Benchmarks for GPS Mathematics Curriculum

Eighth Grade

Content Standard 1: Number Sense

Students will use numbers to count, measure, compare, order, scale, locate and label, and use a variety of numerical representations to present, interpret, communicate and connect various kinds of numerical information.

By the end of Grade 8, students should know and be able to:

  • Use a variety of representations of numbers
  • Define, recognize, and order real numbers including scientific notation
  • Relate very large and very small numbers to place value and exponential form

Content Standard 2: Operations

Students will add, subtract, multiply, and divide with whole numbers, fractions, decimals and integers, and develop strategies for selecting the appropriate computational and operational methods for solving problems.

By the end of Grade 8, students should know and be able to:

  • Identify and apply appropriate operations to write and solve problems including exponentiation and square roots
  • Use appropriate computational methods
  • Applies rules of order of operation to solve problems

Content Standard 3: Estimation and Approximation

Students will make estimates and approximations, and judge the reasonableness of results.

By the end of Grade 8, students should know and be able to:

  • Apply and explain appropriate estimation strategies in problem solving situations involving multi-step problems

Content Standard 4: Ratios, Proportions, and Percents

Students will use ratios, proportions, and percents to represent relationships between quantities and measures and solve problems involving rations, proportions, and percents.

By the end of Grade 8, students should know and be able to:

  • Solve and explain multi-step problems involving rations, proportions, and percents

Content Standard 5: Measurement

Students will make and use measurements in both customary and metric units to approximate, measure and compute length, area, volume, mass, temperature, angle, time, and money.

By the end of Grade 8, students should know and be able to:

  • Create and explain multi-step word problems involving measurement

Content Standard 6: Spatial Relationships and Geometry

Students will analyze and use spatial relationships and basic concepts of geometry to construct, draw, describe and compare geometric models and their transformations, and use geometric relationships and patterns to solve problems.

By the end of Grade 8, students should know and be able to:

  • Identify and draw figures to precise measurements

Content Standard 7: Probability and Statistics

Students will use basic concepts of probability and statistics to collect, organize display and analyze data, simulate events, and test hypotheses.

By the end of Grade 8, students should know and be able to:

  • Interpret, construct, and explain graphs and data representations

Content Standard 8: Patterns

Students will discover, analyze, describe, extend and create patterns, and use patterns to describe mathematical and other real world phenomena.

By the end of Grade 8, students should know and be able to:

  • Represent and describe mathematical relationships and use them to solve problems

Content Standard 9: Algebra and Functions

Students will use algebraic skills and concepts, including functions, to describe real world phenomena symbolically and graphically, and to model quantitative change.

By the end of Grade 8, students should know and be able to:

  • Apply algebraic and numerical properties and solve multi-step equations

Content Standard 10: Discrete Mathematics

Students will use the concepts and processes of discrete mathematics to analyze and model a variety of real world situations that involve recurring relationships, sequences, networks, combinations, and permutations.

By the end of Grade 8, students should know and be able to:

  • Use systematic listing and counting strategies including simple combinations and permutations

GRADE 8

Content Standard 1: Number Sense Students will use numbers to count, measure, compare, order, scale, locate and label, and use a variety of numerical representations to present, interpret, communicate and connect various kinds of numerical information.

PERFORMANCE STANDARD
Evident when student: / STRATEGIES/ACTIVITIES / MATERIALS/RESOURCES / ASSESSMENT
  1. Orders number using scientific notation.
D/M /
  • Modeling
  • Cooperative learning
  • Self-monitoring
  • Discussion/discourse
  • Investigations
  • Inquiry
  • Mental math
  • Computer software activities
  • Calculator activities
  • Use of manipulatives
  • Pictorial representations
  • Concrete models
  • Pencil and paper activities
  • Games
  • Memorization
  • Journal writing/math logs
  • Posted visual cues
  • Draw a picture
  • Role play/act it out
  • Find a pattern
  • Guess, check and revise
  • Work backward
  • Make a table
  • Make an organized list
  • Estimation
  • Fact families
  • Skip counting
  • Real-life applications
  • Daily warm-up activities
/
  • Decimal squares
  • Base ten blocks
  • Money
  • Calculators
  • Number tiles
  • Fraction pies
  • Flash cards
  • Fraction dice
  • Decimal dice
  • Number line (-50 – 50)
  • Rulers
  • Thermometer
  • Color tiles
  • Cubes
  • Geoboards
  • Numerical cards
  • Fraction dominoes
  • CMT prep materials
  • Dry-erase coordinate grids
/
  • Impact Math Course 3 Chapter 3, 4 Test and/or
  • Impact Math Course 3 Performance assessments Chapters 3,4
  • CMT
  • District assessments
Other assessments may include:
  • Impact Math Course 3
- Pretest
- Lab Investigations
- Student work
  • Teacher observations
  • Math journals
  • Teacher created assessment tools
  • CMT scoring rubrics
  • Daily warm ups

  1. Develops and uses an intuitive sense of the magnitude of numbers (including very large and very small numbers) and relate them to place value and exponential form.
M
  1. Locates points on the number lines and scales including fractions, decimals and integers.
R
  1. Uses inequalities to compare fractions, decimals and integers.
M
  1. Develops and applies number theory concepts including: prime, composite, factors, multiples, divisibility, as appropriate.
R
  1. Defines, recognizes and orders real numbers.
D/M
  1. Understands, represents and uses numbers in a variety of equivalent forms to solve problems.
D

GRADE 8

Content Standard 2: Operations Students will add, subtract, multiply, and divide with whole number, fractions, decimals and integers, and develop strategies for selecting the appropriate computational and operational methods for solving problems.

PERFORMANCE STANDARD
Evident when student: / STRATEGIES/ACTIVITIES / MATERIALS/RESOURCES / ASSESSMENT
  1. Adds, subtracts, multiplies, divides integers and finds opposites and absolute values.
R /
  • Modeling
  • Cooperative learning
  • Self-monitoring
  • Discussion/discourse
  • Investigations
  • Inquiry
  • Mental math
  • Computer software activities
  • Calculator activities
  • Use of manipulatives
  • Pictorial representations
  • Concrete models
  • Pencil and paper activities
  • Games
  • Memorization
  • Journal writing/math logs
  • Posted visual cues
  • Draw a picture
  • Role play/act it out
  • Find a pattern
  • Guess, check and revise
  • Work backward
  • Make a table
  • Make an organized list
  • Estimation
  • Fact families
  • Skip counting
  • Real-life applications
  • Daily warm-up activities
/
  • Fraction pies
  • Calculators
  • Base-ten materials
  • Money
  • Decimal squares
  • Fraction dice
  • Spinners
  • Flash Cards
  • Algebra balance
  • Number line (-50 – 50)
  • Algebra tiles
  • Inter chips
  • CMT prep materials
/
  • Impact Math Course 3 pretest
  • CMT
  • District assessments
Other assessments may include:
  • Impact Math Course 3
- Lab Investigations
- Student work
  • Teacher observations
  • Math journals
  • Teacher created assessment tools
  • CMT scoring rubrics
  • Daily warm ups

  1. Uses precise math vocabulary and symbols
  2. Integers
  3. Exponents
  4. Roots
  5. Associative properties
  6. Commutative properties
  7. Distributive properties
M
  1. Selects and uses appropriate method for computing from among mental math, estimation, paper and pencil and calculator.
M
  1. Creates, and solves multi-step story problems involving fractions, decimals, mixed numbers, money and explains how the solution was determined (including problems with insufficient or extraneous information.)
R
  1. Evaluates expressions using rules of order of operations.
D/M
  1. Applies exponents and rewrites factors using powers and roots.
M
  1. Multiplies fractions and mixed numbers by whole numbers, fractions and mixed numbers.
  • Cross factoring
  • Improper fractions
R
  1. Adds, subtracts, multiplies, and divides rational expressions.
R

GRADE 8

Content Standard 3: Estimation and Approximation Students will make estimates and approximations, and judge the reasonableness of results.

PERFORMANCE STANDARD
Evident when student: / STRATEGIES/ACTIVITIES / MATERIALS/RESOURCES / ASSESSMENT
  1. Estimates fractions, mixed numbers involving any computational skill.
R /
  • Modeling
  • Cooperative learning
  • Self-monitoring
  • Discussion/discourse
  • Investigations
  • Inquiry
  • Mental math
  • Computer software activities
  • Calculator activities
  • Pencil and paper activities
  • Games
  • Draw a picture
  • Guess, check and revise
  • Estimation
  • Daily warm-up activities
/
  • Calculators
  • Rulers
  • Decimal squares
  • Base-ten blocks
  • Money
  • Fraction pies
  • Balance scale
  • Capacity containers
  • Cuisenaire rods
  • Tiles
  • CMT prep materials
/
  • CMT
  • District assessments
Other assessments may include:
  • Impact Math Course 3
- Pretest
- Lab Investigations
- Student work
  • Teacher observations
  • Math journals
  • Teacher created assessment tools
  • CMT scoring rubrics
  • Daily warm ups

  1. Assess the reasonableness of answers using paper, pencil, mental math, formulas, calculator and computer.
R
  1. Develops, applies, and explains a variety of estimation strategies in problem situations involving quantities and measures.
R
  1. Rounds fractions and mixed numbers to the nearest ½ or whole.
R
  1. Applies estimation strategies to solve and defend solutions in multi-step problems.
M

GRADE 8

Content Standard 4: Ratios, Proportions, and Percents Students will use ratios, proportions, and percents to represent relationships between quantities and measures and solve problems involving rations, proportions, and percents.

PERFORMANCE STANDARD
Evident when student: / STRATEGIES/ACTIVITIES / MATERIALS/RESOURCES / ASSESSMENT
  1. Uses ratios, proportions and percents to solve problems (extend applications).
R /
  • Modeling
  • Cooperative learning
  • Self-monitoring
  • Discussion/discourse
  • Investigations
  • Inquiry
  • Mental math
  • Computer software activities
  • Calculator activities
  • Use of manipulatives
  • Pictorial representations
  • Concrete models
  • Pencil and paper activities
  • Games
  • Memorization
  • Journal writing/math logs
  • Draw a picture
  • Find a pattern
  • Guess, check and revise
  • Work backward
  • Make a table
  • Make an organized list
  • Estimation
  • Real-life applications
  • Surveys
  • Daily warm-up activities
/
  • Decimal/fraction decimals
  • Percent dice
  • Fraction dice
  • Decimal dice
  • Flash cards
  • Base ten material
  • Decimal square
  • Fraction models
  • Two color counters
  • Cuisenaire rods
  • Calculator
  • Rulers
  • CMT prep materials
/
  • Impact Math Course 3 Chapter 2 Test and/or
  • Impact Math Course 3 Performance assessments Chapters 3,4
  • CMT
  • District assessments
Other assessments may include:
  • Impact Math Course 3
- Pretest
- Lab Investigations
- Student work
  • Teacher observations
  • Math journals
  • Teacher created assessment tools
  • CMT scoring rubrics
  • Daily warm ups

  1. Uses dimensional analysis to determine equivalent rates.
D
  1. Finds percents of whole numbers and the percent a given number is of another number.
R
  1. Uses real world problems to develop an understanding of scaling concepts.
I
  1. Develops, uses, and explains applications of direct and indirect variation.
I

GRADE 8

Content Standard 5: Measurement Students will make and use measurements in both customary and metric units to approximate, measure, and compute length, area, volume, mass, temperature, angle, time, and money.

PERFORMANCE STANDARD
Evident when student: / STRATEGIES/ACTIVITIES / MATERIALS/RESOURCES / ASSESSMENT
  1. Creates and solves one and two-step word problems involving measurement.
M /
  • Modeling
  • Cooperative learning
  • Self-monitoring
  • Discussion/discourse
  • Investigations
  • Inquiry
  • Mental math
  • Computer software activities
  • Calculator activities
  • Use of manipulatives
  • Pictorial representations
  • Concrete models
  • Pencil and paper activities
  • Games
  • Memorization
  • Journal writing/math logs
  • Draw a picture
  • Role play/act it out
  • Find a pattern
  • Guess, check and revise
  • Work backward
  • Make a table
  • Make an organized list
  • Estimation
  • Real-life applications
  • Daily warm-up activities
/
  • Rulers
  • Protractors
  • Geoboards
  • Safe-T measuring set
  • Mychron timers
  • Calculators
  • Lateral area set (geometric solids)
  • Geometric volume set
  • Meter sticks
  • Yard sticks
  • Tape measures
  • Balance scales
  • Weights – metric
  • Weights – customary
  • Measuring containers
  • Thermometers
  • CMT prep materials
/
  • Impact Math Course 3 Pretest
  • CMT
  • District assessments
Other assessments may include:
  • Impact Math Course 3
- Lab Investigations
- Student work
  • Teacher observations
  • Math journals
  • Teacher created assessment tools
  • CMT scoring rubrics
  • Daily warm ups

  1. Estimates, makes and uses measurements in realistic situations.
R
  1. Uses formulas and scales to determine measures.
R
  1. Uses the concepts of length, perimeter, area, volume, angle measure, capacity, weight and mass to solve problems, using both metric and customary units.
Volume
  • Rectangular solids
  • Cylinder
Length
  • Circumference
  • Diameter
  • Radius
R
  1. Solves problems involving conversion of units.
R
  1. Understands and applies the relationship between precision of measurements and accuracy of calculations.
I
  1. Estimates and measures area, perimeter, and angles of given polygons in customary and metric units.
R
  1. Identifies appropriate metric and customary measurement units and use appropriate measurement tools including rulers, protractors and compasses.
R

GRADE 8

Content Standard 6: Spatial Relationships and Geometry Students will analyze and use spatial relationships and basic concepts of geometry to construct, draw, describe and compare geometric models and their transformations, and use geometric relationships and patterns to solve problems.

PERFORMANCE STANDARD
Evident when student: / STRATEGIES/ACTIVITIES / MATERIALS/RESOURCES / ASSESSMENT
  1. Locates points on a Cartesian plane using ordered points.
M /
  • Modeling
  • Cooperative learning
  • Self-monitoring
  • Discussion/discourse
  • Investigations
  • Inquiry
  • Mental math
  • Computer software activities
  • Calculator activities
  • Use of manipulatives
  • Pictorial representations
  • Concrete models
  • Pencil and paper activities
  • Games
  • Memorization
  • Journal writing/math logs
  • Draw a picture
  • Role play/act it out
  • Find a pattern
  • Guess, check and revise
  • Work backward
  • Make a table
  • Estimation
  • Real-life applications
  • Daily warm-up activities
/
  • Safe-T measurement set
  • Geoboards
  • Geo reflector mirror
  • Color cubes
  • Tanagrams
  • Pentominoes
  • Globe
  • Pull down coordinate grid
  • Geo solids
  • Pattern blocks
  • Polyhedral models
  • Miras
  • CMT prep materials
/
  • Impact Math Course 3 Chapter 5 Test
  • CMT
  • District assessments
Other assessments may include:
  • Impact Math Course 3
- Pretest
- Lab Investigations
- Student work
  • Teacher observations
  • Math journals
  • Teacher created assessment tools
  • CMT scoring rubrics
  • Daily warm ups

  1. Identifies and draws geometric shapes and figures to precise measurements.
M
  1. Uses the Pythagorean theorem to find the length of the hypotenuse of the missing leg of the right triangle.
D
  1. Finds the hypotenuse or missing leg of special right triangles.
D
  1. Describes and uses fundamental concepts and properties of and relationships among geometric shapes, points, lines, planes, angles including incidence parallelism, perpendicularity and Pythagorean theorem.
R
  1. Identifies, draws, and describes lines of symmetry in plane figures.
R
  1. Constructs symmetrical patterns and designs.
R
  1. Identifies and constructs geometric transformations.
R
  1. Identifies and describes congruent and similar figures.
R
  1. Relates two-dimensional and three-dimensional representation.
R
  1. Describes the geometry in nature and real world applications.
M
  1. Solves real-world problems using geometric concepts.
R
  1. Uses the results of a function table to draw a graph of a solution to an equation containing two variables.
I

GRADE 8

Content Standard 7: Probability and Statistics Students will use basic concepts of probability and statistics to collect, organize, display and analyze data, simulate events, and test hypotheses.

PERFORMANCE STANDARD
Evident when student: / STRATEGIES/ACTIVITIES / MATERIALS/RESOURCES / ASSESSMENT
  1. Interprets and constructs bar, line, pictographs and stem and leaf plots.
R /
  • Modeling
  • Cooperative learning
  • Self-monitoring
  • Discussion/discourse
  • Investigations
  • Inquiry
  • Mental math
  • Computer software activities
  • Calculator activities
  • Use of manipulatives
  • Pictorial representations
  • Concrete models
  • Pencil and paper activities
  • Games
  • Memorization
  • Draw a picture
  • Role play/act it out
  • Fid a pattern
  • Guess, check and revise
  • Work backward
  • Make a table
  • Make an organized list
  • Estimation
  • Real-life applications
  • Surveys
  • Daily warm-up activities
/
  • Graph paper masters
  • Rulers
  • Graph pull down chart
  • Playing cards
  • Probability kit
  • Spinners
  • Dice (number)
  • Fraction models
  • CMT prep materials
/
  • Impact Math Course 3 Chapter 9 Test and/or
  • Impact Math Course 3 Performance assessments
  • CMT
  • District assessments
Other assessments may include:
  • Impact Math Course 3
- Pretest
- Lab Investigations
- Student work
  • Teacher observations
  • Math journals
  • Teacher created assessment tools
  • CMT scoring rubrics
  • Daily warm ups

  1. Interprets and constructs double bar graphs, double line graphs and circle/pie graphs.
R
  1. Identifies information from graphs, tables, and charts.
R
  1. Determines certainty and impossibility of events.
R
  1. Makes predictions based on sample data.
R
  1. Solves problems involving expected outcomes or predictions.
M
  1. Computes mean, median, mode and range.
R
  1. Creates and solves problems involving mean, median, mode, and range, elementary notions of probability and fairness(including justifying answers).
R
  1. Determines the probability of simple and compound events.
M

GRADE 8

Content Standard 8: Patterns Students will discover, analyze, describe, extend and create patterns, and use patterns to describe mathematical and other real-world phenomena.

PERFORMANCE STANDARD
Evident when student: / STRATEGIES/ACTIVITIES / MATERIALS/RESOURCES / ASSESSMENT
  1. Uses patterns and relationships to identify the nth term in a sequence.
M /
  • Modeling
  • Cooperative learning
  • Self-monitoring
  • Discussion/discourse
  • Investigations
  • Inquiry
  • Mental math
  • Computer software activities
  • Calculator activities
  • Use of manipulatives
  • Pictorial representations
  • Concrete models
  • Pencil and paper activities
  • Games
  • Memorization
  • Journal writing/math logs
  • Draw a picture
  • Role play/act it out
  • Find a pattern
  • Guess, check and revise
  • Work backward
  • Make a table
  • Make an organized list
  • Estimation
  • Real-life applications
  • Function tables
  • Function machines
  • Daily warm-up activities
/
  • Tanagrams
  • Pattern blocks
  • Color tiles
  • Color cubes
  • Calculators
  • Number cards
  • Dominoes
  • Attribute blocks
  • CMT prep materials
/
  • Impact Math Course 3 Chapter 10 Test
  • Impact Math Course 3 Chapter 2 Performance assessments
  • CMT
  • District assessments
Other assessments may include:
  • Impact Math Course 3
- Pretest
- Lab Investigations
- Student work
  • Teacher observations
  • Math journals
  • Teacher created assessment tools
  • CMT scoring rubrics
  • Daily warm ups

  1. Uses patterns and relationships to represent and solve problems.
M

GRADE 8