Ms. Olshow: [email protected]. Mr. Grant: [email protected]
Math Department Grading Policy
Assessments..............................................................................65%
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Homework ....................................................................................15%
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G8 ~ Syllabus
Unit 1: Solving Multi-step Equations ------------3 weeks
Unit 2: Exponents and Scientific Notation-------3 weeks Unit 3: Roots and Pythagorean Theorem--------3 weeks Unit 4: Geometry: Angle Relationships---------2 weeks Unit 5: Transformations--------------------------5 weeks |
Unit 6: Measurement: Volume-------------------3 weeks
Unit 7: Modeling with Linear Functions ----------3 weeks Unit 8: Modeling with Linear Functions----------5 weeks Unit 9: Systems of Linear Equations-------------6 weeks Unit 10: Statistics and Linear Functions----------2 weeks |
NYS Math Standards
8.EE.1 - Apply the properties of integer exponents to create equivalent expressions.
8.EE.2(a) - Evaluate square root and identify which is a perfect square or irrational number. 8.EE.2(b) - Evaluate cube root symbols to determine which is a perfect cube or irrational number. 8.EE.3 - Estimate very large and very small numbers using the power of 10. 8.EE.4 - Perform operations with scientific notation. 8.EE.5(a) - Compare different proportional relationships in different ways (graphs, equations…) |
8.EE.5(b) - Interpret the slope of a graph as the unit rate.
8.EE.6(a) - Determine slope between any two distinct point on a graph. 8.EE.6(b) - Interpret the equation y=mx+b from a graph. 8.EE.7(a) - Solve linear equations without using distributive properties. 8.EE.7(b) - Solve linear equations by expanding expressions using distributive properties. 8.EE.8(a) - Solve systems of linear equations by a graph using real world problems. 8.EE.8(b) - Solve systems of linear equations algebraically using real world problems. |
Unit 2: Functions
- 8.F.1 - Determine the output (input) by knowing the function and input (output).
- 8.F.2 - Compare functions represented in an different way(equation, graph, table, and/or context).
- 8.F.3 - Determine which functions are linear and non-linear and give examples.
- 8.F.4(a) - Determine the rate of change and initial value from a table, graph, and equation.
- 8.F.4(b) - Interpret the rate of change and initial value into the context of the situation.
- 8.F.5 - Sketch a graph and describe where it is increasing, decreasing, constant, linear, and nonlinear.
Math on the Spot Videos
Ratios & Proportions Lessons Video
Below is a list of possible learning objectives for each learning target. Amount of class periods spent on each objective may vary depending on each specific class. Please note that additional objectives may be needed based on the needs of each specific class.
TARGET F: I can identify a linear function
TARGET H: I can use scatter plot to make predictions
TARGET F: I can identify a linear function
- Identify what a linear function looks like graphically
- Use an equation to graph a line
- Recognizing a linear function in a table
- Identify what a linear functions looks like algebraically.
- Mastery Quiz F:
TARGET H: I can use scatter plot to make predictions
- Construct a scatter plot
- Identify the type of association evident in the scatter plot
- Identify a good line of best fit
- Draw a line of best fit
- Calculate the equation for the line of best fit
- Use the line of best fit to make predictions
- Use the line of best fit to make predictions -application problem
- Mastery Quiz H:
- Teacher Task/Assessment
- Solve linear systems using substitution
- Solve linear systems using elimination
- Writing linear systems from word problems
- Solve linear systems with two different representation
- Mastery Quiz I
- Teacher Task/Assessment
- Examine no solution problems graphically & algebraically
- Examine infinitely many solution problems graphically & algebraically
- Examine one solution problems algebraically and graphically
- Mastery Quiz J
- Teacher Task/Assessment
- Culminating Project / Presentations
Percents
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TARGET K: I can identify a linear function
1. Define a functional relationship based on observations
2. Determine whether a relationship represented by a graph is a function.
3. Determine whether a relationship in a table is a function.
4. Determine whether a relationship represented by an equation is a function.
TARGET L: I can describe a functional relationship
1. Determine whether a functional relationship represented by an equation is linear or nonlinear
2. Determine whether a functional relationship represented by a table is linear or nonlinear
3. Determine whether a functional relationship represented by a graph is linear or nonlinear
4. Determine if the function is increasing or decreasing from a graph, equation and/or table.
TARGET M: I can analyze graphs of functions
1. Sketch a graph that shows constant changes over time
2. Sketch a graph that shows changes of increasing at an increasing rate and increasing at a decreasing rate over time
3. Sketch a graph that shows changes of decreasing at an increasing rate and decreasing at a decreasing rate over time.
4. Match a description to the sketch of a graph
TARGET N: I can solve use functions to model relationships & solve problems
1. Model and solve linear relationship given in a description
2. Model and solve linear relationships given by an equation
3. Model and solve linear by comparing two situations represented differently
Essential Questions
Video Links
1. Define a functional relationship based on observations
2. Determine whether a relationship represented by a graph is a function.
3. Determine whether a relationship in a table is a function.
4. Determine whether a relationship represented by an equation is a function.
TARGET L: I can describe a functional relationship
1. Determine whether a functional relationship represented by an equation is linear or nonlinear
2. Determine whether a functional relationship represented by a table is linear or nonlinear
3. Determine whether a functional relationship represented by a graph is linear or nonlinear
4. Determine if the function is increasing or decreasing from a graph, equation and/or table.
TARGET M: I can analyze graphs of functions
1. Sketch a graph that shows constant changes over time
2. Sketch a graph that shows changes of increasing at an increasing rate and increasing at a decreasing rate over time
3. Sketch a graph that shows changes of decreasing at an increasing rate and decreasing at a decreasing rate over time.
4. Match a description to the sketch of a graph
TARGET N: I can solve use functions to model relationships & solve problems
1. Model and solve linear relationship given in a description
2. Model and solve linear relationships given by an equation
3. Model and solve linear by comparing two situations represented differently
Essential Questions
- What is a function? Describe what it means for a situation to have a functional relationship?
- What is the relationship between the input and output of a function?
- How can you represent a function (linear or nonlinear) using real-world contexts, algebraic equations, tables of values, graphical representations and/or diagrams?
- In what ways can different types of functions be used to model various situations that occur in the real world?
- What are the advantages of representing the relationship between quantities symbolically? Numerically? Graphically?
- How do you determine which linear function has a greater rate of change using the graph? Using the equation? Using a table of values?
- How can proportional relationships be used to represent authentic situations in life and solve actual problems?
- In what way(s) do proportional relationships relate to functions and functional relationships?
- What information does the slope provide about the graph, the situation, the table of values, and the equation?
- What does it mean for a context to have a slope of 0? What does it mean for a context to have an undefined slope?
- How can you determine if a linear function represents a proportional relationship? How is this confirmed using an equation, a table of values, and/or a graph?
- What strategies can be used to solve multi-step equations? What situations will produce equations with no solutions? What situations will produce equations with infinite solutions?
- How can you solve systems of linear equations numerically, graphically, or algebraically (using substitution or elimination)? When is each strategy most effective to use?
- What does the solution to a system of equations means in the context of the problem?
- Students may mistakenly believe that a slope of zero is the same as "no slope" and then confuse a horizontal line with a vertical line.
- Students may interchange the meanings of x (independent variable) and y (dependent variable), particularly when graphing the line of an equation.
- Students may struggle with distinguishing between combining like terms on one side an equation and eliminating a variable while balancing an equation.
- I can define a function and represent a function in various ways, including mappings, input-output tables, graphs, and/or equations.
- I can show the relationship between inputs and outputs of a function by graphing ordered pairs on a coordinate grid.
- I can generate additional inputs and outputs that are elements of a given continuous function.
- I can write a function rule to represent inputs and outputs from a table of values.
- I can describe the properties of a function that is represented as an equation, a table of values, a graph, or a verbal representation.
- I can compare the properties of two functions that are represented in different forms (tables, graphs, equation, or verbal representation).
- Conceptual Understanding:
- Describing the properties of a function
- Representing a function in a variety of ways
- Distinguishing between functions and non-functions, using a variety of representations
- Understanding how inputs and outputs relate to the graph of a function and an equation
- Using physical models (such as pattern blocks) to create a function representation
- Creating a graphical representation of a scenario, equation, table of values, and/or scenario
- Understanding how to extract key features from different representations to compare the representations
- Procedural Fluency:
- Creating an input-output table for a function and finding specific input or output values
- Representing a function with a graph or mapping
- Rinding a function rule to satisfy a function table
- Comparing the rates of change in equations, graphs, and/or tables of values
- Application:
- Determining possible values of a function given a real-world context, and excluding values that do not make sense in the context of the scenario
- Describing what the input and output represent in the context of a real-world problem
- Comparing functions from different representations within real-world contexts
- Determining which value(s) for a function do not make sense in the context of the real-world scenario
Video Links
- Relations and Functions
- Graphing Linear Equations
- Writing Linear Equations
- Direct Variation