Valley Stream Central HS District

Valley Stream Central HS District CAP Project August 2009

SAT Math Scope and Sequence

Curriculum Writers

David Aguado – Project Supervisor, North High School Rebekah Williams – Central High School Caryn Simon – South High School

Administration

Dr. Marc F. Bernstein, Superintendent of Schools Dr. Thomas Troisi, Assistant Superintendent of Curriculum and Instruction Mrs. Jill Vogel, District Director of Guidance Ms. Maureen Henry, South High School, Principal Mr. Cliff Odell, North High School, Principal Dr. Joseph Pompilio, Central High School, Principal Dr. Kathleen Walsh, Memorial Junior High School, Principal

Table of Contents I. Rationale

II. Resources

III. Course Outline

IV. Daily Lesson Plans

V. Assessments

VI. Works Cited

Rationale

In the past, the Valley Stream Central High School District offered an SAT Preparation course as an elective to its 11th and 12th graders in conjunction with the Princeton Review. After the Spring 2009 semester, the High School District cut ties with the Princeton Review. This curriculum represents the new elective offered to the 11th and 12th grade students and will be implemented in September 2009. The purpose of this CAP was to review several SAT Math Preparation tools and prepare an outline for the new elective. In this process, teachers also reviewed numerous new SAT Preparation review books in order to select a workbook for the course. The committee chose the SAT Math Workbook by Kaplan.

This document contains the Scope and Sequence that will be used throughout the course. Also included is an outline of each chapter and the suggested number of days for each topic. Daily lesson plans have been prepared. Although it is the individual teacher’s responsibility to prepare assessments for this course, sample quizzes are provided. Resources

The workbook chosen for this course contains all topics listed in the outline. However, teachers may find it necessary to supplement some topics. The College Board workbook, The Official SAT Study Guide, is a good resource for additional practice problem. This book not only contains review material but contains 8 full – length practice examinations. Another good resource for teachers to use is the Math Workout for the SAT by Cornelia Cooke. Although this covers most of the same topics as the Kaplan book, it gives the teacher another tool to prepare the students for the SAT.

Teachers should also use the College Board website (http://www.collegeboard.com) for additional information related the SAT examination.

Additional information may be found on the following websites:

http://www.petersons.com/testprepchannel/new_sat.asp?sponsor http://www.act-sat-prep.com/ http://www.kaptest.com http://education.yahoo.com/college/essentials/practice_tests/sat/ http://www.rocketreview.com/ http://www.princetonreview.com http://www.barronstestprep.com/ http://www.testprepreview.com/sat_practice.htm http://www.syvum.com/sat/ http://www.tamingthesat.org/practice.html

Daily Lesson Plans

Chapter (NA); Sub - Topic (Course Introduction) (Day 1 of 1)

Aim: What is expected of us in the SAT Math elective?

Objectives: 1. Understand the course requirements 2. Be aware of the due dates of the signed contract and SAT registration 3. Realize that the quarter grade is a combination of a Math score and a Verbal score

Anticipatory Set / Do Now:

Various students will be asked to read paragraphs from the syllabus aloud. The students will learn that they will be asked to read quite a bit in this class. The students must read clearly and loud enough for everyone in the room to hear them.

Guided Practice:

Students are always concerned with the grading policy for a course they are taking and this one is no different. The grading policy is as follows:  One grade is submitted each quarter by the SAT Math and Verbal teachers.  70% of each student’s quarter grade is based upon class work quizzes, homework, participation and attendance

Quizzes 20% Homework 20% Class Participation and 30% Attendance  30% of each student’s quarter grade is based upon the completion of one take home diagnostic exam and proof of registration for the SAT.

Diagnostic 1 20% Registration for the SAT 10%

 The score that you earn on each diagnostic exam does NOT affect your quarter grade.  Fall Semester: o If you are a senior, you must register for the December SAT exam o If you are a junior, you must register for the January SAT exam  Spring Semester: o You must register for the June SAT exam

Closure:

Students will receive their materials for this class. They will receive two books. The SAT Math Workbook by Kaplan will be brought to class every day. The Official SAT Study Guide by the College Board will stay in the classroom as it contains full length practice SAT examinations.

Homework:

Students will be required to sign the bottom of the syllabus and have a parent do the same. This will be collected next class. Chapter (1); Sub - Topic (How to Prepare for the SAT) (Day 1 of 1)

Aim: How do we prepare for the SAT?

Objectives: 1. Understand the format of the SAT exam 2. Differentiate between the Regular Math questions and the Grid – Ins 3. Realize that the math questions will be arranged in order of difficulty 4. Apply the 7 general SAT strategies for approaching each section

Various students will be asked to read paragraphs from pages 3 and 4 aloud. This brings us to the 7 General SAT Strategies.

Guided Practice:

We will discuss each of the 7 General SAT Strategies: 1. Think About the Question First 2. Pace Yourself 3. Know When a Question is Supposed to be Easy or Hard 4. Move Around Within a Section 5. Be a Good Guesser 6. Be a Good Gridder 7. Two – Minute Warning: Locate Quick Points

Closure:

Students will read the Chapter 1 Summary to themselves. They will be given an opportunity to ask any questions they may have. Students will also hand in their signed forms from the syllabus.

Homework:

Students will read the pages ix and x in their workbook. These pages educate the students on how to use the book to improve their SAT Math score. Chapter (2); Sub - Topic (Introduction to SAT Math) (Day 1 of 2)

Aim: What should we expect on the SAT?

Objectives: 1. Utilize the 5 step method for solving SAT Math questions 2. Solve problems using the “Picking Numbers” technique (Plugging In) 3. Solve problems using the “Backsolving” technique (PITA)

Various students will be asked to read pages 9 and 10 aloud. This introduces us to the first four steps.

Guided Practice:

Picking numbers is one of the most valuable tools that can be used to solve SAT Math Questions. The first example on page 11 is the students first opportunity to use this. We will often refer to this strategy as “Plugging In”.

After solving the problem, this should be put in the students’ notebook.

How to Recognize a Plugging – In Question  There are variables in the answer choices  The question says something like in terms of…  Your first thought is to write an equation  The question asks for a percentage or fractional part of something, but doesn’t give you any actual amounts

How to Solve a Plugging – In Question  Don’t write an equation  Pick an easy number and substitute it for the variable  Work the problem through and get a target score then circle it  Plug in your number – the one you chose in the beginning – to the answer choices and see which choice produced your correct answer

With some math problems, it’s easier to work backward from the answer choices then to try the problem using methods from traditional math classes. Students can use this “Backsolving Strategy” which we often call PITA (Plugging In the Answers).

The first example on page 12 will be completed as a class. The students should understand that they should always start by plugging in choice (C) because the answers are displayed in order. This often helps eliminate answer choices.

Independent Practice:  The students will get an opportunity to plug in on the second problem on page 11  The students will get an opportunity to use PITA on the second problem on page 12

Closure:

The students will answer the following Plugging – In question.

Jill spent x dollars on pet toys and 12 dollars on socks. If the amount Jill spent was twice the amount she earns each week, how much does Jill earn each week in terms of x. A) 2(x +12) B) 2x + 24 C) D) E)

Homework:

Students will be required to bring in a calculator next class and for the remainder of the course. Chapter (2); Sub - Topic (Introduction to SAT Math) (Day 2 of 2)

Aim: How do we solve Grid – In Questions?

Objectives: 1. Successfully grid in questions on the SAT 2. Understand which calculators are permitted on the SAT

Students will attempt the following Easy level question by using PITA.

If 4 less than the product of b and 6 is 44, what is the value of b? A) 2 B) 4 C) 6 D) 8 E) 14

Guided Practice:

 The students will read pages 13 – 15 aloud on Grid – In questions. The directions for this section of the SAT are the same on every test. If you understand how to grid – in correctly, you do not have to waste valuable time reading the directions.  Pages 15 – 17 discuss how calculators can help improve your SAT score. We will read these allowed and the students will ask questions. Independent Practice:

The students will answer each of the following Grid – In Questions. Whatever they do not complete will be finished for homework.

1) What value of x satisfies both of the following equations?

2) Of the 6 courses offered by the music department at her college, Kay must choose exactly 2 of them. How many different combinations of 2 courses are possible for Kay if there are no restrictions on which 2 courses she can choose?

3) Of the 6 courses offered by the music department at her college, Kay must choose exactly 2 of them. How many different combinations of 2 courses are possible for Kay if there are no restrictions on which 2 courses she can choose?

4) If , what is one possible value for x ?

1) 2) 3) 4) Closure:

The students will read the section on page 17 entitled “Wrapping it Up”. This will introduce the students to the SAT Math Practice sections which focus on individual topics.

Homework:

Students will complete the remaining Grid – In Questions Chapter (3); Sub - Topic (Number Operations) (Day 1 of 1)

Aim: How do we answer questions on the SAT concerning Number Operations?

Objectives: 1. Solve problems using the order of operations (PEMDAS) 2. Recall and apply the properties of numbers 3. Add, subtract, multiply and divide signed numbers

Anticipatory Set / Do Now: 1)

Guided Practice:

After reviewing the order of operations questions from the “Do Now”, we will review the basic properties of number operations:  Distributive Property  Commutative Property  Associative Property

Independent Practice:

Students will answer questions 1, 2, 7, 8, and 15 on pages 23 – 24. We will go over these together.

Closure:

Students will answer questions 9 – 11 on pages 23 – 24. If time permits, we will review these as a class. If not, the answers are displayed with explanations on page 26.

Homework: Complete practice set on pages 23 – 24. Chapter (4); Sub - Topic (Number Properties) (Day 1 of 1)

Aim: How do we answer questions on the SAT concerning Number Properties?

Objectives: 1. Apply the definitions of integers, prime numbers, factors and multiples 2. Solve problems involving a remainder 3. Differentiate between the union and intersection of sets

Students will review what was covered in the last class by reviewing some of the “100 Essential Math Concepts”. They will read pages 214 and 216 silently.

Guided Practice:

As a class, we will review the definitions of integers, prime numbers, factors and multiples. An understanding of these concepts is essential to solving SAT questions.

We will complete pages 31 – 33 # 1 – 3, 7 – 8, 15 – 17.

Students will complete pages 31 – 33 # 4, 9 – 12, 18, 20.

Closure:

Students will complete page 32 # 14. Students who can correctly answer this question have a solid understanding of what an integer and remainder is.

Homework: page 31 – 33 # 6, 13, 19, 21 Chapter (5); Sub - Topic (Averages) (Day 1 of 2)

Aim: How do we use the average pie chart to answer SAT questions concerning average?

Objectives: 1. Use the average pie chart to solve problems concerning arithmetic mean 2. Differentiate between the mean, median and mode and calculate each 3. Determine the missing number when given a group of numbers and the mean of them

The students will become familiar with the average pie chart:

This line running horizontally represents where the students should divide to find the missing value. The line running vertically represents where the students should multiply to find the missing number. Guided Practice:

We will answer the following easy level question together using the chart: 6) The average of 3 numbers is 22, and the smallest of these numbers is 2. If the other two numbers are equal, each of them is A) 22 B) 30 C) 32 D) 40 E) 64

Students will answer following medium and hard level questions using the chart:

12) Caroline scored 85, 88, and 89 on the three of her four history tests. If her average score for all tests was 90, what did she score on her fourth test? A) 89 B) 90 C) 93 D) 96 E) 98

14) The average of 8, 13, x, and y is 6. The average of 15, 9, x, and x is 8. What is the value of y? A) –1 B) 0 C) 4 D) 6 E) 8

Closure: Students will answer page 39 # 6 and 7. This will ensure they can successfully use the chart before attempting the homework.

Homework: Page 39 # 1 – 5, 9 – 11 Chapter (5); Sub - Topic (Averages) (Day 2 of 2)

Aim: How do we solve SAT questions concerning arithmetic mean, median and mode?

Objectives: 1. Differentiate between the mean, median and mode and calculate each 2. Solve hard level average questions

The students will complete Page 39 # 8, 12 – 15. They should be using the average pie chart.

Guided Practice:

We will review the definition of median and mode. The students will use these definitions to solve problems on the SAT.

Together, we will complete Page 39 # 16 – 20, 24.

The students will complete Page 39 # 21 – 23, 25.

Closure:

They will be working on the independent practice until the bell. Whatever they do not complete will be done for homework. Homework: Read Page 219 # 37 – 41 from the “100 Essential Math Concepts”. They will also complete any remaining problems from Page 39 – 41.Chapter (6); Sub - Topic (Ratios and Rates) (Day 1 of 2)

Aim: How do we solve SAT problems concerning rates?

Objectives: 1. Set up a ratio and express in simplest form 2. Find the average rate when given two units of measure 3. Convert one unit of measure to another (ie – How many minutes is 3.5 hours?)

The students will read page 218 of the “100 Essential Math Concepts”. This should give them the necessary tools to solve rate questions.

Guided Practice:

As a class, we will complete Page 49 # 4.

Students will complete Page 49 – 50 # 1 – 3, 5 – 10.

Closure:

Students will display and explain their solutions to Page 49 – 50 # 1 – 3, 5 – 10.

Homework: Page 50 – 51 # 11 – 15 Chapter (6); Sub - Topic (Ratios and Rates) (Day 2 of 2)

Aim: How do we solve SAT problems concerning ratios?

Objectives: 1. Use ratio box to solve SAT questions

The students will complete Page 50 – 51 # 16 – 18. Number 16 and 17 give the students an opportunity to Plug – In on rate and ratio questions.

Guided Practice:

We will use the ratio box to solve the following question:

John has red marbles and blue marbles in a ratio of 1:2. If he has a total of 24 marbles, how many red and blue marbles does he have?

Students will practice using the ratio box by completing Page 51 # 19 – 21.

Closure: Students will attempt a hard level question on ratios. They will complete page 51 # 22. We will go over this together.

Homework: Page 52 – 53 # 23 – 32 Chapter (7); Sub - Topic (Percents) (Day 1 of 2)

Aim: How do we solve math problems that involve percents?

Objectives: 1. Apply the percent equation to solve simple percent problems 2. Use the percent translation technique to answer difficult percent problems. 3. Plug appropriate values into percent problems to make problems easier.

Students will be asked to complete the following question: What percent of 5 is 6? After, I will ask the students to explain how they arrived at their answers. I expect that some students will say they used the percent proportion, . We will review the proportion together as a class. Then, I will teach the students another percent method where they translate percent proportions into fraction problems. Students will fill in the following chart:

English Math Equivalents % (percent) Divide by 100 of Multiply what Variable is, are, were, did, does Equals

We will try the same problem as earlier using the percent translation technique. Students will see that the two methods are the same, however, many will find the translation technique easier. By showing both techniques, students will be allowed more flexibility to solve a percent problem. Guided Practice:

As a class, we will complete two easy, and one medium question from the workbook. Easy: p.65 – 68 # 1, 4 (Plug-in) Medium: p65-68 #14

Students will complete p.65 – 68 #8 (easy), 18 (medium)

Closure:

Students will answer question 16 on p. 67 in their workbooks. This question includes the need for plugging in and tests their percent application technique. I will poll the class for the correct multiple-choice answer.

Homework:

Students will complete p.65 – 68 #1-15 (exclude numbers 3,7,10) Chapter (7); Sub - Topic (Percents) (Day 2 of 2)

Aim: How do we solve math problems that involve a percent of change or a profit or loss?

Objectives: 1. Use the percent of change formula. 2. Differentiate profit/loss questions from percent of change questions. 3. Apply the idea that a percent increase/decrease is really an increase or decrease of that number from 100%.

Represent a profit of 25% as a decimal. 100% + 25% = 125% or 1.25 Represent a loss of 25% as a decimal. 100% - 25% = 75% or .75

Students will then be asked to complete the following question:

After getting a 20 percent discount, Jerry paid $100 for a bicycle. How much in dollars did the bicycle originally cost? (p.67 #20)

Hint: What percent of the original price of the bike did Jerry pay? Rewrite the question using the percent translation technique.

Translation: $100 is 80% of the original cost of the bike. Application:

Guided Practice:

After going over the “Do Now” we will complete question #21 on page 67 in the workbook. Then, I will introduce the percent of change formula. As a class, we will look at questions 7 and 10 on p. 65-66.

Students will complete p.65 – 68 #19 (medium), 21 (hard) Closure:

Students will answer question 7 on p. 242 in their workbooks. This question includes the need for plugging in and tests their knowledge on percent of change, and profit/loss. I will poll the class for the correct multiple-choice answer.

Homework:

Students will complete p.67 – 68 #17, 23, 24, and 25 Chapter (8); Sub - Topic (Powers and Roots) (Day 1 of 1)

Aim: What are the laws of exponents?

Objectives: 1. Formulate the basic power rules including multiplying, dividing, adding and subtracting powers with the same base. 2. Build rules for fractional powers, the power of zero, the power of one, and negative powers (supplemental). 3. Solve radical equations with the use of the calculator and the “PITA” technique.

Students will complete the following examples: 1. 2. 3.

After reviewing the power rules, I will ask the students to complete the following acronym and chart in their notebook.

Guided Practice:

After going over the “Do Now” we will complete questions 5,7,17 on page 77-78 in the workbook. Then, I will review radical operations with the students. They will be asked to write the following examples in the “Do Now” section:

1. 2. 3. 4. 5.

Students will complete p.77-79 # 1, 2, 6, and 11.

Closure:

The students will answer the following medium ranked question. I will poll the class for their answers.

If w is a positive integer, then

If time allows, students will also be asked to solve question 7 on p.236 in their workbooks.

Homework:

Students will complete all of the remaining questions from pages 77 – 79 in their workbooks. Chapter (9); Sub - Topic (Graph- Data Analysis) (Day 1 of 1)

Aim: How do we interpret data on the SAT?

Objectives: 1. Draw on prior knowledge such as the average pie, percent applications, and percent of change to answer questions regarding charts.

Work with your designated partner to answer question 2 on p.87 in your workbook.

Challenge yourselves to find a fast method to answer this question. Remember that it is an “easy” question, and therefore it should not eat up all of your time.

Guided Practice: After going over the “Do Now” we will complete questions 1,4, and 6 from pages 87-88 in the workbook. Each of these questions reviews a strategy from the past such as the average pie, the percent application or the percent of change formula.

Students will answer the questions 3 – 11 odd on pages 87 – 89 in their workbooks. After they are finished, they should check their answers with their designated partners from the “Do Now” activity.

Closure:

Students will answer question 12 on p.237 and question 14 on p.275 in their workbooks.

Homework:

Students will complete the remaining questions from p.87 –89 for homework. Chapter (10); Sub - Topic (Basic Algebra) (Day 1 of 1)

Aim: How do we answer algebra questions on the SAT?

Objectives: E.1. Solve problems using polynomial operations. 2. Factor polynomials using the greatest common factor, the difference of two perfect 3. squares or reverse foil. 4. Solve absolute value questions with the use of “PITA” or the isolation of the absolute 5. value expression and the branching off of two equations.

In your workbook, turn to p.95 and answer questions 1, 3, and 12.

Guided Practice:

After reviewing the basic algebra questions from the “Do Now”, we will complete questions 6, 17 and 20 from pages 95-96 to review the necessary methods used to solve function and absolute value questions.

Students will answer questions 4, 13, 15, 18, 21 and 24 on p.95-96 in their workbooks. Closure:

Students will answer question 26 on p.97 in their workbooks.

Homework: Complete questions 1 – 29 on pages 95- 97 in the workbook. Chapter (11); Sub - Topic (Advanced Algebra) (Day 1 of 2)

Aim: How do we use the “Plugging In” technique to solve complicated algebra problems on the SAT?

Objectives: 1. Use the “Plugging In” technique to answer questions with variables. 2. Choose variables that satisfy the conditions for each “Plugging In” question. 3. Check all five answer choices and adjust their assigned values for each variable should they find more than one correct answer choice.

Students will answer question 1 on p.107 in their workbooks. We will review the basics of the “Plugging In” method together.

Plugging In: 1. Assign values for variables. 2. Establish a target value. 3. P.O.E. down!

Guided Practice:

As a class, we will continue to solve questions that use the “Plugging In” method (p.107 #4).

We will also look at questions that may have more than one correct answer depending on the values that the students choose to plug in. It is for this reason that students must be reminded to always check all five answers before selecting their final answer. If the students should find that more than one answer choice works within a given problem, they must change their assigned values and try the problem again until they have only one correct answer. p.107 #5 is a good example practice where the students may find more than one correct answer.

We will also complete question 10 on p.107.

Students will answer questions 3, 11, and 22 on p.107-109 in their workbooks.

Closure:

Students will answer question 11 on p.237 in their workbooks.

Homework: Complete questions 1 – 11 on pages 107-108 in the workbook.

Chapter (11); Sub - Topic (Advanced Algebra) (Day 2 of 2)

Aim: To review solving function questions, quadratics equations, and direct and indirect variation questions.

Objectives: 1. Factor and solve quadratic equations. 2. Find the solution set of absolute value and quadratic inequalities. 3. Distinguish the difference between the direct variation and indirect variation method to solve word problems.

Students will answer the three following (medium ranked) questions.

7) If , what is the value of x?

A) B) C) 4 D) 8 E) 16

7) If , all of the following are possible values of x EXCEPT

A) –3 B) –2 C) 0 D) 2 E) 3 9) If , which of the following is NOT a possible value of x?

A) –10 B) –5 C) –3 D) 5 E) 10

Guided Practice:

After reviewing the “Do Now”, the class will discuss the differences between direct and indirect variation. I will ask the class to make a chart under their “Do Now” section to compare and contrast the different ways that two variables can be related. I will ask the students to supply an example for each type of variation.

Direct Variation Indirect Variation Def: When one variable increases Def: When one variable increases, the (decreases), the other variable increases other variable decreases (vice-versa). (decreases).

Example: Example:

Formula: Formula:

Next, the class will complete the following two medium ranked questions. 7) The volume of hydrogen in a balloon varies inversely with the applied pressure. At an applied pressure of 200 tons, the volume of hydrogen in the balloon is 3 cubic feet. What is the applied pressure in tons, when the volume of hydrogen in the balloon is 40 cubic feet? A) 0.6 B) 13.3 C) 15 D) 163 E) 237

12) If x varies directly as , and x = 4 when y = 3, then what is the value of x when y = 12?

A) 8 B) 16 C) 36 D) 48 E) 64

Also, question 12 on p.108 in the workbook.

Students will answer questions 14,15,19, and 25 on pages 108-109 in the workbook.

Closure:

Students will answer question 11 and 15 on page 271 in their workbooks.

Homework: Complete questions 13 – 26 on pages 108-109 in the workbook. Chapter (12); Sub - Topic (General Word Problems) (Day 1 of 2)

Aim: What are the different approaches that can be used to solve SAT word problems?

Objectives: 1. Apply the different vocabulary terms for multiplication, division, addition, and ‘ subtraction to translate the word problem information from English to algebra. 2. Use the “ PITA” charting technique to answer word problems.

Students will answer question 2 and 6 on p.119 in their workbooks. Question 2 challenges students to translate words into math. Question 6 is a word problem that requires very careful reading.

After the students answer the “easy” level questions, I will poll them for their answers. I expect most students to answer question 6 incorrectly. This will hopefully alert the students to the trickiness of the problem. I will remind the students at this time that SAT Math isn’t tough because it tests tough concepts; its tough because ETS can be pretty tricky. More than half of all math errors are caused by misreading the question, so be sure to READ CAREFULLY.

Guided Practice:

As a class, we will complete questions 18, 8 and 22. As we work on question 18, we will review operation vocabulary. I will stress “special cases” where the order of the numbers must be switched. For example: 3 less than 5 translates to 5 – 3; 3 subtracted from 5 translates to 5 – 3.

Question numbers 8 and 22 both involve the “PITA” charting technique. After the class decides that the questions will best be completed using this technique, we will review the “PITA” steps. P lugging I n T he A nswer (PITA) 1) Label Answer Choices 2) Start with “C” 3) P.O.E. down!

Students will answer questions 3, 7, and 14 on p.119-120 in their workbooks.

Closure:

Students will answer the following “easy” level question:

5) Elvis gives his chauffeur a gold suit and gives his cook a diamond ring. If the suit is worth one fifth of what the ring is worth, and if the two items together are worth $4,800, then how much is the ring worth?

A) $800 B) $960 C) $3,840 D) $4,000 E) $4,200

Homework: Complete questions 1 – 18 on pages 120-121 in the workbook. Chapter (12); Sub - Topic (General Word Problems) (Day 2 of 2)

Aim: To practice the “PITA” technique (day 2).

Objectives: 1. Use the “ PITA” charting technique to answer word problems.

Students will be asked to complete question 26 on p.121 in their workbook with a designated partner. The “hard level” question requires the use of the “PITA” charting. Some lower scoring students will need the help of their partners to complete the question, while other higher scoring groups can use their partner to check their answers.

Guided Practice:

As a class, we will work on a few word problems that incorporate different mathematical topics and/or different SAT strategies. These topic/strategies include percents, direct/ indirect variation, plug-in, and PITA.

Practice Problems: p.121-122 # 19, 24, 25 and 29

Students will answer questions 20, and 33 on p.121-122 in their workbooks.

Closure:

Students will answer the following “medium” level question: 8) Lori is 15 years older than Carol. In 10 years, Lori will be twice as old as Carol. How old is Lori now?

A) 5 B) 12 C) 20 D) 25 E) 30

Homework: Complete questions 19 – 33 on pages 121-122 in the workbook. Chapter (13); Sub - Topic (Logic Word Problems) (Day 1 of 2)

Aim: To review probability.

Objectives: 1. Explain the definition of probability. 2. Review the counting principle, tree diagrams, and combinations.

Students will complete question 3 and question 12 on pages 133-134. After the “Do Now” we will define probability as the likelihood that a certain event will occur.

Guided Practice:

As a class, we will work on different word problems that incorporate the counting principle, reasoning strategies, and the formula.

Students will also be given a handout that contains two questions that answer the question “How many different ways is it possible to arrange a group of items?

Practice Problems: 12) Four chefs are available to cook four different meals. If each chef is to cook one of the meals, in how many ways could the four chefs be assigned to the four meals? A) 4 B) 8 C) 16 D) 24 E) 64

16) Six children, one boy and five girls, must stand in a line. If the boy cannot stand first or last in line, how many different ways could the children be arranged? A) 720 B) 480 C) 360 D) 240 E) 120 The class will also complete p.133-135 # 4, 6, and 9 in the workbook.

Students will answer question numbers 2, 5, 14 and 15 on pages 133 – 135 in their workbooks. Closure:

Students will complete question 18 on p.266 and question 6 on p.273 in the workbook.

Homework: Complete questions 1-15 on pages 133 – 135 in the workbook (omit number 7 and 11). Chapter (13); Sub - Topic (Logic Word Problems) (Day 2 of 2)

Aim: To continue to review probability and work on pattern questions.

Objectives: 1. Use the “Plugging In” technique to simplify probability and logic questions. 2. Identify a pattern within a pattern to solve a question in less time.

Students will complete question 18 on p. 136 in their workbooks. In order for the students to solve this question, they must use the “plugging in” method. After the class is finished, we will review the “plugging in” method and apply it to a few more practice problems.

Guided Practice:

As a class, we will use the plugging in method to complete p. 136 # 21. We will also look at question 22 on p.136 together. This question requires the use of a Venn Diagram.

After, I will guide the students through a pattern question. The students will write down the following question in their workbooks.

9) A craftsman creates necklaces out of beads. He uses colored beads in a repeating pattern of gray, lime, opal, ruby, clear, white, black and so on. If the first bead on a necklace is gray, what is the color of the 86th bead?

A) Gray B) Lime C) Opal D) White E) Black

The students will be asked to write out the repeating pattern: G L O R C W B Next, they will be asked to count how many colors there are in the sequence. (7) After, they will be asked to find out how many times 7 will evenly divide into 86. (12 with a remainder) Lastly, I will ask the students to tell me what 7 x 12 is and what color this answer represents. (84 and B) The students will finally count two more colors until they land on the 86th bead’s color. (Lime) The class will also complete p. 246 #6 in their workbooks.

Students will answer question numbers 11, 16 and 20 on pages 134 – 136 in their workbooks.

Closure: Students will complete question 15 on p.247 in the workbook.

Homework: Complete p.136 in the workbook (omit number 24) Chapter (14); Sub – Topic (Lines and Angles) (Day 1 of 1)

Aim: How are the properties of lines and angles used?

Objectives: 1. Apply the properties of complementary, supplementary, alternate interior, and vertical angles. 2. Investigate the relationships between parallel and perpendicular lines. 3. Solve problems involving line segments, midpoints, and ratios of segments.

Active Learning Strategies: Partner activity, matching activity

Anticipatory Set / Do Now: Have students in even rows write everything they know about parallel lines. Have students in odd rows write anything they know about perpendicular lines. Next, students will slide next to their partner and share what they wrote. Partners may add to each others’ lists. Finally, the class will share their information together.

Procedures: 1. Students will complete p.145 #1 & 2 individually. When reviewing these problems, go over the definition of vertical angles, straight angles, right angles, and supplementary angles. 2. Complete p.145 #3 as a class. First, draw a picture and label it. Use POE to determine that correct answer. 3. Review the properties of two parallel lines cut by a transversal. What is true about all small angles? All large angles? Any small plus any large angle? Let students work in pairs on #11 and then review as a class. Guided Practice: Work in pairs on #13 and 14. Then share/review as a class.

Assessment / Evaluation: Students will complete a matching activity reviewing the vocabulary of lines and angles and their definitions and pictures.

Closure: Review the matching solutions.

Homework: Complete p.145-147. Name______Date______

Do Now: Write down ANYTHING you can think of related to PARALLEL LINES.

Name______Date______

Do Now: Write down ANYTHING you can think of related to PERPENDICULAR LINES. Name______Date______Match each term to its picture and description.

1. Vertical angle Two lines that meet at 90 degree angles.

2. Right angle Two equal angles that are formed by two intersecting lines and are opposite each other.

3. Supplementary angles An angle that has 180 degrees and makes a straight line.

4. Parallel lines The point on that divides a line segment into two congruent parts.

5. Straight angle Congruent angles formed when two parallel lines are cut by a transversal.

6. Perpendicular lines Angles that add to 180 degrees and form a straight line.

7. Alternate interior angles Lines that will never intersect.

8. Acute angle An angle with more than 180 degrees.

9. Obtuse angle An angle that has 90 degrees.

10. Midpoint An angle with less than 90 degrees.

Chapter (15); Sub – Topic (Triangles) (Day 1 of 3)

Aim: How can we solve basic triangle problems?

Objectives: 1. Find the interior and exterior angles in a triangle. 2. Find the area of a triangle 3. Use the Pythagorean Theorem to find the side of a triangle.

Active Learning Strategies: Partner work, exit ticket

Anticipatory Set / Do Now: Let students solve p.153 #1 independently. Go over the question together and review the property that every triangle has 180 degrees and the property of supplementary angles.

Procedures: 1. Have students read #2 and identify the best strategy to apply. (PITA) Solve the question together using PITA. 2. Let students determine the strategy to apply to solve #3 (plug in). Solve the question together using plugging in. 3. Read #13 together. Ask what formula we need to use (area) and write down the formula. Ask students how we can find the base and height that the formula uses. Use the Pythagorean Theorem to determine the base and height. Apply the area formula to find the correct answer.

Guided Practice: Work in pairs on #6, 14-15. Then share/review as a class.

Assessment / Evaluation: Monitor students as they work in pairs.

Closure: Give students an incorrectly solved area problem. Ask students to determine if the question is solved correctly and if not, to identify the mistake and correct it. (Ex- using a side that is not an altitude as the height.)

Homework: p.153 #4, 6, 16-19. Chapter (15); Sub – Topic (Triangles) (Day 2 of 3)

Aim: How can we solve problems with special right triangles?

Objectives: 1. Solve problems involving special right triangles. 2. Identify the Pythagorean triples.

Active Learning Strategies: Partner and small group work

Anticipatory Set / Do Now: Ask students to identify all of the special right triangles that they have heard of. Classify them as special angles or Pythagorean triples. Show students the special right triangles on the SAT formula page and show examples of possible ratios of the sides. Ask students where they might find each of the special triangles (in a square or an equilateral triangle).

Procedures: 1. Work as a class to solve p.154 #9. Identify the special triangle and the ratio of the sides. Use the ratio to find the indicated side. 2. Let students work on #12 in pairs and then go over as a class.

Guided Practice: Work in small groups on # 22, 23. Then share/review as a class.

Assessment / Evaluation: Monitor students as they work in pairs/groups.

Closure: Challenge students to recall all five special triangles.

Homework: p.154 #5, 10, 20, 21, 25. Chapter (15); Sub – Topic (Triangles) (Day 3 of 3)

Aim: How can we practice solving difficult triangle problems?

Objectives: 1. Apply the triangle inequality theorem 2. Solve difficult level triangle problems.

Active Learning Strategies:

Anticipatory Set / Do Now: Ask students if it is possible to make any three line segments into a triangle. Use strips of paper to show a set of three sides that does not form a triangle.

Procedures: 1. Review the triangle inequality theorem. Given any two sides, add them and subtract them to determine the possible side lengths in between the two results. 2. Let students apply the triangle inequality theorem to solve p.154 #7. Guided Practice: Have students work in pairs or small groups on p.157 #26-30

Assessment / Evaluation: Monitor students’ progress as they work in groups. Have students put their solutions on the board and explain their steps.

Closure: Let students complete an exit ticket applying the triangle inequality theorem.

Homework: Complete p.158 #31-34 Chapter (16); Sub – Topic (Quadrilaterals and other Polygons) (Day 1 of 1)

Aim: What are the properties of quadrilaterals and other polygons?

Objectives: 1. Know the definition of a quadrilateral and apply the property of the sum of the angles of a quadrilateral. 2. Apply the properties of parallelograms, rectangles, and squares. 3. Solve problems involving the area and perimeter of a quadrilateral or polygon. 4. Determine the sum of the interior angles of a polygon other than a quadrilateral.

Anticipatory Set / Do Now: Draw a quadrilateral on the board. Ask students to name the shape. Ask students for any special properties of all quadrilaterals (they have 360 degrees). If students name incorrect shapes (parallelogram, trapezoid, etc.), talk about what is special about each of those.

Procedures: 1. Show students a polygon with more than four sides. Ask students how many degrees are in the shape. Let the students know that there is a formula, but they can find the degree measure without memorizing another formula. Have students divide the polygon into triangles. They know each triangle has 180 degrees, so multiply the number of triangles they made by 180 to find the total number of degrees in the polygon. 2. Work together to solve p.169 #2. Review the properties of a rectangle and the definition of perimeter as you work backwards to find each side of the figure. Review the area formula for a rectangle to find the answer. 3. Read #14 together. Ask students what strategy they can use since they don’t have any measurements to work with. Encourage students to write down the area formula and then plug in numbers that could work as the base and height of the triangle. Use the dimensions to find the base and height of the bigger triangle and then find its area. Guided Practice: Have students work in pairs or small groups on p.170 # 7, 8, 19, 20.

Closure: Let students look at #15. Have students write down the first thing they would do to solve this question (break it into familiar shapes). If there is time, let the students continue to solve the problem.

Homework: p.169 #1, 3-6, 12-16. Chapter (17); Sub – Topic (Circles) (Day 1 of 2)

Aim: How can we solve problems involving the area and circumference of a circle?

Objectives: 1. Identify the diameter and radius of a circle and know that all radii of a circle are congruent. 2. Use the area and circumference formulas. 3. Anticipatory Set / Do Now: Ask students to recall the three basic steps to solving a geometry question. (Draw a picture, label your picture, write and substitute into relevant formulas.)

Procedures: 1. Read p.181 #1 together. Ask students to state the steps we should follow. Draw a picture. Write the are formula, substitute they area, and solve for the radius. Finally, write the circumference formula and substitute the radius in to find the answer. 2. Have students read #6 and give the first step (write the area formula). Have students use the area formula to find the radius independently. Ask the students where we should label the radius in the diagram (there are two radii in the picture). Remind the class to always look for all radii and diameters when they see a circle diagram and that all radii or diameters are equal. Ask the class what else we need to know to find AB (OA). Tell the students to look for basic shapes and apply their properties. In this case, there is a right triangle, so they can use the Pythagorean theorem. Let students use the formula or identify the 6-8-10 triangle. Finally, find the difference between OB and OA to find AB.

Guided Practice: Have students work in pairs or small groups on p.181 #2, 7, 9

Closure: Have students complete an exit ticket independently where they are given an area and asked to find the circumference.

Homework: p.181 #4, 8, 11, 14. Chapter (17); Sub – Topic (Circles) (Day 2 of 2)

Aim: How can we find the arcs and angles in a circle?

Objectives: 1. Apply the relationship between central angles and arcs and know the number of degrees in a circle. 2. Determine the area of a sector of a circle. 3. Apply the properties of a line tangent to a circle.

Anticipatory Set / Do Now: Ask the students to figure out how many degrees the minute hand on the clock has to move before the period will be over. Let students recall that there are both 360 degrees and 60 minutes in a circle. When converting one set of units to another, we can use a proportion.

Procedures: 1. Look at p.183 #13. Ask the students what they will need to do even before they read the question. Have students draw a picture to match the problem. Label the arc that is 12 pi, and then determine the total circumference. Ask the students why the answer is not 4 pi (the arc between the two endpoints). First, it’s too easy for a medium level question and second, because the shortest distance is a straight line. Let students volunteer how to use the circumference to find the radius. Next, use special right triangles to find the hypotenuse of the isosceles right triangle. 2. Have students read #10 together. Ask students what a tangent line means. Recall the property that a tangent line always makes a right angle with the radius of the circle. Let students plug in for x and use the Pythagorean theorem to find the solution.

Guided Practice: Let students work independently on # 5.

Assessment / Evaluation: Monitor students’ progress as they work. Call on students to describe the steps to get through the problem.

Closure: Have students complete an exit ticket.

Homework: p.181 # 3, 12, 15. Chapter (18); Sub – Topic (Multiple Figures) (Day 1 of 1)

Aim: How can we solve problems with multiple figures?

Objectives: 1. Solve problems involving overlapping figures. 2. Identify the basic shapes in complicated figures and apply their properties. 3. Determine the relationships between inscribed circles and squares.

Anticipatory Set / Do Now: Let students look over the difficult level questions on p.190. Ask the students what makes these questions look intimidating (they have unfamiliar shapes). Remind the students that they know all of the basic shapes and their properties, they just need to identify what shapes are being combined or overlapped in these difficult figures.

Procedures: 1. Have students identify the overlapping shapes in #6. What are the important parts of a circle to identify? What types of triangles should we look for? Review the basic steps of geometry. Label the picture with the given information. Use the radius to find the area of the circle. Ask the students if the radius has any other significance (it’s also the height of the triangle). Let the class know that often the key to these questions is identifying a side that is shared between the two shapes. Use the area of a triangle formula to find the base. Ask the students what other piece we need to find (the overlapping section). What type of triangle do we have (isosceles right triangle or 45-45-90). Use a ratio to determine the area of the sector. Let students determine how to combine these three areas to find the area of the total figure. 2. Work through question #8 together, again letting the students identify the common parts of the overlapping figures and the area formula to find each area. Since the final answer, a ratio, will be a fraction, we can plug in our own numbers to make the work simpler.

Guided Practice: Let students work in pairs on #4.

Assessment / Evaluation: Monitor students’ progress as they work. Call on students to describe the steps to get through the problem.

Closure: Have students complete an exit ticket.

Homework: p.189 # 1-3, 5, 7. Chapter (19); Sub – Topic (Coordinate Geometry) (Day 1 of 1)

Aim: How can we solve problems involving coordinate geometry?

Objectives: 1. Plot points on the coordinate plane. 2. Determine the slope of a line given two points. 3. Solve problems involving the equation of a line. 4. Determine the length and midpoint of a line segment given the coordinates of its endpoints.

Anticipatory Set / Do Now: Let the students solve p.197 #1 independently. Go over the correct answer and review where the positive/negative x and y-values lie on the coordinate plane.

Procedures: 1. Read p. 198 #9. Ask students to share the first thing they would do. Encourage the students to start by sketching a graph and plotting the points. Assign one student the job of timing how long it takes to make a sketch with the two points to show students it is worth the small amount of time it takes. Then, have the students make the line into the hypotenuse of a right triangle, count the length of the sides, and use the Pythagorean Theorem to find the length of the line. 2. Ask students to describe the meaning of slope. Have students give several methods of finding a slope. Ask for three volunteers to find slope each using a different method. Give each student two ordered pairs and have one use the slope formula, one use a graph and count rise over run, and the third use linear regression. Ask the class to vote for which method they think will be easiest and fastest. Give the class another set of ordered pairs and let them choose their own method to find the slope.

Guided Practice: Students can work in small groups on p.197 #3, 7, 14, 15.

Closure: Have students write on an index card how they would describe to a friend how to find the slope and distance between two ordered pairs.

Homework: p.197 #1, 2, 4-6, 8, 10-13. Chapter (20); Sub – Topic (Solids) (Day 1 of 1)

Aim: How can we find the surface area and volume of a solid?

Objectives: 1. Determine the surface area of a rectangular solid. 2. Solve problems involving the volume of a solid.

Anticipatory Set / Do Now: Ask the students to name some common solids. Have the students attempt to draw a cube and another rectangular solid. Point out the volume formulas on the reference information. Ask the students to describe surface area and how it is found.

Procedures: 1. Draw a rectangular solid on the board and assign it a length, width, and height. Ask the students to find its surface area. Ask how many sides we need to find the area of. Find each area and help students recognize that there are three pairs of sides. Ask the students what we need to do with the six areas. 2. Let students read and begin p.207 # 4 independently. Ask them to point out the trick in the question. (There are two different sets of units.) Let them describe how to deal with this trick. Encourage the students to change the 1 foot into inches. Ask them if it matters if we change the units before or after finding the volume. Let them try it both ways to see if they get the same result.

Guided Practice: Students can work in pairs on p.207 #5, 7, 9.

Closure: Have students write on an index card how they would describe to a friend how to find the slope and distance between two ordered pairs.

Homework: p.207 #1-3, 6, 8, 10. Assessments

Name ______SAT Math Date ______Chapters 1 – 3

Directions: Answer 6 out of the 8 questions below. Write your final answers in the answer box on the right of this page. (5 points each)

1. If , then x = A) 37 B) 39 C) 41 D) 74 E) 78

1. If , what is the value of ? A) –4 B) 0 C) 1 D) 2 E) 3

2. If and , what is the value of ? A) 3 B) 5 C) 15 D) 25 E) 30 3. If , what is n in terms of x? A) 4x + 1 B) 2x + 1 C) 2 – x D) 1 – 2x E) 1 – 4x

4. How many different positive three – digit integers can be formed if the three digits 4, 5, and 6 must be used in each of the integers? A) Three B) Four C) Six D) Eight E) Nine

5. If k is a positive integer, which of the following must represent an even integer that is twice the value of an odd integer? A) 2k B) 2k + 3 C) 2k + 4 D) 4k + 1 E) 4k + 2

6. If , what is the value of x?

7. If , what is the value of ab?

Name ______SAT Math Date ______Chapters 4 – 6

1. The total cost of 3 equally priced mechanical pencils is $4.50. If the cost per pencil is increased by $0.50, how much will 5 of these pencils cost at the new rate? A) $7.50 B) $8.00 C) $9.00 D) $9.50 E) $10.00

2. Which of the following could be the remainders when 4 consecutive positive integers are each divided by 3? A) 1, 2, 3, 1 B) 1, 2, 3, 4 C) 0, 1, 2, 3 D) 0, 1, 2, 0 E) 0, 2, 3, 0

3. If the average (arithmetic mean) of x and 3x is 12, what is the value of x? A) 2 B) 4 C) 6 D) 12 E) 24 4. How many seconds are there in m minutes and s seconds?

A) 60m + s B) m + 60s C) 60(m + s) D) E)

5. If the sum of consecutive integers from –22 to x, inclusive, is 72, what is the value of x? A) 23 B) 25 C) 50 D) 75 E)94

6. In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5 to 2. How many pounds of cashews will there be in 4 pounds of this mixture?

7. What is the greatest of 5 consecutive integers if the sum of these integers equals 185? 8. For all positive integers j and k, let j R k be defined as the whole number remainder when j is divided by k. If 13 R k = 2, what is the value of k? Name ______SAT Math Date ______Chapters 7 – 10

1. If 20 percent of x is 10, what is x percent of 10?

A) 50 B) 30 C) 20 D) 10 E) 5

2. If , what is the value of x?

A) 4 B) 6 C) 8 D) 27 E) 64 COST PER ITEM

NUMBER OF ITEMS SOLD TEAM T-SHIRT CAP A 50 25 B 45 18 C 40 30 ITEM PRICE T-shirt $12 Cap $7

3. The first table above shows the number of T-shirts and caps sold by three teams of students at Jacoby High School’s annual fundraiser. The second table shows the price of each item sold. Based on this information, how much more money did team A raise than team C?4. Carlos paid $154.00 for 2 tickets to a concert. This price included a 25 percent handling fee each ticket and a $2 transaction fee for the total sale. What was the price for a single ticket before the additional fees?$95.00$60.80$57.50$57.00$38.005. If 3x – 8 < 12 + 5x, thenx > 10x < 10x > -10x < -10x > 06. What is the value of a, if and ? 1296437. If x and y are positive integers and