## 8.EE.5 Day 4

Day 4 – Finish slope intro

Go over staircase activity with students. Have students apply knowledge to several examples of finding slope from two points on a coordinate plane. Have students interpret y=mx and then go back to their slides, from Thursday. They should graph all of their partner’s equations using desmos.com and then compare them to their predictions on the slide. Finally they should write several sentences comparing the slopes of all partners.

Day 4 Reflection:

The staircase activity was summarized by me asking which ratios students made. I wrote three different examples down and then steered them towards the step height and length ratio. It felt slightly forced, but it was effective. We compared the highest and lowest and then I had students pick one that should be in-between and find that one. Students finished graphs in desmos and reflected on it well. We had time for 3 examples that students had to think through and try y=2x (I graphed two ordered pairs and then they had to find the equation and interpret the slope from the equation). We used this equation to move from y=kx to y=mx as students found out that k was the same thing as slope. Students then graphed y=3x on their own with slope. Then they did y=1/4x. Some students shared back that they graphed it in the form of (1/4)/1 as the slope while others just graphed 1/4. Homework was p.184 #1,2 p. 185,7 #1,2,3,16,17. HW is pulling slope from graphs (the reverse of what we did in class). Should start with negatives tomorrow to cement this understanding as students will blindly try it tonight.

## 8.EE.5 Day 3

Day 3 – Slope Discovery

Students will spend the majority of the class working on the staircase slope discovery activity. Students will try to discover how to mathematically describe slope without the conventional terminology of “rise over run” and without being told what to measure. The point is try and mathematically describe why a certain staircase is steeper than another and prove it by measurement. Hopefully students will eventually arrive at comparing a ratio of step height to length.

Day 3 Reflection:

I don’t think this lesson went great. It could be because it was the first time I taught this lesson and so I wasn’t sure of the best questions to ask students as I circulated. I also think that asking students to arrive at a ratio comparison of vertical change to horizontal change is a reach. In the end students got close because of hints I gave, but only 1 student out of more than 50 arrived at the ratio of step height to step length.

## 8.EE.5 Day 2

Day 2 – Estimating Proportional Graphs

• Students took a screenshot of their desmos.com graph and put into a google slide.
• Students then took the equations of their 3 partners and made a line tool where their partner’s equations would be roughly compared to their own.
• The hope here is that students begin to see how steepness is related between proportional relationships by their constant of proportionality which we will transition to calling slope in the next two days.
• Students then work on linear (and proportional) table and graph identification in their book.

Day 2 Reflection:

This day went well. All students seemed to utilize Desmos.com well and I was able to quickly assess if they correctly got an equation for their graph as I walked around and checked computer screens. Both classes took a review of y=kx as they never saw the “k” before. I ran through an example of my own, they discovered my equation and then in turn were able to discover those – this was for the benefit of the students who could not find their own equation (about 80% in per 1 and 60% in per 6).

## 8.EE.5 Day 1

Day 1

• Review/scaffold proportional relationships.
• Students created proportional relationships by measuring an action for a time limit. They found their personal unit rate.
• Students graphed proportional relationships on desmos.com using a table and then created their equation and checked it by graphing over their points on the line via desmos.com.

Day 1 Reflection

The activity went well. Time was not always the independent variable as originally anticipated (i.e. how much time until a person blinks). Some groups finished early, be ready for students to move on past this.

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