Meaningful Practice

If there is one resource I would recommend it is Kagan: thoroughly, wholeheartedly its Kagan.  I stocked up our teacher resource library at our school this summer have been enjoying their ideas to make my classroom a bit more interesting ever since.

We are working on our number unit in year 8 at the moment and studying decimals.  I was getting a bit bored with decimals, I mean the real world connections can only be so exciting before students start to resent adding up shopping items or items at a restaurant.  Kagan suggested something called a round table activity.  It was simple, it was not an example of how us maths teachers try to convince our students, "honestly!!  You will use this in your personal lives!!!!"  It was rather a simple activity, which took me about 5 minutes to plan and had my whole class chatting, working, engaging in meaningful work.  And with a few years under my belt, those meaningful and engaging lessons mean more to me then the few times I can make those superficial real work connections, because lets face it, I use my phone calculator when I am in a supermarket more often then I should probably admit.  So, the activity was simple.  I wrote out a number of slips of papers with x= a decimal and y= a decimal and that is the only resource you need for this activity.

1)  I tell students to work with their shoulder partner.  Students are sitting in table of four so they were to decide who will be partner 1 and who will be partner 2.

2)  Then I wanted to create a cheesy buzz, so I asked partner 1 to tell the person beside them their favourite feature about them.  Then I asked partner 2 to tell partner 1 their favourite memory of the other.  awwwwwww.

3)  Students were given the slip of paper and I told them that they would take turns answering questions.  If it was your turn you would answer the question on a white board whilst your partner watched.  If you got it right, your partner would praise you and tell you that it was correct.  If you did not get it right, your partner would coach you, help you find your mistake and reach the right answer.

4)  I then proceeded to call out things like x+y, x squared, y divided by x until I thought the activity had run its course.

It was great fun for me, because all of my groups were engaging in practicing their decimal work and the students enjoyed the change from a traditional lesson.

Simultaneous Equations

I have a pretty high flying group of year 8's and I wanted to give them a bit of a challenge.  I used twitter as I usually do to look for inspiration and probably not surprisingly, when I searched simultaneous equations the main theme that appeared was students complaining that they had to learn simultaneous equations when they will NEVER use them in their real lives.  But actually, as geeky as it might be, this is one of the things that you might actually use in real life if you know how to use simultaneous equations in context.  Now I didn't find the most inspiring example to start with, but because my students are clever and because they love to learn they still got right involved.  I put this questions on the board:

The admission fee at a small fair is$1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

I let students work in groups and just asked them to try and calculate how many adults and children attended the fair.  Students naturally began with trial and error which is what I expected.  Also, my most clever mathematician decided to form an equation to start to solve for a variable.  

I had my class split into three levels, and the weakest ones sat looking at each other so in retrospect I should have differentiated tasks.  I stepped in and asked the weakest group to try and form equations to represent what we knew.  So they did come up with a + c =2200 and 4a + 1.50c = $5050.  

All groups at this point now had something they could realistically achieve.  I allowed students to take turns going up to the board, I stepped in a few times to offer a few hints and eventually we solved the problem.  I then gave students a couple more problems and as to be expected they got more efficient at solving them.  

The best part for me, was the fact I spent the majority of time at the back of my classroom watching the groups work.  I realized how I had fallen into the teacher talk style of lessons too often lately and whilst my students were being productive, making progress and developing their skills they weren't inspired, excited or really engaged in lessons like they were on that day.  It was a gentle reminder that even the most "when will we need this" topics can be interesting when students know when they can use it and they aren't being prescribed steps to solve something new.  

Domain and Range Interactive Notebook

I really am loving this new approach to taking notes.  Even with older students.  I usually teach domain and range in a typical Ben Stein, "Bueller" style.  How do you REALLY make x and y values interesting, exciting, connected to the real world, worthy of a teenagers attention?  Well I couldn´t think of any other way than to say DO IT basically, until the wonderful world of pinterest got me onto interactive notebooks. 

Here are the notebooks my IB Maths Studies students created in order to find the domain and range of various functions.  I´m still learning how to format my blog.  I will try and rotate soon. 

You´ve probably worked out how they use the graphs, but they fold in the right and left flaps in order to isolate the smallest and largest x values and then they write the domain on the graph in the lower right hand corner.  Likewise for the range.  What you can´t see is that there are about five graphs in a pile in the middle of the green cross.  Some of them I left blank so that students could draw their own.  Also, we discussed set notation and used a foldable to take notes.  So fun.  Bueller?  Anyone?

Y=mx+c

Linear functions have been a difficult topic for me in the past but I think I´ve finally nailed it.

It was the first time my year 8 class had encountered linear functions so we started with real world situations.  I know it sounds ridiculous, and it´s a bit embarrassing, but I´ve never started with a real life situations when previously teaching this topic.  I know.  Terrible maths teacher mistake!  The lesson went as such:

• The students started to understand the concept of gradient and how each point increases by the same amount before I even hit them with all of the different variable in the standard equation.  One example we worked with was wages. 

• The wage per hour was $12.50 and we started by calculating how much an individual would earn as their hours increased. 

• Next, we pretended to be business owners and we needed to calculate our employee's wages quickly and efficiently since we are Mathematicians and that´s how we work.  We created an equation so that we could calculate any amount of wages when there is a starting amount and then wages increase with every hour worked.  For example, C=12.50x+50 where someone receives $50 plus $12.50 for every hour that they work.  Since we had just completed real-life graphs it was easy for students to plot a graph to illustrate their calculations with hours on the x-axis and total wages on the y-axis. 

• We then started to consider how the points increase consistently and discuss the concept of gradient or slope.  Also we use the starting point to learn about the y-intercept and how these aspects of the graph connect to the equation.  They got.  They finally got why the gradient is useful, how the equation connects to the graph and how we can take information like the y-intercept and gradient from the equation in slope-intercept form.  PHEW!

Another nice part of this lesson is the way I got students to take notes.  I used an interactive notebook where they created a foldable and we discussed important parts of y=mx+c.  My students enjoyed the alternative method of note taking and I enjoy looking through their books much more!
 

Distance-Time Graphs

This week I taught one of my favourite lessons with my lovely year 8's.  The lesson goes like this:
1)  I start by introducing the basics of the graphs.  Time on the x-axis, distance on the y.
2)  I tell students a story about Ian.  I describe how long it takes Ian to get to a sweet shop where he buys some treats for his friend.  We discuss how far away from home Ian is and how much time he takes before he carries on to his friend Derek's place.  Students place counters on a graph on the white board and we map out what this story looks like graphically.  For example, when he is in the sweet shop, the graph is horizontal.  We also discussed when Ian walked quicker based on the gradient or slope of the graph.
3)  Next, I draw a random graph on the board and ask students to think about a story that the graph could represent.  We discuss and mostly laugh at the randomness of some of my more creative students.
4)  Students work in pairs to do the same thing I did.  They write a story about a journey at the top of a piece of paper.  I ask students to fold a piece the paper so that only the story is revealed.  At the bottom, in the hidden part of the paper, they represent the story graphically.  I ask students to hide their graphs and then exchange them with another group.  Students read the new story, draw a graph on a white board and then unfold the paper to see if their interpretations match. 
5)  If the graphs are different, students analyse who was more accurate and offer some feedback to the other group. 

y=mx+c Revision

I found bbc bitesize to be useful for revising y=mx+c.  I would suggest doing the activity (the link is at the end).  Then go through the revision notes and complete the test at the end to see how well you understand this topic. 

http://www.bbc.co.uk/bitesize/ks3/maths/algebra/graphs/revision/1/