Complementary, Supplementary Algebra

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Objective

SWBAT find missing complementary and supplementary angles.

Big Idea

Students work in heterogenous groups to find missing values and angles using complementary and supplementary angle relationships

Do Now

10 minutes

Students enter silently according to the daily entrance routine. Do Now assignments are handed at the door as students sit down silently to begin their work. These last few weeks of school can be challenging in terms of motivation, so it is important to keep up the positive and try as much as possible to dispel the negative in non-reactionary ways. For example, as students enter, I am narrating positive student behaviors such as:

  • Julissa has come in silently and has already begin her work.
  • Mohammed has already filled out his heading and is tracking the words on paper to show he is reading.
  • Jennifer just underlined the word “equation” in the Do Now.

By “highlighting cooperative behaviors” students are being reminded of expectations in a neutral, non-threatening way. This is a method Lee Canter describes in a lot of his work with assertive discipline.

Students will be working silently for 5 minutes to find the missing angles in the do now example. This is spiraled material that I need to continue giving students for practice as some continue to struggle. It is an extension of the previous lessons. When we review the answer, I show students a strategy if they get stuck: list everything you know and what you are being asked to find. Students will work together, calling on each other in class, to solve this problem. The following video details the vocabulary and facts students need to discuss. As much as possible, I aim to ask questions rather than give out answers, facts, or steps to solve.

Class Notes

15 minutes

After reviewing the answer to the Do Now question, students receive C Notes. First, they must fill out the heading and copy the definitions off the board. After copying the definitions, students must independently and silently draw examples of these two definitions. As I walk around I make sure:

  • Students are including labels in their drawings to show they understand the difference between the terms
    • i.e. including angle measures, squares to indicate complementary angles, or linear pairs for supplementary angles
    • students are labeling the angles appropriately, using three points or an arc to identify the angle

 

We then move on to the third topic, “algebra”. The note included in the worksheets is also included in the notes, students do not have to copy down that summary. They are asked to read it silently and underline or highlight any words they don’t understand or are important. I narrate any actions students take that are positive toward this end, for example:

  • Aleyah underlined missing angles
  • “the value of a variable is not necessarily the same as the measure of an angle”; excellent phrase to highlight Chris!

 

Again, the narration of these positive behaviors let other students know what is important in a positive manner. Now it’s time to see if they understood what they read. I ask them all to add 4 points to the picture to help distinguish and talk about the two angles that make up the right angle. By having students add and label the points themselves, I am hoping to get my few struggling students closer to mastering this basic skill: identifying angles according to three points.

 

 

I guide students to writing an equation like this:

 

 

Once I have helped them to set up the equations, they must work with partners to solve the equation, without answering any questions, because none have yet been included. Once students have been given time to solve (2 – 3 mins), I will ask them to write down the following three questions and answer them within their notes:

1)      What is the measure of angle ABC?

2)      What is the measure of angle CBD?

3)      What is the measure, as an algebraic expression, of angle ABD?

 

This final question may confuse students. Many are still stuck in the concrete state of mind answering #3 thusly,

  • 90 degrees
  • It’s a right angle

For these students, remind them that the question asks for an algebraic expression and that the definition of this term is a mathematical sentence consisting of variable terms. Thus, the answer should be 3x.

Class Work

20 minutes

Students will be working in groups of 4. I will be working with a group of 6 – 8 students lagging in algebraic skills so that I can give them more one-on-one attention in terms of these needs. For this small group I may be doing much of the set-up of the equations in each problem and prioritizing practice in solving equations. This is a skill that needs to be prioritized to get ready for 8th grade math.

All other groups will be determined before the lesson so that I can ensure each group includes a confident and able student peer who will be able to get through most of the class work answers correctly AND be able to lead his team through the work by explaining and guiding. Each group will also be assigned one problem from the Day 151 - classwork to display on the board. Groups must work together to finish this task and will be asked to take any remaining problems home to complete for homework. Students will also be advised that this is a graded assignment.

Working with a small group at the front of the room will also enable me to help the rest of the class with challenging problems like #2. Many students have struggled all year with algebraic translations. Knowing this allows me to foresee this misunderstanding so that I can draw the appropriate picture for this problem on the board as I help my group. Having the drawing (and the drawing only) on the board will help all other groups. One student in my group will be adding the rest of the solution for this problem later in this section of class.

Once there are about 10 minutes left in class, all groups are warned that in 5 minutes we will review the answers and students must have their work on the board ready to display for other students.

Once there are 5 minutes left, all students will stop working and we will line up to walk quietly around the room, observing other students’ solutions and asking questions if something is not understood, or if students disagree with any given answer.

Closing

10 minutes

After answering questions and reviewing the answers to the class work, I give students their homework. I want to use this time to make sure students know how to complete some of the homework items.

I am mostly concerned with the first few problems which include no pictures. These are the types of items students usually struggle to complete correctly on their own. Many are still resistant to the idea of drawing a visual if one is not provided.

The best way to review these problems to ensure buy-in from students is to use whiteboard. Nothing is permanent and it’s fun to use them. Each student receives a white board and dry erase marker and is asked to take 1 minute to read question #1 and begin solving. “No”, I admit to them, “you will most likely not have enough time to solve, this is NOT A SPEED TEST”. Students must be encouraged to show their steps neatly and visibly. When time is up I will narrate the steps students have taken to solve, especially if they have shown a picture or written a correct equation. I also correct any mistakes I may see on students’ boards. Some misconceptions I am actively looking out for include:

  • Incorrect equations
  • Confusing supplementary for complementary sums ( = 180 not = 90)

Using whiteboards can also help me flag students who show nothing on their board or visibly have deep misconceptions about the material. I will be having a separate conversation with them at the end of class where we will jointly find a solution for this problem, may it be review and rewrite this specific part of my notes, show up to tutoring, or research online and print the results (no more than 2 pages) back to me. 

I've also attached and additional practice resource used during study halls or remediation blocks.