Math-8 Core Map Quarter 2
| Subject/Grade Level/Unit Title | Timeframe/Grading Period | Big Idea/Themes/Understandings | Essential Questions | Standards | Essential Skills | Vocabulary | Assessment Tasks | Resources | |||||||||||||||
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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 Qualitative graphs (writing and reading)
Transformations Translations Reflections Rotations Compostions Dilations Similarity
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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
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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?
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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
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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
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Math Chat Writing prompt Classroom assessments Pass paper Judy Dodge exits Exit tickets Daily and weekly spirals Benchmarks IXL |
Glencoe Course 3 Text Big Ideas Text-Grade 8 Holt-McDouglal Mathematics Grade 8 IXL New York State Modules |
