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:

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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.

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We translated and found the hidden difference.

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I threw in a few curve balls:

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

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More translating:

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Then I transitioned into inequalities;

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

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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.

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

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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 29: Why? Why? Why?

In Algebra I used the textbooks exploration in solving one step inequalities. The goal was for students to realize the same properties of equality apply to inequalities.

This went ok.

It is had to differentiate and account for different student ability levels when giving every student the same worksheet. But at times I am feel like I am out of other options, especially when dealing with inequalities. These are my weak spot.

I am throwing around a few ideas of how to have students ask the question for the triangle inequality but that idea is still n the works. If anyone has any activities/ideas for inequalites let me know! I think the hardest thing for me is the similarity between solving a multi-step inequality and solving a multi-step equation.

In Geometry I introduced algebraic proofs by throwing this up on the board:

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Solving for the variable was a piece of cake, justifying each step was brutal.

I really enjoyed asking students WHY they could subtract 8 from both sides. There was a flurry of reasons; they understood that it has something to do with the equal sign but couldn’t quite construct a viable argument as to the exact justification.

This is my first year teaching Geometry so these lessons are definitely at a still-in-the-works point, but I am excited to see how the year develops!

Day 28: half-your-age-plus-seven

I have been at a stand still in finding activities/resources for introducing inequalities that both perplex students and transition naturally into the concept. Last year I started by putting x>3 up on the board and scaffoled my way up to multi-step inequalities. I wasn’t happy with the results; students had a very small base of conceptual understanding, which did not transition smoothly into linear inequalities.

I took a risk today and developed my own introduction. I really wanted to focus on letting students ask the question and approach the concept from a different direction.

I threw this up on the board;

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Then asked students if they had ever heard of the half-your-age-plus-seven rule. Not a single student had. They calculated half Brad Pitt’s age plus seven; 32. I asked them if this had any meaning? A lot of students didn’t believe he was 50, so we Googled it.

After I told them he is married to Angelina Jolee;

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“Brad Pitt is all good according to our rule” I told them.

At this point things started falling into place, we talked about what the rule might mean and decided that it would be creepy if Brad Pitt dated anyone younger then 32.

Up next…

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Professor Xavier they shouted out. Well our rule says 43.5 is the cut off. We talked about possible ways to work around the decimal; round up, round down, keep it. I let the students decide.

We went through who he is married to and finished up with the one:

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I had students write a sentence about what our rule meant, it took a while for it to evolve but they eventually came up with:

It is creepy for Mila Kunis to date anyone under the age of 22.5.

We have been working to translating between words and math so I asked students to translate this into an expression.

If z is Mila,

then z > 22.5

After we talked a little more about if we should include 22.5 in the range of ages then moved into a few notes about inequalities and how to graph them.

Each period I taught the lesson it improved and I tweaked things around. I know there is still plenty to change and the tons of potential to further develop the lesson. What is just as important for me though is I was excited about the lesson. I was not excited about lecturing on how to interpret x > 3. Students feed off that excitement and it becomes a better experience for everyone involved.