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Monthly Archives: January 2016

8.F.5 Day 1,2

Focus Question – How do you recognize a non-linear equation in a graph, table, or equation?

This is a relatively new topic for students. Students should have knowledge of what a linear functions look like so because of this they should be able to contrast to discover, they will have a clue in recognizing nonlinear functions. This should be easily true for graphs, but less easy for tables and equations.

Day: 1

Students will work on the packet linked below in their groups. The packets guide students to discover that if the lines are not straight then they are nonlinear (obviously). They then go down the path to discover that if they try to find rate’s of change for the values in the table then they will vary or not be constant. This should show them how to recognize if a table of values is linear or nonlinear.

https://www.engageny.org/resource/grade-8-mathematics-module-5-topic-lesson-8

After students attempt the problems to to discover the above, I will circulate around the room and check in with each group to make sure this understanding is cemented.

Finally students will complete #4-10 for homework. Which allows them to think through if the equations are linear or nonlinear without graphing or making a table.

Day 2

Have students in groups write down the equations that they thought were linear and which were nonlinear. Have students discuss and find common characteristics that allowed them to discover if they were linear or not.

Use Desmos.com for students to test out their “characteristics” from above. Graph similar equations to see if they are also linear/nonlinear.

Discuss the discoveries as a class and make a list of things to look for in an equation that guarantees it will be nonlinear.

Have students do a few problems from the book p. 330-1 to check for understanding.

Spend the rest of time reviewing for the Functions Test.

 


8.F.4 Day 1

Focus Question – How do you write functions?

This is a skill that the students worked on many days when working on the EE standards so this is mostly a day of review.

  • Have students work individually on page 322 #1-3.
    • Have students do one problem by themselves, check it in groups and then share back as a class.
  • HW: p. 323 #1-6,9,12

8.F.2 Day 1&2

Focus Question – How do you compare functions?

Students worked through p. 314-318 in book with sub. This content is mostly review over concepts they have learned previously – slope, y-intercept, tables, graphs, and equations.

  • Work through examples in the Engage NY packet:
    • https://www.engageny.org/resource/grade-8-mathematics-module-5-topic-lesson-7
    • Order: 1,3,4
      • Emphasize to students they need to compare rates of change (slope) and y-intercepts. They need to practice finding these in tables, graphs, and equations. If they can make a comparison without finding slope, allow it, but have them practice it in addition.
    • Student Homework #1-3
    • Exit Slip in Teacher Packet if time allows.

8.F.1 Day 1 & 2 Take 2

Days 1,2 – What makes a function a function?

Focus Question – What makes a table a function?

  • Intro with: https://www.illustrativemathematics.org/content-standards/8/F/A/1
    • Lessons in order:
      • Introducing Functions
      • Foxes and Rabbits
      • If The Customers
  • Practice and HW: https://www.engageny.org/file/48221/download/math-g8-m5-topic-a-lesson-2-student.pdf?token=Vym_jPNp0XzgJcvox0fQgzRYmm0yQrWoftCelSO_0L0
    • Pages 2,4,5,6

8.F.5 Day 1

Day 5 – Describing Functions Qualitatively

Bellwork – 1 problem of negative exponents review, 1 problem of exponent properties review

Focus Question – How do you describe a function qualitatively from a graph? How do sketch a graph from qualitative information?

  • Examine the difference between Qualitative and Quantitative Data/Information
    • Students will begin by having students examine root words to try and decipher what the meaning of each word would be.
    • Compare them. What is similar and different about them.
    • Use Moneyball example. Tie into the Browns.
      • Watch a clip, and discuss the controversy of using observations and feelings vs. using a statistical analysis.
  • Pass out “Graphing Your Story” Papers and explain that we have been looking at graphs exclusively in a Qualitative sense, now we are going to try to look at them in a Quantitative sense.
    • When thinking about quantitative graphs, it helps to think about them as a story they are trying to tell.
    • Students look at the graphs and write the story it describes.
    • Students then create a story and draw the graph.
    • Students trade stories with someone else and see if their graphs match after a partner tries to draw it.

 


8.F.1 Day 1

Day 1 – What makes a function, a function.

Focus Question – What is a function?

Bellwork – None due to quiz

This day is supposed to just be review as we went over this standard earlier in the year.

  • Go over previous day’s word problem homework.
  • Students take quiz on 8.EE.8b
  • Have students write down the definition of a Function in notes:
    • a rule that assigns exactly one output for every input
  • Students will have to make an equation, table and graph that ARE functions and that ARE NOT functions
    • They can work on this in groups and should check them
    • I will circulate around the room to provide feedback and intervention on the topic where necessary.

Exit Slip – Draw a graph and a table and ask students if they are a function or not.

HW – None


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.