comprehensive unit plan

7/25/2019 Comprehensive Unit Plan

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EDUC 232 Unit Plan Assignment

Anneke Mundel, Fall 2015

Purpose and Developmental Appropriateness:

This Foundations of Algebra unit aims to provide tenth grade (or tenth grade equivalent) students with a solid basis in algebra. It explores

the meaning and relevance of algebra in everyday contexts; in other words, the intent of the unit is to demystify algebra and help studentssee algebra as practical, not merely as an academic pursuit. This unit also provides students with fundamental algebraic tools: anunderstanding of critical vocabulary, an ability to translate between symbols and words, and a capacity to make sense of algebraicexpressions and equations.

As Larson and Keiper (2013) remind us, adolescent learners are growing, developing, and changing at a very rapid pace [O]pportunitiesabound when teaching adolescents because of their newly developing cognitive skills, social interactions, and awareness of the worldaround them (p.4). This unit speaks to tenth graders unique (though varied) developmental needs: For example, the unit deals withsomewhat abstract math concepts (addressing youths growing cognitive abilities), but seeks to ground these concepts in everydayapplications. Similarly, the unit provides youth opportunities for positive social interactions (ex/small group work, partner work), but these

are facilitated by the teachers presence and modeling. Likewise, the units performance assessment provides students the opportunity todo independent work and internet-based research (given youths desire for choice and technological interest / savvy), but the suggestedtimetable, instructor moderation, and potential accommodations help provide the structure that youth may need to be successful.

Enduring Understandings & Essential Questions:

This unit revolves around three enduring understandings and related essential questions, namely that algebra: (a) has real-worldapplicability, (b) is its own special language of sorts, and (c) has problem-solving at its heart. The first understanding is most clearlyaddressed by the summative performance assessment (Real Life Algebra poster/brochure), but is interwoven throughout the unit(addressed on the pre-graffiti board, noted in running student logs, reinforced by home-inspired expressions and a video-short onequations that have impacted the world, integrated into word problems throughout, and revisited in the post-graffiti board). The secondunderstanding, namely of algebras unique language, is the central subject of the lessons on Days 1 through 8. Specifically, thisunderstanding is (a) explored / taught through a mix of direct instruction (PPTs with exercises and worksheets that move through severalcycles of the Gradual Release of Responsibility model) and group work (gallery walk, rotation activity, etc.) and (b) compiled into theKey Algebra Terms graphic organizer. The third understanding - about algebras problem-solving capacity - is somewhat implicit in thefirst part of the unit and would likely be explicit within many students performance assessments (for example: We use algebra when wetry to solve ..). Finally, in the summative unit test, all three understandings and questions are brought to the fore.

Connection Between Learning Goals and Assessments:

In order to address the many specific learning objectives and standards of this unit, a wide variety of formative and summative assessmentsare used. The formative assessments, most of which are ungraded though checked, provide students and the teacher an opportunity todetermine if the planned curriculum is being learned and to adjust instruction if needed. For example: the Comparing Expressions and


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Equations graphic organizer used as an exit assessment on Day 4 clarifies if students understand these key concepts. The review plannedfor the start of Day 5 would then address any noted gaps in understanding. Similarly, the Placemat Equations exercise at the end of Day 6ensures students understand the fundamentals of solving multi-step equations (peers check work and teacher re-checks); were students toshow gaps here, the teacher could potentially adjust the bellringer activity of Day 7 and re-teach elements needed before proceeding withmore complex multi-step equations.

In addition to a variety of formative assessments, there are two summative assessments. The unit test (provided below) evaluates studentsunderstanding of all of the stated objectives (SWBAT) in a rather traditional format. However, the performance assessment is necessary aswell: It both provides the opportunity for student-directed exploration and the having of wonderful ideas and asks students to honetheir peer and self-assessment skills (as they use a checklist and rubric to peer- and self-assess their posters/brochures). Furthermore, itevaluates students grasp of the central understanding of algebras real world applicability, of the objective that SWBAT cite applicationsof algebra in their everyday lives, and of students achievement of the stated 21stCentury Employability skills.

Differentiation:

While it is perhaps not apparent in the pacing calendar, this unit takes diverse learners needs into account a number of ways:

First, this unit provides instruction using diverse methods: it integrates teacher directed instruction, visuals (video-clip, PPT), hands-onexercises (manipulatives in the Hands-On Equations kit), movement (gallery walk, rotation activity), technology (internet-basedresearch and potentially iPads with the Hands-On Equations app), creative expression (poster/brochure performance assessment),whole class discussion, peer-to-peer instruction (Placemat Equations, peer checklist of performance assessment), and so on. As such,this unit seeks to address students varied learning styles and preferences, as well as their multiple intelligences.

Second, this unit provides several aids to students: for example, all students are given a Key Algebra Terms graphic organizer(graphic organizers are known to be helpful to a variety of learners with special needs and ELLs) and receive prompts to add terms.Also, all students are given ample opportunity for review of key concepts (repeated learning is, again, known to be beneficial tolearners with special needs as well as ELLs).

Third, this unit provides for possible accommodations: In the Gallery Walk, questions are color-coded by three levels of difficulty, and

students are allowed to choose the appropriate tier for them. In the Performance Assessment, students who struggle withindependent research (for example: students with particular learning disabilities, vision disabilities, or attention-deficit) may be offeredprint-based materials or pre-screened and selected websites.

Fourth, the many formative assessments in this unit provide the teacher with insights into individual students strengths, interests,weaknesses; as such, the teacher could adjust instruction as needed. As Larson and Keiper (2013) remind us, the practice ofdifferentiating instruction requires flexibility on the part of the teacher to adjust lesson planning to the students rather than requiringstudents to adjust to the curriculum (p.15). Thus, it is in the implementation of this unit that most differentiation would actually takeplace!!


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Unit Title: Foundations of Algebra (Meaning, Expressions, and Equations)

Grade level: 10th

Length of unit: 13+ class periods; almost 3 weeks.

Stage 1 Desired Results

Meaning

Enduring Understandings/Generalizations:

Algebra has real-world applicability.

Algebra is its own language and involves translation betweensymbols and words.

The aim in algebraic problem-solving is to turn unclearrelationships of unknowns and unfamiliars into knowns and

familiars by means of equivalent statements.

Essential Questions:

How can algebra, broadly conceived, help us in our everyday lives?

What is the relationship between mathematical symbols andwords?

Why and how do we use algebraic equations?

Knowledge & Skills Acquisition

Learning Goals: (e.g., Iowa/Common Core standards.)

Iowa Core Math (9th grade)

HSA.REI.B.3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Iowa Core Math (10th

grade)HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context.!

! Interpret parts of an expression, such as terms, factors, and coefficients.

! Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product ofP and a factor not depending on P.

HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. For example, see x4 y4 as (x2)2 (y2)2, thus recognizing it as a difference

of squares that can be factored as (x2 y2)(x2 + y2).

HSA.SSE.B.3


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Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. !

HSA.APR.D.7

(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction,

multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions,and simple rational and exponential functions.

HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels

and scales.

HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or

nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different

foods.

HSA.REI.A.1

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from theassumption that the original equation has a solution. Construct a viable argument to justify a solution method.

HSA.REI.A.2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Iowa Core 21stCentury Skills/Technological Literacy (10th grade)

21.912.TL.4

Essential Concept and/or Skill: Demonstrate critical thinking skills using appropriate tools and resources to plan and conduct research, manage

projects, solve problems and make informed decisions.

Identify and define authentic, realworld problems and significant questions for investigation.

!

Students identify global issues and analyze capabilities and limitations of current and emerging technology resources in order to developand refine investigatible questions.

Plan and manage activities to develop a solution or complete a project.

! Students effectively use multiple technologies and resources to develop a systematic plan for conducting research in order to assesspotential sustainable solutions, or to develop a complete product to demonstrate knowledge and skills.

Collect and analyze data to identify trends, solutions, or make informed decisions.

! Students use technology to gather appropriate data, analyze its application to a task, and assess its effectiveness in order to design,develop, and test possible solutions that assist students in making decisions.

Use multiple processes and diverse perspectives to explore alternative solutions.

Students use multiple perspectives to analyze and evaluate information from a variety of technological resources. Students critically assess


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numerous solutions and investigate them from differing viewpoints.

Iowa Core 21stCentury Skills / Employability (10th)

21.912.ES.1

Essential Concept and/or Skill: Communicate and work productively with others, incorporating different perspectives and cross cultural

understanding, to increase innovation and the quality of work. Work appropriately and productively with others

! Set goals

! Effectively communicate with group and stakeholders

! Demonstrate respectful behavior to group member ideas and opinions

! Manage and resolve conflict when appropriate

! Lead or support when appropriate

! Determine peoples strengths and assign roles accordingly

! Contribute to a team by sharing information and expertise

! Agree to disagree in a respectful manner in a group dynamic

!

Collaborate effectively with other teams/team members toward a common goal! Recognize own and others good effortsUse different perspectives to increase innovation and the quality of work

! Gather input from all group members

! Capitalize on the diversity of group members

! Accept and provide feedback in a constructive and considerate manner

Use all the appropriate principles of communication effectively

! Listen to understand and appreciate the points of view of others

! Listen for comprehension

! Listen for decision making

!

Process information in order to make an informed decision! Ask appropriate questions in seeking clarification

! Read, understand and create information presented in a variety of forms (e.g. words, charts, graphs, diagrams)

! Follow directions

! Express thoughts and ideas clearly and succinctly

! Use appropriate technology to communicateUse appropriate channels of communication (written, verbal, technical, visual)

21.912.ES.4

Essential Concept and/or Skill: Demonstrate initiative and selfdirection through high achievement and lifelong learning while exploring the ways


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individual talents and skills can be used for productive outcomes in personal and professional life.

Perform work without oversight

! Assesses the situation and identify the priority/necessary actions to be taken

! Understand the value of the task in relationship to greater goal

! Understand that incomplete work even if excellentis a failure

!

Model selfconfidence! Know how to find and evaluate appropriate resources

! Implement solutions

! Demonstrate commitment to self/group/societyUse time efficiently to manage workload

! Segment task into logical steps with appropriate estimates of time

! Build a timeline to facilitate completion of the task

! Prioritize steps in proper orderAssess ones own mastery of skills

! Understand the task

!

Identify the depth and breadth of knowledge to be successful at a task! Identify and utilize appropriate measure of knowledge

Set and achieve high standards and goals

! Understand incremental steps for acquiring goals

! Create a written plan

! Set realistic goals that match aptitudes

! Engage in activities to improve skills that are relative to goals

! Demonstrate core values

! Constructively evaluate progress and takes corrective action when necessaryEngage in effective problem solving process

!

Transfer learning from one domain to another! Identify partners and resources germane to the situation

! Evaluate and select the best resources in context of the problem, and allocates them appropriately

! Identify root cause of problem

! Detail a course of action in writing with sequence of steps involvedImplement a solution and makes adjustments when there is need/opportunity for improvement


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Students will know

Key algebraic concepts:

o Variable / unknowno

Expressiono Equationo Like termso Simplifyo Evaluateo Isolate variableso

Distributive propertyo

Inverse operations

The symbolic meaning / equivalent of words signifying

unknowns, the equal sign, parentheses, and operations(addition, subtraction, multiplication, and division):o

Unknowns = a numbero Equal sign = is; is equal to; is the same aso Addition = sum; add; plus; more thano

Subtraction = difference; decreased; minus; less thano

Multiplication = product; times; multipliedo

Division = quotient; shared equally; divided

How to combine like terms

How to evaluate expressions and equations

How to solve one-step equations

How to solve multi-step equations

How to apply algebra to solve word problems

The importance of solving algebraic equations

Students will be able to

Define algebra

Cite applications of algebra in their everyday lives.

Render real life problems into algebraic expressions.

Translate real life problems into algebraic equations and solve.

Translate words into algebraic expressions and expressions intowords.

Translate words into algebraic equations (one-step and multistep)using addition, subtraction, multiplication, and division.

Combine like terms (letters and numbers) to simplify anexpression or equation.

Evaluate expressions and equations by substituting given values forvariables and solving

Solve one-step equations by applying inverse operations.

Solve multi-step equations by simplifying (combining like terms,

using the distributive property) and applying inverse operations.

Critically assess word problems and render these into solvablealgebraic equations.


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systematically.

Resources/Materials:

Worksheets (from New Readers, SV, Contemporary, etc.)

Calculators

Instructor Powerpoints

Poster paper for graffiti boards Pretest

Handout and rubric on performance assessment

Key Algebra Terms graphic organizer

Mini-quiz on Algebraic Expressions

Video: 10 equations that changed the world (linked in PPT; available athttp://www.intmath.com/blog/videos/friday-math-movie-10-equations-that-changed-the-world-10093)

Hands-on Equations kit (from borenson.com) & iPads with Hands-on Equations app

Placemats with 4 multi-step equations each

Gallery walk components: student answer sheets, 10 stations, teacher answer-keys in plastic protectors Unit test

Computers (for student research)

Various texts sharing real-world / everyday algebra applications &/or list of appropriate, pre-screened websites

Editors checklist for peer review of performance assessment

Poster board

Stage 2 Evidence (Assessment)

Types of assessment: Selected-Response (tests, quizzes); Personal Communication (interview, oral exam,

discussion); Written Response (short constructed response questions, entrance/exit slips, essays); PerformanceAssessment (role-play, Simulation, labs, dramatization)


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Diagnostic Assessment:

Short pre-test: Students will work on a short test that covers key unit concepts (translating words into expressions and vice-versa,simplifying expressions, solving one-step equations, solving multi-step equations). The purpose of this pre-test is to ascertainindividual students content knowledge (of algebraic expressions and equations) and tailor the unit accordingly.

Graffiti Boards (Pre/Post): Students will write (and potentially draw) responses on two graffiti boards prior to beginning the unit.

Graffiti Board prompts: Board one:What is algebra? What does it look like? Board two:What are some real-world uses of algebra?The purpose of this activity is to determine students prior knowledge of algebra and of authentic applications of algebra. Thisexercise will be repeated at the end of the unit to determine the class learning gains.

Formative Assessment (Assessment forLearning):

Worksheets (some submitted, some self-checked, some peer-checked)

Class discussions of unit content

Teacher observation of student work

Quick Thumb It checks for understanding (from Gregory & Chapman, p.68)

Graphic organizers of key terms and definitions

Mini-quiz on expressions (Day 3) Exit Comparing graphic organizer (from Gregory & Chapman, p.136) (Day 4)

Placemat equations (Day 6)

Rotation activity on translation (Day 7)

Gallery Walk work, tiered and color-coded (Day 8)

Drafts of brochure / poster text

Peer review checklists

Running logs of real-life algebra applications (in student notebooks)Summative Assessment (Assessment ofLearning):

Post-test: Students will complete a paper-pencil test on key unit concepts (translating words into expressions and vice-versa,

simplifying expressions, solving one-step equations, solving multi-step equations, solving word problems with algebra). They will beasked to show their work.

Real-World Algebra brochure or poster: Students will create a brochure or poster with text and graphics illustrating one ormultiple real-world algebra applications. The express goal is to convince other algebra-skeptical-students of algebras applicability.While students will work with peers during the research, creation, and review processes, each student will be responsible for theirown brochure or poster to be submitted for assessment and then displayed in the classroom. Students also will be responsible forcompleting a self-assessment of their project using a teacher-provided rubric.


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Stage 3 Learning Plan

*see Pacing Calendar below.


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Pre Graffiti Boards

(students may begin as they

enter):Board one:What is

algebra? What does it looklike?Board two:What aresome real-world uses of

algebra?

Discussion of What is

algebra? board & Brief

Introduction of Unit (PPT

with essential questions andmain objectives)

Introduction of Real-

World Algebra

Performance Assessment:

provide handout and rubric/ Encourage students tokeep alogof all real-world

applications they encounterDays 18.

Pre-Test (checked, notgraded): Students work onthis independently. Collect

and review prior to nextday. Students whocomplete early may begininternet research on Real-World Algebra project.

Bellringer: How might you

write projected expressionsin letters and symbols?Discussion of bellringer.

Distribution of graphic

organizer, Key Algebra

Terms

Direct-instruction (PPT)

accompanied byworksheets completedthrough guided,

collaborative, andindependent work:Variables & Expressions

What are variables

and expressions?

How do we translate

between words &letters/symbols?

Homework assignment:Students should come up

with two expressions in

words re: something intheir homes (i.e real-world

scenarios).

Review of homework:

Pairs of students swaphome-made expressions

and translate these intoalgebraic expressions.Discuss whole class.

Direct-instruction(PPT)accompanied byworksheets completed

through guided,collaborative, andindependent work:Simplifying and

Evaluating Expressions

What are like-terms?

How do we simplify?

How do we evaluate?

* Prompt students to addvocab words to KeyAlgebra Terms graphic

organizer.

Mini-quiz on expressions.

Includes quick write at

bottom: what is stillunclear?

Show video 10 equations

that changed the world.

Think-pair-share:(1)Which of these equationshad you heard of? Where?

& (2) How do equationsdiffer from expressions?Whole-class discussionof

topics.

Direct-instruction(PPTwith worksheets, asspecified in Day 2): One-step Equations - Part 1

What are equations?

How do we translate

between words &letters/symbols?

How do we solve

addition and

subtraction equationsthrough inverseoperations?

* Prompt students to addvocab words to organizer.

Exit Comparing

Graphic Organizer:

Define and considerdifferences betweenexpressions and equations.

Review:Key concepts

from Day 4

Direct-instruction (PPT

with worksheets): One-

step Equations Part 2

How do we solvemultiplication anddivision equationsthrough inverse

operations?Hands-on Equations

Activity: After teacherdemo, students work insmall groups to solve one-

step equations usingmanipulatives and balancescale in the Hands-on

Equations kit (fromborenson.com). Studentswho need independent

work may use the iPad appof this activity.

Whole class debriefing of

activity


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Bellringer:The local

library charges $0.10 percopy. You have to make150 copies of a flyer on the

school Carnival Night.How much will it cost?Discuss whole class/

review of one-step

equations and inverse

operations.


with worksheets) on

Multi-step Equations -

Part 1:

What are multi-stepequations?

How do we translatethese from words and

back?

How do we solve? (add

or subtract first, isolate

the variable)

Placemat Equations:

Students are divided intogroups of 4 and given oneplacemat with 4 multi-

step equations. Eachstudent completes oneassigned equation. Others

check, make corrections asneeded, then have teachercheck before exit.

Bellringer Rotation

Activity:Go to differentstations and translate givenmultistep equations into

words.Students must try touse different words thanthose used by previous

students. They may starwords that seemunclear/inaccurate for later

discussion.Discussion whole class /

review of words

representing symbols.


with worksheets) on

Multi-step Equations -

Part 2:

How do we deal withseparated unknowns?(combine whole

numbers and variables,then solve)

How do we deal withparentheses? (vocab:the distributive

property)* Prompt students to addvocab words to Key

Algebra Terms graphicorganizer.

Independent worksheet:Students submit forevaluation.

Return Reviewed

Worksheets / Review of

Two-Step Equations

Concepts

Expressions & Equations

Gallery Walk Activity:

Students are given ananswer sheet with 10spaces. They rotate around

the room with a partner,choosing one of 3 tiered

problems available at 10different stations (mix of

expressions, one-step and

multi-step equations,symbolic and word

problems; color-coded bytier). Students are taskedwith completing the most

challenging questions theycan.Self-assessment:Studentsuse a teacher-providedanswer key to check their

own gallery walk work,

using a different color pen.Gallery walk work is

submitted (for teacherreview) before exit.

Independent Study:

Remind students to reviewmaterials to prepare for unittest.

Summative Assessment:

Unit Test

Begin/continue research

on Real-World AlgebraPerformance Assessment

when done with test.

Teacher may need toreview expectations,instructions (from Day 1)

and prompt students toreview their running logfrom Days 1-8.

Performance Assessment

Work Day. Students workin the computer lab onfinding real-world algebra

examples for their poster /brochure.

(Possible accommodation :students may be given anarray of teacher-provided

texts, articles, etc. so as todo print-based research.Another possible

accommodation: students

may be given teacher pre-

screened websites toperuse.)


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Work Day. Studentsshould be drafting their

brochure or poster text.

Peer-Review:Last 10minutes, students act as

each others editors, using ateacher-provided checklist.


Work Day.Studentsshould be creating theirfinal brochure or poster,

illustrating their text withinteresting headings,graphics, etc.

Homework: Students areasked to complete a self-assessmentof their projects(using the given rubric) toturn-in with their projects.


Student Presentations.

Students take turnspresenting their brochure or

poster to the class.Listening students aretasked with writing down

all unique real-worldalgebra examples.

Post Graffiti Boards:

students are presented withsame graffiti board promptsas on Day 1.

Whole class discussionofpre & post graffiti boards /

discussion of growth.

Introduction of next unit.


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Name: ___________________

Foundations of Algebra Unit Test

This unit test is your opportunity to show what you have learned during our Foundations of Algebra unit. Please be sure to show yourwork throughout. As always, you may use a calculator where needed.

1. Match the following terms with their definitions (5 points):

______ Equation A. another word for an unknown; represented by a letter

______ Evaluate B. to combine like terms

______ Expression C. to solve

______ Simplify D. a statement that says two amounts are equal

______ Variable E. a group of numbers, operation signs, and variables

2. Translate the following words into algebraic expressions or equations, as indicated (5 points):

a. sixteen decreased by a number ______________________________________________________________________

b. twice a number, increased by four ____________________________________________________________________

c. the product of nine and a number is fourteen ____________________________________________________________

d. five divided by the product of x and y __________________________________________________________________

e.

five times a number minus 7 is equal to three times the same number plus 19 ____________________________________

3. Translate the following algebraic expressions and equations into words (5 points):

a. 3x 7 ________________________________________________________________________________________

b. (15 + n) 8 ____________________________________________________________________________________


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c. y 2 ________________________________________________________________________________________

d. 12x = 7x + 20 ___________________________________________________________________________________

e.

z 3 2 = 5 __________________________________________________________________________________

4. Simplify the following expressions (3 points):

a.

7x 8y + 9x = _______________________________

b.

4m 9n 3 + 6n = ____________________________

c. 3m + 2(m n) 5(m + n) = _______________________________

5. Simplify and solve the following equations (6 points):

a. n 6 = 50

b.

8n = 48

c.

4z 8 = 24

d. 12x = 7x + 20


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e.

4a + 17 = a 13

f. 2(a 3) = 16

BONUS POINT: Name the first property you need to use when solving problem f above:_____________________________(Be sure to use the algebraic term! !)

6. Evaluate the following algebraic expressions as indicated (2 points):

a.

What is the value of 3(x 6) + 2y, when x = -7 and y = 10?

b. What is the value of (x + 5)2 , when x = 3?x 5

7. For the following word problems, please (a) translate the text into an algebraic equation; and (b) solve. Remember: it may be helpful tocircle words and create a problem key as well (4 points total).

a.

At a gym, Frank did a certain number of pushups. Tom did 12 more than Frank. The total number both men did was 66. Howmany pushups did Frank do? (2 points)

Equation:


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Solution:

b. Sarai has money in a savings account. If she adds $50 a month for 6 months, she will have three times the amount she has now(not counting the interest). How much money does Sarai have in her savings account now? (2 points)

Equation:

Solution:

8. Algebra has many everyday applications. Please (a) create a word problem from your everyday life, (b) translate this into an algebraicequation, and (c) solve. (3 points)


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Name: ANSWER KEY

Foundations of Algebra Unit Test

This unit test is your opportunity to show what you have learned during our Foundations of Algebra unit. Please be sure to show your

work throughout. As always, you may use a calculator where needed.

1. Match the following terms with their definitions (5 points):

D Equation A. another word for an unknown; represented by a letter

C Evaluate B. to combine like terms

E Expression C. to solve

B Simplify D. a statement that says two amounts are equal

A Variable E. a group of numbers, operation signs, and variables

2. Translate the following words into algebraic expressions or equations, as indicated (5 points): *any variable is acceptable

a. Sixteen decreased by a number 16 n

b. twice a number, increased by four 2n + 4

c.

the product of nine and a number is fourteen 9n = 14 OR n x 9 = 14

d. five divided by the product of x and y 5 xy OR 5 / xy

e. five times a number minus 7 is equal to three times the same number plus 19 5n 7 = 3n + 19

3. Translate the following algebraic expressions and equations into words (5 points): *multiple correct answers possible

a. 3x 7 the product of three and a number decreased by seven; three times a number minus seven; the difference of


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b.

(15 + n) 8 the sum of fifteen and a number minus eight; fifteen plus a number decreased by eight; etc.

c. y 2 the quotient of y and two; a number divided by two; etc.

d. 12x = 7x + 20 the product of twelve and a number is the equal to the sum of seven times the same number and twenty

e.

z 3 2 = 5 a number divided by three, then decreased by two, is five; etc.

4. Simplify the following expressions (3 points):

a. 7x 8y + 9x = 16x 8y

b. 4m 9n 3 + 6n = 4m 3n - 3

c. 3m + 2(m n) 5(m + n) = 3m + 2m 2n 5m 5n = - 7n (the ms cancel out)

5. Simplify where possible and solve the following equations (6 points): * possible work/steps shown.

a.

n 6 = 50n = 50 x 6n = 300

b.

8n = 48n = 48 8n = 6

c.

4z 8 = 244z = 24 + 84z = 32z = 32 4z = 8

d. 12x = 7x + 2012x 7x = 205x = 20x = 20 5


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x = 4

e. 4a + 17 = a 134a = a 13 174a = a 30 (or a + (-30)4a a = -303a = - 30a = -30 3a = -10

f. 2(a 3) = 162a 6 = 162a = 16 + 62a = 22a = 22 2a = 11

BONUS POINT: Name the first property you need to use when solving problem f above: distributive property(Be sure to use the algebraic term! !)

6. Evaluate the following algebraic expressions as indicated (2 points):

a.

What is the value of 3(x 6) + 2y, when x = -7 and y = 10?

3 (-7 6) + 2 (10)3 (-13) + 20

-39 + 20 = -19

b. What is the value of (x + 5)2 , when x = 3?x 5

(3 + 5)2 = (8)2 = 64 = - 323 - 5 - 2 -2

7. For the following word problems, please (a) translate the text into an algebraic equation; and (b) solve. Remember: it may be helpful tocircle words and create a problem key as well (4 points total).


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a.

At a gym, Frank did a certain number of pushups. Tom did 12 more than Frank. The total number both men did was 66. Howmany pushups did Frank do? (2 points)

Possible key: x = Frank x + 12 = Tom

Equation:

x + (x + 12) = 66 OR 2x + 12 = 66

Solution:x = 27 . Frank did 27 push-ups! !

b. Sarai has money in a savings account. If she adds $50 a month for 6 months, she will have three times the amount she has now(not counting the interest). How much money does Sarai have in her savings account now? (2 points)

x = nowEquation:

($50 x 6) + x = 3x

Solution:$300 + x = 3x$300 = 3x x$300 = 2x

$150 = x .. Sarai has $150 in her savings account right now.

8. Algebra has many everyday applications. Please (a) create a word problem from your everyday life, (b) translate this into an algebraicequation, and (c) solve. (3 points) Many answers are possible!! One-step, multi-step, etc. are accepted.Example:(a) Word Problem: Anns son, Elliott, weighs 5 pounds less than he did a week ago (thanks to a stomach flu!) A week ago, he weighed

exactly half of Anns weight of 120 pounds. How much does Elliot weigh now?(b)Algebraic Equation:

x = Elliots weight now120 2 = x + 5


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(c) Solution: x = 55 pounds.

comprehensive unit plan

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