Final Curriculum Project

Mike Barile

Professors Hari Koirala & Jeanelle DayEastern Connecticut State University

EDU 560

Unit TopicSolving One Variable Equations

FocusEvaluating Expressions, Solving and Generating Word Problems

Course: Algebra 1Grade Level: 8th Grade

Learning Activities

Evaluating Expressions Activity #1 (A) Pre-assessment

• In this activity, the teacher would start with pre-assessment of prior knowledge.

• The teacher may have a few word problems on the board such as: – “What number plus 5 = 8?”– “Five times what number = 25?”

• This tests students ability to conceptually solve basic equations before moving onto higher-order thinking needed for solving more complex equations.

Evaluating Expressions Activity #1 (B) Introduction- (I Do, We Do, You Do)

• After the pre-assessment, the teacher will introduce the topic in the form of a “I Do, We Do, You Do” activity.

• I Do-– The students will watch as the teacher solves one variable expressions for various

math functions on the board. • X+5= 7, X-3=4, X(5)= 25, X/2=5,

• We Do-– The teacher will present various problems similar to the previous examples and,

as a class, ask individual students to come to the board to solve them one at a time.

• You Do- – Using their notes and textbooks, students will work individually on various sample

problems. The teacher will circulate the room assisting students when needed.

• Homework- Textbook questions

Evaluating Expressions Activity #2Repeated Practice

• After going over the homework, the teacher will have each student solve one-step problems on the white boards in the room.

– The teacher will start with easier problems (addition/subtraction) and work up to more complex operations (multiplication/division).

– For each round of problems, the teacher will list two problems. • Problem “A”- must be solved by all students• Problem “B”- is a challenge question if “A” is completed

– This allows slower learners or learners with disabiliies enough time to solve the problem, while still challenging advanced learners with more rigor.

• Homework- Worksheet of more challenging problems created by Kutasoftwhere.com – Teachers can print out worksheets or download software to

create their own– https://www.kutasoftware.com/free.html

Solving and Generating Word Problems Activity #3Solving Word Problems

• Teacher will have a warm-up word problem on the board and ask students to solve it by writing their own variable equation.

“Jenn was the leading scorer of her soccer team. She scored 120 goals and had 20 assists in her high school career.”

1. Let (N) represent the total points awarded for soccer goals. Goal points are determined by 2(g), where (g) equals the total number of goals scored. How many points did Jenn earn for her scored goals? Write out the equation.

2. Overall career points are determined by N + A, where A equals the number of assists. Use your answer from Question #1 to determine Jenn’s total career points.

• Teacher will review answers with the students. – N= 2(g), N=2(120)= 240– Career points= 240 + 20= 260 – 260 total career points

• Teacher will then ask students to use their Chromebook to complete more word problems on the Google App, “Math Word Problems Made Easy.”– https://play.google.com/store/apps/details?id=com.nuzedd.WordProblemsMadeSimple&hl=en

• Homework: Students will have to create three of their own word problems that can be solved with a linear equation. They should start simple and increase in difficulty. – Some students’ equations will be very basic, while other more advanced students will be able to create very advanced equations.

Students will be challenged based on their own ability (differentiation).

Solving and Generating Word Problems Activity #4Self-Generating Questions/Review

• Students will work in partners and exchange their word problems. – Students will attempt to solve the first 2/3 word problems. If they

struggle, the student who made them can help them through it.

• The teacher will ask for students to share their third, more complex word problem out loud. – Students will attempt to solve a few of them as a class.

• When they are completed, they will complete a practice quiz made up of similar questions to the quiz on the following day. – The quiz will cover all content from the last four years. – If students complete the practice quiz early, they may practice more

on the Classzone website.• These are fun computer games that correlate with the textbook.

– For example, one game, Chapter 1: Deep Sea Diver, allows students to play as a scuba diver to collect coins that give him oxygen. If the diver runs out of oxygen, students have to solve a few math problems from the section to get more oxygen and continue playing.

• Homework: Study for Quiz

Deep Sea Diver Math GameSolving One Variable Equations

Evaluating Expressions & Solving and Generating Word Problems Activity #5

Assessment Quiz

• Students will complete a quiz based on the lessons from the past four class periods.

• Students will have to demonstrate the ability to:– Evaluate simple expressions– Evaluate more complex expressions

• Using addition, subtraction, multiplication, division, exponents

– Generate expressions to solve word problems– There will also be some bonus questions that lead into

the material from the next section. • Applying the order of operations to evaluate equations• Writing expressions and inequalities

StandardsCommon Core State Standards (CCSS)

• Analyze and solve linear equations and pairs of simultaneous linear equations.– CCSS.MATH.CONTENT.8.EE.C.7

Solve linear equations in one variable.

• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.– CCSS.MATH.CONTENT.7.EE.B.3

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies

– http://www.corestandards.org/Math/Content/7/EE/– http://www.corestandards.org/Math/Content/8/EE/

StandardsNational Math Standards

• Grades 6–8 Expectations: In grades 6–8 all students should–– develop an initial conceptual understanding of different uses of variables– use symbolic algebra to represent situations and to solve problems,

especially those that involve linear relationships– recognize and generate equivalent forms for simple algebraic expressions

and solve linear equations

• Grades 9–12 Expectations: In grades 9–12 all students should–– write equivalent forms of equations, inequalities, and systems of equations

and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases

• http://www.nctm.org/standards/content.aspx?id=312#represent

Materials

• Algebra 1 textbook• Class computer• Student Google Chromebooks • Internet Access• White Boards• Markers• Class projector• Pencils, paper, handouts

Commercial Sources

1. Math Textbook– Algebra 1, McDougal Littell, 2007

2. Classzone Course Resources– www.classzone.com

3. Google App Store• https://play.google.com/store/apps/details?id=com.nuzedd.WordProblemsMadeSimp

le&hl=en

4. Khan AcademyA. Great tool for struggling learners (See Accommodations

page)– https://

www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/why-we-do-the-same-thing-to-both-sides-simple-equations

– https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/linear-equation-word-problems-tu/v/application-problems-with-equation-in-one-variable

5. Kuta Software • https://www.kutasoftware.com/free.html

Student Accommodation Plan • Depending on the needs of a special education student, or student with a math-

based learning disability, I could make any of the following modifications to lessons, assessments, the class environment and/or access to resources.

• Materials: Access to a calculator, math formula resource sheet, study guides

• Tests/Quizzes/Assessment: Advanced notice of exams, extended time, small test-taking environment, modified/alternative tests for content and vocabulary, access to calculator, opportunity to improve, revise or retest exams

• Environment: preferential seating near strong role models

• Instructional Strategies: Check work in progress, allow extra practice, provide concrete examples, have students restate information, chunk long term assignments, use visuals, provide copies of class notes

Student Accommodation Lesson Examples

• My five lessons also include differentiation and extended learning opportunities for lower level or special education students.– I Do, We Do, You Do- Concrete examples– Problem “A” and “B” on the white board

• Opportunity for struggling students to go slower• Opportunity for quicker, more advanced students to challenge

themselves

– Use of educational apps and games to review learning• Chromebook, Google Apps, classzone.com

– Self-generating questions based on student ability

– The Khan Academy provides many short video clips that clarify many difficult mathematical concepts. • Any struggling students, especially special education students, can

access this site for easy to understand video clips on how to complete math problems, in this case, evaluating one step equations. I would provide these links to all students in each appropriate lesson topic.

• Also good for advanced learners who can look at upcoming topics

Khan Academy Video Tutorials

Vertical Curriculum MapK-12, “Equations”

• This vertical curriculum map will outline the preexisting skills necessary to build student ability for evaluating one-step equations.

• It will also outline how these skills will help students as they move forward into grades 9-12.

• The intent of this map is not to outline every math concept K-12, but to show where this lesson fits into the greater scope of math curriculum for solving equations .

Read and write numbers

Vertical Curriculum Map K-12, “Equations”

Basic number operations- addition, subtraction

Equations can have more than one solutionParty needs 1 bag of ice/10 guest. How many bags for

50 guests? 100 guests? Bag= (X)/10

Solving for multiple unknowns(2 or 3 variables) Solve for X,Y & Z

Write number equations- 5 + 5=10

Comparing numbers- greater than, less than

Order of operations

Solving and Graphing visual representations of equations

Solving basic one-step, 2-step equations6-8: Thinking Becomes More Abstract

K-4: Basic Understanding

Integers- positive and negative numbers

Intermediate number operations- multiplication, division,

More complex number operations- Parenthesis, exponent, square roots

9-12: Higher Level Thinking

Applying equations to cross-curricular contentEngineering, Science, Economics

Explain each step of solving an equation and support reasoning

Apply higher level operations to solve equationsQuadratic formula, factoring, square roots

*Major Application to Science!There is a clear connection to all of these math skills and their application to science. Students often have to solve problems, generate hypothesis, explain the steps of experiments, and defend their reasoning on

science labs. Students will often need to use the math skills to the left to write and solve formulas for

different compounds, chemicals and data results.