Test Champions

This idea was recently shared with me by Pietro Tozzi. He is a maths teacher at Gumley House Convent School in London but also works for Pearson (the Edexcel exam board) two days a week. We brought him out to our school in Singapore to do some training for the team about the new A-level in maths. (By the way, if you are looking for an A-level or (I)GCSE trainer, I would highly recommend him.)

During our time together, he shared this idea for returning a test. As it turns out I had a KS3 test to return and tried it out. As I marked I kept track of the best answers for each question. When I compiled this table, I made sure that every student was listed and students with lower scores were listed more frequently, if possible.

The class score represents the fact that among all the students, they have expertise to get full marks; someone scored perfectly on every question.

After passing back the tests, I asked students to get up and meet others who could help them correct their errors. They spent about half an hour up and about, talking over their questions, and making notations (using a coloured pen) on their tests. While they were doing this, I was able to work around the room and talk to those who had difficulties that their peers couldn’t solve.

They enjoyed this way of reviewing and correcting their tests. Having them out of their seats was good for their concentration (for the most part!) and also allowed me to be less conspicuous in my help of a few key students.

I completed this lesson with a fill-in sheet for students to list strengths and targets based on the test. We spent the following lesson with students doing individual work on their targets before we moved on to our next topics of study.

Logarithm Questions Around the Room


Here’s a lesson that worked for me recently. I had six logarithms questions posted around the room. I gave each pair of students some sticky notes and asked them to go around adding to the posters. Each answer had to be different, clearly. (I didn’t even specify that each answer had to be different, actually, the students just assumed that.)

I love that students were out of their seats and talking to each other. They were more energetic about these questions than they would have been about a worksheet. And they were automatically noticing generalisations as the activity went on and more answers got added to the posters. Also the group feel to an activity like this spurs lots of students to try creating an example that is a bit harder than they would suggest normally.


This was a good activity just like this, but I added a little more. Later in the lesson I took pictures of the posters with my iPad. They are set to automatically upload to iCloud, so I accessed them on my classroom computer and could show them on the screen. We talked about a couple of interesting sticky notes and students noted the ones they thought were incorrect. A few of my students like notetaking more than others, so they copied a few examples.

a mathematics lesson that worked

Since posting one of these pictures on twitter, I have been featured by another teaching blog: Resourceaholic. My idea is one of five “gems”; the other four are (also) amazing ideas!

I am glad that the sticky notes idea seems to work for others; a few others have tweeted to say they liked it. Thanks for the feedback, Emma Cox and MathSparkles! Here’s the file I used with the logarithms questions (make a copy to save it to your own Google Drive or download it); the questions are based on a resource by Susan Wall.

What worked for you recently?

Building Collaboration Using Changing Partners Activities

A few classes needed to revise at the end of teaching units and I wanted them to collaborate while they did so. I printed off a class set of these small checklists with the first names of everyone in the class.

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I also printed some review questions onto colourful card. I separated my tables and spread the questions out over the tables, with two or three on each table. I put some tables facing the wall or the windows so that pairs of students would hopefully focus better on just their partner and the question at hand.

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I gave each student a name checklist to glue into their notes and displayed these instructions.

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From time to time there were not two students looking for new partners at the same time. As a result, sometimes they would have to work in a group of three. Other times there was one person who had to wait a minute to start their next problem. However, this didn’t happen too much and overall I would say that the students did a lot of work. Sometimes in a revision lesson such as this one, students get bored and lose momentum. Not so during this lesson. They stayed on task until the end (80 minutes later) and completed loads of questions. In the last few minutes of class we checked their work as I displayed the answers on the board.


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I have tried this with a few classes now and it has worked well every time. It goes most smoothly when the class size is 20 or more. Though I did try it one day when lots of students were at a field trip and I only had seven learners. That still worked but it was a little harder for students to begin and end questions at the same time as others. it devolved into mixed group work instead.

One time I tried this in my class that has a wheelchair student. This also worked smoothy. I positioned her in a place where she wouldn’t be bumped by others walking by. From time to time I prompted students to go over to her since she can’t come to them.

Some tips for myself and others to make this work well:

  1. A class size of 20 or more works best.
  2. It works best if you have enough tables to have at least two empty tables at the start for the first students who finish and find new partners to move to.
  3. Having three questions on each table means students can sit down at the same table a second or third time with different partners and solve different questions.
  4. Make sure the questions are numbered (or lettered) and students write these down as they solve. Then sharing the answers becomes easy.
  5. Mixed revision from several units of study can be done this way. Just mix up the questions around the room.

Do you have ideas about helping students collaborate in math(s) class?


Algebraic Fractions Quiz-Quiz-Trade Activity

One of my classes of students sat an exam lately and I realized they need more practice with adding and subtracting algebraic fractions. There were a collection of misconceptions on the exam, including not taking a common denominator, trying to cross multiply, and cancelling incorrectly. I made a set of cards (split over two files) to use to help practice this tricky manipulation.

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In this quiz-quiz-trade activity, students start with one question each and make sure they can simplify it. I give them a few minutes to check with their partner or with me. My students like to use their mini whiteboards because it lets them change any errors easily.

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Then they get out of their seats and meet someone from another table. They take their mini whiteboards (or their notebooks) with them. Meeting someone else, they quiz each other. After they are satisfied that they both got their questions correct, they trade cards, thus leaving with a different card then the one with which they arrived.

While the students are quizzing each other, I am able to circulate and address misconceptions. The students are quite good at helping each other. After this activity I think they will feel a lot more confident with adding and subtracting algebraic fractions.

When students sit back down, I ask them to do a few of the algebraic calculations in their notebooks so they have a record of what they learned.

I made these cards using Tarsia software, designed for making mathematics activities. Here are two files (pdf) of the cards.


One Easy Way to Never Teach a Boring Lesson Again

I have discovered that I can’t teach a boring lesson anymore. I really wanted to today. I was tired and it was Friday, last period. My grade 9s always seem a bit too boisterous when I am the most exhausted. Sigh. All I wanted was to sit them down, get them to be quiet, and do some mindless, repetitive task. Unfortunately, I had done one thing at the beginning of the year that ruled out a boring lesson.

I told them never to bring their textbooks to class.

As a result, every lesson has to involve some kind of activity. We have to talk, sort, write, create, classify, or debate. I have no choice but to get them doing and moving. Even when I most want to sit down and supervise them, I rarely can.

We talked about the index laws, then did a quiz-quiz-trade activity to practice simplifying complicated expressions using indices. Then we wrote a few of the “best” examples (the hardest are the best, right?) in our notes. Then we solved a corny riddle using indices. “How do you write a song to knock over a cow?” “In beef flat.”

Not using textbooks in class can be tiring. But it helps me cause active learning.

Make Your Own Normal Distribution Questions

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Today we were building our familiarity with the normal distributions. I had a scan of a textbook page with lots of normal distribution sketches, like the one below. I copied them onto yellow card and cut them out, discarding the textbook’s instructions and numbering.

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Each student got a sketch and I asked them to make up a normal distribution question to go with it. Here are my instructions. Students were working on their mini whiteboards.

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The students got out of their seats to solve other their classmates’ problems. There was a lot of collaboration and those who found writing the question hard got plenty of input from their peers. I was free to circulate and able to clarify some important ideas about continuous distributions and the appropriateness of the normal distribution as a model.

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I was impressed by the questions’ variety and ingenuity.

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I don’t think I emphsized thoroughly enough that students need to specify that the data they have chosen to write about is normally distributed. However, students were able to solve a wide range of questions, some more difficult than others.

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This was definitely much more successful than a page of textbook questions!



Collaborative Talking in Math Class

For the next eight weeks I am participating in Exploring the MathTwitterBlogosphere, a project designed to help math teachers meet others in the cyber community we call home. (It is still a good time to join in, if you haven’t yet.)

Mission 1 is to write about what makes my classroom my very own. One thing I prize and make sure I develop in my students is their ability to communicate with each other about their math. I have been doing more and more discussion-based activities in lessons. I want them to talk about their conjectures and developing ideas. It is rare that my students are sitting in silence. They are usually discussing with the person next to them. Often they are moving around the room, talking to others. Even when we are doing “boring” practice questions they are talking.

umar remi probability never sometimes always true

Here two grade 12 students are discussing probability statements that may be never true, sometimes true, or always true. They had to go meet as many others as they can, discussing the statements on their cards, and each time trading cards. Then they go off and meet another person. (This is a quiz-quiz-trade activity.)

To help students communicate with each other, I have mini whiteboards (MWBs) and pens on each group of tables. Students love using them because they can quickly explain their thinking. They feel more free to make mistakes on the MWBs and to help and comment on each other’s work. Since having them always available, I have noticed a big increase in how much students help each other and talk about their thinking.

With the MWBs it is also easy to share the thinking of one or two students with the rest of the class. In another probability lesson, I asked students to visualize and then draw what they thought a certain probability distribution would look like. Then I brought six of the MWBs up to the front to discuss with the class their common and distinctive features. In the end, our discussion focused on just two of the graphs made by students.

fibber's game probability distributions

All this constant discussion helps my students clarify and solidify their developing ideas. This makes my classroom unmistakably mine.

What makes your classroom unique?

Number Sets Activity

Which numbers are real? Rational? Natural? Whole? Here is an easy activity to help meet the number sets objective.

I made this set of cards with numbers from the above sets. As students enter, I’ll give them a card. Then I will ask the students to walk around the room, see what numbers others have, and organise themselves into groups based on their number. The instruction is purposely vague enough that many possible groupings are possible. When students have grouped themselves, I’ll start a group discussion about the way they are grouped. 

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I anticipate (I haven’t tried this activity yet) that I may have to prompt the students to think again about the groupings and ask questions to help them explore the idea of number sets. And then maybe ask if there are some numbers that are “purer” than others. I think students have a sense that whole numbers are more “number-y” than items like 2.4 or negative four fifths.

I think it would be interesting to put students holding whole number cards in the centre of the room and then build the number sets outwards around them. I think this would elucidate the idea of natural numbers being contained in the set of integers, and rational numbers being contained in the set of real numbers.

I think it’s my responsibility to introduce the names for the number sets once students have developed the concepts behind them. I’ll write the names and symbols for them on the board to conclude our discussion.

How do you teach about number sets?

Quiz-Quiz-Trade: Ways of Getting Students Out of Their Seats


My new school’s lessons are usually 80 minutes long. I think I shall try to get students out of their seats (at least) once each lesson – otherwise it is too long for them to be sitting. I also think it’s too long for me to plan in a single block. I can’t imagine any lesson where we work on the same thing for 80 minutes. My attention span isn’t that long and I can’t imagine any teenager’s is either.

Thus begins this series of posts on ways to get students out of their seats. Quiz-quiz-trade was an activity I learned about in Kagan Cooperative Learning (a brilliant book, by the way, which I thoroughly recommend). I have used quiz-quiz-trade regularly for years and adapted it in a few ways.

Print out some cards with questions on them. These could be taken from a textbook, revision sheet, made up by you, or made up by students.
Cut them up.

Give one card to each student. While they are still sitting down, ask them to work through the question and verify that they know the correct answer.
Ask students to get out of their seats and meet someone new. Student A quizzes B, then student B quizzes A. They thank each other, then swap cards and move on to meet someone else.
After several trades, each student has met many other students and has also answered many questions.

Works Well With…
1. Questions that aren’t too long to solve. Or let students take mini whiteboards with them (pictured above).
2. Worksheet or textbook questions that you think are too boring as a worksheet. Just cut the sheet into strips and hand the questions out. Make sure you have enough for each student to get one.
3. Revising for exams. Use past papers cut into questions.

1. Before quiz-quiz-trade, ask students to make up questions to demonstrate their understanding of a topic. Then you can use this questions for quiz-quiz-trade, either immediately or later.
2. You can print the answers on the back (for safety!).

What are some ways you get students out of their seats?

Check back next week for the next post in the Out of Their Seats series.