Last updated: 6/9/2015 ## Math-8 Core Map Quarter 2

Linear Equations

Graph proportional lines-examine Unit Rate, Constant of Proportionality

Examine transformational between y=mx and y=mx+b

Solve real life situations with proportionality

Writing linear equations from one point and slope in slope intercept form

Writing linear equations from two points in slope intercept form

Write equations in point slope form

Rewriting equations of lines into all forms

Systems

Solving system of Equations graphically

Solving systems of equation using substitiution

Solving systems of equations using elimination

Using systems of equation to solve real life problems

Functions

Define functions

Mapping, charting and graphing functions

Explore the idea of a function as a machine

Determine if a relation is a function

Determine if a function is discrete or continuous

Create input-output tables from an eqution or given situation

Explore domain and range

Comparing funcitons from situations

Linear and Nonlinear functions

Types of non-linear functions-exponential, quadratic square root

Determine if a function is linear or non-linear from a table

Compare functions -increasing or decreasing over each other

Transformations

Translations

Reflections

Rotations

Compostions

Dilations

Similarity

Quarter 2

Linear Equations

Examine linear and non linear relationships

Examine proportional and non-proportional linear equations

Solve real life proportional relationships

Examine transformations of lines y=mx and y=mx+b

Direct variation-proportional line, y = mx

Explain connections between slope, constant of variation and constant of proportionality (in proportional line)

Finding constant of variation, from equations and situations

Interpret intercepts and slopes in linear applications

Writing equations of relationships in graphs, charts and tables in slope intercept form

Writing equations of linear relationships in point-slope form

Transfer linear equations from slope intercept form to standard form and visa versa

Systems

Solving systems of equations graphically

Solving systems of equations algebraically using substitution

Solving systems of equations algebraically using elimination

Solving systems of equations through inspection

Solving systems of equations in real life situations

Functions

Examine relations and functions

Determine the independent and independent variables

Determine the domain and range of functions

Linear functions and function notation

Continous and discrete functions

Constructing functions

Examine types of non-linear functions exponential, quadratic and square root

Determine if a function is linear or non-linear from a table

Compare functions increasing or decreasing over each other

Read and write situations that match a qualitative graphs

Transformations

Linear Equations

How do you know if two quantities are proportional?

What are the characteristics of a proportional line?

How can we determine if a linear equation is proportional or not, from equation and graph?

Can you determine a connection between the slope, constant of proportionality?

How can you recognize an direct variation equation?

What coordinates are always involved in proportional lines?

How are direct variation graphs helpful?

How can the slope of the line used to understand a proportional relationship?

How do the y values change as the x increases?

What two pieces of information are needed to write equatioins of the line?

What does point-slope form remind you of?  Where do you think it originates from?

How can we rewrite linear equations to see information that? describes the line?

How can you write an equation of a line when you are given the slope and a point?

How can you write an equation of a line when you are given two points?

How can you use a linear equation in two variables to model and solve real life problems?

Systems

Can you solve a system of linear equation?

How do youi know equations are in fact a system?

What symbols or words need to be there for you to know?

What do the points of intersection mean to each equation of a line?

Can you determine a solution through inspection?

Can we see the solutions to systems of equations graphically?

Can we solve a system graphically?

Can we prove a solution point algebraically?

Can we solve a system algebraically?

What can you do to confirm your solution is correct?

What does it mean if a point is on one line, but not on another?

Can you describe the situation when a system of linear equations has all or no solutions? What does it say about the lines?

How can you use a system of linear equations to model and solve a real-life problem?

Functions

What is a relation?

How is a function different from a relation?

Why is a function decribed as a machine?

What do functions look like when graphed?

How does a vertical line test help determine if a relation is a function?

What are the input and output of funtions described as?

How can you find the domain and range of a function?

How can you decide whether the domain of a function is discrete or continous?

How can you use a linear function to describe a pattern?

How can you recognize when a pattern in real life is linear or non linear?

How can we use function notation to describe a function?

How can we recognize functions that are non-linear?

What characteristics would be different than those that are linear?

How would non-linear functions appear in a table or chart?

How would the chart differ from those that are linear?

How can we determine if one function is increasing or decreasing over another?

How can we describe the intervals of the domain?

Can we examine functions that qualitiative instead of quantitative?

How do qualitative graphs differ from the quantitative graphs?

Transformations

How can we best show or describe a change in position of a two dimensional figure?

After an image is relocated, how can we reference the original and the new image?

What does it mean to have congruent figures?

How can we describe when a figure is slid on a grid?

Does translating a figure change its size?

What affect does the translation have on the coordinates of an image?

What is a reflection?

How can we determine if a figure was in fact reflected?

How does a reflection in the x or y axis affect the image?

Can we reflect through other lines?

How does that differ from reflecting through the axes?

Are their algebraic rules that can be applied to coordinates to result in a reflection?

How are rules developed?

What is symmetry?

What is rotational symmetry?

How many degress does something turn to result in the original position of a given figure?

How can we develop a rotation with a ruler and a compass?

Do we always need a ruler and a compass?

Can we create a rule for each quarter rotation about the origin of the coordinate plane?

Can you develop a process that rotates your grid to determine new position?

How can we move a figure multiple times on the same grid?

How can we distinquish the original image, the second and the last image?

Does performing a translation, reflection or rotation always create a congruent figure?

Why or why not?

What is a dilation?

Does it create a figure with the same shape and size?

How can we enlarge a figure?

How can we shring a figure?

How does the constant (scale factor) affect the size?

Does the figure center around or in the original?

Does it seem like it is generating from a part?

What is the relationship between the distance from the point (center) of  the dilation and the preimage point and the center to the new image point?

Can you develop a rule to be used to enlarge or shrink a figure?

What can we say about the relationship between the new image and the preimage?

Can we prove they are similar?

 (1) 8.F.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) 8.F.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. (1) 8.F.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. (1) 8.F.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. (1) 8.F.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.

Linear Equations

Determine the difference between proportional and non-proportional lines

Recognize proportional and non-proportional lines linear graphs

Recognize proportional lines from tables and graphs

Use the linear equation of direct variation to determine values of x and y coordinates

Interpret x and y intercept

Write the equation of a line from the point and a slope

Write the equation of a line from two points (point slope and y intercept form)

Write the equation of a line in standard form (point slope and y intercept form)

Rewrite equations of lines in multiple forms

Systems

Graph systems of equations and determine the solution

Explain the systems that have all or no solutions and how they appear on a graph

Solve linear systems using substitution

Solve linear systems using elimination

Use linear systems to solve real life problems.

Functions

Determine if a graph is a function

Determine if a table or chart of a relation is a function

Write linear functions in function form

Find the domain and range of a function

Determine the dependent and independent variables of a function

Build a function table

Graph a function

Determine if a function is discrete or continuous

Determine the pattern of a linear function

Compare linear and non linear functions and their differences

Transformations

Translate a figure using words

Translate a figure from translation symbols

Translate a figure by rule on coordinates

Determine a transformation rule for translated points and apply to new point

Recognize that figure stays congruent

Recognize symmetry

Draw lines of symmetry

Reflect a figure over the x-axis

Reflect a figure over the y-axis

Reflect a figure over vertical and horizontal lines  (not axes)

Create rules for reflections

Determine the line of reflection based on the pre-image and post image coordiantes

Determine rotation symmetry

Determine total rotational degrees

Detemine quarter rotational degrees

Determine methods to find rotations using protractor and a ruler

Determine methods without using protractor and a ruler

Create rules for rotations

Perform composite transformations and properly label

Enlarge and shrink size of a figure by using a scale factor

Discover what a dilation is and what piece of information allows you to enlarge or reduce a figure

Determine if new image is similar or congruent

Examine distances from center to preimage point and distance to new image point

Examine proportionality of figures

linear equation

rate of change

slope intercept form

point-slope form

direct variation

constant of variation

proportional lines

non-proportional lines

discrete

continuous

relation

domain

range

function

dependent variable

independent variable

vertical line test

function form

constant of proportionallity

rate of change

unit rate

constant of variation

point slope form

slope intercept form

standard form of a line

systems of equations

quantitative

qualitative

Math Chat

Writing prompt

Classroom assessments

Pass paper

Judy Dodge exits

Exit tickets

Daily and weekly spirals

Benchmarks

IXL

Glencoe Course 3 Text 