* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 8th Grade Pre-Algebra Curriculum Map
Survey
Document related concepts
History of mathematical notation wikipedia , lookup
Line (geometry) wikipedia , lookup
List of important publications in mathematics wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Analytical mechanics wikipedia , lookup
Recurrence relation wikipedia , lookup
Elementary mathematics wikipedia , lookup
Elementary algebra wikipedia , lookup
Partial differential equation wikipedia , lookup
System of linear equations wikipedia , lookup
Transcript
th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities Unit 1 – Integers, Equations, and Inequalities Chapter 1 – Variables, Expressions, and Integers – 12 days Key Skills and Concepts Add, subtract, multiply, and divide integers. Make a scatter plot. 7.NS.1 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. 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. 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. 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. d. Apply properties of operations as strategies to add and subtract rational numbers. Common Core Math Standards 7.NS.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. 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. b. Understand that integers can be divided provided that the divisor is not zero and every quotient of integers (with nonzero 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. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in zeroes or eventually repeats. 1 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions. 8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. RTI Essential Vocabulary Each day includes 30-40 of individualized RTI Instruction including small group instruction, one-on-one tutoring, and computer program. Teacher will utilize MAP and classroom data to determine tiers and subject of instruction. Numerical expression, variable, variable expression, evaluate, verbal model, power, base, exponent, order of operations, integer, negative integer, positive integer, absolute value, opposite, additive inverse, opposite, difference, mean, coordinate plane, ordered pair, scatter plot Writing Order of Operations Activity Program Review Activities Arts and Humanities Coordinate Plane Graphing Characters PCLS Integers – Football, Golf Resources Needed For Unit Student Notes Homework Checks Integer Game Cards Number Lines th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities Dates 8/10 Content Lesson 1.1 Expressions and Variables Learning Target I am learning to evaluate and write variable expressions. Essential Questions HOTQs Connections to Common Core 1. How is a variable useful in writing a numerical pattern? 2. Compare and Contrast: Numerical Expressions and Variable Expressions 8/11 I am learning to use powers to describe repeated multiplications. 1. If x = 2 , what is the value of x2 ? 2. Does anyone have the same answer but a different way of explaining it/completing it? Assignment Bellringer 5 Homework Check 10 Vocabulary 5 Evaluating a Variable Expression 5 Writing Variable Expressions 5 Note Card Activity 10 Review 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Using Exponents 5 Evaluating Powers with Variables 5 Using Powers in Formulas 10 Review 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Program Review Activity 30 Exit Slip 5 Bellringer 5 Homework Check 10 Vocabulary 5 Using Order of Operations 5 6.EE.2 2 Lesson 1.2 Powers and Exponents Lesson Plan 6.EE.1 p. 7 #12-40 EVENS p. 12 #14-36 EVENS 1. Program Review Activity 8/12 Lesson 1.3 Order of Operations I am learning to use the order of operations to evaluate expressions. 2. What is the purpose of the order of operations? What would happen if we did not use them? 6.EE.3 1. Program Review Activity 8/13 Lesson 1.3 Order of Operations I am learning to use the order of operations to evaluate expressions. 2. What is the purpose of the order of operations? What would happen if we did not use them? 6.EE.3 Program Review Activity p. 19 #10-36 EVENS th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities 1. Why is this definition needed? What can we do with this concept? 8/14 Lesson 1.4 Comparing and Ordering Integers I am learning to compare and order integers. 2. How can you use visual information (diagrams or pictures or graphs) of the concept to understand its definition? 6.NS.7 3. Does anyone have the same answer, but a different way of explaining it? Lesson 1.5 Adding Integers I am learning to add integers. 1. How can you use visual information (diagrams or pictures or graphs) of the concept to understand its definition? 2. Does anyone have the same answer, but a different way of explaining it? Lesson 1.6 Subtracting Integers I am learning to subtract integers. 1. How can you use visual information (diagrams or pictures or graphs) of the concept to understand its definition? 2. Does anyone have the same answer, but a different way of explaining it? 7.NS.1 7.NS.1a 7.NS.1b 7.NS.3 7.NS.1 7.NS.1a 7.NS.1c Using Grouping Symbols 5 Evaluating Variable Expressions 10 Order of Operations Puzzle 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Graphing and Ordering Integers 5 Finding Absolute Value 5 Finding Opposites 5 Evaluating Algebraic Expressions 10 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Adding Integers Using a Number Line 5 Adding Integers 5 Evaluating Variable Expressions 5 Integer Game/Review 10 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Subtracting Integers 5 Evaluating Variable Expressions 5 Evaluating Change 5 Integer Game/Review 10 p. 24 #18-50 EVENS p. 32 #14-40 EVENS p. 36 #12-38 EVENS th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities Lesson 1.7 Multiplying and Dividing Integers I am learning to multiply and divide integers. 1. How can you use visual information (diagrams or pictures or graphs) of the concept to understand its definition? 2. Does anyone have the same answer, but a different way of explaining it? Lesson 1.8 The Coordinate Plane Lesson 1.8 The Coordinate Plane Lesson 1.8 Scatter Plots I am learning to identify and plot points in a coordinate plane. I am learning to identify and plot points in a coordinate plane. I am learning to create and make interpretations from scatter plots. 7.NS.2 7.NS.2a 7.NS.2b 7.NS.3 1. Do you see a pattern? Explain. 2. Why is this definition needed? What can we do with this concept? 8.SP.1 1. Do you see a pattern? Explain. 2. Why is this definition needed? What can we do with this concept? 5 Bellringer 5 Homework Check 10 Vocabulary 5 Multiplying Integers 5 Dividing Integers 5 Finding a Mean 5 Integer Game/Review 10 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Naming Points in a Coordinate Plane Plotting Points in a Coordinate Plane 5 5 Program Review Activity 15 Review 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Review coordinate graphing 5 Finish Program Review Activity 25 Students can create their own coordinate graphing activity 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Making a Scatter Plot 5 Extended Response 5 Program Review Activity (Coordinate Graphing Activity) 15 8.SP.1 1. Do you see a pattern? Explain. 2. Why is this definition needed? What can we do with this concept? Exit Slip/Homework 8.SP.1 p. 45 #12-34 EVENS Program Review Activity: Coordinate Graphing Cartoon Characters Finish Coordinate Graphing Activity p. 49 #27-28 Worksheet th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities 3. Does anyone have the same answer, but a different way of explaining it? Review and Chapter 1 Test I am demonstrating my knowledge of variables, expressions and integers on my Chapter 1 Test. Chapter 1 Test See Above Review 5 Exit Slip/Homework 5 Chapter 1 Test and Extended Response 50 Chapter 2 Vocabulary Chapter 2 – Solving Equations – 10 days Key Skills and Concepts Understand properties and simplify expressions. Construct and solve linear equations in one variable to solve problems. 7.NS.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. 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. b. Understand that integers can be divided provided that the divisor is not zero and every quotient of integers (with nonzero 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. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in zeroes or eventually repeats. 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Common Core Math Standards 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 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? 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. 8.EE.7 Solve linear equations in one variable. a. 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). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Essential Additive identity, multiplicative identity, equivalent numerical expressions, equivalent variable expressions, term, coefficient, constant term, like Vocabulary terms, equation, solution of an equation, solving an equation, inverse operations, equivalent equations, inverse operations, absolute value Resources Writing Arts and Humanities PCLS Student Notes Program th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities Word problems involving sports Review Activities Needed For Unit Homework Checks Create own word problem Dates Content Lesson 2.1 Properties and Operations Lesson 2.2 The Distributive Property Lesson 2.3 Simplifying Variable Expressions Learning Target I am learning to use properties of addition and multiplication. I am learning to use the distributive property. I am learning to simplify variable expressions. Essential Questions HOTQs 1. Why is this definition needed? What can we do with this concept? Connections to Common Core Review of 5.NBT.7 2. Why do we not learn properties dealing with subtraction and division? 1. Explain how to use the distributive property to write an equivalent variable expression for 4(10 + x). 1. How do you simplify an expression that has several terms? Review 6.NS.4 Lesson Plan Bellringer 5 Homework Check 10 Vocabulary 5 Properties Flip Chart 5 Using Properties to Simplify Expressions 5 Conversion Factors 15 Review 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 The Distributive Property 5 Using the Distributive Property 5 Writing Equivalent Variable Expressions Finding Areas of Geometric Figures 7.EE.1 Assignment p. 66 #16-36 EVENS p. 76 #12-40 EVENS 15 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Identifying Parts of an Expression 10 Simplifying an Expression 5 p. 81 #10-36 EVENS th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities Simplifying Expressions with Parentheses Writing and Simplifying an Expression Lesson 2.4 Variables and Equations Lesson 2.5 Solving Equations Using Addition or Subtraction Lesson 2.6 Solving Equations Using Multiplication or Division Lesson 2.7 I am learning to solve equations with variables. I am learning to solve equations using addition or subtraction. I am learning to solve equations using multiplication or division. I am learning to solve 1. How is the addition property of equality used to solve an equation? 7.EE.4 2. Solve. Explain the steps and why you could use them to solve. 1. How is the addition property of equality used to solve an equation? 2. Solve. Explain the steps and why you could use them to solve. 1. Explain how the property is used to find the solution. 2. Solve. Justify your steps. 1. How does absolute value help 7.EE.4 8.EE.7 8.EE.7b 7.EE.4 8.EE.7 8.EE.7b 8.SP.1 7.EE.4 10 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Writing Verbal Sentences as Equations 5 Checking Possible Solutions 5 Solving Equations Using Mental Math 5 Writing and Solving an Equation 10 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Solving an Equation Using Subtraction Solving an Equation Using Addition 10 5 Writing and Solving an Equation 10 Review 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Solving an Equation Using Division 10 Solving an Equation Using Multiplication 5 Writing and Solving an Equation 10 Review 5 Exit Slip/Homework 5 Bellringer 5 p. 87 #8-32 EVENS p. 93 #12-28 EVENS p. 99 #8-26 EVENS p. 105 th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities Decimal Operations and Equations with Decimals equations involving decimals. you determine the sign of the sum when adding numbers with different signs? 8.EE.7 8.EE.7b 2. Solve. Justify your steps. Lesson 2.7 Decimal Operations and Equations with Decimals Review and Chapter 2 Test I am learning to solve equations involving decimals. 1. How does absolute value help you determine the sign of the sum when adding numbers with different signs? 7.EE.4 8.EE.7 8.EE.7b 2. Solve. Justify your steps. I am demonstrating my knowledge of solving equations on my Chapter 2 Test. Chapter 2 Test See Above Homework Check 10 Vocabulary 5 Adding / Subtracting Decimals 5 Multiplying Decimals 5 Dividing Decimals 15 Review 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Solving Addition and Subtraction Equations Solving Multiplication and Division Equations 5 5 Writing and Solving an Equation 10 Review 5 Exit Slip/Homework 5 Chapter 2 Test and Extended Response 50 #12-23 ALL p. 105 #24-38 EVENS Chapter 3 Vocabulary th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities Chapter 3 – Multi-Step Equations and Inequalities – 10 days Key Skills and Concepts Construct and solve multi-step linear equations and inequalities in one variable to solve problems. 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. Common Core Math Standards 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 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? 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. 8.EE.7 Solve linear equations in one variable. a. 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). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Essential Inequality, solution of an inequality, equivalent inequalities Vocabulary Writing Create own word problem Program Review Activities Arts and Humanities PCLS Word problems involving sports Resources Needed For Unit Student Notes Homework Checks th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities Dates Content Learning Target Essential Questions HOTQs 1. Solve. Justify your steps. 9/22 9/23 9/24 9/25 Lesson 3.1 Solving Two-Step Equations Lesson 3.2 Solving Equations Having Like Terms and Parentheses I am learning to solve two-step equations. 2. Does someone have the same answer but a different way of explaining it/solving it? Connections to Common Core 7.EE.3 7.EE.4 8.EE.7 8.SP.1 1. Solve. Justify your steps. I am learning to solve equations using the distributive property. 2. Does someone have the same answer but a different way of explaining it/solving it? 7.EE.4 8.EE.7 9/30 Common Assessment 10/1 Lesson 3.3 Solve Equations with Variables on Both Sides I am learning to solve equations with variables on both sides. 1. Solve. Justify your steps. 2. Does someone have the same answer but a different way of explaining it/solving it? 7.EE.3 7.EE.4 8.EE.7 10/2 10/3 Mid-Chapter Quiz I am learning to solve multi-step equations. Mid-Chapter Quiz 7.EE.3 7.EE.4 8.EE.7 Lesson Plan Assignment Bellringer 5 Homework Check 10 Vocabulary 5 Using Subtraction and Division to Solve Using Addition and Multiplication to Solve Solving an Equation with Negative Coefficients Writing and Solving a Two-Step Equation 5 5 Puzzle 5 10 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Writing and Solving an Equation 5 Solving Equations Using the Distributive Property Combing Like Terms After Distributing p. 123 #8-32 EVENS 5 p. 127 #10-36 EVENS Puzzle 10 Review 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Solving an Equation with the Variable on Both Sides 5 Writing and Solving an Equation 5 Special Cases 10 Solving an Equation to Find a Perimeter 5 Exit Slip/Homework 5 Bellringer Homework Check Review Quiz 5 10 5 20 p. 134 #12-30 EVENS No Homework FALL BREAK! th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities 1. Solve. Justify your steps. 10/14 Lesson 3.4 Solving Inequalities Using Addition or Subtraction I am learning to solve inequalities using addition or subtraction. 2. Does someone have the same answer but a different way of explaining it/solving it? 3. Compare and contrast: Inequality Symbols 10/15 I am learning to solve inequalities using multiplication or division. 2. Does someone have the same answer but a different way of explaining it/solving it? 5 Homework Check 10 Vocabulary 5 Writing and Graphing an Inequality 5 Solving One-Step Inequalities 5 Writing and Solving an Inequality 10 Review 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Writing and Graphing an Inequality 5 Solving One-Step Inequalities 5 Writing and Solving an Inequality 10 Review 5 Exit Slip/Homework 5 Bellringer 5 Homework Check 10 Vocabulary 5 Writing and Solving a Multi-Step Inequality 5 7.EE.4 1. Solve. Justify your steps. Lesson 3.5 Solving Inequalities Using Multiplication or Division Bellringer 7.EE.4 3. Justify that your answer was right. p. 143 #12-38 EVENS p. 148 #12-36 EVENS 10/16 Teen Talk 1. Solve. Justify your steps. 10/17 Lesson 3.6 Solving MultiStep Inequalities I am learning to solve multi-step inequalities. 2. Does someone have the same answer but a different way of explaining it/solving it? 7.EE.4 8.SP.1 3. Compare and contrast: Inequality Symbols 10/20 10/21 Review and Chapter 3 Test I am demonstrating my knowledge of solving multi-step equations and inequalities on my Chapter 3 Test See Above Solving a Multi-Step Inequality 5 Combining Like Terms in a MultiStep Inequality 10 Review 5 Exit Slip/Homework 5 Chapter 3 Test and Extended Response 50 p. 153 #10-30 EVENS Unit 1 Review th Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities Chapter 3 Test.