DSCYF EDUCATION UNIT K-U-D (Know, Understand, Do) Chart

Grade/Course Algebra 2

Unit Title: Unit 1: Expressions, Equations, and Inequalities

Content Standards: A.SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Know Understand Do (Note: concepts, facts, formulas, key (Big idea, large (Skills, competencies) vocabulary) concept, declarative statement of an Write expressions to represent Algebraic expressions and equations enduring patterns in pictures, tables, and reflect patterns. understanding) graphs

Properties of real numbers Real numbers are Identify properties of real related in systems and numbers Vocabulary: subsets. algebraic expression, numerical expression, constant, variable, Apply the Properties of Equality mathematical quantity, opposite, and Properties of Inequality to additive inverse, multiplicative solve equations inverse, reciprocal, evaluate, term, constant term, like terms, coefficient, inverse operations, solution of an equation, literal equation, compound inequality , absolute value Unit Essential Question: How do equations help you solve real-world problems?

Key Learning: Expressions, Equations, and Inequalities

DSCYF EDUCATION UNIT Lesson Essential Question 1 Lesson 1 Vocabulary

1.1 Patterns and Expressions algebraic expression, numerical expression, constant, variable, How can patterns in pictures, tables, and graphs mathematical quantity be used to interpret algebraic expressions and equations?

Lesson Essential Question 2 Lesson 2 Vocabulary

1.2 Properties of Real Numbers opposite, additive inverse, multiplicative inverse, reciprocal How can properties of real numbers be used to simplify and solve expressions and equations involving real numbers?

Lesson Essential Question 3 Lesson 3 Vocabulary

1.3 Algebraic Expressions evaluate, term, constant term, like terms, coefficient How are the properties of equality and inequality applied to solve equations and inequalities?

Lesson Essential Question 4 Lesson 4 Vocabulary

1.4 Solving Equations inverse operations, solution of an equation, literal equation What is your plan for solving multi-step problems?

Lesson Essential Question 5 Lesson 5 Vocabulary

1.5 Solving Inequalities compound inequality

How do you solve an inequality?

Lesson Essential Question 6 Lesson 6 Vocabulary

DSCYF EDUCATION UNIT 1.6 Absolute Value Equations and absolute value Inequalities extraneous solution How is it possible to have two answers for the same problem?

Major Unit Assignment

Name Class Date Prentice Hall Algebra 2 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 74 Chapter 1 Project: Buy the Hour Beginning the Chapter Project Have you had your first job yet? If so, you were probably paid an hourly wage. The amount of money you earned for each hour you worked may have been the minimum Wage. This amount, set by the U.S. Department of Labor, is the minimum amount for One hour of work an employer is allowed to pay to employees who meet certain specific criteria. Each state may set its own minimum wage, but where federal and state laws set different rates, the employer is required to pay the greater of the two amounts to all employees to whom the conditions of the federal law apply.*

In this project, you will write expressions that model amounts of money earned. You will write equations and inequalities to determine the number of hours that must be worked to satisfy certain conditions. You will also research the current federal and state minimum wage laws.

Activities Activity 1: Researching Research the current federal minimum wage. Then find out whether the state in which you live has set its own minimum wage. If so, what is that wage? ______

Select a state other than the state in which you live. Research the minimum wage for that state. You might find it helpful to contact the U.S. Department of Labor and state labor commissioners, or to use the Internet to find this data. What state did you select? ______What is that state’s minimum wage? ______

Activity 2: Modeling Suppose you earn the minimum wage determined in Activity 1 for the state other than your own. Suppose that next week you plan to work h hours. Write an expression that models the amount of money (M) you will earn. ______

Suppose that your friend earns the same hourly wage that you earn, but works in a job for which he receives tips. Write an expression that models your friend’s total earnings for a week during which he works n hours and receives

DSCYF EDUCATION UNIT $15 in tips. ______Then, evaluate the expression for n = 10 and explain what this number means. ______explanation: ______

Write an expression that models the sum of your earnings for 3 weeks and your friend’s earnings for 2 weeks if you each work r hours per week and your friend receives $15 in tips per week. Simplify the expression. ______

Write an expression that models the difference between your earnings and your friend’s earnings for a week during which you work h hours, your friend works n hours, and your friend earns t dollars in tips. (Hint: Be sure to consider the fact that you do not know who earns more money!) ______*Source: http://www.dol.gov/dol/topic/wages/minimumwage.htm

Activity 3: Solving Round numbers of hours to the nearest tenth if necessary. Suppose that last week your employer gave you a $.50/h raise and a $20 bonus as a reward for good work. You earned a total of $80 for the week. Let x represent the number of hours you worked that week. Write an equation to model this situation. Then solve your equation and explain the meaning of your solution. Equation:______Solution: ______Explanation: ______

Suppose your friend (still earning minimum wage) receives $20 in tips, and that you (earning $.50/h more than your friend) have earned the same amount of money at the end of a week during which you worked the same number of hours as your friend. Write an equation to model this situation. Then solve your equation and explain the meaning of your solution. Equation:______Solution: ______Explanation: ______

Suppose that your friend wants to earn at least $95 next week and he expects to earn $15 in tips. Write an inequality that models this situation. Then solve and graph your inequality. Explain the meaning of your solution. Inequality: ______Solution: ______Explanation: ______Graph:

Finishing the Project The answers to the activities should help you to complete your project. You should prepare a presentation for the class describing your results. Your presentation should include the data you researched; the expressions, equations, and inequality you used to model the given situations; and the graph of your inequality.

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Reflect and Revise Ask a classmate to review your project. After you have reviewed each other’s presentations, decide if your work is clear, complete, and convincing. If needed, make changes to improve your presentation.

Extending the Project Research the minimum wages set by other states. If they differ from the minimum wage of your state, determine possible factors that might contribute to the differences. Find out what conditions might exist that would allow an employer to pay an employee less than the federal minimum wage.

Name Class Date Prentice Hall Algebra 2 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 76 Chapter 1 Project Manager: Buy the Hour Getting Started Read the project. As you work on the project, you will need a calculator and materials on which you can record your results and make calculations. Keep all of your work for the project in a folder. Checklist Suggestions ☐ Activity 1: researching minimum wages ☐ Select a state in which you are interested.

☐ Activity 2: writing algebraic expressions ☐ Substitute reasonable values for the variables to determine if the expressions make sense.

☐ Activity 3: writing and solving equations ☐ Check that your answers are reasonable. and inequalities

☐ algebraic models ☐ Have you defined the variables in your expressions, equations, and inequality? How does the graph of an equation differ from the graph of an inequality? What does this mean in terms of your solution?

Student Scoring Rubric 4 The expressions, the equations, and the inequality are correct. The graph and all calculations are accurate. Explanations are thorough and well thought out. The presentation is clear and complete.

3 The expressions, the equations, and the inequality have minor errors. The graph and calculations are mostly correct. The explanations and presentation lack detail or contain small errors.

2 The expressions, the equations, and the inequality have major errors.

DSCYF EDUCATION UNIT The graph and calculations contain minor errors. The explanation and presentation contain minor inaccuracies.

1 The expressions, the equations, and the inequality are not correct. The graph is not accurate. Calculations contain major errors or are incomplete. The explanations and presentation are inaccurate or incomplete.

0 Major elements of the project are incomplete or missing.

Teacher’s Evaluation of the Project

Chapter Project Rubric Student Name: ______

CATEGORY 3 2 1 0 Developing persevered to completed most needed key hints needed extensive Autonomy- The complete the of the problem to solve the guidance to work student project without without help problem the problem help The Solution a complete and an appropriate an appropriate an inappropriate Process – The appropriate solution process process that is process or no students work solution process that is almost partially evidence of a showed complete complete process The accurate inaccurate but inaccurate but inappropriate Conclusion/Answe conclusion, logical logical conclusion, not r – The student’s supported by conclusion, conclusion that supported by answer is an valid evidence supported by overlooks or gets facts and logic, or and reasons, evidence and wrong significant there is no appropriate to reasoning but (about the conclusion this problem and incorrect due to problem, the rule, context minor factual computation, error (in details etc.). of problem, in computation, recall of formula, etc.) or minor mistake in reasoning

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Student Assessments (How students will indicate learning and understanding of the concepts in the unit. Note: Can have multiple assessments, one on each page.)

Unit Topic:

Title Performance Task Description Performance Task 1: Your Basil Metabolic Rate (BMR) is the measure of how many calories you burn if you rest all day. Physicians and other health professionals use this rate as an important tool for determining a person’s daily caloric needs. The Harris-Benedict Formula is commonly used to calculate BMR for an individual.

The formulas are slightly different for males and females. A female’s BMR can be expressed as 655 more than the sum of 4.35 times her weight (lb.) and 4.7 times her height (in.) and then less 4.7 times her age (years). The formula for a male is 66 more than 6.23 times his weight (lb.) plus the product of 12.7 and his height (in.) minus 6.8 times is age (years).

a. Use w = weight, h = height, and a= age to write the formula for the BMR of a female and the formula for the BMR of a male. Female BMR = ______Male BMR = ______

b. Calculate your BMR. ______What does that tell you? ______c. Look at each term of the formula. Make a conjecture about what happens to you BMR as you get older, and why. ______

d. Which term of the expression affects the BMR the most? Explain. ______

e. What is the weight of a 16 year-old male with a BMR of 2600 and a height of 5 feet 10 inches? Show or explain your work. ______

Performance Task 2:

DSCYF EDUCATION UNIT Find all possible values of a and b in the figures, given the following conditions: * figure I is a rectangle with sides length a and width b, * figure 2 is an isosceles triangle with 2 congruent sides 2a and the base b, * the perimeters of the two figures are equal * the rectangle has an area between 80 and 100 square units, * the values of a and b are integers. Drawn the figures.

Show your work 

Time (In Days) 2 Differentiation You may choose to assign one problem to some students rather than both. You may want to provide pictures of the figures in Task 2. You may want to allow students to work with a partner or a group. Some students may need assistance setting up the formulas in Task 1.

Revise/Review

Resources & Materials Paper, calculator, ruler, folder for keeping materials together, internet for researching Task 1

Performance Task Rubric Student Name: ______

CATEGORY 3 2 1 0 Developing persevered to completed most of needed key hints needed extensive Autonomy- The complete the the problem to solve the guidance to work student project without without help problem the problem help The Solution a complete and an appropriate an appropriate an inappropriate Process – The appropriate solution process process that is process or no students work solution process that is almost partially complete evidence of a showed complete process The accurate inaccurate but inaccurate but inappropriate Conclusion/Answe conclusion, logical conclusion, logical conclusion conclusion, not r – The student’s supported by valid supported by that overlooks or supported by facts answer is an evidence and evidence and gets wrong and logic, or there reasons, reasoning but significant (about is no conclusion appropriate to this incorrect due to the problem, the

DSCYF EDUCATION UNIT problem and minor factual error rule, computation, context (in details of etc.). problem, in computation, recall of formula, etc.) or minor mistake in reasoning Research: Performance Task (Essay) Students’ Names: ______CATEGORY 5-4 3 2 1 Quality of Information clearly Information relates Information has a Information has Information relates to the main to the main topic tenuous link to the little or nothing to (Double weighting) topic and answers and answers the main topic. do with the main the question. It question. It Some details topic. includes salient includes some and/or examples examples, lucid salient examples, are given, but analysis and clear analysis and links might be irrelevant links to the to the question. to the question. question. Organization Information is very Information is Information is The information (Half weighting) organized with organized with organized, but appears to be well-constructed well-constructed paragraphs are not disorganized. paragraphs and paragraphs and well-constructed, very clear main clear main point. and the main point points. is unclear. Introduction The introduction The introduction The introduction The introduction consists of a very consists of a good consists of a rather does not have an good argument, argument, and weak argument, argument, and does and outlines briefly outlines briefly the and outlines briefly not outline the the factors to be factors to be the factors to be factors to be examined, and is examined, and is examined, but is examined. very consistent consistent with the not very consistent with the essay. essay. with the essay. Conclusion The conclusion The conclusion The conclusion The conclusion deals fully with the deals with the deals partially with does not deal with requirements of the requirements of the the requirements of the requirements of question, and is question, and is the question, but is the question, and is very consistent consistent with the not very consistent not consistent with with the essay. essay. with the essay. the essay. Mechanics No grammatical, Almost no A few Many grammatical, (Half weighting) spelling or grammatical, grammatical, spelling, or punctuation errors. spelling or spelling, or punctuation errors. punctuation errors punctuation errors.

DSCYF EDUCATION UNIT Sources All sources All sources All sources Some sources are (information and (information and (information and not accurately graphics) are graphics) are graphics) are documented. accurately accurately accurately documented in the documented, but a documented, but desired format. few are not in the many are not in the desired format. desired format.

Total marks: ______/ 30 Learning Goals for this Lesson: 1.1 Patterns and Expressions Standards: Use patterns in pictures, tables, and graphs to interpret algebraic Reviews A.SSE.3 Choose and produce an expressions and equations equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Students Will Know Students Will Be Able To: How to use patterns in pictures, tables, and graphs to Use patterns in pictures, tables, and graphs to interpret interpret algebraic expressions and equations algebraic expressions and equations

Lesson Essential Question: How can patterns in pictures, tables, and graphs be used to interpret algebraic expressions and equations?

Activating Strategy: Getting Ready! P.4 You are playing a video game. You reach a locked gate. The lock is a square with nine sections. You can make a key by placing a red or yellow block in each section. Near the gate is a carving of a pattern of squares. (All Getting Ready problems are available on the textbook website)

Key vocabulary to preview and vocabulary strategy: STRATEGY algebraic expression, numerical expression, constant, variable, mathematical quantity

Lesson Instruction Learning Activity 1: Work through Problem 1on p.4 with the students. You Graphic Organizer may prompt them to see how the number of sides is changing from one figure  Table for Learning Activity 2 to the next. The next figure would have to have 7 sides (aka heptagon).  Table for Learning Activity 3

Assessment Prompt for Learning Activity 1: Got It? P.4 Look at the figures from left to right. What is the pattern? Draw the next figure in the pattern. Turn to your shoulder partner and compare. Explain how you figured it out.

Learning Activity 2: Read through the paragraph at the top of p.5. Write the key concepts on the board with the definitions. Ask students for examples of each. Have them write the examples in the notebooks.

Explain to students that tables are an effective way to organize data and

DSCYF EDUCATION UNIT discover patterns. They work much like an “input/output” machine. Adding a Assignment: process column to the middle allows you to “see” what is happening inside p.8 #9-23 odd and 25-35 the machine.

Work through the toothpick problem, Problem 2 on p. 5. Create a table to correspond with the information provided. Ask the students to identify what is happening inside the machine. Use this information to determine how many toothpicks will be in the 20th figure. Then, write an expression to describe how many toothpicks will be in the nth figure.

Assessment Prompt for Learning Activity 2: Got It? P.5. How many tiles will be in the 25th figure in this pattern (it begins with four and adds two each time). Have students make a table to represent this data, with a process column. Tell students, “Share with your partner to review your tables. Raise your hands if they are the same.” Ask if anyone can give the mathematical expression to describe the process.

Learning Activity 3: Work through Problem 3 with the students. Aquarium You want to set up an aquarium and need to determine what size tank to buy. The graph shows tank sizes using a rule that relates capacity of the tank to the combined lengths of the fish it can hold.

If you want five 2 inch platys, four 1 inch guppies, and a 3 inch loach. Which is the smallest tank you can buy: 15-gallon, 20-gallon, or 25-gallon? Use a table to find the answer, with a process column. Walk the students through the process in the middle of page 6 demonstrating how to find the solution.

Assessment Prompt for Learning Activity 3: Got It? p.6 3. The graph shows the total cost of platys at the aquarium shop. Use a table to answer the questions. A. How much do 6 platys cost? B. How much do 10 platys cost? C. Why is the graph in problem 3 a line while this graph is a set of points? Compare your answer with your partner’s. ______

Have the students work in pairs to complete the Lesson Check on page 7. After 10 minutes, call on students at random to describe a rule for each pattern.

Give each pair of students a few Post-It notes to records their responses to items 8 through 15. Have the students post their responses on the board for you to check quickly.

DSCYF EDUCATION UNIT Summarizing Strategy: Exit Slip: Have the students record answers to items 36 and 37 on p.9.

Learning Goals for this Lesson: 1.2 Properties of real Numbers Standards: Reviews N.RN.3 Explain why sums and products Order real numbers. of rational numbers are rational, that the sum of Identify and use properties of real numbers a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational. Students Will Know: Students Will Be Able To: Order real numbers. The set of real numbers has special subsets. Identify and use properties of real numbers

Properties of numbers are relationships that are true for all real numbers, except for zero, in one case.

Lesson Essential Question: How can properties of real numbers be used to simplify and solve expressions and equations involving real numbers?

Activating Strategy: Getting Ready p.11 You use emoticons in text messages to help you communicate. Six emoticons are shown on p.11. How can a set be described that includes five of them, but not the 6 th?

Key vocabulary to preview and vocabulary strategy: Have students work with a partner to create a definition and example for each of the vocabulary terms listed below. Monitor students as they work. Then ask some of them to share their work with the class. opposite, additive inverse, multiplicative inverse, reciprocal

Lesson Instruction: Remind students that the set of numbers has several special subsets of numbers related in particular ways.

Learning Activity 1: Show the students the diagram on the top of p.12 to describe the subsets of real numbers. Distribute the graphic organizer on Real Numbers to the students. Allow them to write the definition of each subset .  Ask the students to work with a partner to write another 2 examples for each subset. Allow each pair of students to place one of their examples on the large picture on the board. Make sure to discuss that each example belongs not only to its subset but all those below it as well.

Work with Problem 1 with the students to answer the multiple choice question: Your school is sponsoring a charity race. Which set of numbers does not contain the number of people p who participate in the race?

DSCYF EDUCATION UNIT a. natural numbers c. rational numbers

b. integers d. irrational numbers

Assessment Prompt for Learning Activity 1: Got It p.12 In problem 1, if each participant made a donation of $15.50 to a local charity, which subset of real numbers best describes the amount of money raised?

Learning Activity 2: Draw a number line on the board with integers from negative 3 to positive 3. Have the students place the numbers -5/2, √2, and 2.66666…

Assessment Prompt for Learning Activity 2: Have the students add the numbers √3, -1.4444, and 1/3 to the number line. Compare your answers with your shoulder partner.

Assignment: p.15 #10-40, 42-48 even, 58-66 even Learning Activity 3: Ordering Real Numbers, when comparing two numbers greater than, or less than signs are more useful than a number line. To compare and 3.8 it is helpful to use the perfect square closest to 17…16 Walk the students through the fact that √16 = 4 and since 17 is larger than 16. Therefore, must be larger than 4 and thus larger than 3.8. So, 3.8 <

Assessment Prompt for Learning Activity 3: Have the students complete Got

DSCYF EDUCATION UNIT It on p.13 to compare and 6.25 using < or >. Then, if a< b and b < c, compare a and c using < or >. Thumbs up if a is bigger. Thumbs up if c is bigger. (If all agree, have students explain to their neighbor how they knew.) (If there is a mixture of responses, ask for student explanations.)

------Learning Activity 4: Review the vocabulary at the top of p. 14: opposite or additive inverse of a number is –a. The sum of a number and its opposite is zero. The reciprocal or multiplicative inverse of a non-zero number is 1/a; the product of them is 1.

Have the students complete the foldable as shown to write the properties of real numbers the definitions and examples.

Ask the students to identify which property is illustrated by each of the following examples:

a. (-2/3) (-3/2) = 1

b. ( 3 x 4 ) x 5 = ( 4 x 3 ) x 5

Assessment Prompt for Learning Activity 4: Got It? p.14 Have the students use the foldable to determine which property is illustrated by the equation 3 ( g + h ) + 2g = ( 3g + 3h ) + 2g. What property of real numbers allows us to justify that a + [ 3 + (-a)] = 3 Tell your neighbor your answer.

Summarizing Strategy: Exit Slip: There are grouping symbols in the equation ( 5 + w ) + 8 = ( w + 5 ) + 8 but it does not illustrate the Associative Property of Addition. How is it different? What property is illustrated?

Learning Goals for this Lesson: 1.3 Algebraic Expressions Standards: Solve equations and simplify expressions using properties of Reviews A.SSE.1.a Interpret parts of an equality. expression such as terms, factors, and coefficients. Students Will Know Students Will Be Able To How the properties of equalities are applied to solve Solve equations and simplify expressions using properties equations. of equality.

DSCYF EDUCATION UNIT Lesson Essential Question: How are the properties of equality and inequality applied to solve equations and inequalities?

Activating Strategy: Getting Readyp.18 Work the following problem with the class. During summer vacation, you work two jobs. You walk three dogs several times a week, and you work part-time as a receptionist at a hair studio. You earn $8 per hour as a receptionist and $20 per week per dog. Your weekly schedule (shown in the chart below) is the same each week. How much will you earn in 10 weeks? Explain.

Monday Tuesday Wednesday Thursday Friday Saturday Walk dogs 8-9am Walk dogs 8-9am Walk dogs 8-9am

Studio 1-5pm Studio 1-5pm Studio 1-5pm Studio 1-5pm Studio Noon- 4pm

Key vocabulary to preview and vocabulary strategy: STRATEGY evaluate, term, constant term, like terms, coefficient

Lesson Instruction

Learning Activity 1: Lead the students through Problem 1, p.18, Which Graphic Organizer algebraic expression models the word phrase “seven fewer than a number t?” Ask the students what operation is usually represented by the word “fewer.” Subtraction The choices are: a) t+7 b) -7t c) t-7 d) 7-t Seven fewer than suggests Addition subtraction. Begin with the number t and subtract 7. Therefore the correct response is “c,” t-7. Multiplication Division To model a situation with an algebraic expression, do the following:

 Identify the actions that suggest operations.

 Define one or more variables to represent the unknown(s)

 Represent the actions using the variables and the operations.

Allow the students to create a foldable brainstorming of all the words they can think of they signify mathematical operations. Allow them 5 minutes to work in a group of 3 or 4 then ask for volunteers to read a word of Activity 5: his/her paper. The other students are to put a check on their paper if they have the same word. If they do not have the word they should add it to Fold paper in four columns or create their paper. Continue until all words have been read, and all students chart as attached to plan to have have a good list of words. You may need to prompt some of them… columns for property, shown quotient…. w/symbol, example with numbers,

DSCYF EDUCATION UNIT Assessment Prompt for Learning Activity 1: Got It? P.18 Which algebraic and description in words expression models the word phrase “two times the sum of a and b.” The choices are: f) a+b g) 2a+b h) 2 (a+b) i) a+2b Shout out your answer on the count of three… 1,2, 3 Discuss results… If necessary have students explain what each of the expressions means in words.

Learning Activity 2: Guide the students through Problem 2 on p.19 You start with $20 and save $6 each week. What algebraic expression models the total amount you save? (You may want to ask what this would look like on a graph… starts at 20, positive y-intercept, and goes up by 6 each week, positive slope, linear, constant rate of change) Assignment: Assessment Prompt for Learning Activity 2: Got It? p.19 You had $150, but you are spending $2 each day. What algebraic expression models this p. 22 # 11 – 37, 39 - 60 situation? Compare your response with your partner’s. Raise your hands if they are the same.

Learning Activity 3: Guide the students through Problem 3 A and B on p. 19 to evaluate the algebraic expressions by substituting in the given value for each variable. Remind the students of PEMDAS (the order of operations).

Assessment Prompt for Learning Activity 3: Got It? p.19 Have the students compute the value of the expression if x=6 and y= -3. Will the value of the expression change if the parentheses are removed? Explain to your partner. ______

Learning Activity 4: Guide the students through writing the algebraic expression to determine the total number of points a football teams scored with 3 touchdowns (6pts. Each), 2 extra point kicks (1 point each), and 4 field goals (3 pts. each)? Follow the plan on p. 20 to emphasize the Know Need and Plan for solving problems. Remind the students that they will encounter problems that are more challenging and must be prepared to write down the problem and steps.

Assessment Prompt for Learning Activity 4: In basketball, teams can score by making 2 point shots, three point shots, or 1 point free throws. What algebraic expression models the total number of points a team scores in a game? If a team makes 10 2 point shots, 5 three point shots, and 7 free throws, how many points does in score in all? Write your answer on a post-it and pass it to your left. If the answer is correct, post it on the board. ------Learning Activity 5: Have the students identify the following from the expression: -4ax + 7w – 6: terms, coefficients, constant terms, and like terms

DSCYF EDUCATION UNIT Remind them from algebra 1 what it means to “combine like terms”!

Have the students work with a partner to complete the table for Learning Activity 5 (attached at the end of this packet, or make a foldable) to write the list of properties listed on p. 21 with the symbols, examples, and words for each.

Utilizing the properties, work through problems 5A & B on p. 21 with the students A. 7 + 3+ 2 - 4 B. –(3k + m) + 2(k – 4m)

Assessment Prompt for Learning Activity 5: Have the students complete Got it? on p. 21 Combine like terms. What is a simpler form of each expression? -4- 7k + 5j + b. –(8a + 3b) + 10(2a -5b)

Summarizing Strategy: Exit Quiz… You have a summer job detailing cars. You charge $5 to wash a car, $25 to wax a car, and $2 to vacuum a car.

1. What algebraic expression models the amount you can earn?

2. If you wash 8 cars, wax 2 cars, and vacuum 6 cars, how much money will you earn in all?

Learning Goals for this Lesson: 1.4 Solving Equations Standards: A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

Students Will Know Students Will Be Able To: Solve equations in one step, multi-step,  Properties of numbers and equality can be used to identity, and no solution solve an equation by finding increasingly simpler equations that have the same solution as the original equation.

 Important properties of equality include reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication and division.

DSCYF EDUCATION UNIT Lesson Essential Question: What is your plan for solving multi-step problems?

Activating Strategy:

Key vocabulary to preview and vocabulary strategy inverse operations, solution of an equation, literal equation

Lesson Instruction

Learning Activity 1 Graphic Organizer:

Review the vocabulary word: equation Graphic Organizer: Word Problem Organizer Review the EQ and the Essential Understanding  http://img.docstoccdn.com/thum Give students the Cornell Notes page and have them record the b/orig/20485139.png following information for the Properties of Equality.  Or (see attached at the end of the unit: Solving Word Problems Graphic Organizer)

Or http://jackiemurphy21.files.wordpress.co m/2013/02/solve.jpg

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Assessment Prompt for Learning Activity 1 - Solving for a variable, using the properties we learned:

In your Collaborative Pairs, 1’s and 2’s: Think Ink Share

1’s solve: 12b = 18

Work should be similar to this:

12b=18

12b/12= 18/12 b= 1 ½ or 1.5

2’s solve: -3a=-15

Work should be similar to this:

-3a = -15

-3a/-3 = -15/-3 a= 5

DSCYF EDUCATION UNIT After you have students share the answers, have them discuss which properties were used to figure out the answer. Share answers with the larger group.

Learning Activity 2

Show students this problem, in their Pairs.

Have students explain to their partner how you solve an equation with the variable on both sides of the equal sign. Share answers and show students the remainder of the problem’s solution. Ask Assignment students why they think you have to put the variable on one side.

Do activity sheet attached at the end of the unit (marked Lesson 1.4)

Assessment Prompt for Learning Activity 2

The Got it problem #3 (see the Activity Sheet marked Lesson 1.4)

They will also need another copy of the Graphic Organizer for Problem Solving.

DSCYF EDUCATION UNIT Learning Activity 3

Have students take notes:

Try this problem in Collaborative Pairs:

Assessment Prompt for Learning Activity 3

With a Partner, solve this problem:

The first half of a play is 35 minutes longer than the second half of the play. If the entire play is 155 minutes long, how long is the first half of the play? Write an equation to solve the problem.

Summarizing Strategy: : Exit Ticket

Independently, solve these problems on a sheet of lined paper. This is your ticket out the door.

Part 1: Make a plan and solve this problem.

The length of a rectangle is 3cm greater than its width. The perimeter is 24cm. What are the dimensions of the rectangle?

(Answer: width= 4.5cm, length = 7.5cm)

DSCYF EDUCATION UNIT Part 2: Find and explain the error(s) in the steps shown:

Error Analysis

12x +10=-2

12x = 8

X= 8/12 or 2/3

(Answer: the second line is incorrect, subtract 10 from each side)

Learning Goals for this Lesson: 1.5 Solving Inequalities Standards: A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

Students Will Know Students Will Be Able To

 Just as properties of equality can be used to solve equations, Create equations and inequalities in properties of inequality and be used to solve inequalities. one

 Properties of numbers and inequality can be used to solve an variable and use them to solve inequality by finding increasingly simpler inequalities that problems. have the same solution as the original inequality.

Lesson Essential Question: How do you solve an inequality?

Activating Strategy:

Here are the number line graphs of two different inequalities.

Compare and contrast the two inequalities and graphs that are shown above.

Similarities Differences

DSCYF EDUCATION UNIT Key vocabulary to preview and vocabulary strategy

Frayer compound inequality

Compound inequalities are two inequalities joined by the word and or by the word or. Inequalities joined by the word and are called conjunctions. Inequalities joined by the word or are disjunctions. You can represent compound inequalities using

words, symbols or graphs.

Lesson Instruction

Learning Activity 1 Graphic Organizer

Interactive Learning: Solve It!  Frayer

Question: You want to download some new songs on your MP3 player. Vocab. (see attached Each song will use about 4.3 MB of space. The amount of storage templates) space on your MP3 is shown at the right. At most how many songs can you download? Explain. (Hint: 1 GB=1000MB) Compound

Purpose: To distinguish between situations that involve equations and Inequality those that involve inequalities

Process: Students may Compare Multiply 7.8 by 1000 to find the number of available and Words like “at most” and “at least” suggest a relationship in which two Contrast quantities may not be equal. You can represent such a relationship with a Chart

ESSENTIAL UNDERSTANDING: Just as you use properties of equations, (Activating you can use properties of inequality to solve inequalities.

DSCYF EDUCATION UNIT Strategy)

Cornell

Notes see

Templates

http://www.ebstc.org/TechLit/not es/cornellbasic.jpg

DSCYF EDUCATION UNIT

Assessment Prompt for Learning Activity 1

Using collaborative pairs, solve this problem to check your understanding.

What is the solution of -2(x+9) +5 ≥ 3? Graph the solution.

Learning Activity 2

DSCYF EDUCATION UNIT Assignment

Assessment Prompt for Learning Activity 2

Compare and Contrast the two plans

Plan 1 Plan 2

DSCYF EDUCATION UNIT Learning Activity 3

Assessment Prompt for Learning Activity 3

Summarizing Strategy

Learning Goals for this Lesson: 1.6 Absolute Value Equations and Inequalities Standards: A.SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

Students Will Know Students Will Be Able To Absolute value is nonnegative Solve and write Opposites have the same absolute value, so an absolute value equation can have equations and two solutions inequalities involving absolute value

Lesson Essential Question: How is it possible to have two answers for the same problem?

Activating Strategy:

Introduce Absolute Value with this song/video (36 sec.)

https://www.youtube.com/watch?v=gT-Be1OE5Ug&feature=player_embedded

Complete a Frayer model, teacher guiding the process

DSCYF EDUCATION UNIT (see attached template)

Key vocabulary to preview and vocabulary strategy absolute value extraneous solution

Lesson Instruction

Learning Activity 1 Graphic Organizer

 Frayer (see attached Lead the students through the Solve It! problem at the beginning of the templates) lesson. http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do? method=scoViewer&internalId=131112100000200&isHtml5Sco=false&fromTa b=DONETAB

You are riding in an elevator and decide to find out how far it travels in 10 min. You start on the third floor and record each trip in a table. Each floor is 12ft high. How far did the elevator travel in all? Justify your answer.

Allow students to discuss the problem and how they think the question can be solved. Let them work together to try and solve it. Allow sharing of the answers. Then, reveal the answer.

Then work on Problem 1 together using this resource: http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do? method=scoViewer&internalId=131112100000201&isHtml5Sco=false&fromTa b=DONETAB

Have partners look at the problem and see if they can figure out how to solve it.

Go over it together.

Assessment Prompt for Learning Activity 1

(TE pg 42 Got It #1)

In your math notebook, record the following problem. Solve the problem. Then hold your hand up so I can check your answer.

DSCYF EDUCATION UNIT What is the solution of 2 │x+9│+3 = 7? Graph the solution

Learning Activity 2

Put the following problems on pieces of paper and allow pairs of students to draw one. Have them solve it and share the answers with the class (using the Smart Board, doc. Camera, or white board.) Have students include the Answer Check by substituting the answer in place of the variable. Assignment 1. 2. 3. Complete this lesson 4. 5. 6. review: (with a partner) Note Taking: Complete this The distance on the number line cannot be negative. Therefore, some worksheet absolute value equations, such as │x│=-5, have no solution. It is important to https://www.pearso check the possible solutions of an absolute value equation. One or more of nsuccessnet.com/sn the possible solutions may be extraneous. papp/iText/products /0-13-318813-2- An extraneous solution is a solution derived from an original equation that is 01/media/HSM12CC not a solution pf the original equation. _A2/Chapter_1/HSM Problem 3 (TE pg43) Checking for extraneous solutions 12CC_A2_01_06_CM. pdf What is the solution of │3x+2│= 4x+5? Check for extraneous solutions.

Step 1: Rewrite the problem as two equations. And solve each equation.

3x+2=4x+5 or 3x+2=1(4x-5)

-x=3 x=-1

Check your answer by substituting the answer.

Since x=-3 does not satisfy the original equation, -3 in an extraneous solution, The only solution to the equation is x=-1.

Assessment Prompt for Learning Activity 2

With a partner, solve this problem and Check for extraneous solutions.

DSCYF EDUCATION UNIT Make sure you students use the Opposite of a Sum Property when simplying.

(TE pg 43 Got It?)

What is the solution of │5x-2│=7x+14? Check for extraneous solutions.

Learning Activity 3

Take Notes: Inequality

The solutions of the absolute value inequality │x│<5 include values greater than -5 and less than 5.

This is the compound inequality x>-5 and x<5, which you can write as -5

(Draw a number line to graph -5 to 5)

You can write an absolute value inequality as a compound inequality without value symbols.

(Problem 4 TE pg 43)

Solving the Absolute Value Inequality │A│

What is the solution of │2x-1│<5? Graph the solution.

Plan out and discuss the problem together:

Is this an “and” problem or an “or” problem? Why?

2x-1 is less than 5 and greater than -5. It is an “and” problem.

│2x - 1│<5

-5 < 2x – 1 < 5

-4 <2x <6

-2

DSCYF EDUCATION UNIT Take Notes: Concept Summary Use the Smart Board, white board, or projector to show students this table and have them copy it into their notes.

Symbols Definition Graphing │x│= a The distance from x to Draw number line to 0 is a units. demonstrate │x│< a {│x│≤ a} The distance from x to Draw number line to 0 is less than a units. demonstrate │x│ >a {│x│≥ a} The distance from x to Draw number line to 0 is greater than a demonstrate units.

Assessment Prompt for Learning Activity 3

With a partner find the solution and graph it:

│3x-4│ ≤ 8? Graph the solution.

Summarizing Strategy

Ticket Out the Door:

Explain what it means for a solution of an equation to be extraneous.

DSCYF EDUCATION UNIT Cornell Notes templates

http://www.ebstc.org/TechLit/notes/cornellbasic.jpg

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DSCYF EDUCATION UNIT

DSCYF EDUCATION UNIT

Lesson 1.6

DSCYF EDUCATION UNIT