BCPS Curriculum Guide
R07-2009
Math 8 Course Map THIS COURSE: Math 8
Is about
using mathematical concepts to introduce Algebraic skills and Geometric concepts as well as exploring statistical data.
Course Questions: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
How are expressions, equations, and inequalities evaluated? What determines into which class a real number falls? How are various charts, graphs, and plots organized to understand collections of data? What is the relationship between angles formed by lines and their measurements? How are geometric figures in the coordinate plane transformed? How is the Pythagorean Theorem used? How are formulas used to find volume and surface area of 3-D figures? How are formulas and proportions used to solve practical problems? How are percents used in real life situations? How can probability be used to make predictions? How are tables, graphs, and rules used to graph linear equations?
BCPS Curriculum Guide
R07-2009 Critical Vocabulary
Exponents Fractions Decimals Percents Equations Graphs Angles 3D Figures
Integers Formulas Inequalities Expressions Transformations Number Systems Proportions Properties Learned in these UNITS Patterns Functions
Algebra
Graphing
Probability
Proportions Geometry
Real Numbers
BCPS Curriculum Guide
R07-2009
Course: Math 8 Unit 1: Algebra…is about… Pacing: 9 weeks Properties of real numbers
applying applying
Key Unit Questions:
Expanding the knowledge of algebra by
simplifying
solving
Equations and inequalities
simplifying
Numeric expressions using order of operations
SOLs: 8.1 8.4 8.15
1. How are the properties of real numbers applied? 2. How are numeric and variable expressions simplified using order of operations? 3. How are 2 step equations and inequalities solved?
Variable expressions using order of operations
The student will a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers; The student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables. Problems will be limited to positive exponents. The student will solve two-step equations and inequalities in one variable, using concrete materials, pictorial representations, and paper and pencil.
Teacher Comments: **Teacher discretion - Multi-step equations and inequalities Holt 8 text 10-2, 10-3, 10-4
Essential Skills & Knowledge
Suggested Activities & Suggested Resources
BCPS Curriculum Guide
R07-2009 Assessments
8.1a
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Simplify numerical expressions containing exponents where the base is a rational number and the exponent is a positive whole number, using the order of operations and properties of operations with real numbers. *** include negative exponents •
8.4
•
-Holt 8 text 2-6, 2-8 -http://janus.astro.umd.edu/astro/ scinote -www.mathplayground.com/howto_ pemdas.html -Holt 8 text 1-1
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to •
8.15
-properties sort -order of operations mneumonic -FRAME with order of operation steps
Substitute numbers for variables in an algebraic expression and simplify the expression by using the order of operations. Exponents used are whole numbers less than 4. Apply the order of operations to evaluate formulas.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to • •
Solve two-step linear equations by showing the steps and using algebraic sentences. Solve two-step inequalities by showing the steps and using algebraic sentences.
-FRAME -Hands On Equations -Algeblocks
Required: Interactive Achievement Test
-Holt 8 1-3, 1-4, 1-5, 2-4, 2-5, 3-6, 3-7, 10-1 -http://www.algebralab.org/lessons/ lesson.aspx?filesAlgebra_Onevariable onestep.xml -http://www.learningwave.com/ chapter/alpha/index.html -mathnet:InteractiveAlgebra: Equationbuster -http://step.nn.k12va.us/math/ middlemath/ppt/solve_one_ step_inequalities.ppt--cached -Holt 8 text 10-2 optional
BCPS Curriculum Guide Course: Math 8 Unit 2: Graphing…is about… Pacing: 4 weeks
Key Unit Questions:
Organizing and analyzing data
by examining
Box & Whisker Plots
R07-2009
Matrices by identifying
by distinguishing and formulating
Patterns in Scattergram s
SOLs: 8.12 8.13
by examining
Frequency Table & Histograms
To examine and create
1. How is data organized with a variety of graphs and plots? 2. How is data compared, and predicted with a variety of graphs and plots? 3. How are inferences made from data? 4. How is data organized in a matrix (matrices)?
Bar, Line, circle , and picture graphs
The student will make comparisons, predictions, and inferences, using information displayed in frequency distributions; box-andwhisker plots; scattergrams; line, bar, circle, and picture graphs; and histograms. The student will use a matrix to organize and describe data.
Teacher Comments:
Essential Skills & Knowledge
Suggested Activities &
Suggested Resources
BCPS Curriculum Guide
R07-2009 Assessments
8.12
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to • Make comparisons, predictions, and inferences, given data sets of no more than 20 items that are displayed in frequency distributions; box-and-whisker plots; scattergrams; line, bar, circle, and picture graphs; and histograms.
8.13
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to •
Describe the characteristics of a matrix, including designating labels for rows and columns.
•
Use a matrix of no more than 12 entries to organize and describe a data set.
•
Identify the position of an element by row and column.
•
Transfer data from a chart to a matrix.
-use real life source (newspaper) to analyze data -number line on floor and students become part of the graph
-convert various tables/charts to matrices -take survey and create matrix of data -M&M activity (CAMS) -Scope & Sequence pages 89-90
Required: Interactive Achievement Tests
-Holt 8 text 4-4, 4-5, 4-6, 4-7 -www.mathteacher.com.au/ year8/ch17_stat/03_freq/freq.htm -http://score.kings.k12.ca.us/ lessons/mandm.html -http://quarknet.fnal.gov/toolkits/ ati/histograms.html -http://www.wisc-online.com/objects. index_tj.asp?objid=TMH1101 -http://teachhealthk-12. uthscsa.edu/curriculum/… -VDOE Box & Whisker
-Holt 8 text page 687 -http://www.kidsnumber.com/ math_magic.php
BCPS Curriculum Guide
R07-2009
Course: Math 8 Unit 3: Proportions…is about… Pacing: 3 weeks
Key Unit Questions:
Using equivalent ratios To solve To identify and apply
Practical problems
SOLs: 8.17 8.3
1. How are proportions used to solve practical problems? 2. How can problems be written that establish a relationship between ratios? 3. How are proportions used to identify and work with similar figures? 4. How are equivalent ratios determined?
Similar figures
The student will create and solve problems, using proportions, formulas, and functions. The student will solve practical problems involving rational numbers, percents, ratios, and proportions.
Teacher Comments:
Essential Skills & Knowledge
Suggested Activities &
Suggested Resources
BCPS Curriculum Guide 8.17
8.3
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to •
Write problems that require establishing a relationship between ratios.
•
Solve problems by using proportions.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to •
R07-2009 Assessments -measure student heights -Holt 8 text 7-1, 7-2, 7-4 and shadows to estimate -www.ehow.com/how_5011076_makeheight of tree or other tall an-altimeter.html object -construct an altimeter using a straw, string, ruler and a weight to create two similar triangles…find heights of different objects
Solve practical problems by using computation procedures for whole numbers, integers, rational numbers, percents, ratios, and proportions.
Required: Interactive Achievement Test
BCPS Curriculum Guide
R07-2009
Course: Math 8 Unit 4: Geometry…is about… Pacing: 6 weeks Pythagorea n Theorem
applying
Key Unit Questions:
Exploring various figures by
finding
Volume & Surface Area
graphing analyzing
Angles
SOLs: 8.10
8.6 8.8 8.9 8.7 8.17
identifying
Coordinate Plane and transformations
Nets of 3D figures
5. How is the Pythagorean Theorem applied? 6. How are square roots determined? (with the use of calculator) 7. How are angles identified and measured ? 8. What are the relationships of the angles between intersecting lines and how are they determined? 9. How are figures in the coordinate plane graphed and transformed ? 10. How are nets of 3D figures identified? 11. How are formulas used to calculate volume and surface areas?
The student will a) verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement; and b) apply the Pythagorean Theorem to find the missing length of a side of a right triangle when given the lengths of the other two sides. The student will verify by measuring and describe the relationships among vertical angles, supplementary angles, and complementary angles and will measure and draw angles of less than 360°. The student will apply transformations (rotate or turn, reflect or flip, translate or slide, and dilate or scale) to geometric figures represented on graph paper. The student will identify applications of transformations, such as tiling, fabric design, art, and scaling. The student will construct a three-dimensional model, given the top, side, and/or bottom views. The student will investigate and solve practical problems involving volume and surface area of rectangular solids (prisms), cylinders, cones, and pyramids. The student will create and solve problems, using proportions, formulas, and functions.
Teacher Comments:
BCPS Curriculum Guide Essential Skills & Knowledge
8.10
Find the measure of a side of a right triangle, given the measures of the other two sides. The measures of the sides of the triangle may be whole numbers no larger than 15 or decimals in tenths.
-protractor activities -FRAME -Scope & Sequence pages • Solve real-life problems involving right triangles by using the 47-51 Pythagorean Theorem -use toothpicks and The student will use problem solving, mathematical communication, marshmallows to illustrate mathematical reasoning, connections, and representations to angles, vertices, and edges • Measure angles of less than 360° to the nearest degree, using appropriate tools. •
Identify and describe the relationships among the angles formed by two intersecting lines.
•
Identify and describe pairs of angles that are vertical.
•
Identify and describe pairs of angles that are supplementary. Identify and describe pairs of angles that are complementary.
•
8.8
Suggested Activities & Assessments
The student will use problem solving, mathematical communication, -use tiles to probe theorem mathematical reasoning, connections, and representations to -ask a carpenter how they • Identify the parts of a right triangle (the hypotenuse and the determine right angles legs). -Scope & Sequence pages 37-40,45 • Verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement. •
8.6
R07-2009
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to •
Identify the geometric transformations (rotation, reflection, translation, and dilation) by using a variety of real-life
-Dry erase coordinate plane boards -Scope & Sequence pages 60-67
Suggested Resources
-Intro to triangles Holt 8 text 5-3 -Holt 8 text 6-3 -http://www.mathisfun.com/ pythagoras.html http://www.doe.virginia.gov/VDOE /EnhancedSandS/mgrade8.doc
-Holt 8 text 5-1, 5-2 - www.kidsport.com/grade 7/math/measuregeo/measuringang les -www.mathleague.com/help/ geometry/angles.htm -http://mathworld.wolfram.com/ Angle.html
BCPS Curriculum Guide examples
8.9
8.7
•
Demonstrate the reflection of a figure over a vertical or horizontal line on a coordinate grid.
•
Demonstrate 90° 180°, 270°, and 360° rotations of a figure on a coordinate grid.
•
Demonstrate the translation of a figure on a coordinate grid.
•
Compute the surface area of a pyramid by finding the sum of the areas of the triangular faces and the base.
•
Compute the surface area of a cone by calculating the sum of the areas of the side and the base, using formulas.
•
Compute the volume and surface area of rectangular solids (prisms), cylinders, cones, and square pyramids, using formulas. Investigate and solve problems involving volume and surface area of rectangular solids (prisms), cylinders, cones and pyramids.
-1997 AIM Activity Spacial Visualization (RMMS) -Scope & Sequence pages 68-69
-Cut a net of each figure to find total area The student will use problem solving, mathematical communication, -Scope & Sequence pages mathematical reasoning, connections, and representations to 56-58 • Construct three-dimensional models, given top, side, and bottom views. Required: Interactive Achievement Test The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
•
8.17
R07-2009
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to •
Write problems that require establishing a relationship between ratios.
•
Solve problems by using proportions.
-Holt 8 text 5-7
-Holt 8 text 6-5, 6-6, 6-7,6-8, 6-9
BCPS Curriculum Guide
R07-2009
BCPS Curriculum Guide
R07-2009
Course: Math 8 Unit 5: Real Numbers…is about… Pacing: 4 weeks
Key Unit Questions:
Representing and applying numbers by Decimals, fractions, percents, scientific notation SOLs: 8.1 8.3 8.5 8.2
Comparing and ordering
solving
Consumer application problems
Classifying and identifing
finding
Percent increase & decrease
Subsets of real numbers
12. How are fractions, decimals, percents, and scientific notation interchanged, compared, and ordered ? 13. How are percents used to solve consumer application problems? 14. How is percent of increase and decrease determined? 15. How do relationships between subsets of the real number system differ? 16. How are the values of square roots placed on a number line?
The student will b) recognize, represent, compare, and order rational numbers expressed in scientific notation c) compare and order decimals, fractions, percents, and numbers written in scientific notation The student will solve practical problems involving rational numbers, percents, ratios, and proportions. Problems will be of varying complexities and will involve real-life data, such as finding a discount and discount prices and balancing a checkbook. The student, given a whole number from 0 to 100, will identify it as a perfect square or find the two consecutive whole numbers between which the square root lies. The student will describe orally and in writing the relationship between the subsets of the real number system.
Teacher Comments:
Essential Skills & Knowledge
Suggested Activities &
Suggested Resources
BCPS Curriculum Guide 8.1
8.3
8.5
8.2
R07-2009
Assessments The student will use problem solving, mathematical communication, -flash cards mathematical reasoning, connections, and representations to -sorts to order -Scope & Sequence pages • Recognize, represent, compare, and order rational numbers expressed in scientific notation, using both positive and negative 3-6 exponents. • Compare and order fractions, decimals, percents, and numbers written in scientific notation. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to •
Solve practical problems by using computation procedures for whole numbers, integers, rational numbers, percents, ratios, and proportions.
•
Maintain a checkbook and check registry for five or fewer transactions.
•
Compute a discount and the resulting (sale) price for one discount.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to •
Identify the perfect squares from 0 to 100.
•
Identify the two consecutive whole numbers between which the square root of a given whole number from 0 to 100 lies (e.g., 2 2 57 lies between 7 and 8 since 7 = 49 and 8 = 64).
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.
•
Illustrate the relationships among the subsets of the real number system by using graphic organizers such as Venn diagrams. Subsets include real numbers, rational numbers, irrational numbers, integers, whole numbers, and natural numbers.
•
Identify the subsets of the real number system to which a given number belongs.
-Create advertising poster or sale flyer -Create a checkbook and go shopping -Scope & Sequence pages 103-106
-Holt 8 text 2-9, 8-1 -www.mathgoodies.com/ lesson/volt/challenge_vol4htm -www.mathplayground.com/ mathvideos/html -http://janus.astro.umd.edu/ astro/scinote -Holt 8 text 8-2, 8-3, 8-4, 8-6, 8-7 -newspapers/flyers/catalogues
-calculator exploration -Scope & Sequence pages 34-36
-Holt 8 text 3-8, 3-9 -FRAME -Flow Chart -Scope & Sequence pages 6-8 -Concept Comparison or Concept Masteryof Rational and Irrational Numbers
-Holt 8 text 3-10
BCPS Curriculum Guide • •
R07-2009
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. Required: Interactive Achievement Test
BCPS Curriculum Guide
R07-2009
Course: Math 8 Unit 7: Patterns and Functions…is about… Pacing: 3 weeks
Key Unit Questions:
Identifying relationships by comparing
Functions and relations
SOLs: 8.14
by graphing
Linear equations
by identifying
Domain, range, IV, DV
17. How do functions and relations differ? 18. How are linear equations graphed? 19. How are domain, range, independent, and dependent variables identified? 20. How are rules determined from a table of values? 21. How are tables of values, graphs and rules related? 22. How are the domain, and range of a function determined? How are domain and range related to independent and dependent variables?
The student will a) describe and represent relations and functions, using tables, graphs, and rules; and b) relate and compare tables, graphs, and rules as different forms of representation for relationships. 8.17 The student will create and solve problems, using proportions, formulas, and functions. 8.18 The student will use the following algebraic terms appropriately: domain, range, independent variable, and dependent variable. 8.16 The student will graph linear equations in two variables, in the coordinate plane, using a table of ordered pairs. Teacher Comments:
BCPS Curriculum Guide Essential Skills & Knowledge
8.14
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.
•
Write a rule that represents a relation from a table of values.
•
Write a table of values from the rule that represents a relation.
•
Write a table of values from the graph of ordered pairs of a relation.
•
Describe and represent relations and functions, using tables, graphs, and rules. Relate and compare different representations of the same relation.
•
8.17 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to • • 8.18
Create problems that involve a functional relationship. Solve problems that involve functions
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.
Suggested Activities & Assessments -charts/tables from real life sources
R07-2009 Suggested Resources
-Holt 8 text 1-7, 1-8, 1-9
-Scope & Sequence pages 107120
-Holt 8 text 12-4 -coordinate with science department experiments -point out alphabetical patterns Required: Interactive Achievement Test
BCPS Curriculum Guide • Determine the dependent variable of a relationship. 8.16 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.
R07-2009 -Holt 8 text 1-7, 1-8, 11-1