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Algebra Foundations

Lesson Plans, PowerPoint’s, and

Supplemental Materials for SBCUSD

Algebra Foundations.

Krystle Burt

University of La Verne

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Table of Contents

Tab 1: Keeping an Interactive Notebook 4-5

Tab 2: Algebra Basics 6-8

Variables and Expressions Adding and Subtracting Real Numbers Multiplying and Dividing Real Numbers

Tab 3: Algebra Properties 9-11

Properties of Real Numbers Combining Like Terms

Tab 4: Expressions 12-14

Simplifying Expressions Evaluating Expressions

Tab 5: Factoring Methods 15-16

Greatest Common Factor Prime Factorization

Tab 6: Equations and Inequalities 17-20

One-Step Equations One-Step Inequalities Two-Step Equations Two-Step Inequalities

Tab 7: Graphs 21-24

Slope The Slope Formula Using Intercepts Slope-Intercept Form Slope-Intercept Form (Point and Slope)

Tab 8: Exponents 25-28

Powers and Exponents Integer Exponents Multiplication Property of Exponents Division Property of Exponents

Tab 9: Fluency Builders 29-30

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Tab 10: Quizzettes 31-32

Tab 11: Quizzette Quizzes 33-34

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Keeping an Interactive Notebook in Mathematics

There are many reasons for students to keep interactive notebooks. Most importantly, it is

a way for them to keep their notes organized. The interactive notebook becomes a study tool for

students when preparing for a quiz or an exam. The majority of the work done in the notebook is

done in class. All of the detail work and finishing touches can be done at home or after all

assignments in class have been completed. Many components make up the notebook and can be

changed based on grade level or content. Included are some of the materials that I use in my

classroom that have made the interactive notebook successful. (A sample notebook is included

for reference)

All About Me

At the very beginning of the year I have the students tell me about themselves. Included

is a little person that they can color to make look like them if they want to. I ask them to tell me

about their family, what they like and dislike, what they want to be when they grow up, and

something else that they are good at. Having this information early in the year provides me with

details about my students that I can use to help shape the curriculum.

Table of Contents

At the beginning of the notebook and after multiple lessons involving the same content, I

have the students create a table of contents. This allows them to keep track of where their work is

in their notebook. All of the student’s page numbers will correspond to my sample notebook, to

make it easier to find their work. This also allows the students to go right to the page they need

to, to help them study or add additional work.

Syllabus

The students are also required to include the syllabus for the course in their notebook.

This is so they can refer back to the rules and requirements of the class. A parent has to sign their

syllabus as well, stating that they too understand the rules and requirement. I have included a

copy of the syllabus so that it can be used by others.

Algebra Foundations Syllabus.docx

The Left Side

The left side of the notebook is used for all of the output information that the students

create. Color should be used on the left side of the notebook, to better help the students process

the information.

The Left Side.docx

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The Right Side

The right side of the notebook is used for notes. These could be lecture notes; however it

is not just limited to that. For better studying techniques the notes should be taken in Cornell

format. This helps the students have an even better study tool that helps them prepare for tests or

quizzes.

The Right Side.docx

The Reflection

The reflection in the interactive notebook is designed for the students to evaluate their

work. It gives them an opportunity to identify their strengths and weaknesses and build upon

them so they can continue to do better. It also gives them an opportunity to express their feelings

about the class. There is an outline that the students can follow to write a proper reflection.

Reflections are typically written right before the students turn in their notebooks for a notebook

check.

The Reflection.docx

Design Your Ideal Teacher

This is an activity that is typically done within the first few days of school. The students

get to create their “perfect teacher” and express things that they would want to see in class. They

get to express how they feel about assignments, classroom rules, and even the organization of the

class. Most students make logical suggestions and if the students feel as though they are helping

establish the atmosphere of the classroom, they are more likely to be willing to follow the rules

and guidelines outlined.

Parent Reflection

The parent reflection is used to show the parent/guardian of the student their progress in

class. It is a way for the parent to see if the student is doing what is asked of them and it helps

them identify learning habits or talents that their child might possess. The parents are able to

comment on the work of their student and ask me any questions that they might have. All of my

contact information is located at the bottom of the form, so that they parent can contact me if

they so desire. I have included a version of the parent reflection that can be edited for the use of

others.

Parent Reflection.pub

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Teacher: Subject: Algebra Foundations Date:

Standard: 4.0 – Student’s simplify expressions before solving linear equations and inequalities in one variable. 2.0 – Students understand and use such operations as taking the opposite, finding the reciprocal…

Objective

Lesson 1:

ASW translate between words and algebra and will evaluate algebraic expressions.

Lesson 2:

ASW add and subtract real numbers.

Lesson 3:

ASW multiply and divide real numbers

Time: Each lesson is designed to span many days based on the scope and sequence of the class. The teacher should determine how much review time is necessary and to plan accordingly. Each lesson includes Diagnostic Tests that should be given at the proper time, which is determined by the teacher.

Assessment:

Quizzette Quiz (Based on Quizzette given for the week).

Diagnostics:

Standard 11 FSD GR 7 NS.doc

Standard 10 FSD GR 6 NS.doc

Standard 2 FSD GR 4-5 NS.doc

Standard 2 FSD GR 6-7 Opposites and Operations with Signed.doc

Standard 2 FSD GR 5 NS.doc

Access Prior Knowledge/Anticipatory Set:

Daily fluency builders will be given to the students, so that they may continue to build upon their fluency in mathematics. These fluencies will be determined based on the individual student.

Students will complete a daily quizzette (determined by the teacher) that re-enforces what they previously learned or content that will help them in solving algebraic expressions.

The students prior knowledge will be accessed through a warm-up that has them add, subtract, multiply, or divide rational numbers. These are basic mathematical operations students will need to be successful in the course (lesson 1).

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The students will practice multiplying and dividing integers. This is important for them to understand before they are give positive and negative numbers in the same problem (lesson 2).

Direct Instruction/Modeling:

Lesson 1:

The teacher will introduce the vocabulary for the unit. (Personal dictionaries are a good way to keep the vocabulary words organized and understandable).

- Variable: is a letter or symbol used to represent a value that can change - Constant: is a value that does not change - Numerical Expression: contains only constants and/or operations - Algebraic Expression: contains variables, constants, and/or operations - Evaluate: to fins the value of an expression - Replacement Set: is a set of numbers that can be substituted for a variable

Students will be introduced how translating algebraic expressions from algebra to words and from words to algebra. Students will also learn how to evaluate expressions, by replacing the variable with a number. These are all basic operations that students can use on a daily basis and will continue to use as they interact with people.

Variables and Expressions.pptx

Lesson 2:

The teacher will introduce the vocabulary for the unit. (Personal dictionaries are a good way to keep the vocabulary words organized and understandable).

- Real Number: is the set of all numbers that can be represented on a number line - Absolute Value: is the distance of a number from zero on the number line - Opposites: two numbers that have a sum of zero - Additive Inverse: a number and its opposite; they are the same distance from zero

The teacher will introduce adding and subtracting integers using a number line. Based on the use of the number line the teacher and the students should compile a list of rules or steps that will help them add and subtract integers without using the number line.

Adding and Subtracting Real Numbers.pptx

Lesson 3:

The teacher will discuss the rules of multiplying and dividing signed numbers The students need to know what the sign of the product or quotient is when positives and negatives numbers are multiplied or divided. The teacher will also introduce the properties of zero. This will be extremely important later when the students are asked to find the slope of a line.

Multiplying and Dividing Real Numbers.pptx

Guided Practice:

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The teacher will provide the students with an I DO, WE DO, YOU DO activity. The teacher will do one problem for the students on the board. The students will not write anything, they will only watch the teacher complete the problem. If there are any questions the teacher should answer them before they move on to the WE DO problems. Students should copy the I DO problem from the board on their worksheet. The teacher will then provide the students with two additional problems that they will do together as a class. The teacher will write/workout the problems on the board. Finally, the teacher will provide the students with ten problems that they are to work out on their own. This activity is still guided due to the I DO, WE DO, YOU DO activity.

Each individual lesson will be accompanied with an I DO, WE DO, YOU DO activity. This particular activity makes a great study guide and can be complied in a flip book. It can also be included in the student’s interactive notebook as well.

Variables and Expressions (1).pub

Variables and Expressions (2).pub

Adding and Subtracting Real Numbers (1).pub

Adding and Subtracting Real Numbers (2).pub

Multiplying and Dividing Real Numbers (1).pub

Multiplying and Dividing Real Numbers (2).pub

Dividing Fractions (1).pub

Dividing Fractions (2).pub

Independent Practice:

Supplemental material should be used to help students with their understanding of the content. These materials may include, but are not limited to, individual worksheets, pairs checks, games, and other activities. Supplemental material should be used at the discretion of the teacher based on the students needs.

Closure/Reflection:

Classwork or an exit ticket is included with most, if not all, of the PowerPoint lessons. This is a good closure activity for the students, but again is at the discretion of the teacher. Producing a list of rules or steps that the students can follow is also a beneficial closure/reflection activity. The teacher should determine the needs of the students and find a closure/reflection activity that meets those needs.

Homework Assigned:

Homework should also be assigned at the discretion of the teacher. Extra problems or the supplemental provided could be used as a homework assignment.

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Teacher: Subject: Algebra Foundations Date:

Standard: 1.0 – Students identify and use arithmetic properties of subsets of integers and rational, irrational,

and real numbers, including closure properties for the four basic arithmetic operations where applicable.

Objective:

Lesson 1

ASW identify and use properties of real numbers.

Lesson 2

ASW combine like terms in an expression with common variables.

Time: Each lesson is designed to span many days based on the scope and sequence of the class. The teacher should determine how much review time is necessary and to plan accordingly. Each lesson includes Diagnostic Tests that should be given at the proper time, which is determined by the teacher.

Assessment:

Quizzette Quiz (Based on Quizzette given for the week).

Diagnostic:

Standard 4 FSD GR 7 AF.doc

Access Prior Knowledge/Anticipatory Set:

Daily fluency builders will be given to the students, so that they may continue to build upon their fluency in mathematics. These fluencies will be determined based on the individual student.

Students will complete a daily quizzette (determined by the teacher) that re-enforces what they previously learned or content that will help them in solving one-step equations.

The students will use their knowledge of adding and subtracting integers to help prepare them for combining like terms (lesson 2).

Direct Instruction/Modeling

Lesson 1:

The teacher will introduce each of the properties to the students. These include: commutative property, associative property, and the distributive property. They will need to understand the general rule for each of the properties and also be able to identify an example of each. It is important to remind the students that the properties hold true for all real numbers and variables that represent real numbers.

Properties of Real Numbers.pptx

Lesson 2:

The teacher will introduce the vocabulary for the unit. (Personal dictionaries are a good way to keep

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the vocabulary words organized and understandable).

- Terms: the parts of an expression that are added or subtracted - Like Terms: contain the same variable raised to the same power - Coefficient: a number multiplied by a variable

In this lesson the teacher needs to stress the importance of combining like terms with common variables only. The teacher could explain to the kids that each variable is like its own fruit, we can combine like fruits, but they are not making a smoothie. The teacher should use different colors or shapes and have the students do the same so that they understand what terms are similar and which are not.

Combining Like Terms.pptx

Guided Practice:

The teacher will provide the students with an I DO, WE DO, YOU DO activity. The teacher will do one problem for the students on the board. The students will not write anything, they will only watch the teacher complete the problem. If there are any questions the teacher should answer them before they move on to the WE DO problems. Students should copy the I DO problem from the board on their worksheet. The teacher will then provide the students with two additional problems that they will do together as a class. The teacher will write/workout the problems on the board. Finally, the teacher will provide the students with ten problems that they are to work out on their own. This activity is still guided due to the I DO, WE DO, YOU DO activity.

Each individual lesson will be accompanied with an I DO, WE DO, YOU DO activity. This particular activity makes a great study guide and can be complied in a flip book. It can also be included in the student’s interactive notebook as well.

Properties of Real Numbers (1).pub

Properties of Real Numbers (2).pub

Distributive Property (1).pub

Distributive Property (2).pub

Combining Like Terms (1).pub

Combining Like Terms (2).pub

Independent Practice:

Supplemental material should be used to help students with their understanding of the content. These materials may include, but are not limited to, individual worksheets, pairs checks, games, and other activities. Supplemental material should be used at the discretion of the teacher based on the students needs.

Closure/Reflection:

Classwork or an exit ticket is included with most, if not all, of the PowerPoint lessons. This is a good closure activity for the students, but again is at the discretion of the teacher. Producing a list of rules or

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steps that the students can follow is also a beneficial closure/reflection activity. The teacher should determine the needs of the students and find a closure/reflection activity that meets those needs.

Homework Assigned:

Homework should also be assigned at the discretion of the teacher. Extra problems or the supplemental provided could be used as a homework assignment.

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Teacher: Subject: Algebra Foundations Date:

Standard: 1.1 – Students use properties of numbers to demonstrate whether assertions are true or false.

Objective:

Lesson 1

ASW use the order of operations and properties of the real number system to simplify expressions.

Lesson 2

ASW evaluate expressions.

Time: Each lesson is designed to span many days based on the scope and sequence of the class. The teacher should determine how much review time is necessary and to plan accordingly. Each lesson includes Diagnostic Tests that should be given at the proper time, which is determined by the teacher.

Assessment:

Quizzette Quiz (Based on Quizzette given for the week).

Diagnostics:

Standard 10 FSD GR 6 AF.doc

Standard 4 FSD GR 4 AF.doc

Standard 4 FSD GR 5 AF.doc

Standard 5 FSD GR 3-5 AF.doc

Access Prior Knowledge/Anticipatory Set:

Daily fluency builders will be given to the students, so that they may continue to build upon their fluency in mathematics. These fluencies will be determined based on the individual student.

Students will complete a daily quizzette (determined by the teacher) that re-enforces what they previously learned or content that will help them in solving one-step equations.

The students will have to know how to evaluate exponents and add and subtract integers in order to simplify expressions. The warm-up for the day will include such. Students also need to recall how to translate words into algebra (lesson 1).

Before the students can evaluate expressions they must be able to simplify expressions. Their knowledge from the previous lesson will help them complete the warm-up by simplifying expressions (lesson 2).

Direct Instruction/Modeling:

Lesson 1:

In this lesson the teacher needs to introduce the students to PEMDAS. It is important that they know

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and understand the order of operations. If they do not they will be unable to simplify expressions properly. The teacher should also remind the students that the algebra properties may be used through simplifying expressions.

Simplifying Expressions.pptx

Lesson 2:

The teacher will introduce evaluating expressions to the students. The teacher should point out that when evaluating expressions the final answer is a real number. This is going to be very similar to simplifying expressions. The students will need to understand that they will replace the variable in the expression with a real number and then simplify.

Evaluating Expressions.pptx

Guided Practice:

The teacher will provide the students with an I DO, WE DO, YOU DO activity. The teacher will do one problem for the students on the board. The students will not write anything, they will only watch the teacher complete the problem. If there are any questions the teacher should answer them before they move on to the WE DO problems. Students should copy the I DO problem from the board on their worksheet. The teacher will then provide the students with two additional problems that they will do together as a class. The teacher will write/workout the problems on the board. Finally, the teacher will provide the students with ten problems that they are to work out on their own. This activity is still guided due to the I DO, WE DO, YOU DO activity.

Each individual lesson will be accompanied with an I DO, WE DO, YOU DO activity. This particular activity makes a great study guide and can be complied in a flip book. It can also be included in the student’s interactive notebook as well.

Simplifying Expressions (1).pub

Simplifying Expressions (2).pub

Evaluating Expressions (1).pub

Evaluating Expressions (2).pub

Independent Practice:

Supplemental material should be used to help students with their understanding of the content. These materials may include, but are not limited to, individual worksheets, pairs checks, games, and other activities. Supplemental material should be used at the discretion of the teacher based on the students needs.

Closure/Reflection:

Classwork or an exit ticket is included with most, if not all, of the PowerPoint lessons. This is a good closure activity for the students, but again is at the discretion of the teacher. Producing a list of rules or steps that the students can follow is also a beneficial closure/reflection activity. The teacher should determine the needs of the students and find a closure/reflection activity that meets those needs.

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Homework Assigned:

Homework should also be assigned at the discretion of the teacher. Extra problems or the supplemental provided could be used as a homework assignment.

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Teacher: Subject: Algebra Foundations Date:

Standard: 11.0 – Students apply basic factoring techniques to second and simple third degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect square of binomials.

Objective:

ASW write the prime factorization of numbers and find the greatest common factor (GCF) of monomials.

Time:

Each lesson is designed to span many days based on the scope and sequence of the class. The teacher should determine how much review time is necessary and to plan accordingly. Each lesson includes Diagnostic Tests that should be given at the proper time, which is determined by the teacher.

Assessment:

Quizzette Quiz (Based on Quizzette given for the week).

Diagnostics:

Standard 11 FSD GR 3-5 NS.doc

Standard 11 FSD GR 6 NS.doc

Access Prior Knowledge/Anticipatory Set:

Daily fluency builders will be given to the students, so that they may continue to build upon their fluency in mathematics. These fluencies will be determined based on the individual student.

Students will complete a daily quizzette (determined by the teacher) that re-enforces what they previously learned or content that will help them in solving problems that deal with greatest common factors and prime factorization.

The students prior knowledge will be accessed through a warm-up that has them determine whether the second number given is a factor of the first number. Students will also be asked to list all of the factors of the given numbers. The students should also be able to identify if integers are prime or composite and if they are composite they should be able to list the factors of that number. By identifying this above information for the given integers students should have an easier time writing the prime factorization and identifying the GCF of monomials.

Direct Instruction/Modeling:

The teacher will introduce the vocabulary for the unit. (Personal dictionaries are a good way to keep the vocabulary words organized and understandable).

- Prime Factorization: all of the prime factors of an integer, written in order from least to greatest. - Greatest Common Factor: the greatest factor that is shared by two or more whole numbers

Students will be shown how to find the prime factorization of an integer, using a factor tree. Students

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will be required to write the prime factorization of integers from least to greatest. The teacher will then introduce how to find the greatest common factor of a pair of numbers. The students should recognize that they are finding the prime factorization of each number to find the GCF. Finally, the students will have to find the GCF of monomials. The same methods will apply when finding the GCF.

Prime Factorization and GCF.pptx

Guided Practice:

The teacher will provide the students with an I DO, WE DO, YOU DO activity. The teacher will do one problem for the students on the board. The students will not write anything, they will only watch the teacher complete the problem. If there are any questions the teacher should answer them before they move on to the WE DO problems. Students should copy the I DO problem from the board on their worksheet. The teacher will then provide the students with two additional problems that they will do together as a class. The teacher will write/workout the problems on the board. Finally, the teacher will provide the students with ten problems that they are to work out on their own. This activity is still guided due to the I DO, WE DO, YOU DO activity.

Each individual lesson will be accompanied with an I DO, WE DO, YOU DO activity. This particular activity makes a great study guide and can be complied in a flip book. It can also be included in the student’s interactive notebook as well.

GCF (1).pub

GCF (2).pub

Prime Factorization (1).pub

Prime Factorization (2).pub

Independent Practice:

Supplemental material should be used to help students with their understanding of the content. These materials may include, but are not limited to, individual worksheets, pairs checks, games, and other activities. Supplemental material should be used at the discretion of the teacher based on the students needs.

Closure/Reflection:

Classwork or an exit ticket is included with most, if not all, of the PowerPoint lessons. This is a good closure activity for the students, but again is at the discretion of the teacher. Producing a list of rules or steps that the students can follow is also a beneficial closure/reflection activity. The teacher should determine the needs of the students and find a closure/reflection activity that meets those needs.

Homework Assigned:

Homework should also be assigned at the discretion of the teacher. Extra problems or the supplemental material provided could be used as a homework assignment.

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Teacher: Subject: Algebra Foundations Date:

Standard: 5.0 – Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

Objective:

Lesson 1

ASW solve one-step equations in one variable.

Lesson 2

ASW solve one-step equations in one variable using multiplication and division.

Lesson 3

ASW solve one-step inequalities using addition, subtraction, multiplication, and division.

Lesson 4

ASW solve two-step equations in one variable.

Lesson 5

ASW solve inequalities that contain more than one operation.

Time:

Each lesson is designed to span many days based on the scope and sequence of the class. The teacher should determine how much review time is necessary and to plan accordingly. Each lesson includes Diagnostic Tests that should be given at the proper time, which is determined by the teacher.

Assessment:

Quizzette Quiz (Based on Quizzette given for the week).

Diagnostics:

Standard 4 FSD GR 6 AF.doc

Standard 5 FSD GR 6 AF.doc

Standard 5 FSD GR 6-7 NS.doc

Standard 5 FSD GR 7 AF.doc

Standard 6-7 FSD GR 4 AF.doc

Access Prior Knowledge/Anticipatory Set:

Daily fluency builders will be given to the students, so that they may continue to build upon their fluency

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in mathematics. These fluencies will be determined based on the individual student.

Students will complete a daily quizzette (determined by the teacher) that re-enforces what they previously learned or content that will help them in solving one-step equations.

The students will solve one-step equations using the operation of addition, subtraction, multiplication, and division. Having the understanding of one-step equations, will help the students solve two-step equations. (Lesson 4)

The students will access their prior knowledge by solve two-step equations. They will use what they know about two-step equations and later apply that to solving two-step inequalities. (Lesson 5)

Direct Instruction/Modeling:

Lesson 1:

The teacher will introduce basic one-step equations. To solve the one-step equations, students will use the operations of addition and subtraction.

Students will also be introduced to negative variables. They will be shown and should understand that you cannot have a negative variable for your answer and that to get rid of the negative variable they must either multiple or divide by negative one. Either operation is acceptable since multiplication and division are inverse operations.

One-Step Equations (addition and subtraction).ppt

Lesson 2:

The teacher will move on to solving basic one-step equations using the operations of multiplication and division. Students should recognize what operation they are supposed to use based on the operation that is given in the original problem.

One-Step Equations (multiplication and division).ppt

Lesson 3:

The students will then be introduced to solving one-step inequalities. All operations addition, subtraction, multiplication, and division will be used to solve these problems.

One-Step Inequalities (all operations).ppt

Lesson 4:

The students should understand the concept of solving one-step equations. In this lesson it is the hope that they can combine their knowledge to solve two-step equations. The students should understand that the ultimate goal is the same: to isolate the variable. It is important to remind the students that whatever they do to one side of the equation they must do to the other side of the equation.

Solving Two-Step Equations.pptx

Lesson 5:

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It is important to review all of the properties of inequalities. Students should recall that when you multiply or divide by a negative number you must flip the inequality. If the student use what they know about solving two-step equations and apply the properties of inequalities there is very little new content presented.

Two-Step Inequalities.ppt

Guided Practice:

The teacher will provide the students with an I DO, WE DO, YOU DO activity. The teacher will do one problem for the students on the board. The students will not write anything, they will only watch the teacher complete the problem. If there are any questions the teacher should answer them before they move on to the WE DO problems. Students should copy the I DO problem from the board on their worksheet. The teacher will then provide the students with two additional problems that they will do together as a class. The teacher will write/workout the problems on the board. Finally, the teacher will provide the students with ten problems that they are to work out on their own. This activity is still guided due to the I DO, WE DO, YOU DO activity.

Each individual lesson will be accompanied with an I DO, WE DO, YOU DO activity. This particular activity makes a great study guide and can be complied in a flip book. It can also be included in the student’s interactive notebook as well.

One-step equations (AS1).pub

One-step equations (AS2).pub

One-step equations (MD1).pub

One-step equations (MD2).pub

One-step inequalities (1).pub

One-step inequalities (2).pub

Two-Step Equations (1).pub

Two-Step Equations (2).pub

Two-Step Inequalities (1).pub

Two-Step Inequalities (2).pub

Independent Practice:

Supplemental material should be used to help students with their understanding of the content. These materials may include, but are not limited to, individual worksheets, pairs checks, games, and other activities. Supplemental material should be used at the discretion of the teacher based on the students needs.

Closure/Reflection:

Classwork or an exit ticket is included with most, if not all, of the PowerPoint lessons. This is a good

20

closure activity for the students, but again is at the discretion of the teacher. Producing a list of rules or steps that the students can follow is also a beneficial closure/reflection activity. The teacher should determine the needs of the students and find a closure/reflection activity that meets those needs.

Homework Assigned:

Homework should also be assigned at the discretion of the teacher. Extra problems or the supplemental materials provided could be used as a homework assignment.

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Teacher: Subject: Algebra Foundations Date:

Standard: 6.0 – Students graph a linear equation and compute the x- and y- intercepts.

Objective:

Lesson 1:

ASW be able to describe the slope as rise over run and will also be able to identify the slope from a graph.

Lesson 2:

ASW find the slope of the line using the slope formula.

Lesson 3:

ASW find the x- and y- intercepts.

Lesson 4:

ASW will write a linear equation in slope-intercept form using the slope and y-intercept.

Lesson 5:

ASW write a linear equation in slope-intercept from using the slope and a point.

Time: Each lesson is designed to span many days based on the scope and sequence of the class. The teacher should determine how much review time is necessary and to plan accordingly. Each lesson includes Diagnostic Tests that should be given at the proper time, which is determined by the teacher.

Assessment:

Quizzette Quiz (Based on Quizzette given for the week).

Diagnostics:

Standard 6-7 FSD GR 7 AF.doc

Access Prior Knowledge/Anticipatory Set:

Daily fluency builders will be given to the students, so that they may continue to build upon their fluency in mathematics. These fluencies will be determined based on the individual student.

Students will complete a daily quizzette (determined by the teacher) that re-enforces what they previously learned or content that will help them in solving one-step equations.

Students will have to solve multi-step equations. This prior knowledge is important because they will be using the same process to solve for the x- and y- intercepts of an equation (lesson 3).

Students will be asked to access their prior knowledge by writing linear equations in slope-intercept form using the slope and a point. The students will also be asked to practice their skills of finding the

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slope when given two points (lesson 5).

Direct Instruction/Modeling:

Lesson 1:

The teacher will introduce the concept of a slope to the students. The teacher should explain to the students that slope is a constant rate of change and the slope of a line is the same between any two points on that same line. By using their knowledge of rise over run students should be able to determine the slope of a line by using a graph.

Slope.pptx

Lesson 2:

The teacher will introduce the students to the slope formula. It is important to show the students how to label their points so that they properly plug in the values. The students will also need to know that when there is a slope of zero the graph is a horizontal line and when the slope is undefined the graph is a vertical line. They should also be able to recognize whether or not the graph has a positive or negative slope.

The Slope Formula.pptx

Lesson 3:

The teacher will introduce the vocabulary for the unit. (Personal dictionaries are a good way to keep the vocabulary words organized and understandable).

- x-intercept: the coordinate of any point where the graph intersects the x-axis - y-intercept: the coordinate of any point where the graph intersects the y-axis

The teacher will show the students how to find the x- and y- intercepts from an equation. The teacher should show the students the cover up method of finding the intercepts. Explain to the students that this works because when the value is covered up that particular value is always zero.

Using Intercepts.pptx

Lesson 4:

In this lesson the teacher will introduce the students to slope-intercept form. The students will need to recall that slope is rise over run. The teacher will give and explain all components of the formula. The students, with the help of the teacher, will identify the slope and y-intercept in different examples. Once the students understand where the slope and y-intercept are located, they will be asked to write formulas given the slope and y-intercept. The teacher should clarify that all the students are being asked to do is plug in values for m and b.

Slope-Intercept Form.ppt

Lesson 5:

In this lesson students will continue working with equations in slope-intercept form. The difference here

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is that they will be asked to write an equation of the line in slope-intercept form given the slope and a point. The teacher should point out that in order to write equations in slope-intercept form you must have values for BOTH m and b. Once both of those values are obtain, one can write an equation.

Slope-Intercept Form (point and slope).ppt

Guided Practice:

The teacher will provide the students with an I DO, WE DO, YOU DO activity. The teacher will do one problem for the students on the board. The students will not write anything, they will only watch the teacher complete the problem. If there are any questions the teacher should answer them before they move on to the WE DO problems. Students should copy the I DO problem from the board on their worksheet. The teacher will then provide the students with two additional problems that they will do together as a class. The teacher will write/workout the problems on the board. Finally, the teacher will provide the students with ten problems that they are to work out on their own. This activity is still guided due to the I DO, WE DO, YOU DO activity.

Each individual lesson will be accompanied with an I DO, WE DO, YOU DO activity. This particular activity makes a great study guide and can be complied in a flip book. It can also be included in the student’s interactive notebook as well.

The Slope Formula (1).pub

The Slope Formula (2).pub

x and y intercepts (1).pub

x and y intercepts (2).pub

Slope-Intercept Form (Identify m and b) (1).pub

Slope-Intercept Form (Identify m and b) (2).pub

Slope-Intercept Form (1).pub

Slope-Intercept Form (2).pub

Independent Practice:

Supplemental material should be used to help students with their understanding of the content. These materials may include, but are not limited to, individual worksheets, pairs checks, games, and other activities. Supplemental material should be used at the discretion of the teacher based on the students needs.

Closure/Reflection:

Classwork or an exit ticket is included with most, if not all, of the PowerPoint lessons. This is a good closure activity for the students, but again is at the discretion of the teacher. Producing a list of rules or steps that the students can follow is also a beneficial closure/reflection activity. The teacher should determine the needs of the students and find a closure/reflection activity that meets those needs.

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Homework Assigned:

Homework should also be assigned at the discretion of the teacher. Extra problems or the supplemental provided could be used as a homework assignment.

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Teacher: Subject: Algebra Foundations Date:

Standard: 2.0 – Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

Objective:

Lesson 1

ASW evaluate expressions containing exponents.

Lesson 2

ASW evaluate expressions containing integer exponents and will simplify expressions containing integer exponents.

Lesson 3

ASW use multiplication properties of exponents to evaluate and simplify expressions.

Lesson 4

ASW use division properties of exponents to evaluate and simplify expressions.

Lesson 5

ASW evaluate expressions containing roots.

Time:

Each lesson is designed to span many days based on the scope and sequence of the class. The teacher should determine how much review time is necessary and to plan accordingly. Each lesson includes Diagnostic Tests that should be given at the proper time, which is determined by the teacher.

Assessment:

Quizzette Quiz (Based on Quizzette given for the week).

Diagnostics:

Standard 2 FSD GR 6-7 Exponents-Computational.doc

Standard 2 FSD GR 6-7 Exponents-Conceptual.doc

Standard 10 FSD GR 7 AF.doc

Standard 2 FSD GR 6-7 Roots.doc

Access Prior Knowledge/Anticipatory Set:

Daily fluency builders will be given to the students, so that they may continue to build upon their fluency in mathematics. These fluencies will be determined based on the individual student.

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Students will complete a daily quizzette (determined by the teacher) that re-enforces what they previously learned or content that will help them in solving expressions that contain exponents.

The students prior knowledge will be accessed through a warm-up that has them multiply positive and negative integers. Students will need to know if the final answer is positive or negative and understand why (lesson 1).

The students will practice writing expressions in exponent form (lesson 3).

The students will simplify expressions that are perfect squares. This will help the students when they have to take square roots (lesson 5).

Students will simplify expressions containing exponents, using the properties of multiplication (lesson 4).

Direct Instruction/Modeling:

Lesson 1:

The teacher will introduce the vocabulary for the unit. (Personal dictionaries are a good way to keep the vocabulary words organized and understandable).

- Power: is an expression written with an exponent and a base - Base: is the number that is used as a factor - Exponent: tells how many times the base is used as a factor (multiplied)

Students will also be introduced on how to evaluate powers. They will also be show how to write powers given the base and an exponent. Understanding how to translate powers is key to understanding how you bases and exponents are used.

Powers and Exponents.pptx

Lesson 2:

The teacher will move on to integer exponents. The students will be reminded of what a base, exponent, and power are. However, in this lesson they will be introduced to negative exponents and an exponent of zero. The teacher will show the students how to simplify and evaluate expressions with negative and zero exponents. Some examples will also include negative exponents in the denominator. Remind the students that factors with negative exponents are not yet simplified.

Integer Exponents.pptx

Lesson 3:

The students will continue working with exponents. They will be introduced to the product of powers property (addition of exponents with the same base). Students will also be shown that exponents can only be added if the bases of the power are the same. The students will also be introduced to the power of a power property (multiplication of exponents).

Multiplication Property of Exponents.pptx

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Lesson 4:

In this lesson students will be introduced to the quotient of powers property (subtracting exponents). They will learn how to simplify fractions that involve powers.

Division Properties of Exponents.pptx

Lesson 5:

The teacher will introduce the vocabulary for the unit. (Personal dictionaries are a good way to keep the vocabulary words organized and understandable).

- Perfect Square: is a number whose positive square root is a whole number

In this lesson the teacher will show the students how to take square roots of numbers and variables. It is important to point out that to solve a square root; they need to find a number that is multiplied by itself.

Roots.pptx

Guided Practice:

The teacher will provide the students with an I DO, WE DO, YOU DO activity. The teacher will do one problem for the students on the board. The students will not write anything, they will only watch the teacher complete the problem. If there are any questions the teacher should answer them before they move on to the WE DO problems. Students should copy the I DO problem from the board on their worksheet. The teacher will then provide the students with two additional problems that they will do together as a class. The teacher will write/workout the problems on the board. Finally, the teacher will provide the students with ten problems that they are to work out on their own. This activity is still guided due to the I DO, WE DO, YOU DO activity.

Each individual lesson will be accompanied with an I DO, WE DO, YOU DO activity. This particular activity makes a great study guide and can be complied in a flip book. It can also be included in the student’s interactive notebook as well

Powers and Exponents (1).pub

Powers and Exponents (2).pub

Integer Exponents (1).pub

Integer Exponents (2).pub

Multiplication Property of Exponents (1).pub

Multiplication Property of Exponents (2).pub

Division Property of Exponents (1).pub

Division Property of Exponents (2).pub

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Roots (1).pub

Roots (2).pub

Independent Practice:

Supplemental material should be used to help students with their understanding of the content. These materials may include, but are not limited to, individual worksheets, pairs checks, games, and other activities. Supplemental material should be used at the discretion of the teacher based on the students needs.

Closure/Reflection:

Classwork or an exit ticket is included with most, if not all, of the PowerPoint lessons. This is a good closure activity for the students, but again is at the discretion of the teacher. Producing a list of rules or steps that the students can follow is also a beneficial closure/reflection activity. The teacher should determine the needs of the students and find a closure/reflection activity that meets those needs.

Homework Assigned:

Homework should also be assigned at the discretion of the teacher. Extra problems or the supplemental materials provided could be used as a homework assignment.

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Fluency Builders

Materials:

Student Folders

Clear Sheet Protectors

Fluency Builders

Goal Sheets

Dry Erase Markers

Erasers

Timer

Crate

Anticipatory Set:

It is important to introduce the students to fluency builders and to make

sure that they understand its importance. Included is a PowerPoint Presentation

that does just that.

Fluency Builders.pptx

Passing out Folders and Pens:

Have the folders ready to go, so you can quickly pass them out. Have the

timer ready to go as well. Tell students when half their time is up. Count down the

last 10 seconds and make sure they stop and do not continue to work.

Some students will continue to work…you’ll want to stop them and point out why doing so works against them.

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Scoring:

Have the students flip the fluency builder over and self-correct. Ask them

to write down the number that they got correct on their score chart. Some students will want to lie about the number they got correct. Again, you want to point out why doing this works against them. The students should include the date

for each fluency taken.

Challenge Sheet.xlsx

Challenge Score:

Each fluency will also need to include a challenge score. The best way to

determine the challenge score for each fluency is to, personally, take the fluency

and then take 80% of the score that you received. This tends to be a good

challenge score for the students. Also, when you tell them “your score” (the

challenge score) they like trying to beat you.

Challenging:

The students will have to reach or exceed the challenge score three days.

Note that they do not need to do so in a row. Once they reach the challenge score

three time, they can challenge. When a student challenges they write directly on

the fluency, and not on the sheet protector. Also, when a student challenges the

teacher grades their fluency. If the student meets or exceeds the challenge score

they get to move on to the next fluency builder and the process repeats itself.

*NOTE – Not all of your students will be on the same fluency builder. If you make

this a fun thing for the students they tend to enjoy participating more. The

students also like competition, so be creative.

I have included a blank fluency sheet and two fluency builders for reference.

Blank Document.doc Adding & Subtracting Positive and Negative Integers.doc Point-slope form.docx

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Quizzette Table of Contents

Add, Subtract, Multiply, & Divide Decimals Decimal Operations.doc Adding & Subtracting Integers Add and Subtract Integers.doc Adding Fractions Adding Fractions.doc Decimals & Fractions on the Number Line Decimals & Fractions on the Number Line.doc Equations Involving Combining Like Terms Equations with Combining Like Terms.doc Equations Involving Distribution Equations with Distribution.doc Evaluating Expressions Evaluating.doc Expanded and Exponential Forms Expanded & Exponential Forms.doc Exponents Exponents on Perfect Squares.doc Graphing Linear Equations Graphing Linear Equations.doc Greatest Common Factor GCF.doc Intercepts Intercepts.doc Multiplication Multiplication.doc Multiplying Monomials and Binomials Multiplying Monomials and Binomials.doc Operations on Polynomials Operations on Polynomials.doc Opposites & Reciprocals Opposites and Reciprocals.doc Order of Operations Order of Operations.doc

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Points on the Coordinate Plane Points on the Plane.doc Positive, Negative, & Fraction Exponents Pos-Neg-Frac Exponents.doc Prime Factorization & Least Common Multiple Prime Factorization & LCM.doc Simplifying Expressions Simplifying Expressions.doc Slope Slope.doc Slopes from Graphs Slopes from Graphs.doc Solving One-Step Equations Solving One Step Equations.doc Square Roots Square Roots.doc Subtracting Integers Subtracting Integers.doc Translating Words to Algebra Translating Words to Algebra.doc Two-Step Inequalities Two-Step Inequalities.doc Verifying Points on the Line Verifying Points on the Line.doc Word Problems and Two-Step Equations Word Problems and Two-Step Equations.doc Word Problems with the Variable on Both Sides Word Problems with the Variable on Both Sides.doc Writing Equations Writing Equations.doc X-Y Tables x-y tables.doc

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Quizzette Quizzes Table of Contents

Add, Subtract, Multiply, & Divide Decimals Decimal Operations.doc Adding & Subtracting Integers Add and Subtract Integers.doc Adding Fractions Adding Fractions.doc Decimals & Fractions on the Number Line Decimals & Fractions on the Number Line.doc Equations Involving Combining Like Terms Equations with Combining Like Terms.doc Equations Involving Distribution Equations with Distribution.doc Evaluating Expressions Evaluating.doc Expanded and Exponential Forms Expanded & Exponential Forms.doc Exponents Exponents on Perfect Squares.doc Graphing Linear Equations Graphing Linear Equations.doc Greatest Common Factor GCF.doc Intercepts Intercepts.doc Multiplication Multiplication.doc Multiplying Monomials and Binomials Multiplying Monomials and Binomials.doc Operations on Polynomials Operations on Polynomials.doc Opposites & Reciprocals Opposites and Reciprocals.doc Order of Operations Order of Operations.doc

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Points on the Coordinate Plane Points on the Plane.doc Positive, Negative, & Fraction Exponents Pos-Neg-Frac Exponents.doc Prime Factorization & Least Common Multiple Prime Factorization & LCM.doc Simplifying Expressions Simplifying Expressions.doc Slope Slope.doc Slopes from Graphs Slopes from Graphs.doc Solving One-Step Equations Solving One Step Equations.doc Square Roots Square Roots.doc Subtracting Integers Subtracting Integers.doc Translating Words to Algebra Translating Words to Algebra.doc Two-Step Inequalities Two-Step Inequalities.doc Verifying Points on the Line Verifying Points on the Line.doc Word Problems and Two-Step Equations Word Problems and Two-Step Equations.doc Word Problems with the Variable on Both Sides Word Problems with the Variable on Both Sides.doc Writing Equations Writing Equations.doc X-Y Tables x-y tables.doc