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8.EE.8b Day 4

Day 4 – Continued review and intervention on solving systems of equations with substitution.

Focus Question – same from day 3

Bellwork: 1 Exp Properties; 1 systems


8.EE.8b Day 3

Day 3 – Review Quiz and Practice

First day after Winter Break. Quiz came back with Per. 3 averaging a 66% and Per. 6/7 averaging a 74% (Students did remarkably better on graphing systems, 8.EE.8a with 81% and 86.5% respectively). We will spend the next two days reviewing and providing intervention and practice for students to retake the assessment one more time as a class.

Focus Question: How do you solve systems of equations using substitution (without graphing)?

Bellwork: 1 Neg Exp; 1 Solve Equations

  • Have students retry quiz in their groups.
    • Students will log into goformative.com and answer questions from there. They will then compare new answers to answers they already have to see if they think they got the question right or wrong. Work will be done on a piece of paper.
    • Emphasize SUBSTITUTION to help them get through difficult problems. Have them write it at the top of their paper.
  • I will circulate around the room to answer questions and provide intervention during this process where necessary.
  • After students finish they will further practice systems of equations word problems (Word Problem W.S. p.52) which is homework. If students finish early they are to check answers and correct where necessary.

8.EE.8 Day 6

Day 6 – Review converting to slope intercept form and graphing.

Students struggled with turning equations into slope intercept before graphing. We went over homework then students tried two more problem in book – p. 238 #1,2. Students then worked on #3 to write equations for a word problem and then graph them to find their solution. Quiz tomorrow over finding solutions to a system of equations by graphing.

HW: P. 241 #15-20


8.EE.8 Day 7

Day 7 – Substituting to Find Point Of Intersection

Increasing complex examples on substituting to find the point of intersection. Examples taken from book page 244 and on. Students will try them first in groups to compare answers and then we will go over them.

I am not sure how to make this into an inquiry or rich task. Thus, students will take notes on example problems and then practice the skill while I circulate and help students who are struggling.


8.EE.8 Day 5

Day 5 – No Solutions and Infinite Solutions

This day is meant to be the last day of finding the systems of linear equations graphically.

Bellwork: Graph an equation with a negative slope.

  1. Take questions on homework.
  2. Have students sketch a graph of what it looks like to have one solution (hint: they just did it for homework repeatedly)
  3. Could there be other outcomes besides one solution? Discuss.
  4. Can you sketch what No Solutions would look like.
  5. Can you sketch what Infinite Solutions would look like.
  6. Run through examples in book on these. Students will also be practicing manipulating equations and moving variables.
  7. See if students can figure out what do with the equations to make them graphable (turn them into slope-intercept).
  8. Ex 1: y-x=1;y=x-2+3
  9. Ex 2:y=2x+;y=2x-3
  10. Ex 3:y=2x+1;y-3=2x-2
  11. Ex 4:y=2/3x+3;3y=2x+15

HW: p. 239 #1-6

Day 5 Reflection

I underestimated the struggle with turning equations into y=mx+b. When I initially asked students to turn the equations into slope intercept form there were an equal amount of students who were able to figure out some of the steps and those that could not. This skill will have to continue to be practiced – must likely during Bellwork.


8.EE.8 Day 4

Day 4 – Practice Graphing Systems and Proving 1 Solution

Bellwork:  Write the equation for a negative slope graph (review).

1) Finish the Celsius vs. Fahrenheit activity by having students finish the following:

http://map.mathshell.org/download.php?fileid=1154
“Will the two equations ever give you the same answer?” “How do you know?”s
“When do they actually give you the same answer?” Use the graph to prove it. Use math to prove it.

2) Go around and check each group’s mathematical proof that (10,50) is the solution to this systems of equation – meaning that both equations will be the same at 10,50.

3) After groups have proven the math, have them get started on the practice sheet (Ch. 3: Lesson 7 Extra Practice: Solve Systems of Equations by Graphing.

3a) Students are expected to graph each system to find the solution or point of intersection and then prove that it works using substitution in each graph.

Intervention: Circulate around the room and assist students who are having difficulty with the practice.

HW: Finish #1-8 on worksheet

Day 4 Reflection

Once I made sure each group could substitute and prove the original CvsF equations students started the worksheet practice. This allowed me time to move around the room and provide intervention for students who had either forgotten how to graph y=mx+b equations or were struggling with doing so. After scaffolding and intervention had been provided I felt confident that every student was leaving with the ability to finish the paper.

 


8.EE.8 Day 3

Standard: ee.8a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Day 1 & 2 established what a point of intersection looks like on a graph (begin with it again to reiterate). Day 3 & 4 need to begin to focus on that these points of intersection “satisfy both equations simultaneously”.

Focus question: What does the solution to a system of two linear equations graphically and mathematically look like?

Bellwork: What did changing the headstart distance of “Half-Speed Julio” do to his linear graph? Can you make a quick sketch to illustrate what you are talking about?

Recap Yesterday: At what time and distance would “Half-Speed Julio” and Rich be at the same place?

[in notes] Give a possible “solution” (there are infinite) to the equation y=2x+3. (hint: your answer will be in the form of an ordered pair)

[referencing homework problem] how many solutions do these two graphs have in common? Can you prove that the solution works for both graphs mathematically?

http://map.mathshell.org/download.php?fileid=1154

  1. Accurate Method vs. Estimation Method
  2. “Can you write an equation for each?”
  3. Graph it using Desmos.com
  4. “Is the estimation method close enough that it is worth using?”
  5. “Mathematically, why do the two equations give you close answers?”
  6. “Will the two equations ever give you the same answer?” “How do you know?”s
  7. “When do they actually give you the same answer?” Use the graph to prove it. Use math to prove it.

Homework: Finish questions 4 and 5.

Day 3 Reflection:

The majority of class was spent on understanding what a solution is and how many solutions a linear equation can have (infinite) vs. most systems of equations (one). I will spend a separate day to teach infinite solutions and no solutions. Students then began the converting Celsius to Fahrenheit activity above, but we only reached graphing the two equations in Desmos. Students had to finish 4 and 5 on their own.

 


8.EE.8 Day 2

Day 2 – continued practice on visually seeing and determining points of intersection.

Bellwork – find the equation of a graph

Go over homework to review 8.EE.6 retake #3

Take 8.EE.6 retake #3

Lesson:

[finish lesson from yesterday]

  1. What if Julio runs at half speed. What will the race look like? (Assume no head start for Rich)
  2. What kind of head start will he need to make it close? To win?

[Day 2 Lesson Start]

http://map.mathshell.org/download.php?fileid=1154

  1. Accurate Method vs. Estimation Method
  2. “Can you write an equation for each?”
  3. Graph it using Desmos.com
  4. “Is the estimation method close enough that it is worth using?”
  5. “Mathematically, why do the two equations give you close answers?”
  6. “Will the two equations ever give you the same answer?” “How do you know?”s
  7. “When do they actually give you the same answer?” Use the graph to prove it. Use math to prove it.

Closure: HW: y=2x+2 and y=3x. At what ordered pair do these two lines intersect. Make a prediction and then graph to see if your prediction is correct or not.


8.EE.8 Day 1

Day 1 – Points on Intersection

http://threeacts.mrmeyer.com/playingcatchup/

Bellwork – Estimation 180, and a y=mx+b from 2 points

  • Watch video – stop at 17 seconds. Show 2 images. “Who is faster?”
    • Write equations for both people and graph them on desmos to prove who is faster.
    • Who will win the 40-yd race?
  • Continue video – stop at 24 seconds. What if we give Rich a 10 yd head start?
    • Write equations and graph them to show who would win this 40 yd race.
    • How close is the finish?
    • How could you prove with math that Julio actually won? By how many seconds?
    • How many seconds did it take for the lines to cross? What does this intersection mean in terms of the race?
    • Finish the video – stop at 31 seconds.
  • What if Julio runs at half speed. What will the race look like? (Assume no head start for Rich)
    • What kind of head start will he need to make it close? To win?

Closure: HW: y=2x+2 and y=3x. At what ordered pair do these two lines intersect. Make a prediction and then graph to see if your prediction is correct or not.

Day 1 – Reflection

We went through the majority of the lesson in class. Students finished at the third bullet point. “What if Julio runs at half speed.” The plan is to pick up there tomorrow. Observations: Many students found speed as sec/yd. When pressed to prove how math shows Julio is still faster than Rich, many students had problems seeing they needed to substitute 40 in for y and solve for x. Maybe make a bigger deal about defining x and y. Or start the question with “how many seconds faster was Julio than Rich?” Several strudents struggling with problem perservering today. Could be a factor of Monday, distractedness, or myself not setting up questions with enough clarity to tackle them efficently.

This is the work that many students struggled to come up with on their own:

image

I decided to make the homework review problems in preperation for a retake quiz tomorrow:

image

 

 

 


8.EE.6 Day 10

Day 10 – Continued Intervention w/ Slope, Graphing, Finding Equations

Estimation 180 for bellwork

Work on the following Khan Academy Lessons:

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-slope/e/line_graph_intuition

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-slope/e/slope-from-a-graph

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-slope-intercept-form/e/graph-from-slope-intercept-equation

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-slope/e/slope-from-two-points

Practice for getting slope-intercept equations from two ordered pairs. (didn’t get to – we did notes on quiz question instead – maybe start class with this tomorrow)

image

Practice for students still struggling with slope triangles: (didn’t get to)

stairsteepMMM

 Day 10 Reflection:

Bellwork went well. We went over quiz. Students wrote into notes the table question and we went over how to solve it. Students then worked with their partners to pick 2 other pairs from the table and go through the same steps to find the same same slope-intercept equation.

Students then worked on Khan Academy lessons while I circulated around the room. Majority of students finished the first lesson. The hope is to get both lessons done tomorrow, review finding the slope and intercept from two points and then take another post-test if time allows.


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