unit plan template - wilday middle...

Roselle (Algebra Honors) Curriculum

Unit Title: 1 Grade: 8

Essential Question(s) Enduring Understanding(s)How can you represent quantities, patterns, and relationships?

How are properties related to algebra?

You can use variables to represent quantities and to write algebraic expressions and equations.

The properties of real numbers describe relationships that are always true. You can use them to rewrite expressions.

Common Core Standards, 2010

A.SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

8.NS.2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Summative Assessment TaskSee attached document

CAR © Bormann & Wright



Learning ExpectationsWAL To/That…

Activities/Instructional Procedures

Student Strategies/Modification/

Differentiation

Formative Assessments Technology Infusion/Resources

Classify numbers as natural, whole, and integers based upon properties for each and develop a rule for classifying rational and irrational numbers.

SWBAT define rational numbers (any integer, fraction or decimal that terminates or repeats) and irrational numbers (any integer, fraction or decimal that does not terminate or repeat).

Have students come to the Smartboard and determine whether a number is rational or irrational.

Rephrasing of information and questions

Allow student who are having trouble to work with partner

Utilize textbook for those having trouble

Small group instruction

Have students complete the Rational Numbers Lesson on Study Island scoring at least 7 correct out of 10 questions.

Have students work within their team to solve equations and determine if the answer is a rational or irrational number.

Exit Ticket

Journal Entry

Do Now

Formative Assessments

Minute Papers

Homework

Stations

Menus

Smartboard

Laptops

Studyisland.com




Projects

Perform all operations utilizing rational numbers

SWBAT take words and represent them with numbers and letters (variables).

Students will be called to the Smartboard to practice this new skill.

SWBAT complete worksheets and show their ability to turn words into algebraic expressions.

Small Group Instruction




Students will be asked to design their own word problems and show an equation which can be used to solve the problem.

Exit Ticket

Journal Entry

Do Now


Minute Papers

Homework

Stations

Menus

Smartboard

Laptops

Interactive Games




Projects

Oral questioning

Observation

Describe a function as a rule which assigns one input exactly one output

Identify the set of ordered pairs consisting of an input and an output

Determine initial rate of change and initial value of a function by reading a table

Identify the set of ordered pairs consisting of an input and an output

SWBAT develop algebraic expressions, equations, and open sentences

Group work: Each group will be given a math phrase in which they have to write an algebraic expression. Students will review their findings with the class.

Independent Practice: Students will rewrite equations using words to represent the equation. Then the students will write equations from information given in a table.

Journal Entry: How can


Independent practice

Guided questioning

Exit Ticket

Journal Entry

Do Now


Minute Papers

Homework

Stations

Menus

Projects

Oral questioning

Observation

Starboard

PowerPoint:

http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html







you tell the difference between an expression and an equation? Give an example of each.

Introduction: Students will be given a function table and scenario in which they must decide what the function rule is.

Students will then be presented with the terms, definitions, and examples from the section. Students will practice examples individually as well as a class before doing group work.

Group Work: Students will discover the function rules, domain, and ranges


Guided questioning

Function Rule Game: http://www.mathplayground.com/functionmachine.html

Starboard

PowerPoint


http://www.mathplayground.com/functionmachine.html





from given tables presented on the starboard. They will then be asked to expand the table adding additional inputs.

SWBAT create function tables from given function rules and create their own inputs so that they can discover the ranges of the function. They will then be asked to try and graph their data and explain what it represents.

Journal Entry: How could a function table help you if you owned your own business?

Utilize a number line to define absolute value and find the absolute value of numbers.

SWBAT discuss absolute numbers (shows the distance from 0 on a number line).


Allow student who are

Students will have a homework sheet with

multiple “absolute value” problems to complete at

Smartboard




having trouble to work with partner



home Students will have a homework sheet with

multiple “absolute value” problems to complete at

home

Exit Ticket

Journal Entry

Do Now


Minute Papers

Homework

Stations

Menus

Projects

Oral questioning

Observation

Explicate square roots. and use a graphing

SWBAT share their explanations of square


Students will use the laptops and calculators to

Smartboard




calculator to explore square roots

Explain and demonstrate their understanding of cube roots

roots and their examples.

SWBAT discuss positive and negative square roots, rational and irrational square roots. They will also learn how to estimate square roots and how to approximate square roots using a calculator.

SWBAT recognize cube roots and practice doing cube roots on the Smartboard with the assistance of other students and the teacher. They will learn perfect and non-perfect cubes and negative cubes and will also learn how to estimate cube roots and how to approximate square roots using a calculator.

SWBAT find the cube and cube root of a number by completing a worksheet.








compete in games using square roots and exponents at the following websites:

http://www.funbrain.com/cgi-bin/ttt.cgi?A1=s&A2=9&A3=0


Exit Ticket: Students will explain square roots in their own words.

Students will complete a worksheet on cubes and cube roots with 85% accuracy.

Exit Ticket

Laptops

Calculators

Squares & Roots Games



Cube Root Practice

http://www.ixl.com/math/ algebra-1/cube-roots

http://www.mathkinz.com/


http://www.mathkinz.com/Exponent/CubeRoot.html
















Journal Entry

Do Now


Minute Papers

Homework

Stations

Menus

Projects

Oral questioning

Observation

Exponent/CubeRoot.html

Smartboard

Laptops

Calculators

Perform all operations utilizing rational numbers

Lesson:

Teacher will introduce the concepts of variables, equations and algebraic expressions. Students will begin learning how to take words and represent them with numbers and letters (variables).





Students will be asked to design their own word problems and show an equation which can be used to solve the problem.

Smartboard

Laptops

Interactive Games





Change fractions into decimals and properly order a series of numbers from smallest to largest.

Students will be called to the smart board to practice this new skill.

Students will complete worksheets and to show their ability to turn words into algebraic expressions.

Lesson (30 minutes):

SWBAT compare and order numbers which include both fractions and decimals. SWBAT convert the fractions to decimals so that the numbers can be compared properly. SWBAT compare and order rational numbers when negative numbers are included in the





Study Island Assessment: Students will be going on Study island and completing 30 problems and will be expected to achieve an 80% or better. (34 minutes)

Smartboard for video and practice

Laptops for studyIsland




Combine rational numbers utilizing different signs with an accuracy of at least 85%

comparison.

Students will be going on Study island and completing 30 problems and will be expected to achieve an 80% or better.

Lesson:

SWBAT work with rational numbers with different signs and explain the impact those signs have on the outcome of the answer.

Students will complete worksheets practicing the skills they learned.

Exit Ticket: students will describe in their own words how to add and subtract rational numbers


I will also use color tiles to help the students visualize adding and subtracting rational numbers

We will watch a video on adding and subtracting with different signs:

http://www.youtube.com/watch?v=UaKu-9G_dD4

Exit Ticket: Students will describe in their own words how to add and subtract rational numbers

Quiz on:

Stem and leaf plots

Scatter plots Completing all

operations on rational numbers with both positive and negative







with different signs.Rephrasing of information and questions



with different signs.

Exit Ticket

Journal Entry

Do Now


Minute Papers

Homework

Stations

Menus

Projects

Oral questioning

Observation

signs Ordering

numbers Utilizing the

distributive property

Use properties to simplify expressions using order of operations (review

SWBAT identify the various laws and

Students will be called to the smart board to practice each of the

Text: Pearson - Algebra 1 Common Core {1.2, 1.3, 1.4, 1.5, 1.6, 1.7}




associative, commutative, distributive, and additive/multiplicative inverse).

Write a numerical expression in simplest form utilizing the various laws and properties

properties of math

Commutative Law of Addition:

http://www.adaptedmind.com/v.php?vId=43

Show why the Commutative Law does not work for subtraction.

Associative Law of addition: http://www.adaptedmind.com/v.php?vId=3

Commutative Law of Multiplication: http://www.adaptedmind.com/v.php?vId=49

Associative Law of Multiplication:

http://www.adaptedmind.com/

properties as they are explained by the teacher.

Students will then practice using each of these laws on a worksheet.

Teacher will have students come to the Smartboard and practice PEMDAS problems on the Khan Academy website

Students will then complete handouts with multiple PEMDAS problems.

Students will then complete problems which require them to add and subtract negative numbers at:

http://www.mathopolis.com/questions/a.php?id=1981&ansno=8456

Integer Operation Notes & Gameshttp://www.mathsisfun.com/positive-negative-integers.html

http://www.funbrain.com/funbrain/cgi-bin/nl.cgi?A1=a&A2=4&A11=1&A12=1

http://www.math-play.com/integers-game.html

Properties Practice & Gameshttp://regentsprep.org/Regents/math/ALGEBRA/AN1/propPrac.htm

http://www.math.com/school/subject2/practice/S2U2L1/S2U2L1Pract.html



















v.php?vId=50

Identity Law of Addition:

http://mathforum.org/dr.math/faq/faq.property.glossary.html

Inverse Property of Addition:

http://www.khanacademy.org/math/arithmetic/number-properties/v/inverse-property-of-addition

Inverse Property of Multiplication:

http://www.khanacademy.org/math/arithmetic/number-properties/v/inverse-property-of-multiplication

Distributive Property of

Students will attempt to get 20 problems correct on the following site which utilizes a number line to practice the adding and subtracting of positive and negative numbers:

http://www.funbrain.com/cgi-bin/nl.cgi?A1=c&A2=3&A3=-2&A4=[-2][0][2][0]&A11=7&A12=7

http://www.quia.com/mc/332021.html


http://www.funbrain.com/cgi-bin/nl.cgi?A1=c&A2=3&A3=-2&A4=%5B-2%5D%5B0%5D%5B2%5D%5B0%5D&A11=7&A12=7












Multiplication/Addition:

http://www.khanacademy.org/math/arithmetic/number-properties/v/the-distributive-property

Distributive Property of Multiplication and Subtraction:

http://www.khanacademy.org/math/arithmetic/number-properties/v/the-distributive-property-2

Distributive Property with real numbers:

http://www.khanacademy.org/math/arithmetic/number-properties/v/distributive-property-example-1













The symmetric Property:

http://www.mathwords.com/s/symmetric_property.htm

The transitive Property:

http://www.mathwords.com/t/transitive_property.htm

Determine the mean, median mode and range of a group of numbers.

Lesson : Teacher will review the concepts of mean, median, mode and range.

Students will be called to the smart board to practice each of the properties as they are explained by the teacher.

Students will be given a worksheet to complete on these concepts.

Small group Instruction Students will be asked to explain in their own words the concepts of mean, median, mode and range and complete a worksheet checking their understanding.

Smartboard

Laptops

Calculators







Construct a scatter plot and describe the relationship between the variables

Describe patterns from a scatter plot such as clustering, outliers, linear and nonlinear association

Introduction: Students will watch a short video on stem and leaf plots and correlations.

Independent Instruction

Modified data

Guided questioning





Review Sheet

Exit Ticket

Oral Questioning

Exit Ticket

Graph Presentations

Video:

http://www.brightstorm.com/math/algebra/introduction-to-statistics/scatterplots-and-correlations/

Starboard

PowerPoint

Starboard

PowerPoint







Construct stem and leaf plots to organize data

Interpret data from graphs and compare how each type of graph is used to show relationships

Will then view a PowerPoint created by the teacher to reinforce the ideas and concepts from the video. Students will work on a scatter plot as a class and discover the correlations.

Group Work: Students will be given sets of data and asked to create stem and leaf plots to represent it. The students will review their findings with the rest of the class to discuss what the plots represent.



Guided questioning

Students will be given varying amounts of data depending on ability.


Guided questioning

Starboard

PowerPoint




Independent Practice: Students will be given several names of data sets and asked to decide on whether they would get a positive, negative, or no correlation between them.

Introduction: Students will be given a set of data and asked to put them in order from least to greatest.

We will then view a PowerPoint on what the

measures of central tendency are and how to compute them. After the students will go back to their list of ordered data

and asked to find the mean median and mode.

Group work:Students will be given the

daily temperatures in

Smartboard

Laptops

Interactive Games




Roselle for the past month and asked to find the measures of central

tendency. Results will be discussed as a class to see

how they compare.

Journal Entry: A mean of a set of data is 7.8, the mode is 6.6, and the median is 6.8. What is the least possible number of data values

Introduction:

Students will be presented with different types of graphs. This will show them what are graphs are best to interpret different kinds of data.

Students will work in groups and be given different types of data that they have to turn into various types of graphs. They will use graph paper,


Review Sheet

Exit Ticket




Find the measures of central tendency by collecting and interpreting sets of data with an accuracy of 17 out of 20.

construction paper, and computers to create their graphs.

Journal Entry: If you took a survey of all of the schools in the state what would you expect the relationship to be between the number of students and the number of teachers in each school to be?

We will then view a PowerPoint on what the measures of central tendency are and how to compute them. After the students will go back to their list of ordered data


Guided questioning



Review Sheet

Exit Ticket

Oral Questioning

Exit Ticket




Given data points, students will develop graphs depicting that data with 90% accuracy.

and asked to find the mean median and mode.

Group work: Students will be given the daily temperatures in Roselle for the past month and asked to find the measures of central tendency. Results will be discussed as a class to see how they compare.

Lesson (30 minutes)

Teacher will introduce the concepts of graphing on the coordinate plane. Students will be introduced to ordered pairs, quadrants, coordinates and midpoints.

Video on graphing





Utilize textbook for those

Graph Presentations

Students will practice these skills at the following two websites:

http://www.khanacademy.org/math/algebra/algebra-functions/e/graphing_points_2

Students will practice these skills at the following two websites:

http://www.khanacademy.org/math/algebra/algebra-functions/e/









coordinates:

http://www.khanacademy.org/math/algebra/algebra-functions/e/graphing_points

Students will practice these skills at the following two websites: (34 minutes)



having trouble

Small group instruction http://www.khanacademy.org/math/algebra/algebra-functions/e/graphing_points

graphing_points_2





















Students will be asked to estimate the midpoints for line segments and then test their estimate by applying the correct formula with 90% accuracy.

Lesson (30 minutes):

Teacher will introduce the concept of finding midpoints of a line segment. They will be shown the logic behind finding the midpoint and then be taught the formula to help them find the exact midpoint.

They will also watch a video of midpoints to help them visually understand what they are doing. The video is at:

http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/midpoint-formula

For 34 minutes, Students will practice finding the





Students will practice finding the midpoints of various line segments at:

http://www.khanacademy.org/math/algebra/pythagorean-theorem/e/midpoint_formula

Smartboard

Laptops

Interactive Games










midpoints of various line segments at:


Solve problems with variables utilizing the distributive property with an accuracy of at least 85%.

Lesson (30 minutes)

Teacher will discuss new vocabulary for expressions with variables, writing expressions and combining like terms.

Students will then work on problems practicing the distributive property. (25 minutes)

Exit Ticket: Students will





Exit Ticket: Students will explain in their own words combining like terms.

Smartboard for video and practice







Reason quantitatively and use units to solve problems by solving one and two step equations with an accuracy of 16 out of 20 on a worksheet.

explain in their own words combining like terms. (9

minutes)

Introduction (12 min)

http://www.montgomeryschoolsmd.org/departments/itv/MathDude/MD_Algebra1_1-2.shtm

The teacher will then demonstrate the process of solving a two-step equation. The students will learn that since we are performing the inverse to undo the operations we will perform all operations

Guided questioning

Teacher will work closely with students who require assistance

Peer tutoring

Oral Questioning

Observation

Exit Ticket

Homework


Smartboard for video

PowerPoint










in the opposite order from the order of operations (SADMEP…the opposite of PEMDAS)

Independent Practice (20 min): Students will be given several examples to solve. During this time the teacher will observe students work and assist any students that require additional help. We will review the answers and processes as a class.

Lesson (Part 2) (10 min): The teacher will put an example on the board of a real world scenario word problem that requires the students to create a two-step equation that they must then solve using the




Explain the reasoning involved in the process of solving equations by using the distributive property

same process as before.

Group Work (20 min): Students, in groups of two, will work on real world scenario word problems that must be turned into two-step equations and solve for the variable.

Exit Ticket (5 min): Students will solve a two-

step word problem to demonstrate their

understanding of the material.

Introduction (12 min): The students will be introduced to solving



Oral Questioning

solving multi-step equations by watching this video:

http://www.montgomeryschools






to solve multi-step equations with an accuracy of 8 out of 10 on a worksheet.

multi-step equations by watching this video:


Independent Practice (20 min):

Game to challenge them:

http://www.quia.com/rr/168572.html

Students will be given 3 multi-step equations to solve. They will need to use their knowledge of combining like terms as well as the distributive property in order to solve the problems. As the

Guided questioning

Peer Tutoring

Observation

Independent Practice

Exit Ticket

md.org/departments/itv/MathDude/MD_Algebra1_1-3.shtm

Game to challenge them:














students are working on their solutions the teacher will observe which students understand the material and ask them to assist any students who are struggling. The teacher will then ask three students to go to the board and show how they solved the problem explaining their work as they progress through the problem.

Group work (25 min):

Students will work in groups of four to problem solve five real world scenarios that require solving multi-step equations. As the groups are working the teacher will circulate around the room observing the




students work and asking guiding questions to any groups having trouble with the problems. Once the groups have completed the problems they will each be asked to present their solution to the class as a group explaining the steps they used to solve the problems.

Exit Ticket (5 min): Students will be given 1 multi-step problem to

solve demonstrating their understanding of solving these types of equations.

Utilize textbook for those Smartboard




Rearrange formulas to highlight and solve for a variable of interest by solving 4 out of 5 formulas on a worksheet.

Introduction (15 min): Students will be shown several formulas from the world of physical science including density, speed, and force. The class will then be asked how they could rewrite these formulas using inverse operations. (i.e. instead of solving for density being given the mass and volume, find the volume from being given the mass and density.)

Group Work (25 min) : Students will be given 2 formulas that they will need to rewrite in order to solve for each variable of interest. Once they have completed this step they will be given problems that require them to use

having trouble




Exit ticket

Formative assessment

Oral questioning

Observation

PowerPoint




their newly discovered formulas to solve.

Exit Ticket: Students will be given the formulas for

pressure and asked to rewrite it for each variable

of interest.Identify solutions to inequalities by writing and graphing them with an accuracy of 8 out of 10 on a worksheet.

Introduction (15 min): Students will be shown examples of inequalities and the process of writing inequalities and graphing the results. The teacher will then show the process of writing an inequality from a graph.

Whole Group (5-10 min):

The students will do examples as a whole group and we will review the examples as a class with students inputting

Large and small group instruction

Peer Tutoring

Homework

Exit Ticket

Smartboard

PowerPoint




their ideas and answers to help guide the whole classes understanding.

Independent practice (10-15 min): The students will be given 4 problems to try on their own. Two problems they will be asked to make a graph from a given inequality. The other two problems will have students write an inequality from a given graph. The problems will be reviewed as a whole class with selected students asked to show their results on the board and explain their reasoning.

Group Work (25 min): Students will be given five




Solve inequalities by using addition and subtraction as well as multiplication and division with an accuracy of 8 out of 10 on a worksheet.

real world scenarios in which they must write inequalities for and the graph. Each group will present their solutions to the class.

Exit Ticket (5 min): Students will be asked to demonstrate their understanding of graphing and writing inequalities.


Students will be shown this video to show how to solve inequalities by isolating a variable on one side of the inequality: http://www.montgomerys


One on One Instruction


Peer Tutoring

Homework

Exit Ticket this video to show how to solve inequalities by isolating a variable on one side of the inequality: http://www.montgomeryschoolsmd.org/departments/itv/MathDude/MD_Algebra1_1-4.shtm








choolsmd.org/departments/itv/MathDude/MD_Algebra1_1-4.shtm

The students should be able to make the connection between this process and how they solved one step equations involving addition and subtraction or multiplication and division.

The students will then be shown how to graph their answers.

Independent Practice (15 min): Students will be given 8 problems to complete that have a combination of addition






and subtraction problems. Some students will be asked to peer tutor other students during this practice in order to reinforce understanding.

Group Work (25 min): Students will work in groups of four to complete six real world problems that will require critical thinking and the ability to write and solve inequalities involving all of the operations. The groups will discuss their results as a class.

Exit Ticket (5 min): Students will be given four inequalities that need to be solved with each operation being




Solve multi-step inequalities by using deductive reasoning with an accuracy of 8 out of 10 on a worksheet.

represented.

Introduction (15 min): Students will be shown a PowerPoint that gives explanations and examples of how to perform a solution of an inequality that requires more than one step. A video may also be shown:

http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/v/multi-step-inequalities

Independent Practice (10 min): Students will be given two real world


One on One Instruction


Peer Tutoring

Homework

Exit Ticket

Smartboard for video or PowerPoint

How to perform a solution of an inequality that requires more than one step. A video may also be shown:











problems involving two-step inequalities. The students will review the solutions as a class, with every student being given the opportunity to input their ideas.

Group Practice (35 min): The students will work in groups of four during this practice. Each group will be required to create four real world word problems that involve inequalities. Two problems must have a multi-step inequality, and the other two must have either addition or subtraction and multiplication or division involved. Once the students have completed their word problems and found solutions they will distribute on word




Create graphs of inequalities using and or, by solving compound inequalities with an accuracy of 16 out of 20 on a worksheet

problem to every other group in the class. Each group will then try and solve the word problems, if possible. We will then discuss the problems as a class.

Exit Ticket (5 min): Multi-step inequality problem.

Introduction (15 min):

Students will be introduced to the idea of compound inequalities by being shown a PowerPoint created by the teacher outlining the process of understanding and graphing these inequalities. Students will

Groups will have varied levels of students

Peer Tutoring


Guided Questioning

Homework

Exit Ticket Smartboard

PowerPoint

Inequality Jeopardy Game:

http://www.superteachertools.com/jeopardyx/jeopardy-review-game.php?gamefile=1294159199







also learn how to solve compound inequalities by isolating the variable.

Independent Practice (15 min): Students will be given problems in which they will need to write and graph a compound inequality when given a situation. Some students will be asked to peer tutor while others are asked to present their answers on the board.

Group Work (30 min): Students will be given five graphs that they need to interpret and turn into compound inequalities. The teacher will watch each group ensuring that all students are




Reason quantitatively and use units to solve problems by solving one and two step equations with an accuracy of 16 out of 20 on a worksheet

participating in the activity. Each group will have the opportunity to present their answers to the class and explain their reasoning.

The students will then remain in their groups in order to play a jeopardy review game on the Starboard.

Exit Ticket (5 min): Compound Inequalities


Power Point Presentation 11-2 solving multi-step equations

Guided questioning

Teacher will work closely with students who require assistance

Peer tutoring

Oral Questioning

Observation

Exit Ticket

Homework


PowerPoint

Power Point Presentation 11-2 solving multi-step equations






The teacher will then demonstrate the process of solving a two-step equation. The students will learn that since we are performing the inverse to undo the operations we will perform all operations in the opposite order from the order of operations (SADMEP…the opposite of PEMDAS)

Independent Practice (20 min): Students will be given several examples to solve. During this time the teacher will observe students work and assist any students that require additional help. We will review the answers and processes as a class.




Lesson (Part 2) (10 min): The teacher will put an example on the board of a real world scenario word problem that requires the students to create a two-step equation that they must then solve using the same process as before.

Group Work (20 min): Students, in groups of two, will work on real world scenario word problems that must be turned into two-step equations and solve for the variable.

Exit Ticket (5 min): Students will solve a two-

step word problem to demonstrate their




Create real-world word problems utilizing their prior knowledge of inequalities with an accuracy of 4 out of 5

understanding of the material

Group Practice (35 min): Students will work in groups of two in order to create five real world word problems that involve inequalities. Three of the problems must have a multi-step inequality, and the other two must have either addition or subtraction and multiplication or division involved. I will leave exemplars for the students to model their work after. All work will be collected and graded.

Peer Tutoring


Exit Ticket

Homework

Quiz


PowerPoint


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