Overview

This Learning Module was designed to teach students the mathematical concept of translating and solving word problems for basic equations. Equations and word problems are typically covered in Algebra 1 classes at the high school level or often introduced in Pre-Algebra classes or middle school mathematics classes. Thus, students engaged in this learning module could range in age from 6th grade students to high schoolers (typically 9th graders). Normally, students' experiences with equations and word problems is centered around a teacher led, student follow approach that does not leave much room for exploration or collaboration on the students' side. In this module, students will be engaged through the use of IXL, Khan Academy instructional videos and practice, collaborative productive struggle activites, independent research, and a final summative group project. Ideally, this classroom would need access to one-on-one tecnology for the students to access. Having access to a computer lab/mobile lab would also suffice. In addition, students will have the opportunity to explore and practice these concepts on paper/pencil as well. The use of technology will enhance the collaborative aspect for this learning module. This method creates a classroom community of learners as opposed to the usual teacher speaks, students listen approach. This learning module should take approximately three weeks of traditional 45/50 minute class periods.

Learning Objectives

The learning objectives for this learning module are as follows. The students will be able to:

Solve linear equations.
Translate algebraic phrases into expressions.
Write and solve linear equations based off word problem contexts.
Create algebraic equations that relate to word problems.
Interpret the meaning of the solution in a given word problem context.
Apply concepts of equations to their own lived experiences.

The Common Core State Standards that align with these learning objectives are:

CCSS.MATH.CONTENT.HSA.CED.A.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
CCSS.MATH.CONTENT.HSA.CED.A3 - Represent constriants by equations... and interpret solutions as vialbe or nonviable option is a modeling context.
CCSS.MATH.CONTENT.HSA.REI.B.3 - Solve linear equations... in one variable, including equations with coefficients represented by letters.
CCSS.MATH.CONTENT.HSA.SSE.A.1 - Interpret expressions that represent a quantity in terms of its context.
CCSS.MATH.CONTENT.HSF.IF.B.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function f(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
CCSS.MATH.CONTENT.HSA.BF.A.1 - Write a function that describes a relationship between two quantities.
CCSS.MATH.CONTENT.HSF.LE.A.1.B - Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
CCSS.MATH.CONTENT.HSF.LE.B.5 - Interpret the parameters in a linear function in terms of a context.

1. Prior Knowledge

For the Student

Before jumping into word problems, students need to be able to:

Successfully solve linear equations.
Identify the slope of a given linear equation.
Graph linear equations on the xy-coordinate plane.

Assigment: Individually, click the links provided to complete the following IXLs:

- S.3: Find the slope of a graph

- S.6: Slope-intercept form: find the slope and y-intercept

- S.7: Slope-intercept form: graph an equation

- S.8: Slope-intercept form: write an equation from a graph

- S.9: Slope-intercept form: write an equation

- S.12: Linear equations: solve for y

*If you are missing questions as you work through the IXL assignment, you have options!

Collaborate with your neighbor! Learn from each other. "No one knows everything, everyone knows something." --Pierre Lévy
Utilize IXL's step-by-step instructions on how to correctly solve to assist you. An screenshot of this can be seen in the image below:

Image Retrieved from: https://www.ixl.com/math/algebra-1/linear-equations-solve-for-y

For the Teacher

Purpose:

Before introducing word problems, make sure your students are proficient in solving, graphing, and understanding the parameters of a linear equation. These concepts are the foundation of prior knowledge students will need in order to successfully comprehend the word problems they will engage in. This section should be used as a formative pre-assessment for the instructor to gauge where their students' current level of knowledge stands.

Method:

The students will work through IXL to complete the assignments given. Utilize the IXL Teacher Dashboard's Live feature. This allows you to see in real time which students are struggling or not working on the assignment. A screenshot of this feature is shown below:

Image retrieved from: ixl.com

The Live Classroom feature changes the students to a red shade if they are consistently missing questions or moving too quickly through the questions/guessing.

In addition to monitoring their IXL progress through the Teacher Dashboard features, be walking amongst students as they work to monitor progress. I have found that simply being physically near the students encourages them to speak up if they need help.

Tips:

Since these skills are prerequisites, some students may finish the IXL assignments quicker than others. Take advantage of this and partner these students with other students who are struggling to remember these skills. Not only does this create a community of learners that depend on each other (and not solely the teacher as the source of knowledge), but also strengthens knowledge levels for all students involved. The students struggling receive peer tutoring and those students tutoring are deepening their comprehension of the concepts by explaining them to others.

2. Equation Terminology

For the Student

Learning Goals:

1. I can translate algebraic phrases into expressions.

2. I can solve linear equations.

Here are the notes for today's lesson:

Translating_20Expressions_20Notes_20Blank.pdf

Assignment: Watch the Khan Academy linked below. As he states in the video, pause the video and try to solve the expressions on your own before playing the remainder of the video to check yourself.

Media embedded February 22, 2020

^{Media Retrieved from:}^{https://www.khanacademy.org/math/cc-fifth-grade-math/imp-algebraic-thinking/imp-writing-expressions/v/translating-expressions-with-parentheses}

Start a Discussion Post: Create a post to discuss the important facts you learned from today's lesson. What was easy? What was surprising or difficult to understand? Name some of the key phrases needed to write an equation. Then, pose a phrase for your peers to translate into an equation and solve in the comments.

For the Teacher

Purpose:

By introducing translating expressions before a complete word problem, the students are not completely overwhelmed by the paragraph of words that comes with a word problem. Focusing solely on translating short expressions helps chunk this lesson into easy-to-understand concepts for the students to master.

Method:

Work through the guided note worksheet with students. Be sure to emphasize key word phrases; use the margins of the worksheet to fill in how "is" represents the equal sign of an equation and so on. Utilize a "I do, we do, you do" method when completing this worksheet. I have found that students grasp the idea quickly once they have seen a couple examples worked out for them. Give students collaborative work time to complete the worksheet examples. Then, when the majority of the class has completed the worksheet, have students come to the board, write out their work for the problems, and explain their ideas when solving. Try to sit aside and let students lead the classroom in this way. Encourage students to engage in a dialogue amogst themselves to debate their ideas - not to just look to the teacher for validation once they are done explaining themselves. A key for the worksheet is provided below:

Materials retrieved from: TeachersPayTeachers - Gina Wilson: All Things Algebra

Tips:

Teachers love to overtake the lesson. It can be easy to rush through the worksheet and simply give all the answers to the students. However, this truly is not beneficial for the students. They learn better when they are given the opportunity to struggle, collaborate, and make connections to their prior knowledge on new concepts. Take a step back and let the students control the thought process of class time. Of course, if class is not going towards the learning objective, step in and redirect the students back on track to reach the learning objective.

3. Creating Equations from Word Problems

For the Student

Learning Goal:

1. I can write and solve linear equations based off word problem contexts.

2. I can interpret the meaning of the solution in a given word problem context.

Notes/Practice: Today's notes are posted below:

Word_20Problem_20Notes_20Blank.pdf

Exit Slip: On your device, go to joinmyquiz.com and enter the code your teacher shares with you.

You will show your knowledge on writing equations from word problems through this Quizzizz.

Create a discussion post: How does today's lesson differ from translating equations that we did in the previous module? Create a situation where you could make an equation to solve it. Use today's notes and/or the Quizzizz to inspire you to connect your own life experiences to create your own word problem. Try to create and solve the equations for your peers' word problems.

For the Teacher

Purpose:

Going through some of the word problem examples as a whole class discussion helps students make connections betweens the translating of equations from the previous module. The more practice students have with word problems, the easier it will be for them to find the key words and phrases to create their equations.

Method:

Navigate through these guided notes similar to the approach in the previous module. Lead students in the first couple examples; be sure to emphasize key words and phrases as you work through the examples. Then, let students break into small groups to complete the remaining word problem examples. Engage students in a jigsaw activity. This method works best if you have groups of four students each. Give each small group 2-3 examples to work through on their own. Then, mix up the small groups so that one student from each group is matched with a group member from each group. Each person in the new groups will have the solutions for different examples. The students then take turns teaching their groups how to correctly solve their examples. A visual representation of how the jigsaw method works is shown below:

Image retrieved from: https://serc.carleton.edu/NAGTWorkshops/coursedesign/tutorial/jigsaw.html

The answer key for the notes are posted below. As the students are working on their jigsaw activity, walk amongst the students to ensure they are correctly solving and explaining the concepts. Do not control the dialogue amongst students, but redirect as needed.

Materials Retrieved from: TeachersPayTeachers - Gina Wilson, All Things Algebra

The Quizzizz Exit slip is a formative assessment to see how the students are comprehending the learning objectives. Either project or write down the code for them to all see and log into the Quizzizz. Quizzizz provides instant feedback on what your students are and are not understanding. It also shows the most missed question for each specific class. The link for the Quizzizz is here.

Tips:

Again, similar to the previous module, try to take a step back and let the students control the flow of the class time. During the jigsaw activity, if you notice students are not in the correct direction of the learning objective, redirect by asking leading questions instead of taking over their conversation. By doing this, your classroom is an environement where students are central to and in charge of their learning.

4. Independent Research: Word Problems in Your World

For the Student

Learning Goals:

1. I can create algebraic equations that relate to word problems.

2. I can appy concepts of equations to my own lived experiences.

Where are the "word problems" in your own life? How does Algebra and equations relate to your lived experiences?

Watch the Khan Academy video below. Work out the examples on a piece of paper. Pause the video and try to write the equation and solve the situation before seeing the answer.

Media embedded February 22, 2020

^{Video Retrieved from: KhanAcademy.com}

Independent Research:

Reflect on your own life. What are some experiences or situations you can think of that you could make into a word problem?
Research more ideas like the ones provided in the Khan Academy video to help you get some ideas flowing.

Create a Discussion Post: Discuss your findings. Share some of the connections you found in your own life that you think would make a great word problem. Explain why you think this situation would fit for a word problem example.

Comment on your peers' updates: On at least two other updates, start a dialogue with your peers. Did their ideas spark any new ones for yourself? Critique their ideas - how would a word problem look for their ideas? how could they improve their ideas?

For the Teacher

Purpose:

This section of the learning module is essential to the upcoming group project where students create their own situation for a word problem. Having students reflect upon their own life and research different examples of word problems will help them in making connections to experiences in their life to a potential word problem.

Method:

The students have been working collaboratively for the majority of this learning module thus far, which is great. However, this section gives students the opportunity to reflect upon their own lives and make their own connections without the influence of their peers or teacher. As students are working, walk amongst them to ensure they are on the right track. Avoid telling students what to search for directly. Pose probing questions to get students reflecting on what situations could be properly modeled by linear equations.

Tips:

If students are struggling to find purpose or find connectins to their lives, lead them to any of the following videos or articles that explain why word problems are so essential and give them more examples to build from.

- Mathnasium: "Why Do I Need to Learn This?"

- Khan Academy Example Videos:

Media embedded February 22, 2020

^{Videos Retrieved from: KhanAcademy.com}

5. Group Project: Applying Word Problems

For the Student

Learning Goals:

1. I can apply concepts of equations to my own lived experiences.

2. I can create algebraic equations that relate to word problems.

3. I can interpret the meaning of a solution in a given word problem context.

Now that you have completed your independent research, you will apply it to create your own word problem that connects to your life. You will work in small groups to collaboratively create a word problem that involves:

A linear equation based word problem that is relevant to your lived experiences.
The word problem created must be a realistic situation.
Your team must solve the word problem created algebraically.
Explain your solution in terms of its context.
Provide a visual display of your project (be creative!).

Some things to think about when brainstorming in your small groups...

What type of information do you need to make a complete word problem?
How much information is "too much" for your problem?
Can you justify why your group chose this specific word problem?

The image below is an example of a previous year's project:

Image Retrieved from: Rantoul Township High School Student Work

Discuss in your small groups...

Does this poster explain the relevance to the author's life?
Is there enough infomation?
What else could be included?
What could be excluded?
How could this be better?

If you and your team are completely lost, go back and reflect on your independent research completed in the last learning module. The grading rubric for your project is posted below for your reference as well.

Creating_20Your_20Own_20Word_20Problem_20Group_20Project_20Rubric.pdf

For the Teacher

Purpose:

This group project will allow students to apply their knowledge learned thus far. Each student will be abe to take thier research they completed independently and collaborate with their group members to create a full presentation that displays their learning.

Method:

Introduce the project and explain the rubric to the students. Showing them an example of what the project should/could look like is helpful for students as well. Encourage students to combine their ideas gathered from their independent research, but let them figure out their final idea. This project should be introduced as a type of productive struggle activity. This means that the students should be figuring out what information they need to make a successful word problem. You should pose probing questions like: what information do you need? how many numbers do you need to create a complete word problem? is this a realistic word problem? If students are struggling to get started, point them back to their independent research. Help them to create the connections between the learning and their lived experiences, but do not tell them what their project should be about. One example of a past project is shown in the image below:

Image retrieved from: Rantoul High School Student Work

Tips:

The end result of the projects should not be exactly the same. The point of a productive struggle is that students will display their knowledge in different ways. Some may choose to display their equations on a graph instead of incorporating artwork. The idea is that their knowledge is put on a visual display that they can explain their thought process from.

6. Peer Review of Projects

For the Student

Learning Goal:

1. I can write and solve linear equations based off word problem contexts.

Partner up with one or two other groups. You will be reviewing each other's projects, providing positive comments, and constructive feedback.

Image retrieved from: https://www.liveyourtruestory.com/2-easy-ways-to-deliver-feedback-infographic-communication/

Each group will...

Present their project - explain the reasoning behind why you chose to create your specific word problem.
Ask the presenting group questions about their project - why did they choose the specific numbers they did? How is their project relevant to their lives?
Record your positive comments and constructive feedback on the rubrics provided below:

Creating_20Your_20Own_20Word_20Problem_20Group_20Project_20Rubric.pdf

Once you recieve your feedback, collaborate with your group and revise your project to make it the best it can be.

Create a discussion post: How did the peer review help your group's project? What aspects did your group do very well? Where did your group need improvement for the project? What ideas did you get from the group's you reviewed?

Comment: Share your thoughts on the peer review process. Do you agree with your peer's perspective? Was it useful to do this? Explain and share your ideas.

For the Teacher

Purpose:

Allowing students to engage in a peer review allows students to reflect upon their own projects, all while providing meaningful feedback to their peers. This also starts the pattern for students to know that they can always improve on their work to make it even better.

Method:

Depending on your class size and time restraints, have student groups partner up or in partner together with two other groups. Three groups collaborating together should be more than enough. Review over the image of how to effectively provide positive comments and constructive feedback with the whole class. Then, allow students to break off and present their projects to their peer groups. Walk amongst the students to ensure that the feedback they are providing and receiving is helpful and following their provided rubric, but do not overtake their dialogue. Allow the students to do the thinking for this activity.

Tips:

This activity may take a couple class periods to complete, but it is worth the time. I would suggest giving at least one (maybe two classes) for groups to present to each other, one for students to discuss their feedback with each other, and one more class for students to revise and improve their projects before final submission.