Unit Plan Template - Wilday Middle Schoolwilday.roselleschools.org/UserFiles/Servers/Server_31533… · Web viewStudents will be asked to design their own word problems and show
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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.
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.
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.
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
Small group instruction
Guided questioning
Function Rule Game: 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).
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.
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
compete in games using square roots and exponents at the following websites:
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).
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.
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
Allow student who are having trouble to work with partner
Rephrasing of information and questions
Utilize textbook for those having trouble
Small group instruction
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)
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:
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.
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.
Small group instruction
Independent Instruction
Guided questioning
Students will be given varying amounts of data depending on ability.
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
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
Independent Instruction
Guided questioning
Allow student who are having trouble to work with partner
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 having trouble
Small group instruction
Allow student who are having trouble to work with partner
Rephrasing of information and questions
Utilize textbook for those
Graph Presentations
Students will practice these skills at the following two websites:
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:
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
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
Small group instruction
Independent Instruction
Oral Questioning
solving multi-step equations by watching this video:
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
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.
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
Rephrasing of information and questions
Allow student who are having trouble to work with partner
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
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.
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.
Introduction (12 min)
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
Independent Practice
One on One Instruction
Small Group 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
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:
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.
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
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
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.
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.