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8.EE.6 Day 6

Day 6 – Summarize Crime Case Activity

Focus Q – How do you find the linear equation of a table without graphing?

  • Have students share back how they arrived at their conclusion
    • Challenge students who only found the unit rate way of graphing if they can find a second way.
    • Showcase graphing the proportional relationships and hep students to arrive at the idea of graphing the equations in the form of y=b-mx
      • Discuss why b-mx makes sense for this problem.
  • Students look at tables and try to determine the linear equation of the table.

8.EE.6 Day 5

Day 5 – Math Mystery Crime Case

Focus Q –  How can math be used to solve a crime?

Have students complete Math Mystery Crime Case activity.

Have students attempt the graphs and discover the proof by graphing anyway they see fit.


8.EE.6 Day 4

Day 4 – Graphing slope-intercept equations

Focus Q – How do you graph equations using slope-intercept form?

  • Bell Work – Finish part C from this task
  • Go over Homework
  • Have students graph the following:
    • y=4x-2
    • y=1/2x+3
    • y=-2x+1
    • y=-3x-4
    • y=-1/3x+1
  • Draw a horizontal line through 3. What is the slope of the line?
  • Draw a vertical line through 2. What is the slope of the line?

8.EE.6 Day 3

Day 3 – Focusing on the Y-Intercept

Focus Q – What does the “b” in the equation y=mx+b represent?

  • Begin by going over the equation comparison paragraph
  • Attempt to derive what the b is referencing. Give another example to showcase what b is referencing:
    • Ex: I need to rent a car. It costs $25 to reserve a car and then $50 per day. What equation describes this relationship?
    • also need examples of negative y-intercept
  • students should be able to identify where the y-intercept is on a table, equation and graph

8.EE.6 Day 2

Day 2 – Bringing y=mx to y=mx+b

*Finish the multiple points on a single line. Similar triangles?

Focus Q – What does a linear equation look like when it is not proportional?

This lesson is all about setting up the need for a y-intercept of “b” in the equation.

  • Where would the equation y=50x start from?
  • When would an equation not start from there? What would that look like?
  • Tech Weigh In Rich Task
    • Compare direct variation to y=mx+b back to back
    • Allow for plenty of time for students to attempt to find the macbook weight.
      • Emphasize that this is the starting weight.
      • It would helpful to find the weight of 1 iPad.

HW:


8.EE.6 Day 1

Day 1 – Deeper into Slope

[this lesson probably should have been done after the EE.5 quiz and that lesson moved to here]

Focus Q  – How do you find the slope between any two points?

The goal of this lesson is to end the period by having students recognize that any two points on a line will be able to provide slope.

  • Estimation bell work. Running a cable from projector to the back of the room. 
  • Put an example on the board of finding the slope of two points graphically – maybe have students create it.
  • Give students a pair of ordered pairs and ask them to find the slope without graphing the two points.
    • Emphasize using the change in y over change in x
  • Practice this several times.
  • Give students a list of points that are on the same line. Assign each group of students two different points from the list.
    • Students share back and discover that all points are actually on the same line.
    • make observations on similar triangles comparison between the pairs of points.
  • Prove the above problem works by giving them another line with multiple points they they have to find the slope through multiple sets of points.

HW: Slope problems from table and 2 ordered pairs. (P.185-6 #4-8,11)

Day 1 Reflection:

The flow was good and lesson went well.

   
    
    
 


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


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