Radnor High School - Radnor Township School District
Radnor Middle School
Course Overview
Math
Course 3
|General Information |
|Credits: N/A Length: Full Year |
|Weighted: N/A Format: Meets Daily |
|Prerequisite: N/A Grade: 7 |
|I. 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 |
|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. |
MARKING PERIOD: 1
Unit: Chapter 1 – Variables and Equations
|Common Core Standards |
|7.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.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.E.1.1-Interpret data shown in complex data displays. |
|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.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) |
|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 bar graphs and histograms to analyze data. Students use order of operations to evaluate numeral and variable |
|expressions, including expressions with powers. Students write variable expressions and write and solve equations using mental math. Students |
|use formulas to find unknown values. |
| |
|At the conclusion of this chapter, students will successfully complete the following skills: |
|Use graphs to analyze data |
|Use order of operations to evaluate numerical expressions |
|Write and evaluate variable expressions |
|Evaluate expressions with powers |
|Write and solve equations |
|Use mental math to solve equations |
|Use formulas to find unknown values |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|Interpreting Graphs |
|1.2 Order of Operations |
|1.3 Variables and Expressions |
|1.4 Powers and Exponents |
|1.5 Equations and Solutions |
|1.6 Variables in Familiar Formulas |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Bar graph, frequency table, histogram, intervals, horizontal axis, vertical axis, whole number, sum, difference, product, quotient, numerical |
|expression, evaluate, order of operations, verbal model, grouping symbols, fraction bar, variable, variable expression, common words and |
|phrases for operations, exponent, base, power, squared, cubed, repeated multiplication, equation, solution, solving an equation, formula, |
|perimeter, area, distance formula, d=r·t, rate, speed |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 1
Unit: Chapter 2 – Integer Operations
|Common Core Standards |
|7.NS.1.a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two |
|constituents are oppositely charged. |
|7.NS.1.b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is |
|positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by |
|describing real-world contexts. |
|7.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. |
|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.1.2-Compare quantities and/or magnitudes of numbers. |
|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.A.3.2-Compute accurately with and without use of a calculator. |
|M7.D.1.1-Recognize, reproduce, extend and/or describe patterns, sequences and relationships. |
|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.2.2-Represent or solve problems using rates, ratios, proportions and/or percents. (Reference: 2.1.8.D, 2.3.8.B) |
|M8.A.3.3-Compute and/or explain operations with integers, fractions and/or decimals. (Reference: 2.2.8.B) |
|M8.D.1.1-Analyze, extend or develop descriptions of patterns or functions. (Reference: 2.8.8.B, 2.8.8.G, 2.11.8.C) |
|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 use a number line to explore integers and absolute value and they add, subtract, multiply, and divide integers. |
|Students find the mean of a data set. Students use the commutative, associate, and distributive properties to evaluate expressions. Students |
|also find and plot points in the coordinate plane. |
| |
|At the conclusion of this chapter, students will successfully complete the following skills: |
|Use integers to represent life situations |
|Add, subtract, multiply, and divide integers |
|Find the mean of a set of integers |
|Use properties to evaluate expressions |
|Use the distribute to simplify expressions |
|Identify and plot points on a coordinate plane |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|2.1 Integers |
|2.2 Adding Integers |
|2.3 Subtracting Integers |
|2.4 Multiplying Integers |
|2.5 Dividing Integers |
|2.6 Number Properties |
|2.7 The Distributive Property |
|2.8 The Coordinate Plane |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Integers, negative integers, positive integers, zero, absolute value, opposites, opposite numbers, number line, variable, variable expression,|
|perimeter, area, identity property of addition, inverse property of addition, sum, signs +/-, rules for addition of integers, opposite, |
|difference, rules for subtraction of integers, identity property of multiplication, product, rules for multiplying integers, multiplication |
|property of zero, multiplicative identity, commutative property, associative property, distributive property, terms, like terms, coefficient, |
|constant term, coordinate plane, x-axis, y-axis, origin, quadrants, ordered pairs, x-coordinate, y-coordinate |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 1
Unit: Chapter 3 – Solving Equations and Inequalities
|Common Core Standards |
|7.RP.2.c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items |
|purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. |
|7.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 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.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions. |
|M7.D.2.2-Create and/or interpret expressions, equations or inequalities that model problem situations. |
|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) |
|M8.D.2.2-Create and/or interpret expressions, equations or inequalities that model problem situations. (Reference: 2.8.8.C) |
|2.1.7.E-Simplify algebraic expressions involving like terms and use algebraic expressions to model real world situations. |
|2.1.7.G-Solve one and two-step equations and inequalities to solve real world problems. |
|2.8.7.C-Create and interpret expressions that model problem situations and create and solve equations and equalities that model problem |
|situations. |
|2.8.7.D-Represent algebraic expressions using concrete models (tiles, blocks). |
|2.8.7.E-Solve one and two-step equations and inequalities. |
|2.5.7.A-Invent, select, use, and justify the appropriate methods, materials and strategies used to solve problems. |
|2.5.7.B-Verify and interpret results using precise mathematical language, notation, and representations, including numerical tables and |
|equations, simple algebraic equations and formulas, charts, graphs and diagrams. |
|2.5.7.C-Justify strategies and defend approaches used and conclusions reached. |
|2.5.7.D-Determine pertinent information in problem situations and whether any further information is needed for solution. |
|Student Objectives: |
|In this chapter, students will solve one and two step equations and inequalities. Students will write and solve each type of equation and |
|inequality to solve real life problems. Students solve equations and find dimensions using formulas for perimeter and area. |
| |
|At the conclusion of this chapter, students will successfully complete the following skills: |
|Solve one step equations using inverse operations of addition, subtraction, multiplication, and division |
|Solve two step equations using inverse operations of addition, subtraction, multiplication, and division |
|Translate verbal expressions/equations into variable expressions/equations |
|Use formulas to solve problems for perimeter and area |
|Solve one step inequalities using inverse operations of addition, subtraction, multiplication, and division |
|Solve two step inequalities using inverse operations of addition, subtraction, multiplication, and division |
|Graph solutions to inequalities |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|3.1 Solving Equations Using Addition or Subtraction |
|3.2 Solving Equations Using Multiplication or Division |
|3.3 Solving Two-Step Equations |
|3.4 Writing Equations |
|3.5 Geometric Formulas |
|3.6 One-Step Inequalities |
|3.7 More Inequalities |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Variable, equation, solution, opposite, like terms, coefficient, equivalent equations, inverse operations, subtraction property of equality, |
|addition property of equality, multiplication property of equality, division property of equality, two-step equation, verbal model, algebraic |
|model, base, height, perimeter, area, area formula for a triangle, area formula for a rectangle, perimeter formula for a rectangle, |
|inequality, solution of an inequality, equivalent inequalities, symbols of inequalities, addition property of inequality, subtraction property|
|of inequality, graph of an inequality, multiplication property of inequality, division property of inequality |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 2
Unit: Chapter 4 – Factors, Fractions, and Exponents
|Common Core Standards |
|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.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. 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: |
|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 |
|Compare and order fractions and mixed numbers |
|Multiply and divide expressions with exponents |
|Read and write numbers using scientific notation |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|4.1 Factors and Prime Factorization |
|4.2 Greatest Common Factor |
|4.3 Simplifying Fractions |
|4.4 Least Common Multiple |
|4.5 Comparing Fractions and Mixed numbers |
|4.6 Rules of Exponents |
|4.8 Scientific Notation |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Prime 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), exponent, |
|power, base, product of powers property, quotient of powers property, rule for negative exponents, rule for zero exponents, scientific |
|notation, standard form, product form |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 2
Unit: Chapter 5 – Rational Number Operations
|Common Core Standards |
|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 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 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.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. 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: |
|Add and subtract fractions with common denominators |
|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 |
|Describe data sets using mean, median, mode, and range |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|5.1 Fractions with Common Denominators |
|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 |
|5.8 Mean, Median, and Mode |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Like terms, simplest form, LCD, improper fraction, mixed number, numerator, denominator, reciprocal, multiplicative inverse, rational number, |
|terminating decimal, repeating decimal, front-end estimation, mean, median, mode, range |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 3
Unit: Chapter 6 – Multi-Step Equations and Inequalities
|Common Core Standards |
|7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the |
|relationship between the circumference and area of a circle. |
|Keystone Connections: (PA Standards) |
|M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions. |
|M7.B.2.1-Develop, use and/or describe measures of length, perimeter, circumference, area or volume. |
|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 |
|2.3.7.A-Apply formulas to determine perimeter and area of polygons and circles, and volume of prisms, pyramids, spheres, cylinders, and cones.|
|2.9.7.G-Approximate the value of (pi) through experimentation. |
|Student Objectives: |
|In this chapter, students solve equations involving the circumference of a circle. |
| |
|At the conclusion of this chapter, students will successfully complete the following skills: |
|Solve equations involving the circumference of a circle |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|6-4 Solving Equations Involving Circumference |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Circle, center, radius, diameter, chord, circumference, pi (π), formulas for circumference |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 3
Unit: Chapter 7 – Ratios, Proportions, and Percents
|Common Core Standards |
|7.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. |
|2.3.7.D-Recognize use and appropriate measures of distance, rate, capacity, are, weight, mass and angles in degrees in real-life situations. |
|2.3.7.F-Use scale measurements to interpret maps and scale drawings. |
|2.3.7.G-Create and use scale drawings and models. |
|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. Students use circle graphs. Students apply |
|percents to solve discount, markup, and other price problems. Students find the probability of simple events. |
| |
|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 problems with percent of increase or decrease |
|Solve percent application problems |
|Solve percent problems using the percent equation |
|Find probabilities of events |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|7.1 Ratios and Rates |
|7.2 Writing and Solving Proportions |
|7.3 Solving Percent Problems |
|7.4 Fractions, Decimals, and Percents |
|7.5 Percentage Change |
|7.6 Percent Applications |
|7.7 Using the Percent Equation |
|7.8 Simple Probability |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Ratio, equivalent, rate, unit rate, proportion, cross products, scale, scale model, percent, base, part, whole, rules for changing between |
|fractions, decimals, percents, percent of change, percent of increase, percent of decrease, percent change formula, markup, discount, retail |
|price, wholesale price, interest, principal, annual interest rate, simple interest formula, percent equation, outcome, event, favorable |
|outcome, probability of an event, theoretical probability, experimental probability, formula for theoretical probability |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 3
Unit: Chapter 8 – Polygons and Transformations
|Common Core Standards |
|7.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 |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|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 Symmetry |
|8.7 Translations and Rotations |
|8.8 Similar Polygons |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Point, 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 |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 4
Unit: Chapter 9 – Real Numbers and Right Triangles
|Common Core Standards |
|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. |
|Keystone Connections: (PA Standards) |
|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) |
|M8.C.1.2-Compute measures of sides of right triangles using Pythagorean Theorem. (Reference: 2.10.8.A) |
|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). |
|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 |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|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 |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Right 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 |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 4
Unit: Chapter 10 – Measurement, Area, and Volume
|Common Core Standards |
|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.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: (PA Standards) |
|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. |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|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 |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Area, 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 |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
MARKING PERIOD: 4
Unit: Chapter 12 – Data Analysis and Probability
|Common Core Standards |
|7.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. |
|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. |
|7.SP.8.b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event |
|described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. |
|7.SP.8.c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to |
|approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to|
|find one with type A blood? |
|Keystone Connections: |
|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. |
|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 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. 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: |
|Make and interpret stem-and-leaf plots |
|Make and interpret box-and-whisker plots |
|Organize data using circle graphs and line graphs |
|Use counting methods to determine the number of choices |
|Use permutations to count possibilities |
|Use combinations to count possibilities |
|Find the odds in favor of events |
|Classify events as independent or dependent and then find their probabilities |
|Materials &Texts |
|Larson, 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, & Assessments |
|ACTIVITIES |
|12.1 Stem-and-Leaf Plots |
|12.2 Box-and-Whisker Plots |
|12.3 Using Data Displays |
|12.4 Counting Methods |
|12.5 Permutations |
|12.6 Combinations |
|12.7 Probability and Odds |
|12.8 Independent and Dependent Events |
| |
|ASSIGNMENTS |
|Lesson Practice Sheets B |
|Associated Chapter exercises |
| |
|ASSESSMENTS |
|Homework 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 |
|Terminology |
|Data, 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, protractor, horizontal and vertical scales, tree diagram, counting |
|principle, probability, permutation, factorial, counting principle, permutation formula, combination, combination formula, complementary |
|events, complementary formula, unfavorable outcomes, odds, probability, find probability of an event, find odds using probability, compound |
|events, independent events, dependent events |
|Media, Technology, Web Resources |
|McDougal Littell Course 3 Easy Planner DVD ROM |
|McDougal Littell Course 3 Power Presentations DVD ROM |
|McDougal Littell resources |
|Teacher developed smart-board documents |
|Scientific Calculator |
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MAJOR UNITS OF STUDY
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