Posted in Inequalities, Questioning

Questions for Inequalities lesson

This is an exploratory lesson for inequalities and absolute value. It involves questioning and students demonstrating their understanding with a visual. I find it difficult to script my question writing because I take cues from my students, but hopefully, this will be a good place to start. You will be tempted to show your students a number line like below. Don’t do this. They will probably use this because they’ve seen it before but don’t limit them. You will be surprised with the visual representations that your students will come up with.

inequalities

This is a 3 lesson series that build upon the last. Inequalities is the first lesson in the series.

x+4<5      What numbers make this statement true? Create a visual representation to show all of the solutions your group finds.

What are some ideas about you have that would help us solve this problem? Try them out and see if you get a solution similar to your visual representation from before.

Discuss successes and failures as a group and what we could learn from them.

-2x > 6      What numbers make this statement true? Create a visual representation to show all of the solutions your group finds.

Solve this one with the same method you used before or another method you hear about when we discussed.  Was this process the same or different? Why do you think it was this way?

-3x+2  ≤  -4      What numbers make this statement true? Can we use the same procedure as before?  Create a visual representation to show all of the solutions your group finds.

Solve this one with the same method you used before or another method you hear about when we discussed.  Was this process the same or different? Why do you think it was this way?

What is a rule that seems to work for all of these? Discuss at your table, everyone has something to add.

Compound Inequalities

-5<x<4       How might this problem be the same and different from the ones before?  What numbers make this statement true? Create a visual representation to show all of the solutions your group finds.

What ideas do you have for solving this? We will share our ideas and discuss.

-9 ≤ 2x + 3 < 5     What numbers make this statement true? Can we use the same procedure as before?  Create a visual representation to show all of the solutions your group finds.

Try to solve this based on our discussion. What are some thoughts you have about this type of problem?

6 > -2x +4 ≥ -12       What numbers make this statement true? Create a visual representation to show all of the solutions your group finds.

Solve this one with the same method you used before or another method you hear about when we discussed.  Was this process the same or different? Why do you think it was this way?

What is a rule that seems to work for all of these? Discuss at your table, everyone has something to add.

5x ≥ 15 or 2x+3 < -13   How would you solve this? Think and discuss with your table and try to find a solution. You can use any method that works.

I would at the end talk about AND and OR symbols and have the students write down what they feel like is important for notes.

The next lesson will explore Absolute Value.

Posted in Questioning, Solving Equations

Solving Equations Questions

When we began our first unit in Algebra we wanted to set the stage for good questioning and not just wrote note taking. Here are a few of the questions we used with our table groups so students would talk and form knowledge about what we were learning. We encourage students to debate with each other and provide solid mathematical evidence to support their thoughts.

  • Variable
    • At your table, discuss the variable in the problem and how you would solve for it: 2x-4=10
  • Operations
    • 4x+8=18 How do you use inverse operations to solve this?
  • Coefficient
    • Locate the coefficient(s), what happens to the coefficient when you solve.
      • 5x=3x+2
  • Expression vs equation
    • How could you make this expression an equation? Now solve at your table.
    • 3.5x+12

When are are finished with each section, we ask the students what they think would be important to write down. Some write a lot, some not as much. It’s important for them to learn how much information they need for their own learning.

Posted in Questioning

Questioning Tab

I loved taking notes. I’m probably one of the few students in my class who took pride in my notebook and wanted neat orderly notes with colorful dividers. I’ve never looked at those notes since the class ended. I don’t remember much about what was in them. I mostly wrote down what the teacher told me to write and didn’t have to think about it much. I don’t want this for my students. I want them to talk about what we are learning, debate their thinking and really dig into the knowledge.

One way I’ve found to do this is to ask guiding questions and then let students discuss at their table. You can search from the side menu through the questioning posts or you can go to the questioning tab at the top where I will curate all the posts with guiding questions. If you have suggestions, please send them through the Google Form link in the menu.

photo by Sean MacEntee https://www.flickr.com/photos/smemon/7118780327