BEDFORD COUNTY PUBLIC SCHOOLS Grade Mathematics Curriculum Guide First 9 Weeks Second 9 Weeks Third 9 Weeks Fourth 9 Weeks 8.2 – Real Numbers 8.1 – Expressions 8.4 – Order of Operations 8.15 – Equations & Inequalities 8.17 – Function Vocabulary 8.14 – Functions 8.16 – Graphing Functions 8.3 – Problem Solving 8.5 – Squares & Square Roots 8.6 – Angles 8.10 – Pythagorean Theorem 8.11 – Area & Perimeter 8.7 – Volume & Surface Area 8.9 – 3-D Figures 8.8 – Transformations 8.13 – Statistics 8.12 – Probability SOL Review # of Weeks Standards/Essential Questions Essential Knowledge/Skills/Understanding Resources Q1 1 Pre-Assessment 8.1 – 8.17 Course Introduction Scavenger Hunt 8.2 - Real Numbers The student will use problem solving, Key Vocabulary VDOE Middle School Math Vocabulary Cards Virginia Department of Education Mathematical Instructional Resources
20
Embed
bcpshelpdeskmiddleschoolmath.weebly.combcpshelpdeskmiddleschoolmath.weebly.com/uploads/6/3/4/6/... · Web viewChapter 5 Lesson 1 Resources/Lessons Order of Operations Algebraic Properties
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
BEDFORD COUNTY PUBLIC SCHOOLSGrade Mathematics Curriculum Guide
First 9 Weeks Second 9 Weeks Third 9 Weeks Fourth 9 Weeks
8.2 - Real NumbersThe student will describe orally and in writing the relationships between the subsets of the real number system.
Essential Question(s)How are the real numbers related?
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Describe orally and in writing the relationships
among the sets of natural or counting numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
Key VocabularyVDOE Middle School Math Vocabulary Cards
BEDFORD COUNTY PUBLIC SCHOOLSGrade Mathematics Curriculum Guide
Prerequisite/Extension SOL5.3a5.5a6.46.6a7.3b
Illustrate the relationships among the subsets of the real number system by using graphic organizers such as Venn diagrams. Subsets include rational numbers, irrational numbers, integers, whole numbers, and natural or counting numbers.
Identify the subsets of the real number system to which a given number belongs.
Determine whether a given number is a member of a particular subset of the real number system, and explain why.
Describe each subset of the set of real numbers and include examples and non-examples.
Recognize that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.†
Venn DiagramDOE Lesson Plans8.2 - Organizing Numbers - Number and Number Sense (PDF) - Investigating the real number system
Resources/LessonsClassifying Real NumbersSubsets of real numbersCreate your own vocabulary flash cards
2 8.1 – ExpressionsThe student willa) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers;b) compare and order decimals, fractions, percents, and numbers written in scientific notation.
Essential QuestionsWhat is the role of the order of operations when simplifying numerical expressions?
How does the different ways rational numbers can be represented help us compare and order rational numbers?What is a rational number?
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Simplify numerical expressions containing: 1)
exponents (where the base is a rational number and the exponent is a positive whole number); 2) fractions, decimals, integers and square roots of perfect squares; and 3) grouping symbols (no more than 2 embedded grouping symbols). Order of operations and properties of operations with real numbers should be used.
Compare and order no more than five fractions, decimals, percents, and numbers written in scientific notation using positive and negative exponents. Ordering may be in ascending or descending order.
Key VocabularyExpressionsRational Numbers
DOE Lesson Plans8.1a - Order of Operations - Following the order of operations8.1 - Ordering Numbers - Comparing and ordering numbers
1 8.4 – Order of OperationsThe student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables.
Essential Question(s)What is the role of the order of operations when evaluating expressions?
Prerequisite/Extension SOL5.76.87.13a
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Substitute numbers for variables in algebraic
expressions and simplify the expressions by using the order of operations. Exponents are positive and limited to whole numbers less than 4. Square roots are limited to perfect squares.
Apply the order of operations to evaluate formulas. Problems will be limited to positive exponents. Square roots may be included in the expressions but limited to perfect squares.
Key VocabularyPEMDAS
DOE Lesson Plans8.4 - Evaluating Algebraic Expressions - Computation and Estimation
Resources/LessonsOrder of Operations LessonOrder of Operation Student Practice
3 8.15a,c – Equations
The student willa) solve multistep linear equations in
one variable with the variable on one and two sides of the equation;
c) identify properties of operations used to solve an equation.
Essential Question(s)How does the solution to an equation differ from the solution to an inequality?
Prerequisite/Extension SOL
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Solve two- to four-step linear equations in one
variable using concrete materials, pictorial representations, and paper and pencil illustrating the steps performed.
Identify properties of operations used to solve an equation from among:
- the commutative properties of addition and multiplication;
- the associative properties of addition and
Key VocabularyEquationLinear Equation
DOE Lesson PlansSolving EquationsProperties of Operations
Resources/LessonsInequality Lesson and Student PracticeInequality Solver
Performance Task must be completed and graded on rubric by the end of Quarter 1
SOL 8.1Differentiated Best of Math I: Frugal Freda's Fruit ForayStudents determine the fraction of edible flesh of Freda's favorite fruits, along with the cost per edible serving.
SOL 8.4Differentiated Best of Math I: Townhouse TribulationStudents determine the number of square feet of brick required for a group of townhouses.Differentiated Best of Math I: Variable DilemmaStudents solve a series of letter equations by substituting numbers.
BEDFORD COUNTY PUBLIC SCHOOLSGrade Mathematics Curriculum Guide
Sample Performance Tasks:Q1 Project Fractions Decimals Percent Scientific NotationNumber Sense Performance Task #1Number Sense Performance Task #2Number Sense Performance Task #3
Q2
1 Benchmark and 8.17 - Function Vocabulary
The student will identify the domain, range, independent variable, or dependent variable in a given situation.
Essential Question(s)What are the similarities and differences among the terms domain, range, independent variable, and dependent variable?
Prerequisite/Extension SOLA.7AFDA.1AII.7
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Apply the following algebraic terms appropriately:
domain, range, independent variable, and dependent variable.
Identify examples of domain, range, independent variable, and dependent variable.
Determine the domain of a function.
Determine the range of a function.
Determine the independent variable of a relationship.
Determine the dependent variable of a relationship.
1 8.14 – FunctionsThe student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship.
Essential Question(s)What is the relationship among tables, graphs, words, and rules in modeling a given situation?
Prerequisite/Extension SOL7.12AFDA.4
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Graph in a coordinate plane ordered pairs that
represent a relation.
Describe and represent relations and functions, using tables, graphs, words, and rules. Given one representation, students will be able to represent the relation in another form.
Relate and compare different representations for the same relation.
BEDFORD COUNTY PUBLIC SCHOOLSGrade Mathematics Curriculum Guide
2 8.16 - Graphing Equations
The student will graph a linear equation in two variables.
Essential Question(s)What types of real life situations can be represented with linear equations?
Prerequisite/Extension SOL6.207.15a
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Construct a table of ordered pairs by substituting
values for x in a linear equation to find values for y.
Plot in the coordinate plane ordered pairs (x, y) from a table.
Connect the ordered pairs to form a straight line (a continuous function).
Interpret the unit rate of the proportional relationship graphed as the slope of the graph, and compare two different proportional relationships represented in different ways.†
Key VocabularyLinear Equation
DOE Lesson PlansGraphing Linear Equations
Pearson Textbook ResourcesChapter 3 Lessons 4 & 5Chapter 11 Lesson 5Resources/LessonsGraphing - match the line with the equationShodor - Graphing SketcherOnline Function Grapher
2 8.3 - Problem Solving
The student willa) solve practical problems
involving rational numbers, percents, ratios, and proportions; and
b) determine the percent increase or decrease for a given situation.
Essential QuestionsWhat is difference between percent increase and percent decrease?
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Write a proportion given the relationship of equality
between two ratios.
Solve practical problems by using computation procedures for whole numbers, integers, fractions, percents, ratios, and proportions. Some problems may require the application of a formula.
Maintain a checkbook and check registry for five or fewer transactions.
Compute a discount or markup and the resulting sale price for one discount or markup.
Compute the percent increase or decrease for a one-step equation found in a real life situation.
Compute the sales tax or tip and resulting total.
Substitute values for variables in given formulas. For example, use the simple interest formula
to determine the value of any missing variable when given specific information.
Key VocabularyPercentDiscountSimple InterestPercent of ChangePercent IncreasePercent Decrease
DOE Lesson PlansDo You Like To Spend Money?The Scoop on Ice CreamPercent of Increase or Decrease
BEDFORD COUNTY PUBLIC SCHOOLSGrade Mathematics Curriculum Guide
Compute the simple interest and new balance earned in an investment or on a loan for a given number of years.
1 8.5 – Squares & Square Roots
The student will
a) determine whether a given number is a perfect square; and
b) find the two consecutive whole numbers between which a square root lies.
Essential QuestionsHow does the area of a square relate to the square of a number?
Why do numbers have both positive and negative roots?
Prerequisite/Extension SOL5.176.56.177.1a7.2A.3
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Identify the perfect squares from 0 to 400.
Identify the two consecutive whole numbers between which the square root of a given whole
number from 0 to 400 lies (e.g., lies between 7 and 8 since 72 = 49 and 82 = 64).
Define a perfect square.
Find the positive or positive and negative square roots of a given whole number from 0 to 400. (Use
the symbol to ask for the positive root and when asking for the negative root.)
Key VocabularyPerfect SquareSquare Root
DOE Lesson PlansPerfect Squares & Square Roots
Pearson Textbook ResourcesChapter 3 Lesson 1
Resources/LessonsSquares and Square Roots Student PracticeSquares and Square Roots Lesson
Performance Task must be completed and graded on rubric by the end of Quarter 2
SOL 8.3Differentiated Best of Math I: Candy DilemmaA box of candies is eaten a fraction at a time. Students determine the number of candies that began in the box.Differentiated Best of Math I: Distribution DilemmaStudents determine the number of movie tickets a seller began with, after giving away different fractional amounts.Differentiated Best of Math I: Dog Years DilemmaStudents determine the 'dog age' of a puppy based on his human age.Differentiated Best of Math I: Easter Bunny FractionsA garden is planted with unusual vegetables in fractional parts. Students determine the missing fractional parts.
BEDFORD COUNTY PUBLIC SCHOOLSGrade Mathematics Curriculum Guide
The students will detemine which locker doors will be open at the end of the experiment.Best of Secondary Math: Maya TempleStudents are required to find the number of nubs in a Mayan Temple built from Legos.Differentiated Best of Math I: Checkerboard DilemmaStudents determine how many squares are on a checkerboard.Differentiated Best of Math I: Division of LaborStudents determine the number of hours 2 people work.Differentiated Best of Math I: Locker DilemmaStudents determine which lockers will be open, and which closed, after other students have open and closed them.
SOL 8.16Differentiated Best of Math, 6-8: Runners' DilemmaTwo friends are running at different speeds. Students determine when one will catch up with the other.
Sample Performance Tasks:Q2 Properties project and rubricAlgebraic Performance Task and RubricAlgebraic (Functions) Performance Task #1 and RubricAlgebraic (Functions) Performance Task #2 & RubricConsumer Math Performance Task & Rubric
Q3
1 Benchmark and 8.6 – Angles
The student willa) verify by measuring and describe
the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles; and
b) measure angles of less than 360°.
Essential Question(s)How are vertical, adjacent, complementary, and supplementary angles related?
Prerequisite/Extension SOL5.12a,b6.137.7G.2
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Measure angles of less than 360° to the nearest
degree, using appropriate tools.
Identify and describe the relationships between angles formed by two intersecting lines.
Identify and describe the relationship between pairs of angles that are vertical.
Identify and describe the relationship between pairs of angles that are supplementary.
Identify and describe the relationship between pairs of angles that are complementary.
Identify and describe the relationship between pairs of angles that are adjacent.
Resources/LessonsInteractive ProtractorGeometric ConstructionsAngles JeopardyComplementary Angles Lesson and Student PracticeSupplementary Angles Lesson and Student Practice
BEDFORD COUNTY PUBLIC SCHOOLSGrade Mathematics Curriculum Guide
Use the relationships among supplementary, complementary, vertical, and adjacent angles to solve practical problems.†
2 8.10 - Pythagorean Theorem
The student willa) verify the Pythagorean Theorem;
andb) apply the Pythagorean Theorem.
Essential Question(s)How can the area of squares generated by the legs and the hypotenuse of a right triangle be used to verify the Pythagorean Theorem?
Prerequisite/Extension SOL5.13a,b6.127.6G.8
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Identify the parts of a right triangle (the hypotenuse
and the legs).
Verify a triangle is a right triangle given the measures of its three sides.
Verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement.
Find the measure of a side of a right triangle, given the measures of the other two sides.
Solve practical problems involving right triangles by using the Pythagorean Theorem.
Resources/LessonsVerify the Pythagorean TheoremPythagorean Theorem CalculatorGrade 8 Math Formula Sheet
2 8.11 - Composite Plane Figures
The student will solve practical area and perimeter problems involving composite plane figures.
Essential Question(s)How does knowing the areas of polygons assist in calculating the areas of composite figures?
Prerequisite/Extension SOL5.96.10a,b,c,d
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Subdivide a figure into triangles, rectangles,
squares, trapezoids and semicircles. Estimate the area of subdivisions and combine to determine the area of the composite figure.
Use the attributes of the subdivisions to determine the perimeter and circumference of a figure.
Apply perimeter, circumference and area formulas to solve practical problems.
The student willa) investigate and solve practical
problems involving volume and
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Distinguish between situations that are applications
of surface area and those that are applications of volume.
Investigate and compute the surface area of a square or triangular pyramid by finding the sum of the areas of the triangular faces and the base using concrete objects, nets, diagrams and formulas.
Investigate and compute the surface area of a cone by calculating the sum of the areas of the side and the base, using concrete objects, nets, diagrams and formulas.
Investigate and compute the surface area of a right cylinder using concrete objects, nets, diagrams and formulas.
Investigate and compute the surface area of a rectangular prism using concrete objects, nets, diagrams and formulas.
Investigate and compute the volume of prisms, cylinders, cones, and pyramids, using concrete objects, nets, diagrams, and formulas.
Solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids.
Compare and contrast the volume and surface area of a prism with a given set of attributes with the volume of a prism where one of the attributes has been increased by a factor of 2, 3, 5 or 10.
Describe the two-dimensional figures that result from slicing three-dimensional figures parallel to the base (e.g., as in plane sections of right rectangular prisms and right rectangular pyramids).†
Resources/LessonsShodor - Surface Area and VolumeSurface Area of Prisms and CubesCone Facts Lesson and Student Practice
1 8.9 - 3-D Figures
The student will construct a three-dimensional model, given the top or bottom, side, and front views.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Construct three-dimensional models, given the top
BEDFORD COUNTY PUBLIC SCHOOLSGrade Mathematics Curriculum Guide
Essential Question(s)How does the knowledge of two-dimensional figures inform work with three-dimensional objects?
Prerequisite/Extension SOLn/a
or bottom, side, and front views.
Identify three-dimensional models given a two-dimensional perspective.
Pearson Textbook ResourcesChapter 8 Lesson 2
Resources/LessonsLevel 1 - Match one view to a 3D ShapeLevel 2 - Math the side view of a 3 D ShapeBuilding 3D Models with 3 views given
1 8.8 – Transformations
The student willa) apply transformations to plane
figures; andb) identify applications of
transformations.
Essential Question(s)How does the transformation of a figure on the coordinate grid affect the congruency, orientation, location, and symmetry of an image?
Prerequisite/Extension SOL5.116.11a,b7.8G.3
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Demonstrate the reflection of a polygon over the
vertical or horizontal axis on a coordinate grid.
Demonstrate 90°, 180°, 270°, and 360°clockwise and counterclockwise rotations of a figure on a coordinate grid. The center of rotation will be limited to the origin.
Demonstrate the translation of a polygon on a coordinate grid.
Demonstrate the dilation of a polygon from a fixed point on a coordinate grid.
Identify practical applications of transformations including, but not limited to, tiling, fabric, and wallpaper designs, art and scale drawings.
Identify the type of transformation in a given example.
Resources/LessonsMath Is Fun TransformationsMister Teacher TransformationsTesselations
Performance Task must be completed and graded on rubric by the end of Quarter 3
SOL 8.6Best of Secondary Math: Tan Pattern Block AnglesStudent will determine the two different angle measurements in the tan pattern block.Differentiated Best of Math I: Tan Pattern Block AnglesStudents determine the value of the angles of the tan pattern block piece.
SOL 8.8Differentiated Best of Math I: Stained GlassStudents determine the amount of glass and metal needed for a stained glass window.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Collect, organize, and interpret a data set of no
more than 20 items using scatterplots. Predict from the trend an estimate of the line of best fit with a drawing.
Interpret a set of data points in a scatterplot as having a positive relationship, a negative relationship, or no relationship.
Key VocabularyScatterplotBest fit linesTrend lineCorrelation
DOE Lesson PlansScatterplotsGraphs
Pearson Textbook ResourcesChapter 9
Resources/LessonsCreate ScatterPlotsPractice with Scatterplots
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Determine the probability of no more than three
independent events.
Determine the probability of no more than two dependent events without replacement.
Compare the outcomes of events with and without replacement
Key VocabularyProbability
DOE Lesson PlansProbability
Pearson Textbook ResourcesChapter 10 Lesson 4
Resources/LessonsProbability Single EventsProbability - Compound EventsMore Probability of Compound Events
5 SOL Review
Essential Questions
Prerequisite/Extension SOL
Key Vocabulary
DOE Lesson PlansVDOE Task CardsVDOE Tasks for SortVDOE Triplet Tasks-Volume
Textbook ResourcesPearson Textbook Resources
Resources/LessonsTestNav
Math SOL Released Tests
VDOE Using Statewide SOL Results to Guide Instruction Powerpoint
Online General ResourcesNational Library of Virtual ManipulativesSmart Exchange lessons for Smartboards