Grade 8 Math

NECAP Standards
Cycle of Review and Revision
K-8 Curriculum Alignment
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Barbara Maling
Director of Curriculum and Instruction

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Grade Eight Math
Scope and Sequence

Students will follow the Connected Mathematics Project Program:
  • Moving Straight Ahead Unit-Students develop an understanding of rate as a characteristic of linear relationships through their use of graphs, tables, and equations. They learn to solve linear equations as well as write them in slope-intercept form given different types of information. 
  • What Do You Expect? Unit- Students develop an understanding of an strategies for analyzing two-stage events. They will also determine the expected value and analyze binomial situations. 
  • Thinking with Mathematical Models Unit-Students will focus on linear functions and data modeling followed up by developing an under- standing of an inverse variation relationship. 
  • Looking for Pythagoras Unit- Students will develop their understanding of the Pythagorean theorem, its uses, square roots and their estimation. 
  • Growing, Growing, Growing Unit-Students focus on exponential growth and decay. Theyalso look at the rules for operating on numerical expressions with exponents. 
  • Students will also do a weekly computational sheet where they practice basic skills. 
  • Eighth Grade Algebra is an option available to students who meet established selection criteria.

YORK SCHOOL DEPARTMENT
CURRICULUM ALIGNMENT
SUBJECT AREA: MATHEMATICS GRADE: 8

Content Standards

Performance Indicators

Instructional Practice

Assessment Tools

Reporting Tools

A. NUMBER:  Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations.  Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers.  It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately.  Estimation should always be used when computing with numbers or solving problems.
WHOLE NUMBER


 


 


 


 


No performance indicator. It is expected that students continue to use prior concepts and skills in new and familiar contexts.
 


 


 


 


RATIONAL NUMBER


 


 


 


 


A.1Students express or interpret numbers using scientific notation from real-life contexts.


a. Use positive and negative integer exponents for powers of ten.


(Connected Mathematics Project-Growing, Growing, Growing) Express very large and very small numbers using scientific notation.


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b. Convert between standard and scientific notation forms and compare the relative size of numbers including the interpretation of numbers as displayed on calculators and computers.


(GGG) Convert between scientific and standard notation both on paper and with a calculator.


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REAL NUMBERS
 


 


 


 


A.2. Students understand the set of real numbers as containing the rational numbers and the irrational numbers.


a. Know that there are real numbers that are not rational numbers.


(Connected Mathematics Project-Looking for Pythagoras) Express square roots in radical form and as "approximately equal to" a rounded decimal form.


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b. Know some common examples of irrational numbers including pi or those arising from square roots.


(LFP) Give examples of familiar irrational numbers.


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c. Use square roots.


(LFP) Determine lengths of diagonal line segments and perimeters of irregular figures using square roots.


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d. Be able to estimate the value of the square roots of whole numbers and place them on the number line.


(LFP) Express lengths of squares in radical form and also in rounded decimal form.  Locate square roots on a number line.


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B. DATA: Students make measurements and collect, display, evaluate, analyze and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students:

  • understand that most measurements are approximations and that taking repeated  measurements reveals this variability;
  •  understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement;
  •  understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.
MEASUREMENT AND APPROXIMATION


 


 


 


B.1. Students understand and use derived measures (measurements expressed as rates).


a. Calculate measures using multiple attributes including speed (distance per time).


(Moving Straight Ahead) Calculate walking rates by measuring distance and time.  Calculate distance given speed and time.


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b. Solve for an unknown component of a measure including finding time given average speed and distance.


 (MSA) Calculate time given speed and distance.


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B.2. Students convert across measurement systems and within a system for different units in derived measures.


a. Approximate metric and customary equivalents given a conversion factor.


(Algebra)  Convert ratios to equivalent ratios using unit analysis

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b. Convert derived measures, including feet per second to miles per hour.


(MSA)  Convert between units in motion problems.

(Algebra)  Convert ratios to equivalent ratios using unit analysis.

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DATA ANALYSIS


 


         

 


B.3. Students use the mean, median, mode, range, and quartiles to solve problems involving raw data and information from data displays.


 


(Comp sheets)  Calculate mean, median mode and range.

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PROBABILITY


 


 


 


B.4. Students understand and apply concepts of probability.


a. Use appropriate terminology to describe complementary and mutually exclusive events.


(What Do You Expect?) Describe complementary and mutually exclusive events.


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b. Use an understanding of relative frequency to make and test conjectures about results of experiments and simulation.


(WDYE) Predict results and test predictions about number of occurrences of a color on a spinner, heads or tails, or outcomes on a die.


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c. Compute probabilities for compound events, using such methods as organized lists, tree diagrams, and area models.


(WDYE) Utilize tree diagrams and area models for more complex probability situations.


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C. GEOMETRY: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct two-dimensional and three-dimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures, students use estimation to check the reasonableness of results.
GEOMETRIC FIGURES


 


         

 


C.1. Students know and use properties of polygons.


a. Apply the triangle inequality.


(LFP) Calculate if three random lengths can form a triangle.

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b. Find the sum of the measures of the interior angles of a polygon.
         

 


 

c. Apply the property that the sum of the measures of the exterior angles of a polygon is 360 degrees.
  

 


C.2. Students know and use angle properties of parallel lines to solve problems and determine geometric relationships.
a. Know and use properties of angles created when parallel lines are cut by a transversal.
  

 


 
b. Use angle properties to determine whether lines are parallel.
 
 


 


c. Know and use properties of angles created by parallel lines and transversals to determine the angle properties of trapezoids and parallelograms, and apply these properties in problem situations.
 


 


C.3. Students know and use the Pythagorean Theorem.


 


(LFP) Determine if a triangle is a right triangle using the Pythagorean Theorem.  Determine missing values in right triangles using the Pythagorean Theorem.


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GEOMETRIC MEASUREMENT


 


 


 


C.4. Students find the volume and surface area of prisms, pyramids, cylinders, and other figures composed of these solids.
a. Apply the understanding that the volume of prisms and cylinders can be found by multiplying the area of a base by the height of the solid.
  

 


 


b. Apply the understanding that the volume of pyramids can be found by multiplying the area of a base by 1/3 the height of the solid.
 


 


 


c. Apply the understanding that the surface area of a figure is the sum of the areas of its faces and find the surface areas of cylinders.
 


 


TRANSFORMATIONS


 


 





No performance indicator. Although no performance indicators are stated, students are expected to continue to use prior concepts and skills in new and familiar contexts.
 


 




        
D.  ALGEBRA: Students use symbols to represent or model quantities, patterns and relationships and use symbolic manipulation to evaluate expressions and solve equations.  Students solve problems using symbols, tables, graphs and verbal rules choosing the most effective representation and converting among representations.
SYMBOLS AND EXPRESSIONS  


 


 


 


 


D.1. Students create, evaluate and manipulate expressions.


a. Create and evaluate expressions using real numbers.


(MSA, Comp sheets) Evaluate expressions with real numbers.  Write variable expressions given a situation.


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b. Add and subtract linear expressions.


(MSA) Add and subtract linear expressions.


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c. Apply the properties of the real number system, including distributive and associative laws, to create equivalent expressions.


(MSA, Comp sheets) Use distributive, associative and commutative properties to create equivalent expressions and solve equations.

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EQUATIONS AND INEQUALITIES


 


 


 


D.2. Students understand and solve problems involving linear equations.


a. Solve any linear equation including linear equations of the form ax + b = cx + d.


(MSA) Use property of equality (golden rule of math) to solve linear equations.


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b. Recognize that, in general, linear equations have just one solution--but know also that some linear equations can have no solution and those linear equations that are identities have every value of x as a solution.  


(MSA) Solve linear equations and recognize when there is no solution or an infinite number of solutions.

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c. Use graphs to estimate solutions to equations and systems of equations, check algebraic approaches, provide alternative solution paths, and communicate the solution to a problem.


(MSA)  Use graphs to estimate solutions to problems.  Use algebraic methods when an exact solution isn't a realistic expectation on a graph.

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D.3. Students understand and solve linear inequalities in one unknown.


a. Represent problem situations as inequalities.


(Thinking with Math Models)  Students will write inequalities to represent situations.  (Algebra)  Write inequalities from a word problem.

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b. Solve linear inequalities.


(TWMM)  Students will solve linear inequalities through symbolic method, using graphs or tables.  (Algebra)  Solve and graph linear inequalities.

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c. Interpret the solutions to linear inequalities.


(TWMM)  Students will explain what their solutions mean to inequalities.  (Algebra)  Find and interpret solutions to linear inequalities.

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FUNCTIONS AND RELATIONS


 


  

 


D.4.  Students understand and use the basic properties of linear relationships, y = kx + b.


a. Understand that a linear relationships are characterized by a constant rate of change.


(MSA) Identify a linear set of data by looking for a constant rate of change in a table or a straight line on a graph.

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b. Understand that the graph of a linear relationship y = kx + b is a line where the slope is k and b is the y- coordinate of the point where the graph crosses the y- axis (i.e., value of y when x = 0).


(MSA) Define slope and y-intercept.  Write equations given a graph by finding the slope (rate of change) and y-in homework

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c. Translate common linear phenomena into symbolic statements and graphs, and interpret the slope and y- intercept of the graph of y = kx + b in terms of the original situation.


(MSA) Write linear equations given computation sheets, homework

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469 U.S. Route 1 York, Maine | Phone: 207-363-3403 | Fax: 207-363-5602 | Contact Us 

Vision
As the tides of the ocean and the strength of the mountain shape our community, the York Schools' commitment to educational excellence and individual achievement shapes the future of each student. 
Mission
The mission of York Schools is to educate, inspire and challenge all learners to be ethical citizens who will make a difference in a changing and complex world.