Day 38: Absolute Value Inequalities

Today was awesome.

I felt like students needed a bit more work on absolute value and thinking about it as a distance sorta thing. I have a ton of whiteboards around my room and a classroom set, neither of which I use very often.

Today I went over five questions and sent half the class to the boards and the other half was working on small whiteboards. After each problem they would flip positions, the fact that students were moving seemed to help their focus.As the day went on I found myself focusing on the student’s ability to translate an absolute value equation into words.

Here’s how things went:

We kicked off the review with this problem. I really focused on asking students what x meant and what the problem translated to in English; “The distance between a number and 12 is 3 units” then asking them to find what numbers were 3 units from 12. We went over a few more that had addition within the absolute value.

We translated and found the hidden difference.

I threw in a few curve balls:

I covered the absolute value part up and asked students to get the black blob on one side.

More translating:

Then I transitioned into inequalities;

Students had no issues translating, FOR REAL. ZERO ISSUES.

I used Fawn’s method of pushing my hands together when we wanted numbers less than 6 units away and spreading them apart for greater than.

I gave em another one; without any help or anything.

There were a few issues when a number went below zero… the concept is there though

Students went over a few more examples till they got bored. I would say at lest 90% of my students were in the swing of things today. Honestly that doesn’t happen very often. It was awesome to see students successful and comfortable with the concept.

The best part… there was no memorizing rules or anything like that. Just thinking about what the inequality and equations were asking for.

Day 37: Absolute Value (again)

I’ll be honest; I didn’t nail absolute value this year. I loved the activity and will do it again next year. However, in less than a month students totally spaced the rules we had covered. AND I had an uneasy feeling in my stomach with the thought of moving forward.

I put these up on the board today as review

Students has a solid understanding of the first two. Half the class could work through c then only a handful were correct on d.

This is a huge red flag, if I let the slide absolute value inequalities would be a train wreck. Here’s the deal; it would be an awful idea to move on and try and force feed the rules of absolute value inequalities. So, I decided to start from the beginning again.

Thankfully Fawn Nguyen has an awesome post on absolute value that was a life saver and here is how I worked through the lesson today.

We started with the idea of distance;

Then eventually added some notation to the thing. There were some great discussions on how distance is always positive and how to work around the whole -4 – 8 thing.

After this point I stopped and really drilled students on translating what the above statements were actually saying. More than just The absolute value of negative six minus four is 10″ and asking students to think about this more as a distance thing.

“The distance between negative four and six IS 10”

My lesson on translating from earlier this year really helped when we jumped to this sorta thing:

The one issue I had here was it felt like students quickly shifted from thinking about absolute value as a distance to a rule where you take the number inside the absolute value and move 6 units to the left and right. Not sure what I think of that right now… I probably could have put more emphasis on translating but it just didn’t feel natural.

We practiced a few more of these then got into some interesting cases:

Tomorrow we are moving into absolute value inequalities continuing along with Fawn’s ideas. I really enjoyed this lesson!

*I missed my first post yesterday… I was out of the classroom again and driving for 9+ hours. 😦

Day 19: Age Estimation

Introducing absolute value is one of my favorite lessons of the year.

Crazy.

Once again credit for this lesson goes out to Dan.

I pretty much followed his structure, just a few things are different which I will mention after we get through the good stuff:

Copy this down in your notes, you will have 21 rows.

For the first entry; students write down the name and their guess. I provide no structure or hints, we have practiced estimating a ton, let things happen.

Team Edward; how old do you think this guy is?

We get through all 21 slides then go through another 21 with their ages

After ask students to total how much they were off for each celebrity then add all those together; the person who was off by the least gets a homework pass. Let them run into problems, don’t take that away from them.

After a while students realize that there is one serious issue; under estimating an age. Say one student guessed Willie was 42 and another 44. Both off by 2, how should we deal with this?

No big deal; drop the negative.

We find the totals again; I made it a competition between my four algebra classes. The lowest 5 went up on the wall and will stay there for the rest of the year.

Finally, we moved into absolute value, smooth transition for students.

In Geometry students started Sam’s lesson on conditional statements. So much good happened here, we only made it through the sketching and first discussion. I couldn’t help but laugh at some of the statements in the slide show. More on this to come tomorrow; here are a few finished products in the mean time.