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Monthly Archives: November 2015

8.EE.5 Day 8 – Quiz Day

Day 8 – Review, EE.5 Quiz, and set-up EE.6

  • Go over HW packet from day before.
  • Students complete the following comparison practice problem:
    • Graph y=5x (don’t give them the equation). Give the equation y=4x. Have students find the equation to a relationship that is between the two.
  • Quiz: 8EE5quiz [#5 needs changed – the table on the right is not proportional and is not fair to put it on a proportional quiz]
  • Students work on the following notes/problem after the quiz:

Based on our definition and examples of direct variation one of the following equations is NOT direct variation.

y=2x+3 | y=(1/2)x

Which one is not direct variation?

Copy and complete the following table for the equation that is not direct variation:

x y
-2
-1
0
1
2

Graph the ordered pairs.

What makes this graph, table, and equation, not a proportional relationship?

Day 8 Reflection:

Students did well on practice review problem.

Quiz is still to be graded.

Students did well on post-quiz activity. 90% chose the right equation. Several had problems making a table. This should probably be reviewed on bell work for next class. Students correctly identified that this equation did not start at the origin and the equation had a +3 making it linear, but not proportional. They had to be reminded about show proportionality through the table by making ratios and show equivalency.


8.EE.5 Day 7

Day 7 – wrap up direct variation comparisons.

  • Bellwork – how many toothpicks are in the 6th term, 100th term – what equation will help you?
  • Finding slope from two points without graphing.
    • Focus on the table from homework (See day 6). Emphasizing change in y interval compared to change in x interval.
  • Making comparisons of direct variations.
  • Students practice direct variation graphs and equations.

Day 7 Reflection:

Students successfully were able to find the toothpicks in the 6th and 100th term, but many didn’t naturally gravitate to creating an equation until they were asked.

Homework went well, we had discussion around are 3.5 and 7/2 both acceptable slopes and that it is important to describe accurately that you are not just putting the y over the x to get the slope, but actually finding the change in y over the change in x.

Homework/Classwork took up a majority of the time in class – about 30 minutes. Several questions were checked periodically for understanding (specifically #7).

The comparisons were rough in one class as near 30% of the class picked each of the persons (below) as the least.

IMG_0411


8.EE.5 Day 6

Day 6 – Direct Variation comparisons

  • students will work on initial comparison of graph and table and then ask to graph an equation that will fall in-between the two linear functions.
    • practice 3 of these.
  • attempt to transition to finding slope from the tables without needing to graph.
    • practice several times
  • homework from the book on getting slope from two points.

Day 6 – Reflection

Students started off bell work with graphing two points and trying to find the slop of the line that passes through it using any method they wanted – (1,3)&(2,6). Most students started well but many had the inverse of the slope so we re-emphasized change in y over change in x. Students then worked on the following problem in their groups:

  
The problem went well. Most students graphed and then found the slope of each line. This allowed us to have many conversations about slope, rate, unit rate are all interchangeable. Students then worked on:

  
Every group was able to successfully provide a slope that worked except for a few that inverted the slope due to the nature of the table having x over y. 

HW: 

 


8.EE.5 Day 5

Day 5 – Equations, Slope, Graphing

[students will need graph paper]

  • have students graph y=2x
    • have students graph y=-2x and write observations comparing the two in hopes of driving conversation towards what a negative slope looks like.
  • After students accomplish this they will be given a graph with a negative slope and asked to graph it.
  • Students will be asked to look at graphs and find the slope and equation (desmos can be used).
  • Students will to compare graphs with tables and equations to determine which have the greatest or least rate of change.

Day 5 – Reflection

Bellwork was finding the slope of a line. We reviewed how slope was change in y over change in x. Students graphed y=2x and then compared it with y=-2x and begin noticing the difference between positive and negative slope. They then graphed y=-3x to show they can graph neg slope. Students then compared a rich problem comparing someone making $5 per hour vs losing 4 per hour. They had to write equations, graph them, and compare the rates of change. Then they finished by trying to graph two equations with fractional slow (y=1/4x and y=-2/3x).

HW: graph 4 equations for slope


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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