Inequalities with index cards

It is amazing how simply index cards can teach two lessons worth of inequalities. 

My first day was teaching solving and graphing linear inequalities in one variable in Algebra I who have already had a good introduction to it.

The second day was compound inequalities.

On the first day, it is my lesson opener to get a feel for what they already know.  I prepare one equation on an index card per student.  I pass them out and they can write on them.  They are instructed to solve and graph.  The cards are of three types of inequalities.  Some are just x<2.  Nothing needs to be done, just graph it.  Some are x+4>10.  It involved one step to solve.  And, the third set include dividing by a negative number.

I instruct the students to work on their card first, then go to the board and write the problem, the work, and the answer with the graph.  They all go up in different colors all over the board. 

Then, I ask, what do you notice?

They notice lots:

• there are different colors
• there are open and closed circles
• some changed their sign

Then, I circle all the ones with changed signs and ask what do they notice.  Note: I haven't gone over if they are correct yet, so the students usually notice that here.  There is usually one person that forgot the rule, so this stands out.  We talk about why they have to flip the signs.

I ask another student to come up and find another group that are similar.  They usually box the ones that are the simplest.  We have a discussion about open or closed circles.  And, finally the ones that are left are the one step problems. 

It is engaged.  Everyone is working.  Everyone is thinking and noticing.  We are grouping, looking for similarities, making comparisons.  And, I get a dipstick for where I need to go with the lesson.

The second day, I have index cards with numbers -5 through +5.  I line them up on the board so they create a number line.  Then, I ask students to come up in pairs.  First I ask for volunteers and the hands go up.  After the first time, kids aren't so sure about volunteering, so I call on one student and ask them to find a partner and come up.

One pair at a time tries to turn the cards around if they aren't true to the following, one at a time:

X>=1 and x<=-2

x>=1 or x<=-2

x>=1 and x>=-2

x<=1 and x>=-2

x>=-2 or x <=1

The audience has a fun time "getting inside the brain's of my volunteers".  It is fun to hear them debate about which card to turn over.  Some go right down and test each one.  Some point and think about each inequality separately.  I have the pair sit down.  I ask the audience if they agree. Often the first try is incorrect so if someone thinks it is incorrect, I ask them to come up and fix it.  Ask the audience again and we are good.  It really gets them thinking about the difference between ands and ors when it comes to compound inequalities. 

Here is my board:

Barbie Bungee is done for the year

I was able to do Barbie Bungee in my Accelerated Algebra 1 and 2 classes plus my class of seniors in Futures basic math.  I wrote about Barbie Bungee with Algebra 2 earlier. 

For my seniors, I wanted to extent it a bit, so we had her jump off our senior balcony.  First we had to figure out how to measure it.  Our only tools were 3 meter sticks and 5 rulers.  Off to work they got.  One went up and hung a meter stick up.  One stood below and reached the meter stick up.  Then another student added a meter stick below this one and then turned it for another, and they filled in with rulers.

It was 4 meters and 41 inches.  How's that for units?  So, it took us a while to convert it to centimeters, but we got to 506 cm. 

They went to work in two groups.  Barbie ended up getting tattooed in one group:

They predicted 48 and 51 rubber bands, pretty close.  Off to the balcony to drop them.  Of course, it coincided with lunch getting out, so we happened to have a big audience.  She jumped and was quite a ways away from the ground.  We went back and one group added 6 more and one group 10 more.  These were just guesses.  The 10 was too much.  55 bands was just barely too much, one less was perfect - 54.  And, the kids wanted to know why the math didn't work the first time.  We brainstormed and they figured out they may have made some tiny errors in actually measuring. 

A great lesson.

One students asked where I came up with these projects.  Blogs and twitter :)

MTBoS - Mission 2: Blog Post about Twitter

Is it Twitter worthy? 
Is it Facebook worthy?
Is it Twitter with a picture worthy?
...is it phone call worthy?
...is it email worthy?
...is it face to face worthy?

I went to NCTM last October and heard Max from @Maxmathforum speak about all the wonderful things Twitter can do, so I guess I have been tweeting since.  He was a good teacher and a good salesman.  Thanks Max!

So many ways to share these days.  I try not to share them in all the forms above.  My current favorite is Twitter.  I think because for me, it is more anonymous.  I tweet @HHSMath  I did do a personal account but I never go there.  I just use the HHSMath one.  I mostly follow math teachers and general teachers to get teaching ideas.  I love that we are all teaching the same stuff around relatively the same time.  My school started after Labor Day, so I do feel a bit behind the game, but then you have all tried your activities, posted, and shared them.  I get to learn from you.  If I need an idea for a lesson, I throw it out there and crowdsource.  I love it. 

Twitter isn't blocked at school and I do have it up in my tabs so I can check it out when I get a quick minute.  I like to look for any interesting updates, pictures, links to news articles about cool math stuff.  Sometimes when I am working at home grading papers, I will have twitter open and reward myself with it.  I must keep grading until there are "10 new tweets" listed, then I can check.  Whatever gets the work done, right.

I also must remember to keep everything appropriate. Twitter really feels like I am open to anyone and feels really like Big Brother.  But, I enjoy reading and sharing, so therefore, I keep it clean.

I love that Twitter is immediate.  There is always someone up and on Twitter.  I like that I get email updates making suggestions for me.  I like that I get updates on my phone via text and email so I know if my phone goes off twice, it is Twitter and I feel important.

I love when something I post gets favorited or retweeted. 

I tell my teacher friends at work that Twitter is the best professional development I have ever been part of.  It doesn't make them curious yet, but I am still working on it.  I try sharing cool stuff I find with them and I give Twitter the credit.  I predict I might get 2 teachers to try it by the end of the school year. 

ZAP game with bananas, French toast, and flying turnips

I love review games with ZAP and so do the kids.  I think a few bloggers have played blog, so I don't know which blog to give credit to.  Basically, I put 16 questions into a powerpoint.  The kids work in groups.  I have individual white boards and individual graphing white boards.  Whichever group gets the correct answer first gets 5 points.  Then, they pick a number 1-16.  This helps adjust the score so it isn't always the smartest group accumulating points.  Some of the ZAP cards are:
multiply your score by 2
subtract (-2) from your score
multiply by 1/2
Zap your score (you go to zero)
Zap all others
Zap all the scores
Sing I'm a little teapot
Do 10 jumping jacks
Switch scores with one other team
Pick a team and give them 4 points

You get the idea.

I have the kids come up with their own name and you can see below we had: infinity, Hillers (our school name), bananas, French Toast, and flying turnips.

I love Cup Stacking!

When the kids saw Cup Stacking on the agenda, they got all excited.  No, it wasn't going to be speed stacking, although that is awesome.

It was Stacking Cups by Dan Meyer.  Such an easy thing, buy some stryofoam cups and voila.  I used it as an opener.  We brainstormed what type of units would be best.  I let them play with how to stack them first and then directed them how I really wanted them stacked.

I gave the groups of 4 each 6 cups and they got to work to figure out how many cups it would take to reach the top of my head.  I wanted each person to do multiple representations of the situation: labeled drawing, graph, equation, and table.  They worked in different orders.  Some drew me in my dress.  They got all the connections I was hoping for.  Great all around.

Here is so student work: