Instructional Design ProjectSolving One-Step Equations

Abigail Grove

Boise State University

EDTECH 503-4202

February 22, 2015

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Table of ContentsPart 1: Topic………………………………………………………………………………... 3Part 1a: Learning Goal…………………………………………………………………………………………….

3Part 1b: Audience Description………………………………………………………………………………. 3Part 2: Analysis………………………………..……………………………………………..

3Part 2a: Needs Assessment Survey………………………………………………………..……………… 3Part 2b: Needs Assessment Data…………………………………………………………………………… 3Part 2c: Analysis of Learners……………………………………………………………………………………. 6Part 2d: Analysis of the Learning Context………………………………………………………..…… 8Part 2e: Analysis of the Performance Context……………………………………………………… 10Part 2f: Analysis of the Content………………………………………………………………………………. 11Part 3: Planning…………………………………………………………..………………….

12Part 3a: Rationale…………………………………………………………………………………………………..… 12Part 3b: Learning Objectives…………………………………………………………………………………….

14Part 3c: Matrix of Objectives, Bloom’s Taxonomy, and Assessments…………………. 15Part 3d: ARCS Table…………………………………………………………………………………………..……… 16Part 3e: Instructor Guide……………………………………………………………………………………………

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Part 3f: Learning Content……………………………………………………………………………….…………

24Part 3f.1: Learning Materials…………………………………………………………………………………….…………………………. 24Part 3f.2: Assessment Materials……………………………………………………………………………………………..……………

25Part 3g: Technology Tools……………………………………………………………………………………… 26Part 4: Evaluation……………………………………………………………………………

28Part 4a: Evaluation Plan…………………………………………………………………………………………… 28Part 4b: Subject Matter Expert Description…………………………………………………………… 30Part 4c: Evaluation Survey……………………………………………………………………………………… 31Part 4d: Expert Review Results………………………………………………………………………………… 31Part 4e: Comments on Change……………………………………………………………………………… 32Part 4f: Reflective Synthesis Paper………………………………………………………………………… 32Part 5: Appendix…………………………………………………………………………… 35Part 5a: Appendix A- Survey…………………………………………………………………………………… 35Part 5b: Appendix B- Operations Key Word Graphic Organizer …………………

37Part 5c: Appendix C- Four Corners Activity Cards ……………….………………………. 38Part 5c: Appendix D- Balancing Equations Table……………….………………………… 41Part 5d: Appendix E- Solving Equations Handout……………….…………………………… 42Part 5e: Appendix F- Summative Assessment……………….………………………………… 43Part 5g: Appendix G- SME Survey Responses ………………………………………

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Part 5f: Appendix H- References……………………………………………………………………..……… 46

Part 1: TopicPart 1a: Learning Goal

Students will solve real-world situations by determining the unknown in a one-operation equation. Part 1b: Audience Description

The learners are sixth grade, female students studying math at the Baltimore Leadership School for Young Women in Baltimore, MD. Passing this course is required for all sixth grade students, leading to diverse learning styles, motivations, and personalities. Contributing to further differences is that students in sixth grade come from elementary schools all over the city and have various learning experiences.Part 2: Analysis ReportPart 2a: Needs Assessment Survey

The needs assessment survey was comprised of seventeen survey questions concerning demographic information, learning preferences, and content knowledge and skills. The survey was designed to give insight into student current knowledge and student learning styles, as well as attitudes about the topic to be covered. The content knowledge section included defining an equation, identifying the unknown, writing an equation, and solving for x in one-step addition, multiplication, subtraction, and division equations. Sixteen students were chosen randomly out of ninety-six to complete the needs assessment survey via a paper copy, only ten surveys were returned. The data was then entered into the online survey sheet for tracking and analysis purposes. The entire survey can be viewed by clicking here as well as in Appendix A.

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Part 2b: Needs Assessment DataDemographics

The demographics questions were about age, how long they have lived in Baltimore City, and what their current grade is in math class. The majority of students surveyed are eleven years old, with one twelve year old and one thirteen year old. Although this information was not a question on the survey, two of the

students have an IEP and the other eight are general education students. Nine out of the ten students have lived in Baltimore for more than five years. The tenth student has lived in Baltimore between two and five years. There is a wide range in current math grades for the students, this data can be seen in the bar graph to the right. Two students have a D, no students have a C, six students have a B, and two students have an A.Learning Preferences and Attitudes

Students were asked how they prefer to learn, what qualities their favorite class possesses, and how they feel when they think about math. The question about learning preferences allowed students to select all of the options that they enjoy and there was quite a bit of overlap amongst the ten students surveyed. The most commonly selected preference was copying examples from the teacher. This learning strategy eliminates student risk,

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reflecting many student’s fear of making mistakes, particularly in math. Six students enjoy watching instructional videos, walking through the problems as a class, and working in groups. Only one student selected “figure it out on your own” as a preference for learning math. Eight of the students selected more than one preference, showing that students like to have variety in their learning environment.

The question about favorite classes had mixed results for classroom qualities. Three students selected “it has fun activities”, three students selected “the teacher explains the problems well”, and two students selected “I do well in that class”. Only one student said she tried harder in that class and that her classmates are helpful.

The most common feeling that students relate to math is excited, which was a surprising result. Again, students could select more than one feeling, resulting in overlap. The next most common, chosen by four students, was that math makes them feel confident. Two students said it makes them feel frustrated, and two said it makes them feel bored. Content Knowledge

Solving one- step equations is the topic for this instruction, so students were asked to rate their understanding of equations, identify a variable, define an equation, write a fact family, and solve for the unknown in different scenarios. None of the students rated themselves as fully understanding

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equations. However, three students did give themselves a four out of five for understanding then proceeded to correctly define the word equation. This is where that trend stopped. Three different students correctly identified the variable. The most common self-rating was three, meaning the student thinks she knows some things about equations, but still has a lot to learn.

Students showed understanding for solving an equation when it was addition, but it did not translate to the other operations. Only three students correctly identified the addition and subtraction fact family, but eight students could solve for x in the addition problem. When it came to subtraction, multiplication, and division, very few students had a strategy and tried to guess. Three were correct for the multiplication problem, four were correct for the subtraction problem, and one was correct for the division problem.

The remaining three questions were word problems requiring students to understand the situation, write the equation, and then solve for the unknown. Three students got each question correct, but each time it was a different three students answering correctly. Without any instruction, one student not only could write an equation for the situations, but rewrote one problem in three different equivalent forms and answered all of the word problems correctly. This information indicates that she will need differentiation when the rest of the class is learning how to write equations. Also, students that have a grasp of how to solve addition problems can analyze their reasoning to help solve when it is a different operation.

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Part 2c: Analysis of the LearnersThe attitudes toward math will play an important role in how students

will assimilate the new skills into their current math knowledge. Most students selected positive emotions of excitement and confidence when taking the survey, but observation in the classroom has shown that many students struggle with confidence and willingness to take risks. Insecurities and frustration often result in shutting down, which makes learning impossible. Encouraging students to be willing to make mathematical mistakes and learn from them will empower students to persevere when a situation becomes difficult or is not immediately clear.

Additionally, how students learn the new information will impact intrinsic motivation. Students in the survey expressed their preferences for a variety of learning strategies, and students will be pushed to learn a variety of strategies for solving the same problem then choosing which strategy each individual prefers to use. This allows for all students to be able to collaborate and to help teach each other in the group setting, while still maintaining autonomy in decision making. Student engagement is the key in any classroom, and when learning equations it is imperative that students see the significance of this skill and are learning in an environment where they are comfortable.

Based on the survey data and classroom observations, students still need development of some prerequisite skills for solving equations that will need to be mastered in order

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to maximize the effectiveness of instruction. The prerequisite skills that students will need to develop include writing equations to represent the given situation, identifying the unknown, and writing fact families. In the survey, only one student actually wrote an equation to solve the world problems. The other nine students just chose an operation to conduct on the two numbers to get their answer with no proof of why that operation was chosen. Prior to learning how to solve equations, instruction will focus on writing equations for different real-world situations and identifying what the variable stands for. Writing fact families is a skill that students have been working on all year intermittently. 30% of the students in the survey were able to correctly identify all four members of the fact family, where 40% identified three correct members, and the remaining 30% were only able to identify two fact family members. Students will need more extensive practice to solidify their understanding of inverse operations. Part 2d: Analysis of the Learning Context

The instruction will take place in a converted YWCA building at the center of Baltimore City that is now a middle and high school for 484 students. The classroom is on the second out of six floors and directly across the hall from the auditorium. This leads to regular noise disruptions from street level and other school activities. The classroom has twenty-five student desks to accommodate the class size that ranges from 20 to 25 students. The room has 4 windows that go to the ceiling on the street side and two sets of French doors that open to the hallway. Only one set of doors can be accessed because the desks are in front of the other set and students are used to entering and exiting through only one door. In the front of the room is the access door for the school’s network and occasionally technicians will walk through the room. A projector is hooked up to a laptop computer on a set of drawers at the front of the room and projects onto a non-functioning smart board. There is a portable whiteboard for instructional writing and teacher examples. The teacher also has speakers available for any sound clips. Wi-Fi is available throughout the building for employees with

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the password. All teachers have a district-provided laptop and teachers associated with this year’s technology initiative have two ASUS tablets. The school has a laptop cart with enough laptops for a class that teacher’s may reserve in advance.

The middle school math department uses the Connected Mathematics 2 curriculum mixed with a teacher-created curriculum in order to ensure that all of the expected grade-level standards are addressed. Some units in Connected Mathematics 2 are specifically for sixth grade, while other units better align with different grade levels. There is a class set of the Connected Mathematics books and students each have a personal workbook to take home with practice problems. For the units not in the curriculum, students receive paper copies or write notes and problems in their classroom math journal. This journal is designed to stay in the classroom, but may be taken home to study as long as it returns to school with the student. For the unit on equations and expressions, the teacher will be using a combination of the Connected Mathematics 2 curriculum and teacher-created resources. Calculators, rulers, algebra tiles, and a variety of math manipulatives are available in the back of the classroom for use and students are encouraged to use models to explain their thinking.

Instructional strategies vary depending on the skill. If it is a review skill or practicing a newly learned skill, then students work with peers to discuss their reasoning. When students are learning a new skill, instruction is a combination of teacher-led and classroom discussion to have students connect new learning with previous learning and build confidence through guided practice. When lessons from the Connected Mathematics 2 book are being used, the students are arranged in groups to answer questions that are carefully designed to guide students to their answer. The teacher then acts as facilitator and poses questions to support student progress. Students are used to a variety of learning activities and classroom arrangements.

The students have a general desire to succeed and understand how math applies to life, requiring only occasional prompting to stay focused on

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the academic task at-hand and to remain positive. There is a high-level of anxiety amongst students in general, accompanied by the statement, “I don’t get it.” Be assured that the statement is not always true, and more accurately reflects stress than a complete lack of understanding. For this reason, it is imperative to encourage students and maintain a positive classroom culture where students build each other up. This is assisted by providing activities consisting of a balance between success and challenge. Added to student anxiety is parent pressure and standardized test scores. This is the first year for a new standardized test called PARCC and many teachers in the school are drilling students with preparation materials.

School begins at 8:30am and ends at 3:30pm. Built into the day is an advisory period similar to a homeroom, where students check in with their advisor to ensure they have completed their homework, are prepared with all of their materials, are in dress code, and have their agenda signed by parents from the previous night. There are six periods throughout the day, lasting fifty-five minutes each and marked by a bell. There are two bell systems that run throughout the day, one for high school and one for middle school. The short bells are for middle school, and the long solid bell is for high school. Students have individual schedules and at this point in the year know where they need to go and have plenty of time to take care of personal business during the five-minute transition time and still report to class before the bell. Part 2e: Analysis of the Performance Context

Solving equations is a foundational skill for every other math class students will take, as well as a general problem solving strategy to apply to life outside of school. In seventh grade, students will be expected to solve proportions using inverse operations. In order to do this, students will need a strong understanding of the way operations are related and how equations work. Not only does solving equations show up in Algebra, which is required for graduation, but it also plays a role in geometry formulas, or even determining what grade a student will need on the final exam in order to

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pass. The primary performance context is future math classes, however students will be posed with a multitude of real-life situations to solve, leading to the understanding that solving equations is a daily task. A few examples of daily situations that require equation solving can be drawn from the initial equation survey. Sharing the cost of a bill at a restaurant is solving an equation. Determining the tax for a purchase is solving an equation. Calculating how long it will take to run home, pick up a forgotten lunch, and make it back to work on time is an equation. Since this school is in an urban area, public transportation abounds and many families do not own cars. The common miles per hour or miles per gallon equations are less applicable and less understandable to this student population. For this reason, students will be given examples to solve while also having the chance to create their own real life examples that apply to their daily lives.

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Part 2f: Analysis of the Content (Flow Diagram)

Part 3: PlanningPart 3a: Rationale

Solving equations is an essential foundational skill for mathematics because the basis of mathematics is solving problems, and equations are the most basic method to solve problems. Students often struggle with analyzing complex situations, and although at first writing equations may appear to be a daunting task, equations turn the complex real-life situations into manageable, procedurally-solved numbers, letters, and symbols. Students need to understand how to write equations, analyze real world problems, and solve equations for the unknown. The common core math domain “equations and expressions” is one of the five domains students must master in sixth grade and the following standards apply specifically to the skill of solving equations:

CCSS.6.EE.B.5“Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?”CCSS.6.EE.B.7“Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q.”

In addition to the state requiring students to learn this skill in sixth grade, students will use this skill in every grade following: in seventh grade to solve two-step equations, in eight grade to calculate slope and solve systems of equations, and in all aspects of high school algebra.

Since solving equations is a procedural skill with step-by-step instructions, the dominant scaffolding strategy is supplantive. Students are directly taught the parts of the equation, how operations relate to each other, how to balance an equation, and how to substitute the solution to check for correctness. The balancing equations activity is designed to be

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both supplantive and generative. Although it is the goal that students will learn to conduct the inverse operation on both sides, the teacher will not directly state it. Rather, the teacher will encourage this understanding through the use of the balancing scale model, class discussion, and guiding questions. It is the hope that students will generate their own realizations as they practice and become comfortable with their own strategies. The other generative piece to this instruction is interpreting what each value, whether number or variable, means. This step is less procedural and requires practice, effort, and perseverance on the part of the learner. The “Real-Life Scenario” assignment that requires students to come up with a scenario to match a given equation is open-ended without much guidance and allows students to explore their understanding to reason about what equations mean in real life.

The dominant pedagogical approach is instructivist and it aligns with the supplantive scaffolding strategy. The summative assessment is testing whether students can perform the skill by the end of the instructional period, aligning with the instructivist approach. The key pieces of instruction will be taught either directly by the teacher, or discovered by students as a result of teacher-guided questioning. Many of the activities are designed to be completed in groups and with activities that connect new learning with past experiences, reflecting a connectivist approach. The students are experiencing equations as a physical activity when they balance the scales and will receive classmate feedback when analyzing word problems for the correct operation. Students know exactly what is expected of them when solving the real-life equations from the specific guidelines in the rubric. The rubric not only serves as an evaluation tool, but it is also a step-by-step guide for what students should do when they solve an equation. Since the goal of this instruction is for students to be able to complete a task, the instructivist approach is most efficient and effective for students to reach the goal in a set amount of time.

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Part 3b: Learning Objectives1. Students will write equation(s) to represent the real-life situation

provided to them.1.1- Students will look for and underline key words to determine which

operation is needed.1.2- Students will identify, by circling, and name the variable for what

they are trying to find.2. Students will get the variable alone on one side of the equation

when given a one-step equation.2.1- Students will determine the inverse operation.2.2- Students will perform the inverse operation on one side of the

equation.2.3- Students will keep the equation balanced.

3. Students will check the solution for each equation that they solve. 3.1- Students will substitute the value back into the original equation.3.2- Students will complete the operation in the original equation.3.3- Students will ensure the new number matches the original equation.

4. Students will interpret the solution.4.1- Students will identify what the variable represents from objective

1.2 by labeling it with words. 4.2- Students will check that the solution makes sense by writing a

summary sentence for each solved equation.

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Part 3c: Matrix of Objectives, Bloom’s Taxonomy, and Assessments

Objective Number

Revised Bloom’s Taxonomy Classification

Scaffolding Strategy

Type of Assessment

1.0 Analyze Supplantive Performance assessment (solving real-life equations rubric)/ summative assessment

1.1 Apply Supplantive Self-assessment( frequency table)

1.2 Analyze Supplantive Performance assessment

2.0 Understand Generative Peer-assessment (balancing equations)

2.1 Remember Generative/ Supplantive

Performance assessment (balancing equations)

2.2 Understand Generative Performance assessment (balancing equations)

2.3 Understand Supplantive Performance assessment (balancing equations)

3.0 Analyze Supplantive Performance Assessment (solving real-life equations rubric)

3.1 Understand Supplantive Self-assessment (solving real-life equations rubric)

3.2 Remember Supplantive Self-assessment3.3 Analyze Supplantive Self-assessment4.0 Create Generative Performance

assessment (day 2 homework)

4.1 Evaluate Generative Performance assessment

4.2 Create Generative Performance assessment

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Part 3d: ARCS TableAttentionA1. Perceptual Arousal The four corners activity engages

students with the physical movement and classmate interaction that they crave while reinforcing the operation recognition.

A2. Inquiry Arousal The teacher will model self-questioning in the example problems and have accountable talk posters and questions posted around the room. The classroom culture is one in which every answer must be followed with a “why”.

A3. Variability Students will be in grouped in various arrangements, partners, groups, and individuals. There will also be pencil-and-paper activities, concrete manipulatives, computer manipulatives, and group discussion.

RelevanceR1. Goal Orientation Students will be informed of the

objective by a student reading the objective and having it posted on the board. Students will understand that equations are the building block for all future math experiences.

R2. Motive Matching Students will be given a time-limit for completing their equation balancing and rewarded to try the next challenging level if they finish early. A list of five equations are given, but students will have the option to pick any two they wish.

R3. Familiarity Equations will be connected to a word problem they have worked on earlier in the year. Students will see that equations are a tool to solving word problems. Also, the operation identification cards from day 1 will be repeated on the solving equations worksheet in day 2.

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ConfidenceC1. Learning Requirements Additionally, the entire class will

support each other when identifying the operation. Students will work in partners when analyzing the real-life situations.

C2. Success Opportunities The opening question where students identify true and false values provides all students will success to begin with a positive attitude.

C3. Personal Control Students will have the rubric for each activity to clearly know what is expected and control their score by completing the rubric independently before the teacher evaluates them.

SatisfactionS1. Natural Consequences Students will be producing real-life

scenarios to match the written equation and connecting it to their life and previous experiences.

S2. Positive Consequences Students will earn higher scores on their activities for following the guidelines set forth in class and the rubric.

S3. Equity Students will be reinforced for each achievement in the balancing equations online activity, when going to the correct operation in the four corners activity, and when completing the rubric to analyze the solving equations handout.

Part 3e: Instructor GuideIntroduction1) In groups of four, students are to analyze the one-step equation, __ - 8 =

21 that is displayed on the projector. The equation has a blank rather than a variable. The students are to come up with as many values as they can that make the equation false, and then as many values as they can that make the equation true. Since some students already know how to solve

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equations, this group discussion will lead to a sharing of ideas and strategies. Also, since there are so many values that make the equation false, all students can achieve success, developing positive attitudes and motivation to begin the lesson.

2) The teacher will establish purpose by informing the students of the objective to solve real-life scenarios using one-step equations. The objective will be written on the board for students to see. Explain that every word problem they have completed in the past could have been solved through the use of equations. Give an example of a word problem from a recent quiz and post it so that all of the students can see it. Tell students that by the end of this topic, they will be able to write equations to help them solve word problems. The teacher will provide the overview for the next two days of instruction. Day one will focus on analyzing real life situations and balancing equations. Day two will focus on checking those solutions and interpreting results to ensure they make sense.

BodyDay 11) Four Corners: Identify the Operation. Around the room the teacher will

have placed four posters with the operations written on them. Each student group receives a set of cards with equations in word form. This set of cards can be found in Appendix C. When the teacher says go, each group member draws a word problem and has 30 seconds to go to the correct operation represented by the world problem. When the 30 second timer goes off, students must share their word problem with the other members at that operation to check if they went to the correct operation. Students may reference their operations key words graphic organizer, example found in Appendix B, created during a previous class. There will be 3 practice rounds, then students will keep track of their accuracy by completing a frequency table and marking the number of correct and incorrect operation identifications. Between each round, students return to their group, shuffle the cards, and draw a new card. This frequency

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table can be found under assessment materials. Key ideas to reinforce include:

a. The relationship between the inverse operations. Most of the word problems could have been solved by setting up either of the inverse operations.

b. Determining what information was missing.2) Variable Review: Ask students what we could put in place of the blank

from the opening activity. Review what a variable means. Have students give words that can be in the place of the variable in a word problem. “A given amount, some number, the unknown…”

3) Teacher Examples: x + 4 = 15 is displayed on the projector. The teacher asks students to draw a scale on their paper and then explains the use of algebra tiles. Students are able to see which tile represents a unit and which tile represents a variable. The teacher will then model by drawing the green rectangle and four yellow squares on the left side, and 15 yellow squares on the right side. Then ask students how we could figure out the value that makes this equation true. Allow students to make suggestions, but do not focus on the correct answer as much as their strategies. Ask students if a square could be taken off of both sides and it would still be equal. Remove the squares until x is alone on the left and explain that this is the goal when solving any equation. Students should have this entire scenario drawn in their math journal and add any ideas that they want to remember. Key ideas to reinforce are:

a. Fact families.b. Inverse operations or “undoing” the operation.c. Keeping the equation equal, what happens to one side of the

equation must happen to the other side.4) Guided practice: Rather than drawing the scale over and over, students

will use mathplayground.com to model the equation on a scale. The entire class will use the teacher’s computer for the first 8 examples, with students managing the computer for at least 5 of the examples. This gets

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students excited and engaged in the activity and the computer provides instant feedback as well as guiding suggestions.

5) Independent practice: Each student will pick up a laptop and complete at least 10 practice problems. Each practice problem is to be copied into the Balancing Equations table that can be found in Appendix D. *For students already confident in solving one-step equations, direct them to select “two-step equations” in the mathplayground.com activity. It is suggested to set a reasonable time limit to encourage focus without producing stress. If 10 practice problems are completed before the time limit is over, challenge those students to try balancing two-step equations. While students practice the teacher is asking guiding and reflection questions to prompt deeper understanding.

6) Think-Pair-Share: With the partner next to them, each student will pick 3 problems to explain. The Balancing Equations rubric, found in the assessment materials, will be used by each partner to assess the other’s understanding. Each partner has a set amount of time to provide evidence of learning. These rubrics will be turned in and then pick a few students to share their new learning that occurred today.

7) Ask students to rate their understanding of the day’s objective to analyze real-life situations and balance equations from 1 to 5 by holding up the corresponding number of fingers.

8) Homework. Write and solve 10 one-step equations. These problems will be added to the student’s classroom portfolio and will give insight into which operations the students are most comfortable with.

Day 21) The teacher will review the objective and engage the students in learning

by picking one from each group to summarize yesterday’s activities. Repeat the goal and that the focus of day two is checking solutions and interpreting results to ensure they make sense.

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2) Project an equation followed by four values to choose from. Only one of the values is true. Ask the students to discuss in their groups which is true and why. Draw a random name from the class roster to then explain which value makes the equation true and why. Key ideas to emphasize include:

a. Fact familiesb. Inverse operations

3) The teacher will explain the meaning of substitution. Show a short video on how ingredients in baking can be used in place of each other. Ask students for other real-world examples of substitution. Some ideas are:

a. Sportsb. Side dishes at restaurantsc. A teacher

4) The teacher then picks a student to distribute the solving real-life equations handout, which can be found in Appendix E. Many of the word problems are from yesterday’s Four Corners activities, so students will have some familiarity with the content to produce confidence and perseverance. The teacher will complete four examples as a whole group discussion with guiding questions. The remaining seven questions are to be completed in partners. Students will have the solving real life equations rubric, found in the assessment materials, to use as a guide when solving the problems. Have algebra tiles and printed balances available for students to use to assist in balancing the equations. Have the steps displayed on the overhead projector while students work. Steps to show are:

a. Determine the operation, underline key wordsb. Determine the variable, circle the letter or key wordsc. Write the equationd. Get the variable alone, balance is keye. Substitute the value back into the equation to determine if it is

correct.

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f. Analyze if the solution makes sense. 5) As a whole class discussion, have students share their solutions and their

reasoning for why the answers make sense. Encourage students to engage in interaction using accountable talk prompts.

a. I agree with her statement because….b. I disagree with her statement because…c. I would like to build upon what ___ said.

6) The teacher will model how to write a real-life scenario from an equation. Example: x/5 = 3 could mean “I have x candy bars and want to share it with five friends. Each friend will get 3 candy bars. Solve for x.”

7) The teacher will display 5 equations on the board. Independently, students will pick 2 equations and write a real-world situation that matches the equations within a set amount of time that allows for thought, but maintains focus. Students are to write the scenarios on index cards that can later be stapled into their math journals. Names are written at the top right of the card.

8) Students will then pass in their real-life scenarios. A different student will be chosen to read each scenario and the class must try to guess which equation it matches. This is an opportunity to critique and revise anonymously so students do not feel threatened and can accept the constructive criticism.

9) For homework, each student must create an equation with a matching scenario and solve it. The best problems will be part of the summative assessment.

Conclusion1) The teacher will review with the steps to solve an equation. Students will

repeat the steps and develop a memory aid.2) The teacher will incorporate student homework questions into a

summative assessment that will track independent student learning.3) Students will take the summative assessment composed of questions

from the survey as well as student created questions. Multiple choice

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problems will be marked either correct or incorrect and situation analysis problems will be labeled with feedback and graded using the criteria in the solving real life equations rubric.

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Part 3f: Learning ContentPart 3f.1: Learning MaterialsLearning Materials

Purpose Timing

Group word problem cards

Students draw a different card for each round to practice identifying the operation. They will be correcting each other by sharing their card to check for the correct operation identification.

Four Corners Opening Activity

Operation Identification Frequency Table

Students use this table to track their ability to determine the correct operation.

The table is filled in while students are playing four corners.

Balancing Equations Table

This table is a place for students to document their work and reflect upon their learning while balancing equations on mathplayground.com

To be used in conjunction with the website

Balancing Equations Rubric

This rubric is for peers to evaluate each other’s understanding of balancing equations.

This assessment occurs at the end of day 1.

Ingredient Substitute Video

This video is to spark the student’s connections to substitution.

This video is played at the beginning of day two

Real-Life Equations

Students can write notes from the four teacher examples and then solve the remaining seven with a partner as practice.

This activity takes place at the end of day two.

Solving Real-Life Equations Rubric

Students can self-check while completing the activity.

This rubric is completed in conjunction with the real-life equations activity.

Summative Assessment

Students will take the assessment independently to check for mastery of each objective.

Day 3

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Part 3f.2: Assessment MaterialsBelow are the rubrics for assessing student understanding. The

summative assessment can be found in appendix F. Operation Identification Frequency Table

Round Number

Correct Operation (multiply, divide, add, or subtract)

Key Words from your card

Did you go to the correct operation?

12345678

Total Correct

Balancing Equations RubricIntended to be filled out by a partner

Student being assessed:________________ Student assessing: ____________________

Excellent(5 points)

Average(3 points)

Unclear(1 points)

Strategies for getting

the variable alone

My partner explained in detail, showing

models, how to get the variable alone

for three equations.

My partner briefly explained how to get the variable alone for three

equations.

My partner was unclear in

explaining how to get the

variable alone.Reflection My partner explained

the mistakes and what was learned using examples.

My partner stated whether the

answers were right or wrong, but did not explain what

was learned.

My partner was unsure of which

ones were correct or

incorrect or why.

Points Possible 10

Solving Real Life Equations Rubric26

Excellent (5 points) Average (3 points) Needs Improvemen

t (1 point)Determine

the Operation

Underlines key words and writes notes for all

problems.

Underlines words, but not all are key words and only for

some problems.

No markings on word problems

Determine the

variable

Circles the unknown and labels it with a variable

for all problems.

Circles the unknown for some

problems.

No markings on the word

problemsWrite the equation

The equation is written and labeled for all

problems.

The equation is written and there

are labels on some problems.

No equations are written

Balance the

equation

The inverse operation is conducted on both sides of the equation with work shown to get the variable

alone for all problems.

The inverse operation occurred on both sides, with

some work for some problems.

No work is shown or the

incorrect operation was used.

Check the solution

The solution was substituted back into the original equation to check

it and all work is shown for all problems.

The solution was substituted back into the original

equation for some problems.

The solution was not checked.

Analyze the

solution

Numbers are clearly labeled for meaning. A sentence summarizes

each solution.

Some numbers are labeled and others

are not.

None of the numbers are

labeled.

Points Possible 30

Part 3g: Technology Tools

Technology Use RationaleProjector and teacher laptop

Teacher visual communication with students. Model the balancing of equations.

This projector allows more preparation to occur before the actual learning so more attention can be directed toward students than the teacher writing on the board.

Student laptops Students practice balancing equations on mathplayground.com.

The laptops not only provide the virtual manipulatives, but also provide instant feedback on accuracy.

Speakers To play the This substitution video will help

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substitution video students connect the current learning with past experiences.

Algebra Tiles and Printed Balances

The manipulatives are to be used in Day 2 to assist solving the equations written from the real-life problems.

The concrete manipulatives move students from the computer checking the equation’s balance to the student ensuring the equation is balanced. This aid is available for students still requiring that visual before conducting the inverse operation.

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Part 4: EvaluationPart 4a: Evaluation Plan

Throughout the creation of this instructional project, evaluation has been occurring in the background to ensure that the instruction will in fact accomplish its intended purpose. Evaluation has occurred at every level of this project as the instructional designer has read, reread, and changed components in response to her own observations as well as the critiques of classmates, subject matter experts, and the instructor.

The evaluation plan for this instructional design project will follow the four-level evaluation model developed by Donald L. Kirkpatrick,Learner Reaction

Learner reaction is a significant indicator on the success of the instruction’s ability to motivate and engage the learner. When learners are engaged and motivated, more learning will occur (Larson and Lockee, 2014). Survey questions will be worded as statements and given to students before their summative assessment to determine learner’s reaction to instruction. Students are to rank their agreement from 1, meaning strongly disagree, to 5, meaning strongly agree for the following survey statements.

I feel confident in my ability to solve equations correctly. I feel confident in my ability to identify the operation in a word

problem. I feel confident in my ability to check my solution to an equation is

correct using substitution. I enjoyed balancing equations on mathplayground.com. The partner feedback from balancing equations was extremely helpful

to my understanding of balancing equations. I enjoyed practicing operation identification through the four corners

game. The solving real life equations rubric was helpful and motivating to

complete the real life equations handout.

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Creating my own scenarios to match numbers and symbols in the equation helped me to relate solving equations to my everyday life.

My learning could have been improved by _______________.Once the students have completed the survey, the instructional

designer, along with other key stakeholders, will analyze the feedback to revise and improve the instruction for future uses. Learning

Learning is the evaluation level that pertains to skill and knowledge acquisition. For this project, learning will be evaluated through many forms of assessment, both formative and summative. Many activities will be evaluated using rubrics that will be completed either by the student, a peer, or the instructor. Students will also be creating and solving their own equations and real life scenarios as formative assessments to be evaluated by the instructor. The summative assessment will be graded by the instructor using the same rubric from instruction.

There are underlying questions about learning that should be answered as a result of the multiple assessments.

Can the learner write an equation by identifying the correct operation in a word problem?

Can the learning solve for the variable by balancing an equation? Can the learner check the solution using substitution? Can the learner analyze reasonableness of a solution by giving

meaning to numbers and symbols?These questions will be answered by the instructional designer and

teacher based on the grades from rubrics and assessments. The answers to these questions will help guide the instructional designer to search for areas of improvement as well as successes in order to revise future instruction on the topic of solving equations.

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BehaviorBehavior identifies if the learning will be applied in the future, referring

back to the performance context established in Part 2e of this project. Solving equations is a skill that students should apply in every math activity now that it has been learned. It is part of geometry, proportions, finances, and daily living. The following questions will be answered by the instructional designer through observations of the same students in future class periods.

Do students write equations before solving geometry problems? Do students write equations before solving proportions? Do students write equations when given word problems to solve? Do students write equations before attempting to solve any

problem?The instructional designer will be responsible for ensuring that this

behavior is assessed in the future and can refer to the classroom teacher for insight as to the level of application that resulted from the instruction for solving equations. Results

Results provide the proof that instruction was worth the time, effort, and resources. Did the benefits meet the expectations? To determine the results for this instruction, student surveys from before instruction will be compared to the summative assessment at the end of instruction. The goal was for students to learn to solve equations, gain confidence, and recognize operations from everyday situations. For the rest of the school year, students will be observed on their use of writing and solving equations in all math contexts. The state standardized tests will also assess this skill to show if growth occurred from one school year to the next.Part 4b: Subject Matter Expert Description

The subject matter expert (SME) is Elisa No, the math department chair and geometry teacher as Baltimore Leadership School for Young Women. The evaluation plan was submitted to Elisa on April 11, 2015, giving her three weeks to review the plan and provide feedback.

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Part 4c: Evaluation SurveyThe SME survey, found here, was designed to produce specific and

targeted feedback about the instructional plan. The questions from the survey are listed below.

Are the goals and objectives clearly stated and appropriate for the targeted learners? Why or why not?

Were you able to understand the instructional guide enough to teach it confidently? Give specific areas where more or less detail may have been helpful or appropriate.

Which activities did you find most engaging while also holding a lot of learning potential? Please explain why.

Which activities might you have replaced? Please provide an alternative activity to teach the same objective.

Was there not enough, just right, or too much overlap on activities and their relating objectives? For example, the four corners activity focused on identifying operations as did the solving real life equations worksheet.

Did activities build upon each other with the proper scaffolding for each objective? Please give examples.

Are the rubrics detailed enough to evaluate learning for the given activity? Do you have any suggestions for improving the rubrics?

Does the summative assessment, in appendix F, cover the desired objectives in enough detail to determine mastery? Why or why hot?

What are some suggestions you might have for improving the instruction on the topic of solving one-step equations?

Part 4d: Expert Review ResultsThe subject-matter expert (SME) had minimal revision suggestions and

agreed with the majority of the strategies and setup for this instruction. She liked the use of the word, “unknown”, in place of variable at the beginning of the instruction and then the process of connecting the two words to establish strong word association. The greatest concern was that the instructional guide would be easily understood and the SME stated that, “by just reading the guide, I felt like I had been present in [the] lesson.” The SME made one suggestion for student grouping, that the initial think-pair-share strategy

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should have an additional step for students to not only partner once, but partner a second time to explain the first partner’s thinking. I agree with the SME that this second partnering is powerful because it extends the student beyond their own thinking and requires them to understand a peer’s thinking well enough to explain it. As a previous sixth grade teacher, the SME was encouraging and positive about the design fitting the needs of sixth grade students, the instruction being scaffolded and engaging, and the assessment aligning to the goals of the instruction. The complete SME responses can be found in Appendix G.Part 4e: Comments on Change

There are not many items to change within the instruction of this lesson, however there is always room for improvement. One area where instruction could be improved is requiring more student talk. Whenever the opportunity arises to allow students to explain their thinking, it should be taken. The SME suggested that students explain a peer’s thinking during a think-pair-share activity. I would also like to add in more of this requirement to other pieces of the instruction. During the balancing equations activity have students partner. One partner controls the computer and explain how and why she is making each action. Then the second partner must explain it back to the first and to another classmate. This repeated discussion can be very powerful and build confidence in those students who may at first be hesitant to speak their thoughts. Part 4f: Reflective Synthesis Paper

My original assumption, that I had been an instructional designer for years, turned out to be far from the truth. At the beginning of this class, I was unfamiliar with the term instructional design, but when I broke down each word it seemed that every teacher must be an instructional designer. Yes, as a classroom teacher I create lesson plans, but rarely do I take the time to survey, break down a skill into its smallest parts, plan every second of instruction, collaborate with key stakeholders, and align all activities for

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one specific goal. In other words, instructional design is more like writing an orchestra than writing a piano solo.

An orchestra is composed of many parts, that must fit together and work together to accomplish a specific purpose. Each piece of the composition is intertwined and developed as it goes along. Although an idea for one instrument may sound amazing alone, when partnered with the other instruments in the orchestra there may need to be adjustments or it may need rewritten altogether. This situation reflects the need of the instructional designer to ensure all components of the instruction mesh together. Technology integration is often helpful, but if it does not support the objective for the day it may need to be revised or replaced by another activity. The same goes for group work, worksheets, teacher lecture, and any other instructional strategy. Just as the composer has to go back, revise, replay, and evaluate, so must the instructional designer make sure that the full message makes it smoothly into the hearts and minds of the audience.

Through my instructional design experience this semester, I have gained new perspective to the daily classroom routine. When students become frustrated, I think more about how I could have prevented this frustration than placing the blame on students. Every day I try to reflect on what could have gone better. In report #1 of this instructional design project, I was surprised to see certain student reactions and skills present on the pre-assessment survey. Now I can see that a short survey could even be a homework assignment to help me prepare for a day of instruction later in the week, it doesn’t have to be a unit-long pre-assessment. I have also re-found the need for more frequent formative assessments. In my undergraduate program we learned to do daily formative assessments, but often the pressure of finishing a unit can take the time away from formative assessments. Although teacher observation is a means for formative assessment, actually having students write down their thoughts each day provides more specific feedback and encourages students to put their thinking on paper. Writing report #2 reiterated the need for well-designed

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assessments and the need for students to know what is expected of them. While working on this project, I have also been practicing theories and approaches in my classroom. The use of rubrics has completely changed student attitudes because there is no longer a mystery behind what is expected of them.

Throughout the entire design process, there has been a connection to how teaching with technology is just as designed as teaching without. Technology is not intended to replace the educator, and can be such a powerful tool when wielded with proper planning and preparation. “Technology should always be used to meet a specific instructional need” (Larson and Lockee, 2014, p.184). Each learning material, including technology, needs a purpose and to match a desired outcome. This does not mean that each outcome needs a specific activity either. As asked by Larson and Lockee (2014), “can I optimize the instruction by addressing several outcomes with one activity?” (p. 153) If the answer is yes, then by all means consolidate learning. Our world is so connected, that many activities can support more than one learning outcome. It is up to the instructional designer to see that the learning material satisfied the defined need.

My future in educational technology will be filled with educational decisions, now made based on the skills learned through playing the role of instructional designer. Long gone are the days of typing up a quick agenda for a daily lesson plan. With each new lesson I can’t help but consider the assumptions and pedagogies as well as rationale for each activity, even if I don’t write it all down. My mindset has changed to one of constant reflection and evaluation as a result of my learning experiences with instructional design and my future in this field will be better as a result.

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Part 5: AppendixPart 5a: Appendix A- Survey

Equations Survey* RequiredWhat is your age? *o  10o  11o  12o  13How long have you lived in Baltimore? *o  1 yearo  2-5 yearso  more than 5 yearsWhat is your current percent grade in math class? *

When learning, do you prefer to... *pick all that are trueo  copy down examples from the teacher?o  watch a video with examples?o  walk through problems as a class?o  try to figure it out on your own?o  work in a group to develop steps?o  a combination of these methods?Think of your favorite subject. Why do you enjoy it? *o  I do well in that classo  It has fun activitieso  The teacher explains the problems wello  My classmates are helpfulo I try harder in that classWhen you think of math, how does it make you feel? *Check all that applyo  excitedo  frustratedo  boredo  confidentRate your understanding of equations from 1 to 5. *

1 2 3 4 5

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No understandin

gUnderstand completely

What is an equation? *o  a set of numbers all added togethero  a list of numbers in ordero two equal expressionsWhat is the variable in the following equation? *5x + 1 = 14o  5o  xo  14o  =Which equations below are part of the fact family for 14.3 + 6 = 20.3? *Pick all that are trueo  20.3 - 6 = 14.3o  20.3 - 14.3 = 6o  6 + 14.3 = 20.3o  14.3 - 6 = 20.3Solve for x. *25 + x = 34

Solve for x. *13x = 52

Solve for x. *153 - x = 98

Solve for x. *x ÷ 27 = 3

Solve for x. Deja, Desmond, and another friend want to purchase some snacks that cost a total of $7.50. They will share the cost of the snacks. How much will each person pay? *x•3 = 7.5

Solve for x. Dirk will rent a bicycle for $15 per hour. He has $65 to spend. What is the maximum number of whole hours that Dirk can rent the bicycle? *

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Solve for x. 2 apples weigh the same as 4 limes. Each apple weighs 4 ounces. How much does 1 lime weight? *Draw a model to help understand the problem.Part 5b: Appendix B- Operations Key Word Graphic Organizer

Total Sum Altogether Combine Plus More Greater Increase

Order Doesn’t Matter

2 + 3 = 3 + 2

Difference How many more Less Fewer Take away Decrease Minus

Order Matters

8 - 5 ≠ 5 - 8

Addition Subtraction

Multiplication Division

Product Repeat Of Times Equal groups Factor

Order Doesn’t Matter

4 x 5 = 5 x 4

Quotient Split Share Equal groups Factor Divisor Part

Order Matters

20 ÷ 4 ≠ 4 ÷ 20

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39

Part 5C: Appendix C- Four Corners Activity Cards

The quotient of u and 12 is 36.

Jenine bought 6 shirts and some number of pants. She had 10 clothing items when she left the store. How many pants did Jenine purchase?

The sum of 3 and c is 7.

The product of 6 and b is 42.

Samuel scored some number of goals. Chad scored 2 more goals

than Samuel. If Samuel scored 8 goals, how

many did Chad score?

Each day, Tanya reads p more pages of her book. How many pages has Tanya read after 2 weeks?

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Caroline needs to create b scrapbooks for her new business. If each scrapbook needs 8 feet of paper, how much paper must Caroline purchase?

30 decreased by w equals

25.

Niya runs 7 miles every day. If a lap around the track is m miles, how many laps will Niya have to run each day?

Destiny is x inches shorter than Deja. If Destiny is 68 inches tall, how tall is Deja?

8 more than v equals 32.

The President’s visit shut down x blocks of the city, which was 4

more than the Governor’s visit. How

many blocks were shut down by the president’s

visit?

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Xena is in the grade 3 grades lower than Jess. If Xena is in Grade x, what grade is Jess in?

Kendal earns 5 times as much money working as a designer than she earned working at a restaurant. If she made d dollars as a designer, how much did she make working at a restaurant?

The difference between b and

13 is 9.

Sarah is 24 years younger than her mother. If Sarah is y years old, how old is her mother?

A third of h is 3.

Every time Darius helps his grandma,

he earns y dollars. If he’s earned $21.35 so far, how many

times has he helped his grandma?

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Part 5d: Appendix D- Balancing Equations Table

Balancing Equations

Original Equation

Describe how you got the variable

alone

The value of x that

makes the equation

true.

Reflection: Did you get it correct on the first try?

Why or why not?

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Part 5e: Appendix E- Solving Real-Life Equations HandoutSolving Real Life Equations

1) Jenine bought 6 shirts and some number of pants. She had 10 clothing items when she left the store. How many pants did Jenine purchase?

2) Samuel scored some number of goals. Chad scored 2 more goals than Samuel. If Samuel scored 8 goals, how many did Chad score?

3) Each day, Tanya reads p more pages of her book. Tanya has read 28 pages after 2 weeks? What value represents p?

4) Caroline needs to create b scrapbooks for her new business. If each scrapbook needs 8 feet of paper and Caroline purchased 56 feet of paper, what doed b represent?

5) Niya runs 7 miles every day. If a lap around the track is m miles and she does 4 laps, what must m equal?

6) Destiny is x inches shorter than Deja. If Destiny is 52 inches tall and Deja is 47 inches tall, give a true value for x?

7) The President’s visit shut down x blocks of the city, which was 4 more than the Governor’s visit. If the governor’s visit shut down 10 blocks, how many blocks were shut down by the president’s visit?

8) Xena is in the grade 3 grades lower than Jess. If Xena is in Grade x and Jess is in Grade 9, what is Grade x?

9) Kendal earns 5 times as much money working as a designer than she earned working at a restaurant. She made $8 an hour working at the restaurant. If she made d dollars as a designer, what value is d?

10) Sarah is 24 years younger than her mother. If Sarah is y years old and her mother is 33, what does y represent?

11) Every time Darius helps his grandma, he earns $3.05. If he’s earned $21.35 so far, how many times has he helped his grandma?

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Part 5f: Appendix F- Summative AssessmentSolving Equations Summative Assessment

Rate your understanding of equations from 1 to 5.1 2 3 4 5

No understandin

gUnderstand completely

What is an equation? o  a set of numbers all added togethero  a list of numbers in ordero two equal expressions

Circle the variable in the following equation.5x + 1 = 14

Solve for x.25 + x = 34

Solve for x. 13x = 52

Solve for x. 153 - x = 98

Solve for x. x ÷ 27 = 3

Solve for x. Deja, Desmond, and another friend want to purchase some snacks that cost a total of $7.50. They will share the cost of the snacks. How much will each person pay?

**** Insert student scenarios here. ****

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Part 5g: Appendix G- SME Survey ResponsesQ: Are the goals and objectives clearly stated and appropriate for the

targeted learners? Why or why not?A: Yes. Students by this point should already know what one-step equations

are and solving for the unknown. As a 6th grade class, instead of using terms such as "variable" in the objective, Ms. Grove used a more familiar term of "unknown" to be appropriate for the targeted learners. The objective is also straight forward and allows me to see that the lesson is designed to help students with real life one-step equation problems.

Q: Were you able to understand the instructional guide enough to teach it confidently? Give specific areas where more or less detail may have been helpful or appropriate.

A: Yes. The instructional guide was very detailed and thorough. By just reading the guide, I felt like I had been present in her lesson.

Q: Which activities did you find most engaging while also holding a lot of learning potential? Please explain why.

A: The activity that I found the most engaging while holding a lot of learning potential was the use of the algebra tiles to help students understand the concept of solving for the variable. It allowed students to get a visual representation of what was happening. In addition, the teacher emphasized the importance of observing how they came to their answer rather than the answer itself.

Q: Which activities might you have replaced? Please provide an alternative activity to teach the same objective.

A: All the activities were great. I might have just added an extra step to the Think Pair Share part of the first day. In addition to students sharing it with their partner, you could also have students grab a new partner and have to show them their old partner's work and explanation.

Q: Was there not enough, just right, or too much overlap on activities and their relating objectives? For example, the four corners activity focused

46

on identifying operations as did the solving real life equations worksheet.

A: I believe that there was just enough activities and their relating objectives. It had a lot of steps that were well scaffolded. It allowed students to be able to learn in different ways and had various points where Ms. Grove could go back to reteach any topics students were not understanding completely.

Q: Did activities build upon each other with the proper scaffolding for each objective? Please give examples.

A: Yes. The activities started off with a basic activity allowing students to understand operations in simple word problems. Then the teacher reviewed variables and moved to an activity that allowed the teacher to explain solving for the unknown using manipulatives. Then, the teacher allowed students to try out their own problems and explain it to their partners. The next day, the teacher started off with lessons using videos to explain the beginning of real world problems with one step equations and gave opportunities for students to solve and think of their own problems.

Q: Are the rubrics detailed enough to evaluate learning for the given activity? Do you have any suggestions for improving the rubrics?

A: Yes. Q: Does the summative assessment, in appendix F, cover the desired

objectives in enough detail to determine mastery? Why or why not?A: Yes. It allowed the teacher to see the student's understanding of

operations, equation solving, and real life equation solving. Q: What are some suggestions you might have for improving the instruction

on the topic of solving one-step equations?A: None! This was great!

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Part 5h: Appendix H- ReferencesKeller, J. M. (1987). “The systematic process of motivational design.”

Performance & Instruction, 26 (9/10), 1-8.Larson, M.B. & Lockee, B.B. (2014). Streamlined ID: A practice guide to

instructional design. New York and London: Routledge Taylor & Francis Group.

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