Wednesday, 6/7 - Review videos for Trimester 3 Math Final
Please click on the following links for review videos. Take good notes to help you study.
1. Transformations- Translations, Rotations, Reflections, and Dilations
Translations- to slide
3:58
www.youtube.com/watch?v=XdjH_EWhCZ0
Rotations: to turn
5:13
https://www.youtube.com/watch?v=pqVKmLVIfl8
Reflections: to flip
4:17
www.youtube.com/watch?v=j1X_UIOvEwA
Dilations- make larger or smaller
6:51
https://www.youtube.com/watch?v=BCllaARDOWI
2. Volume - Cone, Cylinder, Sphere
10:04
www.youtube.com/watch?v=U8sI9alygTc
3. Pythagorean Theorem
12:54
www.youtube.com/watch?v=WqhlG3Vakw8
4. Exponential Functions
6:04
www.youtube.com/watch?v=QJsKTTkIjFk
5. Exponent Rules
9:42
www.youtube.com/watch?v=kITJ6qH7jS0
Please click on the following links for review videos. Take good notes to help you study.
1. Transformations- Translations, Rotations, Reflections, and Dilations
Translations- to slide
3:58
www.youtube.com/watch?v=XdjH_EWhCZ0
Rotations: to turn
5:13
https://www.youtube.com/watch?v=pqVKmLVIfl8
Reflections: to flip
4:17
www.youtube.com/watch?v=j1X_UIOvEwA
Dilations- make larger or smaller
6:51
https://www.youtube.com/watch?v=BCllaARDOWI
2. Volume - Cone, Cylinder, Sphere
10:04
www.youtube.com/watch?v=U8sI9alygTc
3. Pythagorean Theorem
12:54
www.youtube.com/watch?v=WqhlG3Vakw8
4. Exponential Functions
6:04
www.youtube.com/watch?v=QJsKTTkIjFk
5. Exponent Rules
9:42
www.youtube.com/watch?v=kITJ6qH7jS0
8th Grade Cedar Point Reminders for June 10, 2016
- Be at KMS by 6:30 a.m. to board the busses for attendance (we will leave promptly at 6:45 with or without you and ticket is non-refundable)
- Dress appropriately – Shorts and tank tops are acceptable but remember we are representing Kennedy Middle School
- Bring sunscreen or raincoat if necessary
- Bring money for lockers if you chose not to carry things around
- Bring a lunch or bring money for lunch (about $40)
- The bus air conditioning is usually on and it gets cold on the way home especially if your clothes are wet from the water rides (bring a sweatshirt or blanket)
- Items can be left on the bus BUT there is no returning to the bus during the day
- Food/water /small coolers are allowed on the bus trip but returning to the bus during the day cannot be done
- The bus will be cleaned by the students before exiting the bus.
- Buddy System – you must be with another student at all times during the day
- Emergency – The First Aid Stations are located at the front (Snoopy Land) and back of the park - the chaperones will check there periodically.
- Be at the front of the park at 7:00 p.m. and ready for the ride home. We will leave with or without you (your parents won’t be happy if they have to come to get you).
- Parents should be waiting for you at Kennedy between 10:00 and 10:15 p.m. The building will be locked.
- Keep an eye on the sky and dress appropriately for the weather (currently the report is 77 degrees)
Bridge Project
Groups of 1 or 2 will design, construct, and test a bridge built out of flat toothpicks and Elmer's glue. Although class time will be given to work on bridges, some groups will have to work on them at home. Materials needed: flat toothpicks, Elmer's glue, and shoe box Constructions Dates: Blue Print Design: Tuesday, 4/25 Building Days: Wednesday, 4/26 Thursday, 4/27 Monday, 5/8 Friday, 5/12 Monday, 5/15 Monday, 5/22 Wednesday, 5/31 Thursday, 6/1 Friday, 6/2 Due Date (DEMOLITION DAY): Bridges must be completed by Monday, June 5th |
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Week of June 12th to June 15th
Monday, 6/12
8th Grade Math FINAL
Tuesday, 6/13
8th Grade Math FINAL
Wednesday, 6/14
8th Grade Farewell Dance
Thursday, 6/15 - 1/2 Day
Last Day of School
3rd-6th hours - 8th Grade Breakfast
Friday, 6/16
SUMMER VACATION
Monday, 6/12
8th Grade Math FINAL
Tuesday, 6/13
8th Grade Math FINAL
Wednesday, 6/14
8th Grade Farewell Dance
Thursday, 6/15 - 1/2 Day
Last Day of School
3rd-6th hours - 8th Grade Breakfast
Friday, 6/16
SUMMER VACATION
Week of June 5th to June 9th
Monday, 6/5
Check in Bridges
Review for FINAL
1. Transformations- Translations, Rotations, Reflections, and Dilations
2. Volume - Cone, Cylinder, Sphere
3. Pythagorean Theorem
4. Exponential Functions
5. Exponent Rules
Tuesday, 6/6
Demolish Bridges
Wednesday, 6/7
1. Transformations- Translations, Rotations, Reflections, and Dilations
Translations- to slide
3:58
www.youtube.com/watch?v=XdjH_EWhCZ0
Rotations: to turn
5:13
https://www.youtube.com/watch?v=pqVKmLVIfl8
Reflections: to flip
4:17
www.youtube.com/watch?v=j1X_UIOvEwA
Dilations- make larger or smaller
6:51
https://www.youtube.com/watch?v=BCllaARDOWI
2. Volume - Cone, Cylinder, Sphere
10:04
www.youtube.com/watch?v=U8sI9alygTc
3. Pythagorean Theorem
12:54
www.youtube.com/watch?v=WqhlG3Vakw8
4. Exponential Functions
6:04
www.youtube.com/watch?v=QJsKTTkIjFk
5. Exponent Rules
9:42
www.youtube.com/watch?v=kITJ6qH7jS0
Thursday, 6/8
Demolish Bridges
Friday, 6/9
Cedar Point
Monday, 6/5
Check in Bridges
Review for FINAL
1. Transformations- Translations, Rotations, Reflections, and Dilations
2. Volume - Cone, Cylinder, Sphere
3. Pythagorean Theorem
4. Exponential Functions
5. Exponent Rules
Tuesday, 6/6
Demolish Bridges
Wednesday, 6/7
1. Transformations- Translations, Rotations, Reflections, and Dilations
Translations- to slide
3:58
www.youtube.com/watch?v=XdjH_EWhCZ0
Rotations: to turn
5:13
https://www.youtube.com/watch?v=pqVKmLVIfl8
Reflections: to flip
4:17
www.youtube.com/watch?v=j1X_UIOvEwA
Dilations- make larger or smaller
6:51
https://www.youtube.com/watch?v=BCllaARDOWI
2. Volume - Cone, Cylinder, Sphere
10:04
www.youtube.com/watch?v=U8sI9alygTc
3. Pythagorean Theorem
12:54
www.youtube.com/watch?v=WqhlG3Vakw8
4. Exponential Functions
6:04
www.youtube.com/watch?v=QJsKTTkIjFk
5. Exponent Rules
9:42
www.youtube.com/watch?v=kITJ6qH7jS0
Thursday, 6/8
Demolish Bridges
Friday, 6/9
Cedar Point
Week of May 29th to June 2nd
Monday, 5/29 - No School
Memorial Day
Tuesday, 5/30
Complete Exponential Functions TEST
Wednesday, 5/31
Bridge Building Day
Thursday, 6/1
Bridge Building Day
Friday, 6/2
Bridge Building Day
Monday, 5/29 - No School
Memorial Day
Tuesday, 5/30
Complete Exponential Functions TEST
Wednesday, 5/31
Bridge Building Day
Thursday, 6/1
Bridge Building Day
Friday, 6/2
Bridge Building Day
Week of May 22nd to May 26th
Monday, 5/22
Bridge Building Day
Tuesday, 5/23
Exponent Rules Practice
Wednesday, 5/24
Review for Exponential Functions TEST
Thursday, 5/25
Exponential FUNCTIONS TEST
Friday, 5/25
1/2 Day - Complete Apollo 13
Monday, 5/22
Bridge Building Day
Tuesday, 5/23
Exponent Rules Practice
Wednesday, 5/24
Review for Exponential Functions TEST
Thursday, 5/25
Exponential FUNCTIONS TEST
Friday, 5/25
1/2 Day - Complete Apollo 13
Week of May 15th to May 19th
Monday, 5/15
Exponential Functions
Tuesday, 5/16
Pinery
Wednesday, 5/17
Pinery
Thursday, 5/18
Pinery
Friday, 5/19
Pinery
Monday, 5/15
Exponential Functions
Tuesday, 5/16
Pinery
Wednesday, 5/17
Pinery
Thursday, 5/18
Pinery
Friday, 5/19
Pinery
Week of May 8th to May 12th
Monday, 5/8
Bridge Building Day 3
Tuesday, 5/9
Exponential Functions
Wednesday, 5/10
Exponential Functions - Rabbit Population
Thursday, 5/11
Exponential Functions
Friday, 5/12
Bridge Building Day 4
Monday, 5/8
Bridge Building Day 3
Tuesday, 5/9
Exponential Functions
Wednesday, 5/10
Exponential Functions - Rabbit Population
Thursday, 5/11
Exponential Functions
Friday, 5/12
Bridge Building Day 4
Week of May 1st to May 5th
Monday, 5/1
One Grain of Rice
HW: Graph the exponential function for the first fifteen days of doubling the grains of rice
For the x intercept, use 1 as your intervals for the first 15 days. For the y-intercept, use 2000 for your interval.
y = y-intercept (growth factor ^ x)
y = 1/2 (2^x)
Tuesday, 5/2
NWEA Testing - Scores must show 4 points of growth
Wednesday, 5/3
NWEA Testing - Scores must show 4 points of growth
Thursday, 5/4
NWEA Testing - Scores must show 4 points of growth
Friday, 5/5
NWEA Testing - Scores must show 4 points of growth
Monday, 5/1
One Grain of Rice
HW: Graph the exponential function for the first fifteen days of doubling the grains of rice
For the x intercept, use 1 as your intervals for the first 15 days. For the y-intercept, use 2000 for your interval.
y = y-intercept (growth factor ^ x)
y = 1/2 (2^x)
Tuesday, 5/2
NWEA Testing - Scores must show 4 points of growth
Wednesday, 5/3
NWEA Testing - Scores must show 4 points of growth
Thursday, 5/4
NWEA Testing - Scores must show 4 points of growth
Friday, 5/5
NWEA Testing - Scores must show 4 points of growth
Week of April 24th to April 28th
Monday, 4/24
(Day 10) Social Studies CAT Afternoon Session: Students M - Z Afternoon session will begin at 12:10.
Students will be assigned to the following teachers and location for all testing:
Kubiak – Library - Maciejewski thru Moore, Stephen
McGuire – Room 134 – Morgan thru Remilong
Mackewich – Room 139 – Rice thru Smith,Taylor ( Cart # 9)
Desandre - Room 140 – Sonnenfeld thru Vanderworp ( Cart # 8)
Kensicki – Room 113 - Vargas thru Worden (Cart # 3)
Tuesday, 4/25
Blue Prints of Bridge
Wednesday, 4/26
Building Bridge Day 1
Thursday, 4/27
Building Bridge Day 2
Friday, 4/28
Guest Teacher
Monday, 4/24
(Day 10) Social Studies CAT Afternoon Session: Students M - Z Afternoon session will begin at 12:10.
Students will be assigned to the following teachers and location for all testing:
Kubiak – Library - Maciejewski thru Moore, Stephen
McGuire – Room 134 – Morgan thru Remilong
Mackewich – Room 139 – Rice thru Smith,Taylor ( Cart # 9)
Desandre - Room 140 – Sonnenfeld thru Vanderworp ( Cart # 8)
Kensicki – Room 113 - Vargas thru Worden (Cart # 3)
Tuesday, 4/25
Blue Prints of Bridge
Wednesday, 4/26
Building Bridge Day 1
Thursday, 4/27
Building Bridge Day 2
Friday, 4/28
Guest Teacher
Week of April 17th to April 21st
Monday, 4/17
(Day 5)- MATH CAT Afternoon Session: Students A – L Afternoon session will begin at 12:10.
Kubiak – Library – Abriel thru Bommarito, J.
Warehall – Room 134 – Bonser thru Daniels
Karle - Room 122 – Danna thru Furton ( Cart # 9)
Coffey – Room 123 – Gagnon thru Jemison ( Cart # 8)
Clow – Room 114 – Johnston thru Lozon (Cart # 3)
Tuesday, 4/18
(Day 6)- MATH CAT Afternoon Session: Students M - Z Afternoon session will begin at 12:10.
Students will be assigned to the following teachers and location for all testing:
Kubiak – Library - Maciejewski thru Moore, Stephen
McGuire – Room 134 – Morgan thru Remilong
Mackewich – Room 139 – Rice thru Smith,Taylor ( Cart # 9)
Desandre - Room 140 – Sonnenfeld thru Vanderworp ( Cart # 8)
Kensicki – Room 113 - Vargas thru Worden (Cart # 3)
Wednesday, 4/19
(Day 7) – MATH PT Morning Session: Students A – L Morning session will begin at 8:35 a.m.
Thursday, 4/20
(Day 8) – MATH PT Morning Session : Students M - Z Morning session will begin at 8:35 a.m.
Friday, 4/20
(Day 9)- Social Studies CAT Afternoon Session: Students A – L Afternoon session will begin at 12:10.
Kubiak – Library – Abriel thru Bommarito, J.
Warehall – Room 134 – Bonser thru Daniels
Karle - Room 122 – Danna thru Furton ( Cart # 9)
Coffey – Room 123 – Gagnon thru Jemison ( Cart # 8)
Clow – Room 114 – Johnston thru Lozon (Cart # 3)
Monday, 4/24
(Day 10) Social Studies CAT Afternoon Session: Students M - Z Afternoon session will begin at 12:10.
Students will be assigned to the following teachers and location for all testing:
Kubiak – Library - Maciejewski thru Moore, Stephen
McGuire – Room 134 – Morgan thru Remilong
Mackewich – Room 139 – Rice thru Smith,Taylor ( Cart # 9)
Desandre - Room 140 – Sonnenfeld thru Vanderworp ( Cart # 8)
Kensicki – Room 113 - Vargas thru Worden (Cart # 3)
Monday, 4/17
(Day 5)- MATH CAT Afternoon Session: Students A – L Afternoon session will begin at 12:10.
Kubiak – Library – Abriel thru Bommarito, J.
Warehall – Room 134 – Bonser thru Daniels
Karle - Room 122 – Danna thru Furton ( Cart # 9)
Coffey – Room 123 – Gagnon thru Jemison ( Cart # 8)
Clow – Room 114 – Johnston thru Lozon (Cart # 3)
Tuesday, 4/18
(Day 6)- MATH CAT Afternoon Session: Students M - Z Afternoon session will begin at 12:10.
Students will be assigned to the following teachers and location for all testing:
Kubiak – Library - Maciejewski thru Moore, Stephen
McGuire – Room 134 – Morgan thru Remilong
Mackewich – Room 139 – Rice thru Smith,Taylor ( Cart # 9)
Desandre - Room 140 – Sonnenfeld thru Vanderworp ( Cart # 8)
Kensicki – Room 113 - Vargas thru Worden (Cart # 3)
Wednesday, 4/19
(Day 7) – MATH PT Morning Session: Students A – L Morning session will begin at 8:35 a.m.
Thursday, 4/20
(Day 8) – MATH PT Morning Session : Students M - Z Morning session will begin at 8:35 a.m.
Friday, 4/20
(Day 9)- Social Studies CAT Afternoon Session: Students A – L Afternoon session will begin at 12:10.
Kubiak – Library – Abriel thru Bommarito, J.
Warehall – Room 134 – Bonser thru Daniels
Karle - Room 122 – Danna thru Furton ( Cart # 9)
Coffey – Room 123 – Gagnon thru Jemison ( Cart # 8)
Clow – Room 114 – Johnston thru Lozon (Cart # 3)
Monday, 4/24
(Day 10) Social Studies CAT Afternoon Session: Students M - Z Afternoon session will begin at 12:10.
Students will be assigned to the following teachers and location for all testing:
Kubiak – Library - Maciejewski thru Moore, Stephen
McGuire – Room 134 – Morgan thru Remilong
Mackewich – Room 139 – Rice thru Smith,Taylor ( Cart # 9)
Desandre - Room 140 – Sonnenfeld thru Vanderworp ( Cart # 8)
Kensicki – Room 113 - Vargas thru Worden (Cart # 3)
Week of April 10th to April 14th
Monday, 4/10 4/10 (Day 1)- ELA CAT Afternoon Session: Students A – L Afternoon session will begin at 12:10. Kubiak – Library – Abriel thru Bommarito, J. Warehall – Room 134 – Bonser thru Daniels Karle - Room 122 – Danna thru Furton ( Cart # 9) Coffey – Room 123 – Gagnon thru Jemison ( Cart # 8) Clow – Room 114 – Johnston thru Lozon (Cart # 3) Tuesday, 4/11 4/11 (Day 2)- ELA CAT Afternoon Session: Students M - Z Afternoon session will begin at 12:10. Students will be assigned to the following teachers and location for all testing: Kubiak – Library - Maciejewski thru Moore, Stephen McGuire – Room 134 – Morgan thru Remilong Mackewich – Room 139 – Rice thru Smith,Taylor ( Cart # 9) Desandre - Room 140 – Sonnenfeld thru Vanderworp ( Cart # 8) Kensicki – Room 113 - Vargas thru Worden (Cart # 3) Wednesday, 4/12 4/12 (Day 3) – ELA PT Morning Session: Students A – L Morning session will begin at 8:35 a.m. Thursday, 4/13 4/13 (Day 4) – ELA PT Morning Session : Students M - Z Morning session will begin at 8:35 a.m. Friday, 4/14 - Good Friday - NO SCHOOL |
Week of March 20th to March 24th and March 27th to March 31st
M-STEP BOOT CAMP
Monday, 3/20
Complete Check Up from Friday and Volume worksheets
Tuesday, 3/21
MSTEP boot camp
Wednesday, 3/22
Guest Teacher
Thursday, 3/23
MSTEP Boot Camp
Friday, 3/24
Computer Lab
http://sbac.portal.airast.org/practice-test/
Monday, 3/27
MSTEP BOOT CAMP
Tuesday, 3/28
MSTEP BOOT CAMP
Wednesday, 3/29
MSTEP BOOT CAMP
Thursday, 3/30
Computer Lab
https://wbte.drcedirect.com/MI/portals/mi
Friday, 3/31
Computer Lab
https://wbte.drcedirect.com/MI/portals/mi
Performance Tasks
https://www.illustrativemathematics.org/8
http://www.insidemathematics.org/common-core-resources/mathematical-content-standards/standards-by-grade/8th-grade
http://www.insidemathematics.org/performance-assessment-tasks
http://schools.nyc.gov/NR/rdonlyres/638B9380-FE20-422C-9556-8A6D56BD5C80/0/NYCDOEG8RepresentingandInterpreting_FINAL.pdf
Overarching Questions and Enduring Understandings
How might studying geometric relationships increase my understanding of how we use and classify numbers? How can these relationships be used to solve every day and mathematical problems?
8.G.C. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.C.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Knowing the formulas for the volumes of cones, cylinders and spheres and applying them to solve real-world and mathematical problems is also a part of this unit. Within the volume formulas, both square roots and cube roots may arise in problem solving situations.
How might studying geometric relationships increase my understanding of how we use and classify numbers? How can these relationships be used to solve every day and mathematical problems?
8.G.C. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.C.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Knowing the formulas for the volumes of cones, cylinders and spheres and applying them to solve real-world and mathematical problems is also a part of this unit. Within the volume formulas, both square roots and cube roots may arise in problem solving situations.
Week of March 13th to March 17th
Monday, 3/13 Volume of Cones V cone = 1/3 × pi × r^2 × h Tuesday, 3/14 Volume of Cones V cone = 1/3 × pi × r^2 × h Wednesday, 3/15 Volume of a Cylinder Volume: π × r² × h Thursday, 3/16 Volume of Spheres V =4/3 x pi x r ^ 3 Friday, 3/17 Check Up on Volume |
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Week of March 6th to March 10th
Monday, 3/6 Working with Radicals Review Tuesday, 3/7 REVIEW for TRIMESTER 2 FINAL- Linear Systems, Equations, Pythagorean Theorem, Radicals Wednesday, 3/8 TRIMESTER 2 FINAL Thursday, 3/9 Complete Final Friday, 3/10 - 1/2 Day |
Week of February 27th to March 3rd
Monday, 2/27 Pythagorean Theorem Tuesday, 2/28 Pythagorean Theorem Wednesday, 3/1 Pythagorean Theorem Thursday, 3/2 CHECK UPS on Pythagorean Theorem Friday, 3/3 Review |
Overarching Question
How do exponent rules and scientific notation help represent, develop, and analyze exponential relationships?
Essential Focus Questions
1. How can you tell if a function is linear or non-linear by looking at the graph of the function?
2. How does a table of values for a non-linear function differ from the table of values for a linear function?
3. How can you recognize exponential growth or decay from a graph, function rule, table, or real-world situation?
4. What are some differences between linear and exponential functions as seen in their tables, graphs, and rules?
5. How is using scientific notation helpful in representing and comparing quantities? Why does scientific notation involve using a power of ten in the expression?
6. How might using exponents be helpful in comparing populations? What strategies might help in these comparisons?
In this unit students continue building the idea of a function. They will work with the idea that a function assigns each input exactly one output and distinguish between linear and nonlinear functions. Many examples of non-linear functions exist, and students should compare and contrast these nonlinear patterns to linear patterns. In this unit, students compare and contrast exponential and linear functions noting similarities and differences between the two functions.
Students will continue to explore modeling of mathematical situations with multiple representations, from unit 2, by conducting simulations that model exponential growth and decay. They first learn to represent and recognize exponential patterns in a table of values. Examining the recursive pattern, students will see that unlike linear functions with a constant rate of change, exponential functions change by varying amounts. For example the consecutive y values 2,6,18,54 increase by 4,12,and 36. However, exponential functions also have a common factor. In the previous example, each successive y value could be found by multiplying the previous value by 3. Students use common factors to rewrite y values in expanded and exponential form. For example, 2, 2•3, and 2•3•3 or 2•30, 2•31, 2•32. (Students have had experience using exponents to denote powers of 10 in fifth grade, and writing and evaluating numerical expressions with exponents in sixth grade.) By attending to the structure of these numerical expressions, students may also represent the exponential functions with an explicit rule, y=2•3x-1 although symbolic representation of exponential functions is not explicitly called for in the standards until high school.
As students explore exponential relationships and use multiple representations to solve interesting exponential growth and decay problems, scientific notation is naturally used to represent very large and very small quantities. Technology, such as graphing calculators and spreadsheets, display numbers in forms like "3E+10" that students will need to use knowledge of scientific notation to interpret. As students compare populations of exponential relations, they develop and apply properties of exponents. For example, they know from elementary school that division can be used to find that 243 is 9 times larger than 27. In exploring exponential growth, they might have also expressed these numbers in exponential form and represented the related expression, 35/33 or 3•3•3•3•3/3•3•3 which they can deduce is 32. They will also perform similar operations with expressions written in scientific notation. These calculations should be done by using the understanding of the concepts of exponents.
In high school, work with exponential expressions extends to rational exponents. Students will also use properties of exponents to interpret expressions for exponential functions and identify the percent rate of change. They move from finding solutions to exponential problems in tables and graphs in eighth grade to symbolic manipulation using logarithms.
How do exponent rules and scientific notation help represent, develop, and analyze exponential relationships?
Essential Focus Questions
1. How can you tell if a function is linear or non-linear by looking at the graph of the function?
2. How does a table of values for a non-linear function differ from the table of values for a linear function?
3. How can you recognize exponential growth or decay from a graph, function rule, table, or real-world situation?
4. What are some differences between linear and exponential functions as seen in their tables, graphs, and rules?
5. How is using scientific notation helpful in representing and comparing quantities? Why does scientific notation involve using a power of ten in the expression?
6. How might using exponents be helpful in comparing populations? What strategies might help in these comparisons?
In this unit students continue building the idea of a function. They will work with the idea that a function assigns each input exactly one output and distinguish between linear and nonlinear functions. Many examples of non-linear functions exist, and students should compare and contrast these nonlinear patterns to linear patterns. In this unit, students compare and contrast exponential and linear functions noting similarities and differences between the two functions.
Students will continue to explore modeling of mathematical situations with multiple representations, from unit 2, by conducting simulations that model exponential growth and decay. They first learn to represent and recognize exponential patterns in a table of values. Examining the recursive pattern, students will see that unlike linear functions with a constant rate of change, exponential functions change by varying amounts. For example the consecutive y values 2,6,18,54 increase by 4,12,and 36. However, exponential functions also have a common factor. In the previous example, each successive y value could be found by multiplying the previous value by 3. Students use common factors to rewrite y values in expanded and exponential form. For example, 2, 2•3, and 2•3•3 or 2•30, 2•31, 2•32. (Students have had experience using exponents to denote powers of 10 in fifth grade, and writing and evaluating numerical expressions with exponents in sixth grade.) By attending to the structure of these numerical expressions, students may also represent the exponential functions with an explicit rule, y=2•3x-1 although symbolic representation of exponential functions is not explicitly called for in the standards until high school.
As students explore exponential relationships and use multiple representations to solve interesting exponential growth and decay problems, scientific notation is naturally used to represent very large and very small quantities. Technology, such as graphing calculators and spreadsheets, display numbers in forms like "3E+10" that students will need to use knowledge of scientific notation to interpret. As students compare populations of exponential relations, they develop and apply properties of exponents. For example, they know from elementary school that division can be used to find that 243 is 9 times larger than 27. In exploring exponential growth, they might have also expressed these numbers in exponential form and represented the related expression, 35/33 or 3•3•3•3•3/3•3•3 which they can deduce is 32. They will also perform similar operations with expressions written in scientific notation. These calculations should be done by using the understanding of the concepts of exponents.
In high school, work with exponential expressions extends to rational exponents. Students will also use properties of exponents to interpret expressions for exponential functions and identify the percent rate of change. They move from finding solutions to exponential problems in tables and graphs in eighth grade to symbolic manipulation using logarithms.
Week of February 20th to February 24th
Monday, 2/20
No School - Midwinter Break
Tuesday, 2/21
Exponent Rules
Wednesday, 2/22
Exponent Rules
Thursday, 2/23
High School Counselors in Media Center
Friday, 2/24
Complete Career Cruising
Monday, 2/20
No School - Midwinter Break
Tuesday, 2/21
Exponent Rules
Wednesday, 2/22
Exponent Rules
Thursday, 2/23
High School Counselors in Media Center
Friday, 2/24
Complete Career Cruising
Week of February 13th to February 17th
Monday, 2/13
Finalize Summative Assessments of Transformations
Tuesday, 2/14
Present Transformations
Wednesday, 2/15
Transformations
Thursday, 2/16
Computer Lab- Put High School Classes into Computer
GET- Sheet signed
Friday, 2/17- No School
Monday, 2/13
Finalize Summative Assessments of Transformations
Tuesday, 2/14
Present Transformations
Wednesday, 2/15
Transformations
Thursday, 2/16
Computer Lab- Put High School Classes into Computer
GET- Sheet signed
Friday, 2/17- No School
Week of February 6th to February 10th
Monday, 2/6 Review for TRANSFORMATIONS TEST Tuesday, 2/7 TRANSFORMATIONS TEST Wednesday, 2/8 TRANSFORMATIONS TEST Thursday, 2/9 TRANSFORMATIONS TEST Friday, 2/10 TRANSFORMATIONS TEST |
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Week of January 30th to February 3rd
Monday, 1/30 Rotations Introduction Tuesday, 1/31 Rotations Rules - Memorize them 90 degrees counterclockwise P (x,y) becomes P'(-y, x) -90 degrees clockwise (y, -x) 180 degrees counterclockwise and clockwise (-x,-y) Wednesday, 2/1 Rotations WS 1-6, 7,9,11,13 Thursday, 2/2 Rotations Check Up Friday, 2/3 Dilations - To resize something. In general English it means to make larger. But in Mathematics it means to make larger or smaller. |
Week of January 23rd to January 27th
Monday, 1/23 Translations Tuesday, 1/24 Reflections Wednesday, 1/25 Reflections Thursday, 1/26 Reflections Friday, 1/27 CHECK UP on Translations and Reflections |
Week of January 16th to January 20th
Monday, 1/16 No School - MLK Day Tuesday, 1/17 No School - Ice Day Wednesday, 1/18 Transformations Thursday, 1/19 Translations Friday, 1/20 Translations |
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Overarching Question
How can transformations demonstrate congruence and/or similarity?
Essential / Focus Questions
1. What does it mean for figures to be similar and/or congruent?
2. How can you use a sequence of transformations to exhibit similarity and congruence of two-dimensional figures?
3. What attributes of two-dimensional figures stay the same with given transformations? Why?
4. What attributes of two-dimensional figures change with given transformations? Why?
5. How can you use coordinates to describe the effects of transformations on two-dimensional objects?
In this unit, students build a concept of what it means for figures to be congruent and similar. They use geometric transformations to justify congruence and similarity of figures.
Students have many related prior experiences. In seventh grade, students explored ratios within and among similar figures in their development and use of proportional reasoning. In solving problems with similar figures, students may have informally used a variety of transformations to set up and solve problems with scaled figures. For example, they might have had to reflect a figure to more readily identify which of its parts correspond with another figure in order to form ratios or identify scale factors. In fourth grade students are introduced to line symmetry and identify line symmetric figures. They informally use reflections as they begin to identify parts of figures that reflect over the line of symmetry onto congruent parts. In this eighth grade unit, students build on this experience as they reflect figures (and each of its parts) over lines. On the other hand, standards from earlier grades do not explicitly attend to rotational symmetry. While students may have been introduced to angles as measures of “turn” or rotations, it is likely that students have limited experience rotating figures outside of their informal experiences with similar figures in seventh grade. As such, the unit begins with students exploring rigid transformations and the related effects on figures.
For each of the rigid transformations (translations, rotations, and reflections) students verify through experiments and a variety of tools (e.g., hinged mirrors, MIRAs, tracing paper, protractors, angle rulers, straight edges, compasses, and dynamic geometry software) that angles are taken to congruent angles, line segments to congruent line segments, and parallel lines to parallel lines. As such, students build an understanding of congruent figures and informally prove congruence of figures by giving a sequence of transformations that moves one figure to another. Students also begin their study of dilations that will become more formal in high school. Here they understand that figures are similar if they can use a sequence of rotations, reflection, translations, and dilations to map one figure onto another including the notions of scale factor that were developed in seventh grade. They also use coordinates to describe the effects of all transformations on two dimensional figures. They may also create and use rules to transform figures.
Finally, students will use transformations as strategies to solve problems and make informal arguments about relationships among angles in triangles and those that are created when parallel lines are cut by a transversal.
How can transformations demonstrate congruence and/or similarity?
Essential / Focus Questions
1. What does it mean for figures to be similar and/or congruent?
2. How can you use a sequence of transformations to exhibit similarity and congruence of two-dimensional figures?
3. What attributes of two-dimensional figures stay the same with given transformations? Why?
4. What attributes of two-dimensional figures change with given transformations? Why?
5. How can you use coordinates to describe the effects of transformations on two-dimensional objects?
In this unit, students build a concept of what it means for figures to be congruent and similar. They use geometric transformations to justify congruence and similarity of figures.
Students have many related prior experiences. In seventh grade, students explored ratios within and among similar figures in their development and use of proportional reasoning. In solving problems with similar figures, students may have informally used a variety of transformations to set up and solve problems with scaled figures. For example, they might have had to reflect a figure to more readily identify which of its parts correspond with another figure in order to form ratios or identify scale factors. In fourth grade students are introduced to line symmetry and identify line symmetric figures. They informally use reflections as they begin to identify parts of figures that reflect over the line of symmetry onto congruent parts. In this eighth grade unit, students build on this experience as they reflect figures (and each of its parts) over lines. On the other hand, standards from earlier grades do not explicitly attend to rotational symmetry. While students may have been introduced to angles as measures of “turn” or rotations, it is likely that students have limited experience rotating figures outside of their informal experiences with similar figures in seventh grade. As such, the unit begins with students exploring rigid transformations and the related effects on figures.
For each of the rigid transformations (translations, rotations, and reflections) students verify through experiments and a variety of tools (e.g., hinged mirrors, MIRAs, tracing paper, protractors, angle rulers, straight edges, compasses, and dynamic geometry software) that angles are taken to congruent angles, line segments to congruent line segments, and parallel lines to parallel lines. As such, students build an understanding of congruent figures and informally prove congruence of figures by giving a sequence of transformations that moves one figure to another. Students also begin their study of dilations that will become more formal in high school. Here they understand that figures are similar if they can use a sequence of rotations, reflection, translations, and dilations to map one figure onto another including the notions of scale factor that were developed in seventh grade. They also use coordinates to describe the effects of all transformations on two dimensional figures. They may also create and use rules to transform figures.
Finally, students will use transformations as strategies to solve problems and make informal arguments about relationships among angles in triangles and those that are created when parallel lines are cut by a transversal.
Overarching Question
Why is more than one equation sometimes needed to solve a problem?
Essential/ Focus Questions
1. Under what circumstances is it possible to have more than one solution that fits a given situation?
2. What are some possible ways to solve simultaneous equations?
3. What are the characteristics of a system of equations that yields zero, one, or multiple solutions?
4. Given a system of equations, how would you decide which of the listed methods is most efficient to solve the system: graphing, substituting, or combining equations?
5. How can you check whether a point is the intersection point of a system of equations?
The focus of this unit is on developing a conceptual understanding of the connections between algebra and geometry in viewing systems of equations. Students explore situations where multiple solutions are possible and write equations to represent these situations. Graphing technology is used to explore solutions to systems of linear equations.
In order to become proficient in solving systems of equations in a variety of ways, students need to become skilled in converting back and forth between the slope-intercept and standard forms of equations. This will allow students to graph equations(even if not given in slope-intercept form) in order to find the solution(s) to the systems. It also allows students to use the substitution method by first solving for x or y in the equations. The other method explored in this unit is the combining equations method. After practicing and comparing these three methods of solving systems, students should be able to make decisions about methods that will be most feasible for a given system.
Why is more than one equation sometimes needed to solve a problem?
Essential/ Focus Questions
1. Under what circumstances is it possible to have more than one solution that fits a given situation?
2. What are some possible ways to solve simultaneous equations?
3. What are the characteristics of a system of equations that yields zero, one, or multiple solutions?
4. Given a system of equations, how would you decide which of the listed methods is most efficient to solve the system: graphing, substituting, or combining equations?
5. How can you check whether a point is the intersection point of a system of equations?
The focus of this unit is on developing a conceptual understanding of the connections between algebra and geometry in viewing systems of equations. Students explore situations where multiple solutions are possible and write equations to represent these situations. Graphing technology is used to explore solutions to systems of linear equations.
In order to become proficient in solving systems of equations in a variety of ways, students need to become skilled in converting back and forth between the slope-intercept and standard forms of equations. This will allow students to graph equations(even if not given in slope-intercept form) in order to find the solution(s) to the systems. It also allows students to use the substitution method by first solving for x or y in the equations. The other method explored in this unit is the combining equations method. After practicing and comparing these three methods of solving systems, students should be able to make decisions about methods that will be most feasible for a given system.
Week of January 9th to January 13th
Monday, 1/9
Solving Systems with substitution Flipchart
HW: 3 problems on back of check-up
Tuesday, 1/10
Solving systems with substitution
Wednesday, 1/11
Early Release
Solving systems with substitution
Thursday, 1/12
Quiz On Solving systems with substitution
Friday, 1/13
http://www.advanc-ed.org/survey/public/1147035
Learning about High School Courses in Computer Lab
Week of January 2nd to January 6th
Wednesday, 1/4
Linear Systems Substitution Method
Thursday, 1/5
Linear Systems Substitution Method
Friday, 1/6
Linear Systems Substitution Method
Wednesday, 1/4
Linear Systems Substitution Method
Thursday, 1/5
Linear Systems Substitution Method
Friday, 1/6
Linear Systems Substitution Method
Week of December 19th to 23rd
Monday, 12/19
Christmas Party
Tuesday, 12/20
Complete Linear Systems Check Up
Wednesday, 12/21
Finish movie- Christmas with the Kranks
Monday, 12/19
Christmas Party
Tuesday, 12/20
Complete Linear Systems Check Up
Wednesday, 12/21
Finish movie- Christmas with the Kranks
Week of December 12th to December 16th
Monday, 12/12 Practice finding solution of system by graphing HW: WS Graphing Systems of Equations Tuesday, 12/13 Check Up - System of Linear Equations Graphing Method Wednesday, 12/14 Change Linear Equations into slope-intercept form Thursday, 12/15 Practice Changing linear equations into slope-intercept form Friday, 12/16 Check Up on Linear Systems |
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Week of December 5th to December 9th
Monday, 12/5 FRIST DAY OF NEW TRIMESTER MythBusters Video and Worksheet. Tuesday, 12/6 Trimester Goals- Math, Home, and School Planned Christmas Party- 1,2,5 Hours will be Tuesday, December 20th 6th hour will be Monday, December 19th Wednesday, 12/7 Introduction to System of Equations A system of equations is when you have two or more equations using the same variables. The solution to the system is the point of intersection. This point will be an ordered pair Thursday, 12/8 Continue with System notes and worksheet. HW: #9, 10, 12, & 13 on Graphing Linear Systems worksheet Friday, 12/9 Computer Lab |
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Week of November 28th to December 2nd
Monday, 11/28 Review for FINAL Tuesday, 11/29 Giving Back to the Community Field Trip Students will report to 1st hour. They will be called down to the cafe at 8:45 am. Wednesday, 11/30 Trimester 1 FINAL Thursday, 12/1 Trimester 1 FINAL Friday, 12/2 No School - Records' Day |
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Week of November 21st to November 25th
Monday, 11/21
Review for Linear Relationships TEST
Tuesday, 11/22
Linear Relationships TEST
Wednesday, 11/23
1/2 Day - Turkey Legs and Pie Princess during 5th and 6th hour
Thursday, 11/24 - NO SCHOOL
Happy Thanksgiving
Friday, 11/25 - NO SCHOOL
Monday, 11/21
Review for Linear Relationships TEST
Tuesday, 11/22
Linear Relationships TEST
Wednesday, 11/23
1/2 Day - Turkey Legs and Pie Princess during 5th and 6th hour
Thursday, 11/24 - NO SCHOOL
Happy Thanksgiving
Friday, 11/25 - NO SCHOOL
Week of November 14th to November 18th
Monday, 11/14 Using the table, find the Slope and y-intercept Tuesday, 11/15 Slope and y-intercept Wednesday, 11/16 Graphing a linear function Thursday, 11/17 Graphing a linear function Friday, 11/18 Check Up on graphing a linear function |
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Week of November 7th to November 11th
Monday, November 7th Multi-Step Equations See one, do one, teach one Tuesday, November 8th - No School Voting Day Wednesday, November 9th Check Up on solving multi-step equations. Foldable notes and a calculator may be used. Thursday, November 10th Using the slope and y-intercept of an equation graph a line on a grid. HW: Worksheets if not completed in class Friday, November 11th Guest Teacher |
Week of October 31st to November 4th
Monday, 10/31 - Happy Halloween Halloween Math Tuesday, 11/1 Create foldable notes for solving multi-step equations HW: None Wednesday, 11/2 Practice solving multi-step equations focusing on using the distributive property and combining like terms HW: Worksheet if not finished in class Thursday, 11/3 Practice solving multi-step equations focusing on when variables appear on both sides. HW: Worksheet if not finished in class Friday, 11/4 Check Up on solving multi-step equations. Foldable notes and a calculator may be used. |
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Week of October 24th to October 28th
Monday, 10/24 Review for TEST on: Great Mathematicians, Number Sense, Properties of Mathematics, Simplifying Expressions, Solving Equations, and Unit Rate Tuesday, 10/25 TEST on functions, order of operations, combining like terms, one and two step equations, integers Wednesday, 10/26 Complete TEST Thursday, 10/27 1/2 day Friday, 10/28 Computer Lab |
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Week of October 17th to October 21st
Monday, 10/17 One Step Equations H.W.: Worksheet- Front Side Additive Inverse Back Side - Multiplicative Inverse Tuesday, 10/18 Two Step Equations Wednesday, 10/19 Two Step Equations Thursday, 10/20 Two Step Equations Friday, 10/21 Check Up on 2 step equations |
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Overarching Questions
Representing and Making Sense of Linear Functions
What does it mean when we see constant and predictable changes in a table of data or a graph? How does transforming algebraic expressions and equations facilitate finding solutions to problems?
Representing and Making Sense of Linear Functions
What does it mean when we see constant and predictable changes in a table of data or a graph? How does transforming algebraic expressions and equations facilitate finding solutions to problems?
Week of October 10th to October 14th
Monday, 10/10 Myth Busters Tuesday, 10/11 Review of Worksheets Wednesday, 10/12 Check Up on Functions Thursday, 10/13 Check Up on Functions Friday, 10/14 One and Two Step Equations |
Week of October 3rd to October 7th
Monday, 10/3 Functions HW: ordered pairs ws Tuesday, 10/4 Computer Lab Wednesday, 10/5 Function Table Thursday, 10/6 Order of Operations Friday, 10/7 Computer Lab |
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Week of September 26th to September 30th
Monday, 9/26 Understand and define: domain, range, relation, and function HW: Function or Not a Function Worksheet Tuesday, 9/27 Practice identifying domain, range, relations, and functions HW: Ordered Pairs and Function Table Worksheets Wednesday, 9/28 NWEA TESTING Thursday, 9/29 NWEA TESTING Friday, 9/30 NWEA TESTING |
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Week of September 19th to September 23rd
Monday, 9/19
Check Up on Adding and Subtracting Integers
Tuesday, 9/20 and Wednesday, 9/21
Sub. Challenge Day.
Myth Busters
Thursday, 9/22
challengeday.org
Friday, 9/23
Math Warm Ups
Review Check Ups on Integers
Monday, 9/19
Check Up on Adding and Subtracting Integers
Tuesday, 9/20 and Wednesday, 9/21
Sub. Challenge Day.
Myth Busters
Thursday, 9/22
challengeday.org
Friday, 9/23
Math Warm Ups
Review Check Ups on Integers
Week of September 12th to September 16th
Monday, 9/12 Addition of integers Tuesday, 9/13 Adding Integers with like signs Wednesday, 9/14 Adding Integers with unlike signs Rule: Find Differences of Absolute Values and keep sign of the majority Card Game HW: addition of positive and negative integers Thursday, 9/15 Subtraction of Integers Friday, 9/16 Computer Lab |
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Welcome Back to School Week
Monday, 9/5 Labor Day Tuesday, 9/6 First Day of School 5 Fun Math Facts about you Entrance and Dismissal Procedures Wednesday, 9/7 Golden rule "Treat others the way you want to be treated." Math Autobiography HW: Parents- Getting to know your math student. Due Friday Thursday, 9/8 Math Warm Ups Why do we learn math? Friday, 9/9 Math Warm Ups Sharing what kind of after-school activities we participate in |
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