A trial of expert groups

A topic I find interesting to teach is graphs. I like graphing at pretty much all levels, although once you get away from just straight lines it is exponentially better (pun intended).

Teaching graphs I try to focus on linking features of the graph and features of the equation, and piecing together what the graph looks like one clue at a time.

 What type of equation is it? 
Looks like a parabola.
Is the x positive or negative? What does that tell us?
It's negative, so it curves down.
It's got a number added to the end? What does that tell us?
It moves up the y axis.

I favour matching activities and assigning "possible" equations to graphs rather than dealing with definites where they can check points or use a table of values.

I've also focused on categorising graphs and exploring their features by looking at a lot of graphs and equations to help make those links. There's a great exploration of this idea at exzuberant (A Visit to the Function Zoo). With a lower-achieving General Maths class I've used Geogebra printouts of graphs with their equations on them in a hands-on categorising activity. I just get them to put them into groups of graphs that they think are similar. Then look at what is similar, and what is different. Where do those differences come from in the equation? What do they look like in the graph?

Today I tried another approach. It was with a Year 10 5.1 class, so they don't really need to know about these graph types, but they are supposed to have seen them or graphed them using tables of values or something, so I figured we'd try this anyway. Extra knowledge can't hurt, and lots of them will do General Maths and it might help to have seen these wacky graphs before.

Here's how it worked:

• Students are given a card with a letter-number coordinate. Letters are from A-E and numbers are from 1-5. 
• (I was going to add this in but realised there wasn't enough time) Whole class to place a series of images of graphs into 5 categories based on the shape of the graphs. 
• Assign a letter to each group of tables.
• Students go to the table with a letter that matches their coordinate. Each table has a different type of graph to become ‘experts’ on. They have a worksheet with questions (each) and a set of graphs (to share) with their equations written on them. Students have to work together (and with the teacher’s help when needed) to answer the questions and learn all about that type of graph. The questions are all about the properties of the graph and links between graph and equation.
• Students now move to tables based on the number in their coordinate. This is arranged in such a way that each table has at least one expert on each type of graph. Each person has 5 minutes to share their knowledge about the graph type.

The Good:

• Some students who were not usually engaged in their work were more serious because they knew they would have to explain it to others.
• Many students benefited from working with people they didn't usually work with.
• Some students made the connections between the transformations of different graph types very well. (and what does adding or subtracting a constant do to this graph? What a surprise.)
• It changed our routine up a bit. Always worth doing.

The Bad:

• Some students seemed to understand well enough in their first group, but were not confident enough to explain it to others without any support.

Next Time:

• I think I'd prefer using expert groups for an idea that is well within the ability range of the kids rather than something at the edge of what's expected of them, just for the confidence thing. Although it certainly showed which students could cope with these new and challenging ideas.
• On that note it might also be a good revision activity - break the topics down into small bits and share those around. Then most students should already have some idea of the content and just need the extra time to fine tune their knowledge.
• More time if possible. Maybe a good activity for a double period rather than a single. This would leave time to do some prep activity (like the categorising that I left out) and add other elements.
• After the expert sharing time, I went over things together as a class. This meant that weaker groups had an opportunity to fill in gaps of knowledge, and it acted as a nice summary. I would then like to follow this up with an individual activity like a little quiz or worksheet, to check their understanding. Maybe the group with the highest score could get a prize, to show what good experts and teachers they are.

Some more foldables

From year 7, Angles and Shapes topic:
 

And some types of triangle - sorry for the bad photos!

Some foldables

I've had a pdf about different foldables to use in Maths for a really long time, waiting in a large "To Do" pile, and recent blog and Pinterest readings have inspired me further. So I've had a go at it a few times. Here is the only one I have a picture of so far:

I put the index law name and question type on the front then the rule inside with an example, so they can work like flashcards. I love seeing the students go back and check these as we do questions.

Explaining where to write everything was probably the hardest part!

This one is by a student who rarely does their work, but asked me to keep this in my folder for them because they didn't have their book that day and thought it would get ruined in their bag. So that was a nice bonus! Hopefully she brings her book sometime and actually glues it in!

There will be lots more to come when I collect some books and take some more photos.

Not-really-Frayer Models

I was introduced at a Professional Learning day to the Frayer Model. I got my year 10 students to do it for Congruent and Similar Triangles one day when I was away, so I don't know how successful that was.

Then on Pinterest I saw some great examples with a "Number of the Day" in the centre and different information about the number around the outside. I really liked them. No longer a Frayer Model, I don't know what to call it, possibly a concept map?

I've been using some variations with different classes. I'll have to mark some books in order to get some photos, but here is one from Extension 1 (a student's work) and one from Extension 2 (me jotting down some answers to check theirs as they go):

I've really enjoyed this idea with the seniors. They seemed keen too, and I think when I teach Extension 2 next year I will regularly use this type of this to keep previous topics fresh in their minds as we move on and review prerequisite knowledge at the start of new topics.

A Growing Addiction

The time that Pinterest is absorbing in my life continues to grow, so I need to resolve to actually use some of these ideas. I want to acutally use this pinboard as a working space of teaching ideas. Add things, but also use them and remove them. I'm determined to do what I can and adapt lots of the fun primary ideas I find to my classes.

Of course some great ideas just don't come at the right time, and will have to wait. I won't teach symmetry or time again until next year, for example. 

So I have started by printing out the comics I'd gathered, laminating them and adding them to the comics section of my classroom.

Year 7 start "Angles and Shapes" next week, so I think I'll get some paddle-pop sticks and have a go at these as posters:

Year 10 after their exam next week will be doing some algebra that includes indices (I think - I haven't planned that far ahead!). I've been considering with some classes that we do too much teaching that is one topic per lesson then move on rather than frequently returning to the ideas and mixing things up more. I'm considering adapting this idea to index laws:

The centre could be a term in index form, and the categories could be multiplication, division and powers of powers (where they write a question that gives that answer) and expanded form. Maybe if the powers are lowish they could also have a substitution category where they pick a value for the pronumeral and evaluate the term. Then we could do one per lesson as we finish the topic and then later when we are revising.

BINGO!

I love bingo. It seems to me that students do more drill questions playing bingo than they are willing to do in any other format, and don't care in the slightest that all they are doing is repetitive drill questions.

I know that as a classroom activity it is not exactly Quality Teaching, there is no deep conceptual understanding or exploration or critical thinking, but I like to think of it as a more engaging alternative to textbook work. I don't care for textbooks, especially in the junior years.

I used excel to randomly generate sheets, which means answers will sometimes be repeated. Usually I let them cross off multiples all at once, since I won't ask two questions with the same answer.

I generally write one question at a time and then every 10 or so go through the answers with the class so they can check if they missed any and to discuss method as we solve them. In some classes kids shout out a lot so this works well. With others I have found it works better to write up a few questions at a time then wander around helping people during the time everyone takes to find the answers. Obviously it depends how hard the questions are too.

All of my Bingo files are in this folder, and it contains the following items:

• Algebra Bingo (a, b and ab terms), and some questions.
• Algebra Bingo (with binomial answers in a, b, and constants), and some questions.
• Algebra Bingo Multiplication and Division (ab, ac, bc, and abc terms)
• Area Bingo (answers in centimetres squared) (Designed to work well as easy answers to square, rectangle, parallelogram, kite, rhombus, triangle questions), and some questions.
• Fractions Bingo (Good for simplifying, ok for multiplication and division too, or a mix, could also do "What fraction is x of y?" questions), and some questions.
• Indices Bingo (I used for the index laws for multiplication, division and power of a power), and some questions.
• Surds Bingo (Good for simplifying, adding and subtracting..?)
• Ratio Bingo (I used questions on simplifying ratios), and some questions.
• Also my colleagues and a class created a great powerpoint of student-written questions for area bingo as part of their year 7 area unit.

I've also used other versions where I've just given the students a range of values to choose from and had them draw their own grid. It's much easier as long as the values are simple (e.g. numbers from -10 to 10) and avoids repetitions. I've also given them a number plane to draw some points on and rolled two dice to randomly generate points.

Tarsia

I love Tarsia. I have been using it as part of my year 7 Weekend Homework Menu quite successfully and as classwork or revision with other groups. It always takes longer than I expect for them to finish the puzzle and some kids just don't seem to have any experience with puzzles and take a while to understand what they have to do.

We also used them in our transition-to-high-school Maths Olympiads, with giant puzzles on coloured card to make it more interesting. I've sometimes done one large copy when I work with a class, and had some students solve that one and blu-tac it to the wall. (As well as their smaller copies, as you can see. They seem to be very proud when they finish them!)

Maths Taboo

I know someone else has done this, but I couldn't find it at the time I needed it, so I made my own. At first it was geared towards School Certificate content only, as revision for my lovely year 10s last year, then I added stage 5.2 and 5.3 content for further revision later.

If you haven't played Taboo, the idea is to give clues to get your team members to guess the top word, without using any of the words below (the 'taboo' words).

The file is here, it requires editing to make sure the tables aren't split across pages and so forth. And I recommend adding more, as I plan to in future.

Mathematical Chinese Whispers

This is a versatile game based on pictorial consequences. Everyone gets a long thin strip of paper and a pen or pencil and sits in a circle. In the original, everyone draws a picture, then passes their paper to the next person. They write a description of that picture, then fold the paper so that only the description is visible, then pass it on again. The next person draws the description, describes that picture, and so on. At the end you unfold the paper and see how much the picture has changed.

I first adapted this to become "Graphical Consequences", which I played last year with My Lovely Year 10s when finishing up a unit on graphs. I started the pieces of paper off with an equation, which they had to sketch and so on. They made lots of mistakes but loved it.

I have since tried equations/solutions, expanding/factorising, equivalent fractions, and simple question/answer versions, with that class again and this year with year 7. I love that this game gets everyone involved together, and that you get to sit on the floor.

Other ideas (I'm sure there are many many many more that would work):

• inequalities/solutions
• inequality/graph on the number line
• coordinates/point on the number line
• integration/differentiation
• decimal/fraction/percentage
• index notation/expanded notation
• basic numeral/expanded notation
• convert between Hindu-Arabic/Roman Numerals/Egyptian Numerals/any other system
• Trig - between exact values and expressions
• Simplifying surds