Graphic Organizer for Unit 1
http://oaklandk12-public.rubiconatlas.org/c/etc/getFile.php?originalFile=8_1Graphic%2B8_20_13.png&FileID=D4B4B6D0-551D-49CB-9146-849DAB4CE94D&download=8_1Graphic+8_20_13.png&CurriculumLinkID=18261&YearID=2014&
http://oaklandk12-public.rubiconatlas.org/c/etc/getFile.php?originalFile=8_1Graphic%2B8_20_13.png&FileID=D4B4B6D0-551D-49CB-9146-849DAB4CE94D&download=8_1Graphic+8_20_13.png&CurriculumLinkID=18261&YearID=2014&
Essential/Focus Questions
- How are algebraic expressions and equations used to model linear functions? What do the slope and y-intercept of a line represent in a these models?
- How do you know when a table, graph, or equation represent a function?
- How can you solve an equation using a table? using a graph? using symbolic manipulation?
- In what ways can you describe and compare linear functions?
- How can you recognize when a linear function is a proportional relationship in a table? in a graph? in an equation?
Vocabulary
vocab.pdf | |
File Size: | 57 kb |
File Type: |
Solving Equations
solving_equations.pdf | |
File Size: | 415 kb |
File Type: |
This link is to the first of 5 on learnzillion.http://learnzillion.com/lessons/2734-understand-onesolution-equations
This link is to the first of 6 on learnzillion.
http://learnzillion.com/lessons/3146-solve-linear-equations-with-rational-numbers-by-using-integers
This link is the first of many on khan academy.
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-solving-equations
This link is to the first of 6 on learnzillion.
http://learnzillion.com/lessons/3146-solve-linear-equations-with-rational-numbers-by-using-integers
This link is the first of many on khan academy.
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-solving-equations
Slope, Equations, Graphing, Functions
graphing-equations.pdf | |
File Size: | 608 kb |
File Type: |
graphing-slope.pdf | |
File Size: | 675 kb |
File Type: |
This link is to the first of 5 on learnzillion.
http://learnzillion.com/lessons/1195-display-all-possibilities-in-a-proportional-relationship-by-graphing
This link is to the first of 7 on learnzillion.
http://learnzillion.com/lessons/1341-make-lines-from-right-triangles
This link is to the first of 5 on learnzillion. **These were viewed together as a class.**
http://learnzillion.com/lessons/2962-understand-a-function-as-a-type-of-relation
This link is the first of 6 on learnzillion.
http://learnzillion.com/lessons/1189-identify-a-function
This link is the first of 4 on learnzillion.
http://learnzillion.com/lessons/3304-define-a-linear-function
This link is the first of 5 on learnzillion.
http://learnzillion.com/lessons/1834-determining-the-constant-rate-of-change
This link is the first of 4 on learnzillion.
http://learnzillion.com/lessons/3536-describe-function-relationships-using-graphs
This link is the first of many on khan academy.
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-relationships-functions
http://learnzillion.com/lessons/1195-display-all-possibilities-in-a-proportional-relationship-by-graphing
This link is to the first of 7 on learnzillion.
http://learnzillion.com/lessons/1341-make-lines-from-right-triangles
This link is to the first of 5 on learnzillion. **These were viewed together as a class.**
http://learnzillion.com/lessons/2962-understand-a-function-as-a-type-of-relation
This link is the first of 6 on learnzillion.
http://learnzillion.com/lessons/1189-identify-a-function
This link is the first of 4 on learnzillion.
http://learnzillion.com/lessons/3304-define-a-linear-function
This link is the first of 5 on learnzillion.
http://learnzillion.com/lessons/1834-determining-the-constant-rate-of-change
This link is the first of 4 on learnzillion.
http://learnzillion.com/lessons/3536-describe-function-relationships-using-graphs
This link is the first of many on khan academy.
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-relationships-functions
comparing_functions.pdf | |
File Size: | 676 kb |
File Type: |
You will be learning the following standards in this unit:
CCSS: Mathematics, CCSS: Grade 8, Expressions & Equations
8.EE.B. Understand the connections between proportional relationships, lines, and linear equations.
8.F.A. Define, evaluate, and compare functions.
CCSS: Mathematics, CCSS: Grade 8, Expressions & Equations
8.EE.B. Understand the connections between proportional relationships, lines, and linear equations.
- CCSS.Math.Content.8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
- CCSS.Math.Content.8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis atb.
- CCSS.Math.Content.8.EE.C.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
- CCSS.Math.Content.8.EE.C.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.F.A. Define, evaluate, and compare functions.
- CCSS.Math.Content.8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1
- CCSS.Math.Content.8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
- CCSS.Math.Content.8.F.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
- CCSS.Math.Content.8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
- CCSS.Math.Content.8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Links to other resources:
Equations of Attack: When one end of a wooden board is placed on a bathroom scale and the other end is suspended on a textbook, students can "walk the plank" and record the weight measurement as their distance from the scale changes. The results are unexpected— the relationship between the weight and distance is linear, and all lines have the same x‑intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find.
http://illuminations.nctm.org/LessonDetail.aspx?id=L782
Amazing Profit: Students use equations to determine eBay profit on new technology. EBay is an online auction agency. For a limited time after a “new” product’s street release date, it is possible to track the profit that sellers make for auctioning them on eBay. Students use previous data of selling prices to derive a linear equation for the “closing bid price” on a product.
http://illuminations.nctm.org/LessonDetail.aspx?id=L799
Finding Our Top Speed: This lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. Finally, students plot the data they have collected.
http://illuminations.nctm.org/LessonDetail.aspx?id=L254
Bouncing Ball: Students develop their skills in collecting and recording data using the real-world situation of a bouncing tennis ball. They use the data collected to formulate the relationship between the dependent and independent variable in their experiment.
http://illuminations.nctm.org/LessonDetail.aspx?id=L246
Exploring Linear Data: Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
http://illuminations.nctm.org/LessonDetail.aspx?id=L298
Geology Rocks Equations: In this lesson, students explore linear equations with manipulatives and discover various steps used in solving equation problems. Students use blocks and counters as tactile representations to help them solve for unknown values of x.
http://illuminations.nctm.org/LessonDetail.aspx?id=L786
Building Bridges: In this lesson, students transition from arithmetical to algebraic thinking by exploring problems that are not limited to single-solution responses. Values organized into tables and graphs are used to move toward symbolic representations. Problem situations involving linear, quadratic, and exponential models are employed.
http://illuminations.nctm.org/LessonDetail.aspx?id=L247
Exploring Equations Further: Starting from the concrete notion of weights and balance and moving to symbolic expressions and representations of functions, this i-Math investigation has focused on some of the issues that arise along the way. In this part, this connection is extended to functions. More sophisticated tools allow for a greater diversity of investigations.
http://illuminations.nctm.org/LessonDetail.aspx?id=L564
Seeing Math:
In these exercises, you use technology to reveal the connection between symbolic and graphic representations of equation solving. In these challenges, you'll use an interactive tool called the Function Analyzer.
http://seeingmath.concord.org/resources_files/FunctionAnalyzer.html
This applet allows students to explore how change the values of slope and
y-intercept change the graph of a linear equation.
http://www.shodor.org/interactivate/activities/SlopeSlider/
An online lesson introducing the lines and slope.
http://mathforum.org/cgraph/cslope/
Students pass a "hand squeeze" around a circle and measure the amount of time that it takes for the hand squeeze to pass around the circle.
http://math.rice.edu/~lanius/Algebra/hndsq.html
Equations of Attack: When one end of a wooden board is placed on a bathroom scale and the other end is suspended on a textbook, students can "walk the plank" and record the weight measurement as their distance from the scale changes. The results are unexpected— the relationship between the weight and distance is linear, and all lines have the same x‑intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find.
http://illuminations.nctm.org/LessonDetail.aspx?id=L782
Amazing Profit: Students use equations to determine eBay profit on new technology. EBay is an online auction agency. For a limited time after a “new” product’s street release date, it is possible to track the profit that sellers make for auctioning them on eBay. Students use previous data of selling prices to derive a linear equation for the “closing bid price” on a product.
http://illuminations.nctm.org/LessonDetail.aspx?id=L799
Finding Our Top Speed: This lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. Finally, students plot the data they have collected.
http://illuminations.nctm.org/LessonDetail.aspx?id=L254
Bouncing Ball: Students develop their skills in collecting and recording data using the real-world situation of a bouncing tennis ball. They use the data collected to formulate the relationship between the dependent and independent variable in their experiment.
http://illuminations.nctm.org/LessonDetail.aspx?id=L246
Exploring Linear Data: Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
http://illuminations.nctm.org/LessonDetail.aspx?id=L298
Geology Rocks Equations: In this lesson, students explore linear equations with manipulatives and discover various steps used in solving equation problems. Students use blocks and counters as tactile representations to help them solve for unknown values of x.
http://illuminations.nctm.org/LessonDetail.aspx?id=L786
Building Bridges: In this lesson, students transition from arithmetical to algebraic thinking by exploring problems that are not limited to single-solution responses. Values organized into tables and graphs are used to move toward symbolic representations. Problem situations involving linear, quadratic, and exponential models are employed.
http://illuminations.nctm.org/LessonDetail.aspx?id=L247
Exploring Equations Further: Starting from the concrete notion of weights and balance and moving to symbolic expressions and representations of functions, this i-Math investigation has focused on some of the issues that arise along the way. In this part, this connection is extended to functions. More sophisticated tools allow for a greater diversity of investigations.
http://illuminations.nctm.org/LessonDetail.aspx?id=L564
Seeing Math:
In these exercises, you use technology to reveal the connection between symbolic and graphic representations of equation solving. In these challenges, you'll use an interactive tool called the Function Analyzer.
http://seeingmath.concord.org/resources_files/FunctionAnalyzer.html
This applet allows students to explore how change the values of slope and
y-intercept change the graph of a linear equation.
http://www.shodor.org/interactivate/activities/SlopeSlider/
An online lesson introducing the lines and slope.
http://mathforum.org/cgraph/cslope/
Students pass a "hand squeeze" around a circle and measure the amount of time that it takes for the hand squeeze to pass around the circle.
http://math.rice.edu/~lanius/Algebra/hndsq.html