## Desmos, Progressions & Supplementary Angles

Summer!  The time to catch up on sleep, projects around the house and blog posts.  This post is the 3rd in a 3 part series I started back in February. I spent two days working with Candace and her 7th grade students on complementary and supplementary angles.  I wrote posts on the complementary angle activity builder (day 1) and the opening activity on day 2.  Finally, here’s the post on the Desmos Supplementary Angles Activity Builder.

In this post:

1. Lesson guide for the  Supplementary Angles Activity Builder
2. Extension question
3. Connection to grade 8 standards/highlighting common core progressions.
4. Closing thoughts & ticket out the door

***********************************************************************

## Desmos Supplementary Angles Activity Builder

Slide 1 : Since it was the second day moving angles with sliders, students jumped right in and got to work.

Slide 2:  As students are writing, the overlay allows you to read their responses in real time. Take this opportunity to address SMP #3 & 6 when possible.  Ask students to

• Refine their explanation by using academic language (precision of language)
• Fix grammatical mistakes.
• Elaborate on a thought. (mathematical precision)
• Connect their thinking to other aspects of mathematics.

Student Responses:

************************************************************

Slide 3 & 4:  These 2 slides were designed to connect geometry with linear equations. This process was also done the day before with complementary angles, which is why one student stated the equation, x + y = 180, in her response above.

By definition, supplementary angles occur when the sum of 2 angles equals 180˚ Therefore when a student creates a 0˚ angle and a 180˚ angle, the supplementary angle sign doesn’t pop up.   This situation should be addressed during the whole class discussion on slide 5.

Since students ran through a similar question series with complementary angles, many just skip to slide 4, fill in the chart and input the equation.  A few students are compelled to enter in ALL the possible points, as shown below. 🙂

************************************************************

Slide 5:  This planned stop prepares students for the upcoming discussion. This is where I’ll write the shared supplementary angle pairs on the board for all students to see.

**************************************************************

Slides 6 & 7: For the learners who require more scaffolding, The slide 5 class discussion combined with slides 6 & 7 will walk them through the rest of the activity.  For students who have already finished this section, you may wish to present them with the extension question given in part 2 of this post.

******************************************************************

Slide 9 & 10:  When searching Teacher.Desmos.com/browse, I came across Kate Nowak’s activity builder, Measuring Circles.  It included the slide to the right.  I loved it!!

1. Proportional reasoning is a main topic in 7th grade.  Any opportunity to spiral back to it is welcomed.
2. I love the overlay aspect of displaying the class consensus.
3. In my adaption, I used rectangles as opposed to circle.
4. Now this activity integrates geometry, linear equations and proportional reasoning.

**********************************************************************

## Extension Question

When I c0-taught this lesson, we discussed that the example, 0 + 180 = 180, does not represent supplementary angles but didn’t connect this fact to the graph of x + y = 180. I wish I had. So…

Extension Question:  The line representing supplementary angles, x + y = 180, goes on forever in 2 directions.  As discussed earlier, not all points that add up to 180˚ describe supplementary angles.

• What part of the graph represents supplementary angle pairs?
• What part of the graph does not represent supplementary angle pairs?

*****************************************************************

Common Core Standards have been developed in a specific sequence or Progression. Proportional reasoning in 6th grade leads to discussing the constant of proportionality in proportional data in 7th, and then expands the conversation to include understanding the slope of both proportional and non-proportional relationships in 8th.

Here’s a list of areas to discuss in an 8th grade classroom.

• Function or non-function
• Function:  There’s one output for each input.  If 30˚ is the input, the only output could be 150˚
• Proportional or non-proportional
• Not proportional:  As one angle increases the other angle decreases
• Linear or non-linear
• Linear:  The graph is a decreasing line
• Discrete or Continous
• Continuous:  The angles 20.08˚ and  159.92 are a possibility.
• Identify the x and y intercepts.
• Y-intercept:  (0, 180) When the first angle is 0˚, the second angle is 180˚
• X-intercept (180, 0)  When the first angle is 180˚, the second angle is 0˚
• These 2 situations do not represent pairs of supplementary angles.
• Determine the slope and explain what it means
• Slope is -1.  As the first angle increases by 1 degree, the second angle decreases by 1 degree.
• Identify the independent and dependent variables
• X:  angle 1, independent variable
• Y:  angle 2, dependent variable
• Equation forms
• Standard:  x + y = 180
• Slope-intercept:  y = -x + 180
• Point-slope:  (y-150) = -(x-30)
• Test your equations on Desmos
• Write a compound inequality to display the supplementary pairs
• See below

***********************************************************************

## Closing Thoughts

Shedding light on the overlapping parts of math can build and strengthen students’ conceptual understanding of math.  By the end of this lesson, the 7th graders clearly understood the equation, x + y = 180 and it’s connection to supplementary angles.  Their ticket out the door was to describe the meaning of the x, y & 180.

I went into designing the supplementary and complementary activity builders for 7th grade.  The goal was to discuss the 2 relationships while connecting them to linear equations.  The more I mulled over the connection, the more I thought about 8th grade. With a little tweaking, the general idea behind this activity can be applied it to the 8th grade function and equation standards.