems involving percents expressed to one decimal place (e.g., 12.5%) and whole-number percents greater than 100 (e.g., 115%)". It becomes easy to start asking myself if I've really taught that students what I was supposed to teach. Did I go over the concept too superficially? Should I have gone into more detail? What about the kids who struggle with the concept of decimals, fractions or percents--how do I help them succeed? And if I try to focus on the students who are struggling and fill the gaps in their understanding, what should the kids who find this easy be doing?

(You may have already heard an easy answer to this, such as, "You just work with the struggling students in small groups while the independent workers work independently"; unfortunately, the reality of working with students in the classroom often precludes easy answers. I have a couple elements of solutions and hypotheses to propose. I also have a couple good questions. But I can confess right now that I don't have any easy answers or solutions that will 100% work in your class for 100% of your students 100% of the time.)

The problem-solving rubric proposed in the book, "Thinking Mathematically"

Where I Got Stuck

Last September, I taught Chapter 5: Measurement of Circles in September. And I did Chapter 1: Number Relationships in October. And after that, I realized that I had no interest in continuing. I couldn't figure out why. It didn't make any sense to me--I love doing math. I love teaching math. I love the rigour involved in preparing lessons that are pedagogically sound, and that explore the nuance of the mathematics curriculum. Why wasn't I looking forward to the next unit?

So I did what I usually do: I started hypothesizing. Maybe I didn't change the program enough from last year (I don't like teaching the same thing the same way twice). Maybe I wasn't precise enough in my examples or definitions (perhaps students weren't fully understanding). Maybe I didn't want to write notes on the board (in retrospect, that was certainly part of the answer). Maybe I should ditch the textbook entirely and plan my year based only on the curriculum. No matter how much I personalize the program and add in my own activities, by starting with a textbook, I'm automatically following someone else's plan, and that limits my creativity. (I looked at my long-range plans, and they looked dreadfully boring.) Maybe I'm experienced enough now that I don't need to curriculum as a guide (I have a pretty good feel for what a grade 8-level problem should be). Maybe if I taught using just the curriculum, I could cover the entire thing in one year. Well, anyway, as much of the curriculum as anyone can cover, since there are so many curriculum expectations, how can anyone cover them all anyway?

When I prepare my units, I try to start with the end in mind. I look around for any great resources (after all, why create something from scratch when I can take something good and make it great with the same amount of effort?), and I try to match them up against the curriculum and organize them in a way that should make sense to students. You can sort of see my process when I compiled the resources, "Nelson Math Grade 8 Long-Range Plans", "Jump Math Grade 8 Long-Range Plans", and "Ontario Curriculum Long-Range Plans". I tried to take the best parts of all three of those documents, and structure them in a way that would make everything as clear as possible to the students. As far as I was concerned at the time, a perfect lesson should cover all the curriculum expectations in an organized and structured manner, and should define all terms, hypotheses and theorems along the way. A perfect lesson should be rigorous, precise, and provide excellent examples for students to follow. You can see the result of that hypothesis in "Chapter 1: Number Relationships".

A Possible Solution

So here is the working hypothesis I tested last year: if I can find a way to teach mathematics so that the kids learn the same way that I like to learn, then they will have more fun and I will have more fun. (Oh, and also, we will all learn more and other stuff too.)

With that in mind, I started to re-design my curriculum so that, instead of teaching a bunch of theory, taking notes, and then trying out some problems, we tackled the big problems first.

The advantage to doing it this way is that the students started asking better questions, generating better hypotheses, and becoming more independent. The short-term downside was that many of the students felt destabilized. The structure I was using to teach had changed, and they justifiably felt unsure of what to expect. To be fair, I felt a bit destabilized myself. I like having structure.

And that brings us to the reason why we are all here today. How can we teach the way we want to teach while still retaining structure? How can we avoid the extremes of "too much flexibility" (which makes it difficult to plan, and to make sure that we are going to teach what needs to be taught) and "not enough flexibility" (where we can't adapt what we are teaching to the needs of the students)?

Well, there's a resource that helps tremendously with that problem.

The "Curriculum and Connections" Resource

Continuum and Connections

This collection of documents, created by the Ontario Ministry of Education, is a fantastic way to organize a flexible framework for mathematics. The documents cover grade 7 through grade 10, and distinguish between applied and academic at the high school level. The best part is that each of the documents is broken up into the strands for each grade.

For example, grade 7 and grade 8 mathematics have a section devoted to each of the following: (1) Fractions; (2) Integers; (3) Patterning and Algebraic Modelling; (4) Perimeter, Area and Volume; (5) Proportional Reasoning; and (6) Solving Equations. Furthermore, each of those sections are broken down into the 5 strands we are supposed to evaluate in those grades: Number Sense and Numeration; Measurement; Geometry and Spatial Sense; Patterning and Algebra; and Data Management and Probability.

The way the "Curriculum and Connections" resource is put together on the EduGAINS website, is unfortunately difficult to work with on a daily basis. I needed something that I could just put on the wall, and check off as I went, something that I could refer to quickly and easily. So, last year, I took some time to compile all the units (by grade level) into a series of 1-page documents containing all of the important information. Click here for the full "Curriculum and Connections" resource.

Covering All the Curriculum Expectations

One of the big advantages to teaching this way is that I no longer worry about "covering the curriculum". There are only six units in the entire year, and I can break them up however I want. In addition, I know I'm going to cover each strand once in every unit, so I'm never going to be in a position where, "Oh, no! I have to teach fractions sometime in the next three weeks so that I can get a grade for the report card!"

Using the Curriculum and Connections framework, I'm going to cover every strand multiple times each semester, so I really just need to make a judicious choice of what I'm evaluating.

Here are two examples of units that I've taught this past year, using the "Curriculum and Connections" framework.

1. Understanding the Relationship Between Percents, Fractions and Decimal Numbers

This is an overview of our strategy wall, after doing one project together.

This unit was based on the Curriculum and Connections grade 8 "Fractions" section. I co-constructed the learning goal and success criteria with the students, but I already had a good idea going in what I wanted to do. The big idea was to understand that "fractions, decimals and percents are just different ways of representing numbers" (you can see that on the top-right, in yellow), and that the same number can always be represented (at least) three different ways.

The student work you see on the board is for two problems, "Nana's Lemonade" and "Dueling Discounts", created by Dan Meyer. For an overview of how I structured this unit, see the post in its original context. At

2. From Patterning to Algebra

Finished Strategy Wall (1). This is what our strategy wall looked like at the end of this problem.

This unit was based on the grade 8 Curriculum and Connections section, "Patterning and Algebraic Modelling". For the students, I named it "From Patterning to Algebra" because that was more meaningful to them. The big idea was to "Understand that pattern rules, tables of values and graphs are simply different ways of representing patterns" (in yellow at the top left). We created our success criteria together, and we added definitions as the unit progressed, to help students learn the terminology that goes with the ideas they were expressing. You can see how I structured that unit in this post. I also included the following evaluation in that unit.

2016-03-04 From Patterning to Algebra - Pattern Rule

Distinguishing Between Skills (Computing) and Reason (Problem-Solving)

Now that we have a framework upon which to base our teaching, the next problem is, "What do we put in that framework?". This is where we get more into the art of teaching, rather than the science. I'll do my best to show you what I do, and hopefully some of that will be useful for you, but most probably, at least some of this won't work with your style of teaching, so please look at this with a grain of salt.

The Ontario mathematics curriculum identifies 7 important mathematical processes: (1) problem solving; (2) reasoning and proving; (3) reflecting; (4) selecting tools and computational strategies; (5) connecting; (6) representing; and (7) communicating. I find it difficult to address all of these processes using just one teaching strategy. I suspect that it would be difficult to reach every student in the classroom using just one teaching strategy as well.

There are two main types of activities that I use to structure student learning. The first is called "Number Talks", and is based on the book "Making Number Talks Matter" by Humphreys and Parker. The book is available on Amazon, but if you bug your school's numeracy coach enough, they might be able to find a copy for you. The second type of activity I like to use are "Three-Act Math" problems, which is (sort of) Dan Meyer's take on three-part math lessons.

Number Talks are 20-minute lessons that cover the skills or computing aspect of solving relatively straightforward problems. Essentially, I chose a problem that I hope will get students to come up with good strategies. Each successive Number Talk builds on the one before it, until students have developed a variety of effective and efficient ways to solve "skill" problems. I will do one or two examples with you during our workshop, but in the meantime, this is how I introduced Number Talks to my class this past year.

Number Talks have replaced the "exercises" portion of my math class. I used to spend a lot of time worrying about the exact best way to structure exercises so that students develop a variety of strategies, and are challenged but not overwhelmed (here is an example of a series exercises for exploring square roots and squares). Now, with Number Talks, I instead use what students have learned so far, and where I want them to go, to choose a problem that I think will help them develop the type of strategies that will help them with a particular skill.

Three-act math lessons are where students get to work in groups to solve complicated problems and develop reasoning, proving and reflecting skills. With good three-act math problems, students form a hypothesis, test the hypothesis, maybe solve the problem, and then reflect on their solution. Often, at the end, they will realize that their solution was inaccurate, partially accurate or reasonably precise, at which point they can reflect on the usefulness of their mathematical models. Over time, they often realize for themselves the statistics aphorism:

All mathematical models are wrong. Some are useful.

I'm going to do an example of a three-act math problem with you as well, and we'll talk about how to make them as effective as possible for your students.

Trials and Errors

In no particular order, here are a couple of the questions that I am struggling with right now. I have elements of answers, but I don't have a coherent global theory that answers all of the problems.

  • How to emphasize group work vs. individual work? (Should one count more than the other? How much time should students spend working individually or in teams?)
  • How do you make sure that every student has learned from their work? (What kinds of activities help you determine what a student has, in fact, learned?)
  • How do you evaluate students when you are constantly giving them feedback? (If you give them questions or next steps, how does that affect your grading of their work?)

Overview and Comments

Here is what I hope to cover during this in-service:

  • Introduction to "Curriculum and Connections" (large group)
  • Choose an order in which to do the 6 units proposed in Curriculum and Connections (randomly generated groups of 2-3)
  • Go through the planning process for one of those units:
    • Do a Number Talk to teach the skills section of the problem (large group)
    • Do a 3-act math problem to teach the problem-solving side of it (randomly generated groups of 2-3)
    • Do an evaluation (exit ticket or math journal entry) to evaluate summatively (plan in groups of 2-3, do the problem individually)

I hope to add pictures of the work we did together to this post, so that we can refer back to it later. If you have questions or comments, please add them below.

UPDATE: Pictures from the Workshop

Thanks for coming out, everyone! This was a lot of fun, and I learned a lot.

Fold and Cut

Fold and Cut

Prologue

  • Ontario Grade 8
    • Curriculum and Connections: Patterning and Algebra
      • "Sort and classify quadrilaterals by geometric properties, including those based on diagonals, through investigation and using a variety of tools"
    • Ontario Curriculum
      • 8m40 (Overall Expectations) demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric properties in the real world
      • 8m41 (Overall Expectations) develop geometric relationships involving lines, triangles, and polyhedra, and solve problems involving lines and triangles
      • 8m43 (Geometric Properties) sort and classify quadrilaterals by geometric properties, including those based on diagonals
      • 8m45 (Geometric Properties) investigate and describe applications of geometric properties in the real world

Act I

  • Is there a way to fold a triangle so that it can be cut out by using only one cut?

Act II

  • Suggest attempting a simpler problem. Ironically, both of the following are easier.
  • Or maybe watch one failed attempt at cutting a triangle out in one cut

Act III

  • One possible solution for cutting out the triangle in one cut (view as image)

Sequel

  • Try cutting out a parallelogram in one cut. Try other polygons.
  • Can you cut out the letters of the alphabet using this theorem?
  • Check out Erik Demaine's awesome site
  • Numberphile explains the "Fold and Cut Theorem"

https://www.youtube.com/watch?v=ZREp1mAPKTM

Ontario Math Continuum and Connections

Introduction

I've been trying to find a more flexible way to approach teaching mathematics to students, one that shows students that everything they learn over the course of a year is interconnected. The Continuum and Connections resource does a really good job of breaking the grade 7, grade 8, grade 9 and grade 10 math curriculums into units containing all five strands. However, the documents are a bit too large to work with on a daily basis. This is my attempt at making this resource into something that is immediately useful in the classroom.

It is still important to refer to the curriculum to make sure that all expectations are covered, but on a day-to-day basis, I really find this document easier to work with.

Overview

There are six units for each of the grades. In each of those units, I have placed the plans for grades 7, 8, 9 and 10. This makes it a bit easier to compare across grades, but unfortunately takes a couple extra moments if you are looking for all the plans for just one grade.

  1. Fractions;
  2. Integers;
  3. Patterning and Algebraic Modelling;
  4. Perimeter, Area and Volume;
  5. Proportional Reasoning; and
  6. Solving Equations.

Here are the download links for the full document:

Curriculum and Connections

The "Continuum and Connections" (link to page) documents are definitely worth consulting in their original context. In case that ever goes offline, I have also mirrored the documents here:

 

Fractions

 

Integers

 

Patterning and Algebraic Modelling

 

Perimeter, Area and Volume

 

Proportional Reasoning

 

Solving Equations

 

From Patterning to Algebra

From Patterning to Algebra

Learning Goal and Success Criteria

Over the course of this chapter, we want students to understand that pattern rules, tables of values and graphs are simply different ways of visualizing patterns. There are a number of specific expectations that we want to cover, listed in the following photos.

Vocabulary

Before starting, we added a number of new words to our strategy walls. Students don't need to memorize the words, but they do need to understand them and be able to use them when they are working.

Graduation

The first project we worked on for this section was, "Graduation". Here, we wanted to start really using tables of values, pattern rules and graphs to solve problems. Here is a variety of answers, with comments on each. I kept one hypothesis, and then a bunch of graphs and tables of values.

New Success Criteria

After completing the "Graduation" problem, we constructed new success criteria based on what we learned. Here they are.

New Success Criteria

Exit Ticket

This exit ticket tested each student's ability to use what they learned in small groups, by applying it to a specific problem. Students were allowed to use everything from their strategy walls, including the success criteria, to do this problem. However, the problem was done individually, in class.

Word: 2016-03-04 From Patterning to Algebra - Pattern Rule PDF: 2016-03-04 From Patterning to Algebra - Pattern Rule

2016-03-04 From Patterning to Algebra - Pattern Rule

Understanding the Relationship Between Percents, Fractions and Decimal Numbers

Understanding the Relationship Between Percents, Fractions and Decimal Numbers

In this chapter, students are supposed to understand the relationship between percents, fractions and decimal numbers, and that they are three ways to represent the same thing.

Dueling Discounts

The first problem we did together was called "Dueling Discounts" by Dan Meyer. We studied the problem on the attached page. Students learned how to deal with percentages and decimal numbers.

Nana's Lemonade

The next problem we studied was "Nana's Lemonade", also by Dan Meyer. Here, students were studying how ratios, equivalent ratios and proportions work in real life situations.

Cinnamon Toast Crunch

Cinnamon Toast Crunch

cinnamon-toast-crunch-3.jpg

Prologue

Play this video for students. You may have to play it more than once before they are ready to ask questions.

[wpvideo EdgORK0d]

Act I

  • Write, "What do you want to know?" on the board
  • Allow students time to ask questions. All questions are valid. Don't answer any of them just yet.
    • Optional: After each question ask, "Who wants to know the answer to this question?". Write that number beside the question.
  • Answer all questions on the board.
    • If a student asks for information about the price or the number of grams, give them access to the photos in Act II.
    • If a student asks a good, math-related question, circle it and tell students you would like to know the answer to that. A good starter question is, "Which box of cereal is the best deal?", but there are many other problems that students can explore based on this video.
    • Hopefully someone asked something like, "What does this have to do with math?" Give moving speech about how math is life. You get bonus points for moving kids to tears during this speech.

Act II

Cinnamon Toast Crunch 1

Cinnamon Toast Crunch 2

Cinnamon Toast Crunch 3

Act III and Sequel

[Placeholder text. Will be updated once students are finished the problem.]

Grade 8 Mathematics: Multi-Strand Long-Range Plans

Grade 8 Mathematics: Multi-Strand Long-Range Plans

The Problem

I was trained to do math in a very classical fashion. Start by what you are certain that you know, and build from there. Pedagogically, this makes a certain amount of sense: once you can figure out where students are, you can build on it.

Using traditional textbooks to teach a math course, implies that you should start with a chapter that students understand well, and from there, go to a chapter that would (a) use what they've already learned, to (b) extend their understanding. In theory, this sounds like a good idea. In practice, there are nuances. With each new group of students (and with each new chapter), you need to figure out which students know what, and how to best get them where they need to be. And using a traditional textbook, it can be hard to figure this out.

I like planning long-term. I've used Nelson Math to create grade 8 long-range plans, and to create grade 7 long-range plans. I've used Jump Math for grade 8 long-range plans as well. And I've compared Nelson Math and Jump Math for grade 8 and for grade 7. There is something comforting about having a plan and knowing where you want to go next.

But every year, as the realities of teaching the students in my class have set it, I've either heavily modified or completely abandoned those plans. (Helmuth von Moltke might have something to say about that!)

Download for Word: 2016-01-25 Grade 8 Math Multi-Strand Long-Range Plans

Download as PDF: 2016-01-25 Grade 8 Math Multi-Strand Long-Range Plans

A Possible Solution

So, here's my next idea. I am certain it is at best an imperfect solution, but it's better than the other solutions I've tried so far. These plans are based on the EduGains' "Continuum & Connections" resources, which date from 2010. I've mirrored them here, in case that website goes down at any point.

The original documents are:

While I have only been working with this system for a few months, I have found a number of benefits:

  • It implicitly covers all of the grade 8 Ontario math curriculum (though I find I still need to refer to the curriculum regularly to make sure).
  • It allows for flexibility in what I teach next. For example, while focusing on fractions, I could cover algebraic expressions and experimental and theoretical probability as two different facets of the same idea, rather than as two different "chapters".
  • It allows me to evaluate all of my strands simultaneously. Hopefully, I'll never be stuck again trying to do just one more chapter so that I can have a mark for report cards.
  • It allows for more fluidity in my strategy walls. I don't have to throw out everything from the last chapter in order to make room for the new chapter.

The downside I have seen with this method is that some students perceive this approach as less structured. They miss the reassurance of knowing they are going to do chapter 10, starting with section 10.1 and going through section 10.8, and knowing that there will be a quiz at the halfway mark and a test at the end. And I have to say that I do miss that structure as well to a certain extent. But so far, I feel like the tradeoff is worth it.

 

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.

Stick or Switch? The Missing Ace Problem

Stick or Switch? The Missing Ace Problem

Prologue

[wpvideo Ytdf27NB]

Act I

Is it better to stick or switch?

Act II

  1. What's your hypothesis: stick or switch?
  2. What's the theoretical probability of your hypothesis?
  3. How would you set up an experiment to test the experimental probability?
  4. Will the experimental probability exactly match the theoretical probability?

Act III and Sequel

Here is the problem in its original context. The history of this problem is fascinating. The Time Everyone "Corrected" the World's Smartest Woman