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 Task
See attached document
Learning Expectations
WAL 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
Projects / Smartboard
Laptops
Studyisland.com
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
Allow student who are having trouble to work with partner
Rephrasing of information and questions
Utilize textbook for those having trouble / 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
Formative Assessments
Minute Papers
Homework
Stations
Menus
Projects
Oral questioning
Observation / Smartboard
Laptops
Interactive Games
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 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 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? / Small group instruction
Independent practice
Guided questioning
Small group instruction
Guided questioning / Exit Ticket
Journal Entry
Do Now
Formative Assessments
Minute Papers
Homework
Stations
Menus
Projects
Oral questioning
Observation / Starboard
PowerPoint:
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html
Function Rule Game: http://www.mathplayground.com/functionmachine.html
Starboard
PowerPoint
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). / Rephrasing of information and questions
Allow student who are having trouble to work with partner
Utilize textbook for those having trouble
Small group instruction / Students will have a homework sheet with multiple “absolute value” problems to complete at home Students will have a homework sheet with multiple “absolute value” problems to complete at home
Exit Ticket
Journal Entry
Do Now
Formative Assessments
Minute Papers
Homework
Stations
Menus
Projects
Oral questioning
Observation / Smartboard
Explicate square roots. and use a graphing calculator to explore square roots
Explain and demonstrate their understanding of cube roots / SWBAT share their explanations of square 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. / Rephrasing of information and questions
Allow student who are having trouble to work with partner
Utilize textbook for those having trouble
Small group instruction
Rephrasing of information and questions
Allow student who are having trouble to work with partner
Utilize textbook for those having trouble
Small group instruction / Students will use the laptops and calculators to 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
http://www.funbrain.com/cgi-bin/ttt.cgi?A1=s&A2=17&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
Journal Entry
Do Now
Formative Assessments
Minute Papers
Homework
Stations
Menus
Projects
Oral questioning
Observation / Smartboard
Laptops
Calculators
Squares & Roots Games
http://www.funbrain.com/cgi-bin/ttt.cgi?A1=s&A2=9&A3=0
http://www.funbrain.com/cgi-bin/ttt.cgi?A1=s&A2=17&A3=0
Cube Root Practice
http://www.ixl.com/math/ algebra-1/cube-roots
http://www.mathkinz.com/Exponent/CubeRoot.html
Smartboard
Laptops
Calculators
Perform all operations utilizing rational numbers
Change fractions into decimals and properly order a series of numbers from smallest to largest.
Combine rational numbers utilizing different signs with an accuracy of at least 85% / 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 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 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 with different signs. / Small Group Instruction
Allow student who are having trouble to work with partner
Rephrasing of information and questions
Utilize textbook for those having trouble
Allow student who are having trouble to work with partner
Rephrasing of information and questions
Utilize textbook for those having trouble
Small group instruction
Allow student who are having trouble to work with partner
I will also use color tiles to help the students visualize adding and subtracting rational numbers
Rephrasing of information and questions
Utilize textbook for those having trouble
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.
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)
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 with different signs.
Exit Ticket
Journal Entry
Do Now
Formative Assessments
Minute Papers
Homework
Stations
Menus
Projects
Oral questioning
Observation / Smartboard
Laptops
Interactive Games
Smartboard for video and practice
Laptops for studyIsland
Quiz on:
· Stem and leaf plots
· Scatter plots
· Completing all operations on rational numbers with both positive and negative signs
· Ordering numbers
· Utilizing the distributive property
Use properties to simplify expressions using order of operations (review associative, commutative, distributive, and additive/multiplicative inverse).
Write a numerical expression in simplest form utilizing the various laws and properties / SWBAT identify the various laws and 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/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 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 / Students will be called to the smart board to practice each of the 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
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 / Text: Pearson - Algebra 1 Common Core {1.2, 1.3, 1.4, 1.5, 1.6, 1.7}
Integer Operation Notes & Games
http://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 & Games
http://regentsprep.org/Regents/
math/ALGEBRA/AN1/propPrac.htm
http://www.math.com/school/
subject2/practice/S2U2L1/
S2U2L1Pract.html
http://www.quia.com/mc/
332021.html
Determine the mean, median mode and range of a group of numbers.
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
Construct stem and leaf plots to organize data
Interpret data from graphs and compare how each type of graph is used to show relationships
Find the measures of central tendency by collecting and interpreting sets of data with an accuracy of 17 out of 20.
Given data points, students will develop graphs depicting that data with 90% accuracy. / 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.
Introduction: Students will watch a short video on stem and leaf plots and correlations.
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.
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 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, 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 and asked to find the mean median and mode.