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: