ov… · Web viewI. Course Description. The goal of this course is to develop an understanding of rational numbers and their operations and begin to apply that understanding to

Radnor Middle SchoolCourse Overview

MathCourse 3/Intro to Algebra

Honors

General InformationCredits: N/A Length: Full YearWeighted: N/A Format: Meets DailyPrerequisite: N/A Grade: 7

I. Course DescriptionThe goal of this course is to develop an understanding of rational numbers and their operations and begin to apply that understanding to equations and inequalities in order to prepare for Algebra 1. These ideas will be integrated throughout the content strands of algebra, geometry, measurement, and data analysis and probability, with a focus on algebraic development. Students will also learn various problem solving strategies to solve appropriate applications within the strands listed above. The students will also begin the Algebra 1 course.

Grade 7 Course 3/Intro to Algebra Honors Last ModifiedJune 15, 2012

MARKING PERIOD: 1Unit: Chapter 2 – Integer Operations

Common Core Standards7.NS.1.c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world context.7.NS.2.b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world contexts.

Keystone Connections: (PA Standards)M7.A.2.1-Complete calculations by applying the order of operations.M7.A.3.2-Compute accurately with and without use of a calculator.M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions.M8.A.2.1-Complete calculations by applying the order of operations. (Reference: 2.2.8.A)M8.A.3.3-Compute and/or explain operations with integers, fractions and/or decimals. (Reference: 2.2.8.B)M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)2.2.7.A-Complete calculations by applying the order of operations.2.2.7.B-Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions. 2.4.7.B-Develop numeric relationship expressions to arrive at a conclusion. (e.g. commutative, associative, distributive, and transitive properties, substitution, and numerical patterns) identify

Student Objectives:In this chapter, students add, subtract, multiply, and divide integers.

At the conclusion of this chapter, students will successfully complete the following skills: Add, subtract, multiply, and divide integers


MAJOR UNITS OF STUDY

Materials &TextsLarson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal Littell.

Lesson Practice Sheets B Study Guides (optional) Lesson Note Taking Guides (optional)

Activities, Assignments, & AssessmentsACTIVITIES

2.2 Adding Integers2.3 Subtracting Integers2.4 Multiplying Integers2.5 Dividing Integers

ASSIGNMENTS Lesson Practice Sheets B Associated Chapter exercises

ASSESSMENTSHomework will be assigned on a daily basis. Grades will be based on quizzes and tests. In addition, teachers may use homework, group activities, and/or projects for grading purposes. The Radnor Middle School grading system and scale will be used to determine letter grades.

Lesson Assessment/Quizzes Chapter Tests

TerminologyNegative integers, positive integers, zero, identity property of addition, inverse property of addition, sum, signs +/-, rules for addition of integers, difference, rules for subtraction of integers, identity property of multiplication, product, rules for multiplying integers, multiplication property of zero, multiplicative identity

Media, Technology, Web Resources McDougal Littell Course 3 Easy Planner DVD ROM McDougal Littell Course 3 Power Presentations DVD ROM McDougal Littell Classzone.com resources Teacher developed smart-board documents Scientific Calculator


MARKING PERIOD: 1

Unit: Order of Operations (Lessons 1.2, 1.4)

Common Core Standards7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Keystone Connections: (PA Standards)M7.A.2.1-Complete calculations by applying the order of operations.M8.A.2.1-Complete calculations by applying the order of operations. (Reference: 2.2.8.A)2.1.7.B-Simplify equivalent numeric expressions involving four basic operations, grouping symbols, exponents, and square roots.2.2.7.A-Complete calculations by applying the order of operations.2.2.7.B-Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions.2.2.7.F-Describe appropriate uses of scientific calculator, pencil and paper and mental math.2.2.7.H-Check the reasonableness of an answer.2.4.7.D-Use and explain algorithmic procedures for computing and estimating with whole numbers, fractions, decimals and integers.

Student Objectives:In this chapter, students use order of operations to evaluate numeral and variable expressions, including expressions with powers.

At the conclusion of this chapter, students will successfully complete the following skills: Use order of operations to evaluate numerical expressions Evaluate expressions with powers



Lesson Practice Sheets C Study Guides (optional) Lesson Note Taking Guides (optional)


1.2 Order of Operations 1.4 Powers and Exponents

ASSIGNMENTS Lesson Practice Sheets C Associated Chapter exercises



Terminologywhole number, sum, difference, product, quotient, numerical expression, evaluate, order of operations, grouping symbols, fraction bar, common words and phrases for operations, exponent, base, power, squared, cubed, repeated multiplication



MARKING PERIOD: 1Unit: Chapter 4 – Factors, Fractions, and Exponents (Lessons 4.1, 4.2, 4.4, 4.3)

Common Core Standards7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 7.NS.2.b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world contexts.7.NS.2.c. Apply properties of operations as strategies to multiply and divide rational numbers.7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Keystone Connections: (PA Standards)M7.A.1.1-Express numbers in equivalent forms.M8.A.1.1-Represent numbers in equivalent forms. (Reference: 2.1.8.A, 2.1.8.B) M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions. M8.A.1.1-Represent numbers in equivalent forms. (Reference: 2.1.8.A, 2.1.8.B)M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)

Student Objectives:In this chapter, students use factorization trees to write the prime factorization of numbers and also factor monomials. Students find the greatest common factor and least common multiple of numbers and monomials. They use these quantities to simplify, compare, and order fractions and mixed numbers.

At the conclusion of this chapter, students will successfully complete the following skills: Write the prime factorization of numbers Find the greatest common factor of two or more numbers/monomials


Simplify fractions Find the least common multiple of two or more numbers/monomials




4.1 Factors and Prime Factorization 4.2 Greatest Common Factor4.3 Simplifying Fractions 4.4 Least Common Multiple




TerminologyPrime number, composite number, factor, prime factorization, factor tree, monomial, common factor, greatest common factor (GCF), relatively prime, simplest form, equivalent fractions, multiple, common multiple, least common multiple (LCM), least common denominator (LCD),



MARKING PERIOD: 1Unit: Chapter 5 – Rational Number Operations (Lessons 5.2, 5.3, 5.4, 5.6, 5.7, 5.5)

Common Core Standards7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.7.NS.2.c. Apply properties of operations as strategies to multiply and divide rational numbers.7.NS.2.d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.7.NS.3. Solve real-world and mathematical problems involving the four operations with rational number.7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Keystone Connections: (PA Standards)M7.A.3.2-Compute accurately with and without use of a calculator.M8.A.3.3-Compute and/or explain operations with integers, fractions and/or decimals. (Reference: 2.2.8.B)M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions. M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)2.2.7.A-Complete calculations by applying the order of operations.2.2.7.B-Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions.

Student Objectives:In this chapter, students add, subtract, multiply, and divide fractions and mixed numbers. Students write fractions and mixed numbers as decimals and vice versa. Students add, subtract, multiply, and divide decimals. Students estimate answers to decimal operations. They use operations with fractions and decimals to solve real world problems.


At the conclusion of this chapter, students will successfully complete the following skills: Add and subtract fractions with different denominators Multiply and divide fractions and mixed numbers Convert between fractions and decimals Identify rational numbers Add, subtract, multiply, and divide decimals Solve equations with fractions and decimals




5.2 Fractions with Different Denominators 5.3 Multiplying Fractions 5.4 Dividing Fractions 5.5 Fractions and Decimals 5.6 Adding and Subtracting Decimals 5.7 Multiplying and Dividing Decimals




TerminologyLike terms, simplest form, LCD, improper fraction, mixed number, numerator, denominator, reciprocal, multiplicative inverse, rational number, terminating decimal, repeating decimal,

Media, Technology, Web Resources


McDougal Littell Course 3 Easy Planner DVD ROM McDougal Littell Course 3 Power Presentations DVD ROM McDougal Littell Classzone.com resources Teacher developed smart-board documents Scientific Calculator


MARKING PERIOD: 1Unit: Chapter 7 – Ratios, Proportions, and Percents (Lessons 7.4, 7.1, 7.2, 7.3, 7.6, 7.7)

Common Core Standards7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.7.RP.2.a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.7.NS. 2.a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.7.EE.4.a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?7.EE.4.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Keystone Connections: (PA Standards)M7.A.2.1-Complete calculations by applying the order of operations.M7.A.2.2-Solve problems using ratios, proportions, percents and/or rates.


M7.B.1.1-Add or convert measurements.M7.B.2.2-Construct, interpret and/or use scale drawings to solve real-world problems.M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions. M8.A.2.2-Represent or solve problems using rates, ratios, proportions and/or percents. (Reference: 2.1.8.D, 2.3.8.B)M8.B.1.1-Convert measurements. (Reference: 2.3.5.D)M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)2.1.7.D-Distinguish between ratios and rates and solve proportions that represent real world problems.2.2.7.C-Create and solve word problems involving ratios, proportions, and percents including determining percentage, rate, and base.2.11.7.B-Compute and compare unit rates, ratios and slopes in real world situations.

Student Objectives:In this chapter, students find ratios and unit rates and write and then solve proportions. Students solve percent problems by using proportions and the percent equation. Students convert among fractions, decimals, and percents.

At the conclusion of this chapter, students will successfully complete the following skills: Find ratios and unit rates Write and solve proportions Solve percent problems using proportions Convert between fractions, decimals, and percents Solve percent problems using the simple interest formula




7.1 Ratios and Rates 7.2 Writing and Solving Proportions 7.3 Solving Percent Problems 7.4 Fractions, Decimals, and Percents 7.6 Percent Applications7.7 Simple Interest





TerminologyRatio, equivalent, rate, unit rate, proportion, cross products, scale, scale model, percent, base, part, whole, rules for changing between fractions, decimals, percents, simple interest



MARKING PERIOD: 1Unit: Chapter 4 – Factors, Fractions, and Exponents (Lessons 4.8)

Common Core Standards7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 7.NS.2.b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world contexts.7.NS.2.c. Apply properties of operations as strategies to multiply and divide rational numbers.7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Keystone Connections: (PA Standards)M7.A.1.1-Express numbers in equivalent forms.M8.A.1.1-Represent numbers in equivalent forms. (Reference: 2.1.8.A, 2.1.8.B) M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions. M8.A.1.1-Represent numbers in equivalent forms. (Reference: 2.1.8.A, 2.1.8.B)M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)

Student Objectives:In this chapter, students multiply and divide expressions with exponents and simplify expressions with negative exponents. Students also read and write numbers in scientific notation and use scientific notation in real world problems.

At the conclusion of this chapter, students will successfully complete the following skills: Read and write numbers using scientific notation Multiply and divide numbers in scientific notation





4.8 Scientific Notation




Terminologyscientific notation, standard form, product form



MARKING PERIOD: 2Unit: Chapter 8 – Polygons and Transformations (Lessons 8.1-8.8)

Common Core Standards7.RP.2.b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.7.EE.4.a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?7.EE.4.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.7.G.1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.7.G.3. Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; given an informal derivation of then relationship between the circumference and area of a circle.7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Keystone Connections: (PA Standards)M7.C.1.1-Define and/or apply basic properties of two- and three-dimensional geometric shapes.M8.B.2.1-Determine the measurement of a missing side(s) or angle(s) in a polygon. (Reference: 2.3.8.C, 2.9.8.D)M8.C.1.1-Identify, use, and/or describe properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders. (Reference: 2.9.8.D)2.9.7.A-Draw, construct and label figures incorporating perpendicular and parallel lines, perpendicular bisector of a line segment and angle bisector using a protractor and compass.2.9.7.B-Identify, draw, label, measure, and list the properties of complementary,


supplementary, vertical, and adjacent angles and use properties to determine missing angles.2.9.7.C-Draw, label, and classify polygons as regular or irregular up to decagon. 2.9.7.E-Construct parallel lines, draw a transversal, measure and compare angles formed such as alternate interior and exterior angles. 2.3.7.C-Measure and construct angles using a protractor.

Student Objectives:In this chapter, students solve equations to find angle measures involving supplementary and complementary angles and angles formed by a line intersecting parallel lines. Students classify angles, triangles, and quadrilaterals, and they find angle measures in polygons. Students identify and name congruent polygons and use the special rules for identifying congruent triangles. Students identify reflective figures and their lines of symmetry. They reflect, translate, and rotate figures in a coordinate plane. Students also use similar polygons to find missing measures.

At the conclusion of this chapter, students will successfully complete the following skills: Solve equations to find angle measures Classify angles and triangles Classify quadrilaterals Find angle measures in polygons Identify and name congruent polygons Reflect figures and identify lines of symmetry Translate and rotate figures in a coordinate plane Use similar polygons to find missing measures




8.1 Angle Pairs 8.2 Angles and Triangles 8.3 Quadrilaterals 8.4 Polygons and Angles 8.5 Congruent Polygons 8.6 Reflections and Symmetry8.7 Translations and Rotations 8.8 Similar Polygons





TerminologyPoint, line, ray, plane, angle, vertex, degree, straight angle, right angle, supplementary, complementary, vertical angles, perpendicular lines, parallel lines, transversal, alternate interior angles, alternate exterior angles, corresponding angles, angle symbols (m∠, ∠, right angle), acute angle, right angle, obtuse angle, acute triangle, right triangle, obtuse triangle, equilateral triangle, isosceles triangle, scalene triangle, tick marks, arc marks, sum of angles in a triangle, quadrilateral, parallelogram, rhombus, trapezoid, sum of angles in a quadrilateral, diagonals, parallel symbol, polygon, regular polygon, hexagon, heptagon, octagon, sum of angle measures, formula, measure of one angle formula, congruent, congruent angles, corresponding parts, congruence symbol (≅), SSS, SAS, ASA, naming polygons, congruence statement, transformation, reflection, image, pre-image, line of symmetry, x-axis, y-axis, line of reflection, rules for reflections, translation, rotation, translation rules, rotation rules, clockwise, counter-clockwise, coordinate notation, prime, similar polygons, similarity symbol (∼), similarity notation, proportional side lengths, scale factor



MARKING PERIOD: 2Unit: Chapter 9 – Real Numbers and Right Triangles (Lessons 9.1-9.4)

Common Core Standards7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Keystone Connections:M7.A.1.1-Express numbers in equivalent forms.M7.A.3.1-Apply estimation strategies to a variety of problems.M8.A.1.1-Represent numbers in equivalent forms. (Reference: 2.1.8.A, 2.1.8.B)M8.A.3.1-Determine the appropriateness of overestimating, underestimating or calculating an exact answer in problem-solving situations. (Reference: 2.2.8.F) 2.1.7.C-Distinguish between and order rational and irrational numbers.2.2.7.D-Identify and distinguish between rational and irrational numbers (e.g. (pi), square roots). M8.C.1.2-Compute measures of sides of right triangles using Pythagorean Theorem. (Reference: 2.10.8.A)2.10.7.A-State the Pythagorean Theorem and apply it to real world problems.

Student Objectives:In this chapter, students find and approximate square roots and classify real numbers as rational or irrational. Students solve real world problems involving square roots including problems that use the Pythagorean Theorem and problems that involve special right triangles.

At the conclusion of this chapter, students will successfully complete the following skills: Find and approximate square roots of numbers Identify real numbers as rational or irrational Use the Pythagorean Theorem to solve problems including real world problems




9.1 Square Roots


9.2 Rational and Irrational Numbers (Click to see note) 9.3 The Pythagorean Theorem 9.4 Using the Pythagorean Theorem




TerminologyRight angle, isosceles triangle, scalene triangle, equilateral triangle, square root, radical expression, perfect square, radical sign, negative square root, positive-or-negative or plus-or-minus symbol (±), irrational number, real number, rational number, integer, whole number, leg, hypotenuse, Pythagorean Theorem, converse, Pythagorean triple



MARKING PERIOD: 2Unit: Chapter 10 – Measurement, Area, and Volume (Lessons 10.1-10.7)

Common Core Standards7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.7.EE.4.a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?7.EE.4.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.7.G.1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Keystone Connections:M7.B.2.1-Develop, use and/or describe measures of length, perimeter, circumference, area or volume.M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions. M8.B.2.2-Use, describe and/or develop procedures to determine measures of perimeter, circumference, area, surface area and/or volume. Reference: 2.3.8.A, 2.3.8.D M8.C.1.1-Identify, use, and/or describe properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders. (Reference: 2.9.8.D)M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)2.3.7.A-Apply formulas to determine perimeter and area of polygons and circles, and volume of prisms, pyramids, spheres, cylinders, and cones.2.3.7.E-Compare and analyze perimeters, areas, volumes of similar figures.2.9.7.D-Identify, name, draw, and list all properties of spheres, prisms, cylinders, and cones. 2.9.7.G-Approximate the value of (pi) through experimentation.

Student Objectives:In this chapter, students find the areas of parallelograms, trapezoids, and circles. Students


identify solids. Students draw nets of prisms, pyramids, cylinders, and cones and use them to find surface areas. Students also use formulas to find the volumes of solids.

At the conclusion of this chapter, students will successfully complete the following skills: Find the areas of parallelograms and trapezoids Find the areas of circles Classify and sketch solids Find surface areas of prisms, cylinders, pyramids, and cones. Find volume of prisms, cylinders, pyramids, and cones.




10.1 Areas of Parallelograms and Trapezoids 10.2 Areas of Circles 10.3 Three-Dimensional Figures 10.4 Surface Areas of Prisms and Cylinders 10.5 Surface Areas of Pyramids and Cones 10.6 Volumes of Prisms and Cylinders 10.7 Volumes of Pyramids and Cones




TerminologyArea, base, height, circle, radius, diameter, pi (π), trapezoid, parallelogram, rhombus, base of a parallelogram, height of a parallelogram, base of a trapezoid, height of a trapezoid, formula for


area of a parallelogram, formula for area of a trapezoid, circumference, area formula for circles, circumference formula for circles, solid, polyhedron, face, prism, pyramid, cylinder, cone, sphere, edge, vertex, net, surface area, formula for surface area of a prism, formula for surface area of a cylinder, slant height, formula for surface area of pyramid, formula for surface area of a cone, volume, formula for volume of a prism, formula for volume of a cylinder, formula for volume of pyramid, formula for volume of cone



MARKING PERIOD: 2Unit: Chapter 7 – Ratios, Proportions, and Percents (Lesson 7.8)

Common Core Standards7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Keystone Connections: (PA Standards)M7.A.2.1-Complete calculations by applying the order of operations.M7.B.2.2-Construct, interpret and/or use scale drawings to solve real-world problems.M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions. M8.A.2.2-Represent or solve problems using rates, ratios, proportions and/or percents. (Reference: 2.1.8.D, 2.3.8.B)M8.B.1.1-Convert measurements. (Reference: 2.3.5.D)M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)

Student Objectives:In this chapter, students find the probability of simple events.

At the conclusion of this chapter, students will successfully complete the following skills: Find probabilities of events




7.8 Simple Probability

ASSIGNMENTS


Lesson Practice Sheets C Associated Chapter exercises



Terminologyoutcome, event, favorable outcome, probability of an event, theoretical probability, experimental probability, formula for theoretical probability



MARKING PERIOD: 2Unit: Chapter 12 – Data Analysis and Probability (Lessons 12.8)

Common Core Standards7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.7.SP.7.a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.7.SP.7.b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?7.SP.8.a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Keystone Connections: (PA Standards)2.7.7.B-Design and conduct an experiment with dependent and independent events and determine the probability of each.2.7.7.C-Write and solve a problem situation requiring probability in a real-world event.2.7.7.D-Conduct an experiment and discuss the differences between the experimental and theoretical probabilities.

Student Objectives:In this chapter, students apply these counting methods to find the probability and odds of simple events. Students also learn to distinguish between and find the probabilities of independent and dependent events.

At the conclusion of this chapter, students will successfully complete the following skills: Classify events as independent or dependent and then find their probabilities





12.8 Independent and Dependent Events




Terminologyprobability, find probability of an event, compound events, independent events, dependent events



MARKING PERIOD: 2Unit: Chapter 5 – Rational Number Operations (Lesson 5.5)

Common Core Standards7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.7.NS.3. Solve real-world and mathematical problems involving the four operations with rational number.7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Keystone Connections: (PA Standards)M7.A.3.2-Compute accurately with and without use of a calculator.M8.A.3.3-Compute and/or explain operations with integers, fractions and/or decimals. (Reference: 2.2.8.B)M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions. 2.2.7.A-Complete calculations by applying the order of operations.2.2.7.B-Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions.

Student Objectives:In this chapter, students find the mean, median, mode, and range of a data set.

At the conclusion of this chapter, students will successfully complete the following skills: Describe data sets using mean, median, mode, and range




5.8 Mean, Median, and Mode





Terminologymean, median, mode, range



MARKING PERIOD: 2Unit: Chapter 12 – Data Analysis and Probability (Lessons 12.1-12.3)

Common Core Standards7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.7.SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Keystone Connections: (PA Standards)M7.E.1.1-Interpret data shown in complex data displays.M7.E.2.1-Describe, compare and/or contrast data using measures of mean, median, mode or range.M7.E.3.1-Determine or calculate theoretical or experimental probability.M7.E.4.1-Draw conclusions and, make predictions based on data displays.M8.E.1.1-Choose, display or interpret data (tables, charts, graphs, etc.). (Reference: 2.6.5.A, 2.6.8.E, 2.7.8.D)M8.E.3.1-Calculate the probability of an event. (Reference: 2.7.8.E) M8.E.4.1-Draw conclusions, make inferences and/or evaluate hypotheses based on statistical and data displays. (Reference: 2.6.8.C, 2.7.8.E)2.6.7.E-Collect and represent data using stem and-leaf plot and box-and-whisker plots.2.6.7.F-Explain data displayed on a spreadsheet. 2.6.7.G-Examine examples of valid and invalid surveys and the sample used.


Student Objectives:In this chapter, students make-and-interpret stem and leaf plots, box-and-whisker plots, circle graphs, and line graphs. Students decide which graph or plot is most appropriate for a data set. Students use tree diagrams, the counting principle, permutations, and combinations to count choices or possibilities.

At the conclusion of this chapter, students will successfully complete the following skills: Make and interpret stem-and-leaf plots Make and interpret box-and-whisker plots Organize data using circle graphs and line graphs




12.1 Stem-and-Leaf Plots 12.2 Box-and-Whisker Plots 12.3 Using Data Displays




TerminologyData, mean, median, range, outcome, probability of an event, stem-and-leaf plot, box-and-whisker plot, lower quartile, upper quartile, lower extreme, upper extreme, inter quartile range, circle graph, line graph

Media, Technology, Web Resources McDougal Littell Course 3 Easy Planner DVD ROM


McDougal Littell Course 3 Power Presentations DVD ROM McDougal Littell Classzone.com resources Teacher developed smart-board documents Scientific Calculator


MARKING PERIOD: 3

Unit: Chapter 1 – Expressions, Equations, and Functions

Common Core Standards Interpret parts of an expression, such as terms, factors, and coefficients. Understand that a function is a rule that assigns to each input exactly one output. The

graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Keystone Connections:A1.1.1.4 Use estimation strategies in problem solving situations.A1.1.2.1 Write, solve, and/or graph linear equations using various methods.A1.1.3.1 Write, solve, and/or graph linear inequalities using various methods.A1.2.1.1 Analyze and/or use patterns or relations.A1.2.1.2 Interpret and/or use linear functions and their equations, graphs, or tables.

PA State Standards2.8.A1.D. Demonstrate an understanding and apply properties of functions (domain, range) and characteristics of linear functions.

Student Objectives: Writing and evaluating algebraic expressions Using expressions to write equations and inequalities Representing functions as verbal rules, equations, tables and graphs

Materials &TextsAlgebra 1 Larson series –McDougal, Littell & Co. 2007 ed. ‐ ‐



Evaluate Expressions


Apply Order of Operations Write Expressions Write Equations and Inequalities Use a Problem Solving Plan Represent Functions as Rules and Tables Represent Functions as Graphs


ASSESSMENTSHomework will be assigned on a daily basis. Grades will be based on quizzes and tests. Additionally, teachers may use homework, group activities, and/or projects for grading purposes. The Radnor Middle School grading system and scale will be used to determine letter grades.


TerminologyVariable Algebraic expressionEvaluate and algebraic expression Power ExponentBaseOrder of operationsVerbal modelRateUnit rateEquation

Open sentenceSolution of an equation or inequalityFormulaFunctionInputOutputDomainRangeIndependent variableDependant variable

Media, Technology, Web Resources McDougal Littell Algebra I Easy Planner DVD ROM McDougal Littell Algebra I Power Presentations DVD ROM McDougal Littell Classzone.com resources Teacher developed smart-board documents Scientific Calculator www.learningupgrade.com


MARKING PERIOD: 3

Unit: Chapter 2 – Properties of Real Numbers

Common Core Standards Use rational approximations of irrational numbers to compare the size of irrational

numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram

Keystone Connections:A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).

PA State Standards

Student Objectives: Performing operations with real numbers Applying properties of real numbers Classifying and reasoning with real numbers



Activities, Assignments, & AssessmentsACTIVITIES Use Integers and Rational Numbers

Add Real Numbers Subtract Real Numbers Multiply Real Numbers Apply the Distributive Property Divide Real Numbers Find Square Roots and Compare Real Numbers

Grade 8 Algebra 1 Honors Last ModifiedApril 24, 2012




TerminologyWhole numbersIntegersPositive IntegerNegative integerRational numberOppositesAbsolute valueConditional statementIf-then statementCounter exampleAdditive identityAdditive inverseMultiplicative identity

Equivalent expressionsDistributive propertyTermCoefficientConstant termLike termsMultiplicative inverseSquare rootRadicandPerfect squareIrrational numberReal numbers

Grade 8 Algebra 1 Honors Last ModifiedApril 24, 2012


Grade 7 Course 3/Intro to Algebra Honors Last ModifiedApril 24, 2012

MARKING PERIOD: 4

Unit: Chapter 3 – Solving Linear Equations

Common Core Standards Give examples of linear equations in one variable with one solution, infinitely many

solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Keystone Connections:A1.1.2.1 Write, solve, and/or graph linear equations using various methods.

PA State Standards

Student Objectives: Solving equations in one variable Solving proportion and percent problems Rewriting equations in two or more variables




Solve One Step Equations ‐ Solve Two Step Equations ‐ Solve Multi Step Equations ‐ Solve Equations with Variables on Both Sides Write Ratios and Proportions


Solve Proportions Using Cross Products Solve Percent Problems Rewrite Equations and Formulas




TerminologyInverse operations, equivalent equations, identity, ratio, proportion, cross product, scale drawing, scale model, scale, literal equation



MARKING PERIOD: 4

Unit: Chapter 4 – Graphing Linear Equations and Functions

Common Core Standards Compare properties of two functions each represented in a different way

(algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Keystone Connections:A1.2.1.1 Analyze and/or use patterns or relations.A1.2.1.2 Interpret and/or use linear functions and their equations, graphs, or tables.A1.2.2.1 Describe, compute, and/or use the rate of change (slope) of a line.

PA State Standards2.8.A1.D. Demonstrate an understanding and apply properties of functions (domain, range) and characteristics of linear functions.2.11.A1.B. Describe rates of change as modeled by linear equations.

Student Objectives: Graphing linear equations and functions using a variety of methods Recognizing how linear equations and functions affect their graphs Using graphs of linear equations and functions to solve real world problems


Lesson Practice Sheets C Study Guides (optional)


Lesson Note Taking Guides (optional)


Plot Points in a Coordinate Plane Graph Linear Equations Graph Using Intercepts Find Slope and Rate of Change Graph Using Slope Intercept Form ‐ Model Direct Variations Graph Linear Functions




TerminologyQuadrantsolution of an equation in two variablesgraph of an equation in two variableslinear equationstandard form of a linear equationlinear function x-intercepty-interceptsloperate of changeslope-intercept formparalleldirect variationconstant of variationfunction notationfamily of functionsparent linear function




Documents

ov… · Web viewI. Course Description. The goal of this course is to develop an understanding of rational numbers and their operations and begin to apply that understanding to