Learning Unit
Planning Guide
Title / Solving One- and Two-Step EquationsTeacher / Team / Algebra I Team
Grade / 8-9 / Subject / Algebra I
(What decisions do I need to make as I develop a Learning Unit?)
Decision 1: Concept Map of Learning Unit
Unit / Topic Concept
Solving One- and Two-Step EquationsUnit Summary – Paragraph Description
The student will solve linear equations using addition, subtraction, multiplication and division. Students will express rational numbers in equivalent form, simplify numerical and algebraic expressions, evaluate simple algebraic expressions and formulas, and translate algebraic expressions and equations.Major Concepts / Skills
Link to Content Standards
What key knowledge and skills will students acquire as a result of this unit?
CRCT Domains/EOCT Domains - QCC Objectives
(List by heading (domain) followed by numbered QCC’s)
QCC 1: Solve problems throughout this course that involve selecting appropriate approaches and tools, using estimating strategies to predict computational results, and judging reasonableness of results.QCC 3: Communicates mathematical ideas by using language and symbolism by reflecting upon and clarifies thinking about mathematical ideas and relationships, formulating mathematical definitions and expressing generalizations discovered throughout investigations, expressing mathematical ideas both orally and in wiring, interpreting written presentations of mathematics and asking clarifying and extending questions related to mathematics about which they have read or heard.
QCC 8: Students will solve linear equations using a variety of methods such as manipulatives and technology.
QCC 9: Students will solve problems involving linear equations.
QCC 6: Students will distinguish between relations and functions, and identify the domain and range.
CRCT Domain Algebraic Fundamentals 1.1:Students solve problems that involve selecting appropriate approaches and tools, using estimating strategies to predict computational results, or judging reasonableness of results
CRCT Domain Algebraic Fundamentals 1.2: Students formulate mathematical definitions, interpret written presentations of mathematics, express generalizations, and express mathematical ideas in writing.
CRCT Domain Solving Equations and Inequalities: Students solve word problems involving linear equations, inequalities, and systems of linear equations.
CRCT Domain Functions and Their Graphs: Students solve problems by connecting patterns to the concept of functions; using patterns, relations, and functions to analyze, write, or sketch linear functions and their graphs; making a distinction between relations and function; and identifying the domain and range of a finite set of points.
Knowledge and Skills:
(Reference CRCT / End of Course Content Descriptors)
Students will express rational numbers in equivalent form; simplify numerical and algebraic expressions, evaluate simple algebraic expressions and formulas, translate words into algebraic expressions and equations, represent problem situations with algebraic expressions and equations.Students will identify and apply properties of the real number system such as the Commutative, Associative, and Distributive Properties.
Students will solve linear equations using a variety of methods.
Decision 2:
What are the Essential Questions of the Unit?
Make sure there is at least one essential question for each major concept or skill. Most important essential questions also need extending / refining questions. All essential questions should be posted in the classroom.
- How do you determine the value of a variable in an equation?
- How are the signs, symbols, and words used in math?
- Why is PEMDAS important?
- How do you use numbers to represent words to write and solve an equation?
Decision 3:
What is the Performance / Product or Project that is the Culminating Activity of the Unit?
What evidence will show that students understand?
This is a summary description.
Describe in detail the product(s)/project(s).
The student will create a mathematical BINGO card with solutions from linear equations using addition, subtraction, multiplication and division. To formulate their equations solutions students will express rational numbers in equivalent form, simplify numerical and algebraic expressions, evaluate simple algebraic expressions and formulas, and translate algebraic expressions and equations.Student Assignment Page for the Culminating Activity
Essential Question of the Culminating Activity:
What essential questions will guide this unit
and focus teaching and learning?
Why is it important to use mental math in real life situations? How are opposite operations used to solve equations?Paragraph Description of the Culminating Activity (including curriculum and unit goals)
You have been hired by a book company to create a new type of mathematical BINGO. Your job is to develop a 5x5 BINGO card (attached) containing the solutions to one- and two-step equations of varying styles (i.e. 5x + 3 = 8; 8=3 + 5x)Steps or Task Analysis of the Culminating Activity:
What student products/performances will provide evidence of desired learning?
By what criteria and scoring tools will student products/performances be evaluated?
Student will design a 5 x 5 BINGO card with solutions from 32 one-and two-step equations they have created. Students will submit 32 equations which satisfy the following criteria: (4) 1 step equations using addition(4) 1 step equations using subtraction
(4) 1 step equations using multiplication
(4) 1 step equations using division
(4) 2 step equations using multiplication and addition
(4) 2 step equations using multiplication and subtraction
(4) 2 step equations using division and addition
(4) 2 step equations using division and subtraction
The equations must :
- display a variety of operational styles (the variable must be in a variety of positions in the equations).
- Be neatly typed or written
- Contain 4 of each “type” of one-and two-step equations
- Contain neat and adequate work showing the solution circled or highlighted
- Have solutions represented on a 5 x5 BINGO card that is neat and legible, completely filled out (all 24 spaces are to be filled out in random with one free space), and the back of the BINGO card must be headed with class, date, and name.
Decision 4: Culminating Activity Rubric
for One-Step and Two-Step Equations
SCALE
CRITERIA /
Excellent/
Skilled
3
YES
/Adequate
2
/Needs Improvement
1
NO
Equations
- Varied in operational style
- Neat
- Number of Equations
Typed or written neatly
(32-24) / Only 2-3 styles are apparent.
Errors are present and mistakes are apparent
(17-9) / Only 1 style of equation is apparent.
Not neat or legible; many mistakes which effect the game
(8 or less)
Work
- Neat
- Adequate work shown
- Answer circled or highlighted
All equations have supporting work
YES / Errors are present and mistakes are apparent
Most equations have supporting work / Not neat or legible; many mistakes which effect the game
Few or no equations have supporting work
NO
Bingo Card
- Neat/legible
- Completely filled out
- Personalized
YES
YES / Errors are present and mistakes are apparent / Not neat or legible; many mistakes which effect the game
NO
NO
Grading Criteria for Rubric:
Letter Grade / Number Grade / CriteriaA / 100-95 / Only 1 (#2) in any ONE section
B / 85 / Any combination of #2’s and #3’s
C / 75 / Only 1 (#1) in any section
D / 70 / 2-4 (#1’s) in any section
F / 50 / 5 or more #1’s in any section(s)
What sequence of teaching and learning experiences will equip students to develop and demonstrate the desired understandings?
Consider the WHERE elements as you plan student learning. Use the WHERE elements to self-check your planning!
W-How will you help students know where they are headed and why (e.g. major assignments, performance tasks, and criteria which the work will be judged by)?
H- How will you hook students through engaging and thought provoking experiences (e.g., issues, problems and challenges) that point towards big ideas, essential questions and performance tasks?
E-What events, real or simulated, can students experience to make ideas and issues real? What learning activities will help students to explore the big ideas and essential questions? What instruction is needed to equip students for the final performances?
R-How will you cause students to reflect and rethink to dig deeper into the core ideas? How will you guide students in rehearsing, revising, and refining their work based on feedback and self-assessment?
E-How will students exhibit their understanding about their final performances and products? How will you guide them in self-evaluation to identify strengths and weaknesses in their work and set future goals?
Decision 5: Acquisition Lessons and Activities
(Hint: You must have at least one acquisition lesson for each essential question in your unit) (See Decision 2)
The 3 Phases of an Acquisition Lesson
Part 1- Beginning of the Lesson
- Linking Prior Knowledge
- Motivate Learner
- Goal Setting with Essential Questions
Part 2 – Middle of the Lesson
- Moving towards knowledge and Skills
- Vocabulary
- Declarative Content
- Procedural Content
- Collaborative Pairs in Distributed Summarizing and distributed guided practice
- Re-teaching, Monitoring, Enrichment, Acceleration, Mastery Options
- Formative Assessment is primary focus for Assessment
(GOAL = CONTINUOUS IMPROVEMENT)
Part 3– End of the Lesson - Summarizing
- Learner Summarizes, summarizes, summarizes
- Assignments match learners’ preparation and learning level, NOT COVERAGE
- Learners answer the overall unit Essential Question
PART #1 Launch Activity - Hook
How will you create interest? = Motivational Activity
How will you link prior knowledge? = Cognitive Activity
Link to Previous Knowledge: KWL method “What do you already know about equations?” and reference the Essential Question: How do you determine the value of a variable in an equation? (see attached)TW place various algebra tiles on the overhead which represent several equations. TW ask students to write what equations they think are being represented (ex. X-2=5, 10=x+15). SW pair and share what they came up with.
Acquisition Lesson Planning
PART #1
Essential Question:(with key questions if necessary)
How do you solve linear equations using addition and subtraction?PART #2
Activating Thinking Strategies:
(ex. KWL, Word Maps, Wordsplash, etc.)
Key Vocabulary (Word Wall)
“Word Splash”: TW place vocabulary terms on a transparency: solution, reciprocal, opposites, equivalent equations, distributive property, inverse operations, variable, open sentence, constant. SW brainstorm and generate complete statements which predict the relationship between each term and a broader topic. SW then pair and compare with another student(s)and share their statements with the class. TW place statements on overhead or other visual.PART #2
(Distributed Guided Practice and / or Distributed Summarizing in Pairs / Graphic Organizers)
- TW provide review examples of adding and subtracting integers.
- TW introduce 1-step equations by modeling equations and their solutions with algebra tiles and reference graphic organizer (attached) for solving 1-step equations (key note: inverse operations)
- Guided Practice Classwork without algebra tiles. SW write, solve, and check (10) 1-step equation problems (teacher will randomly choose 10 problems).
Decision 6: What Extending / Refining Lessons / Activities Will Be in the Unit?
(Hint: Most important essential questions should have thinking skills activities)
Cause / Effect
/Compare / Contrast
/ Constructing Support / ClassifyingJustification
/ Induction / Deduction / EvaluationError Analysis
/ Example to Idea / Idea to Example / AbstractingAnalyzing Perspectives / Writing Prompts
Make sure that the most critical / important acquisition lessons also have
extending / refining lessons or activities
PART #2 Extending/Refining Activity
(Thinking Skills and / or Writing Prompt)
- TW place several equations completed INCORRECTLY on the overhead/board and ask student to find the errors and correct. SW pair and share their answers.
- Writing in Math: SW write a problem you could solve using x – 3 = 10. Share with the class and TW write all problems down showing how many different problems can be represented with x – 3 = 10.
PART #3 Summarizing Strategies:
(Ex. Ticket Out the Door, 3-2-1, etc., Answer essential question)
- Ticket Out the Door= SW put answer to the following questions on a “ticket” to leave the room.
- What operation do you use to solve an addition problem? Subtraction problem?
- Solve and show steps: -17 = x – 9
- Refer back to original Unit Essential Question and ask for feedback.
PART #3 Assignment and / or Assessment
TW assign 10 problems to solve for homework to be checked tomorrow. (* make sure to vary operational styles/placement of variable in problems).Decision 7: What Resources or Materials Will Be Needed for This Unit?
- Algebra Tiles (class set and overhead set)
- Graphic Organizer for 1- and 2- step equations
Additional Comments or Suggested Modifications
Let L/D student use algebra tiles to solve homework equations and actually draw algebra tiles beside the problem; cut problems down to 5-7 for homework.Graphic Organizer for Adding and Subtracting 1-Step Equations
Equation: Are you adding or subtracting?
EXAMPLES:
AddingSubtracting
Inverse Operation isInverse Operation is
Subtraction Addition
Solve for the variable
Ticket Out the Door
SW put answer to the following questions on a “ticket” to leave the room:
1. What operation do you use to solve an addition problem?
Subtraction problem?
2. Solve and show steps: -17 = x - 9
PART #1 Launch Activity - Hook
How will you create interest? = Motivational Activity
How will you link prior knowledge? = Cognitive Activity
TW ask for input on summer jobs held and how much they made per hour; then ask for prices of items wanted (car, shoes, clothing, etc.). Question: How many hours must you work at _____ dollars per hour to buy that item? Do a couple of these with the students.Ex. Student made $7.00/hour; wants a pair of shoes that cost $150.00; how many hours would they have to work? Make up equation: 7(x)=150
Acquisition Lesson Planning
PART #1
Essential Question:(with key questions if necessary)
How do you determine the value of a variable in multiplication and division equations?PART #2
Activating Thinking Strategies:
(ex. KWL, Word Maps, Wordsplash, etc.)
Key Vocabulary (Word Wall)
Review word splash from Lesson 1 and add multiplicative inverse, ratio, inverting.PART #2
(Distributed Guided Practice and / or Distributed Summarizing in Pairs / Graphic Organizers)
TW provide examples of multiplying and dividing with integers for review. SW will answer, pair, and share.TW introduce 1-step equations by pairing and share. TW give examples of multiplying and division equations to be solved by students individually; then SW pair up and discuss solutions. Students will reference the graphic organizer (attached) for 1-step equations with multiplying and dividing.
SW pair and share with guided practice: 10 problems of teacher/student choice on board or overhead; SW write, show work, solve and check.
Rubric for Solving Equations:
(Use to evaluate each equation solved for classwork/homework)
Each equation/problem is worth 5 points.
(1)point: Writing the Problem
(1)point”: Showing work/Operation
(1)point: Showing and circling answer
(1)point: check equation
(1)point: correct answer
Decision 6: What Extending / Refining Lessons / Activities Will Be in the Unit?
(Hint: Most important essential questions should have thinking skills activities)
Cause / Effect
/Compare / Contrast
/ Constructing Support / ClassifyingJustification
/ Induction / Deduction / EvaluationError Analysis
/ Example to Idea / Idea to Example / AbstractingAnalyzing Perspectives / Writing Prompts
Make sure that the most critical / important acquisition lessons also have
extending / refining lessons or activities
PART #2 Extending/Refining Activity
(Thinking Skills and / or Writing Prompt)
Comparison: Explain how dividing by 2 is the same as multiplying by ½.PART #3 Summarizing Strategies:
(Ex. Ticket Out the Door, 3-2-1, etc., Answer essential question)
Ticket out the Door: Read this problem:2/3 x = 24 and as your “ticket out the door”, be prepared to tell me what you need to do first.
PART #3 Assignment and / or Assessment
TW assign 10 problems to solve for homework to be checked tomorrow (* make sure to vary operational styles of problems).Decision 7: What Resources or Materials Will Be Needed for This Unit?
- Graphic Organizer for multiplying and dividing 1-step equations.
- Overhead
- Wordsplash from Lesson 1
Graphic Organizer for Multiplying and Dividing 1-Step Equations
Equation: Are you multiplying or dividing?
:
Inverse Operation
Is Division
or multiplying
by the Reciprocal
Solve for the variable
PART #1 Launch Activity - Hook
How will you create interest? = Motivational Activity
How will you link prior knowledge? = Cognitive Activity
Hook: TW place a transparency filled with various terms (ex. 5x, b, 3, 6x, 2b, 7y, 5n, 6n+9, 8, etc.); SW discuss and MATCH like terms.Acquisition Lesson Planning
PART #1
Essential Question:(with key questions if necessary)
How do I solve 2-step equations?PART #2
Activating Thinking Strategies:
(ex. KWL, Word Maps, Wordsplash, etc.)
Key Vocabulary (Word Wall)
Anticipation Guide: TW put up or distribute the anticipation guide for 2-step equations; SW answer with YES or NO the following questions regarding 2-step equations:- 5x + 3= 15 is an example of a 2-step equation.
- To solve –12x +8+5x=14, you would subtract 14 first.
- Is –10 the solution to 9x-5x-19=21?
- Is –12 the solution to ¾ x +1=-8?
- Is 1/8 the reciprocal of 8?
- Is 4 the solution to 2(x-3)=5?
PART #2
(Distributed Guided Practice and / or Distributed Summarizing in Pairs / Graphic Organizers)
TW present warm-up problems on variables and integers (p. 145 Algebra I McDougal Littell)SW complete guided practice with teacher (use examples from Ch. 3 from Algebra I McDougal Littell); SW work together and pair and share.
TW present notes on graphic organizer (attached) on 2-step equations.
SW solve guided practice classwork on 2-step equations (10 assorted problems with work and checks).
Decision 6: What Extending / Refining Lessons / Activities Will Be in the Unit?