Activity 1: Save the Zogs
Rationale
The purpose of this activity is for students to develop procedural fluency with graphing and writing linear equations. The game provides many examples of linear equations for students to consider, and the handout keeps the focus on relationships between the position variables. The dynamic environment of the game will allow for some exploration of the effect the m and b have on the equation y=mx+b. The purpose of including this lesson in the unit is to familiarize students with linear equations and their corresponding graphs so that the students are able to think critically when proceeding to considering linear relationships that are not based on position variables. The specific standards can be found covered can be seen in the next section.
Standards
The activity covers Common Core Georgia Performance Standards (CCGPS) for 8th Grade. The detail of standards could be found here.
Activity Links
Save the Zogs
Materials Needed
Access to website (http://www.mathplayground.com/SaveTheZogs/SaveTheZogs.html), computer lab, student handout (see attached file), paper, pencil.
Formative Question
See the handout attached below.
Sequence of Lesson
Warm-up: Introduce the unit to the class. Discuss how the class will be exploring linear and quadratic relationships. Give some examples of linear relationships (e.g. price of vegetables and weight of vegetables, price of house and square footage of house, time and plant growth, distance and time for a car traveling at 50 mph). Ask students to think of some other examples of quantities that they think might have a linear relationship. The discussion does not need to go into specifically whether the students are describing linear relationships or not. Rather, the idea is for students to understand that the goal of this unit is to use mathematics to describe the relationship between two variables.
Lecture: The lecture should cover the ideas needed for students to be able to graph and interpret linear equations. This section is specifically for obtaining a procedural understanding of writing an equation in y=mx+b form.
Description: The purpose of this activity is for students to practice graphing linear equations. The game provides a way for students to graph given linear equations and to find the linear equations for given graphs. At this point, students should be developing procedural fluency of linear equations. The purpose of the handout is for the students to maintain a sense of understanding the relationships between the variables instead of solely relying on memorized techniques (e.g. rise over run).
1. Allow the students to go to the website and to play the game for 10 minutes or so before handing out the handout.
Note: You can also assign the students to play the game for homework and come to class so they are immediately ready to jump into answering the questions.
2. Pass out the handouts.
3. Ask the students to answer the questions in the handout (in groups or individually) on a piece of paper.
Note: You can also project the questions on the screen.
4. After the students have completed their handouts, bring the class back together and have students share their linear/non-linear graphs with the class (Students can redraw them on the board or hold up their paper if their graphs were drawn big enough). Facilitate a discussion that centers around how students determined the values for their equations. This includes a discussion on the justification questions on the handout. Some possible questions include
Post-Activity: After the students complete the “Save the Zogs” activity, ask each of the students to write down what they learned and what they had trouble understanding during the lecture. Collect the responses from the students and be sure to address the troubling concepts in the following days.
Common Misconceptions and Difficulties
1. Students may have difficulty understanding how the m and b in y=mx+b affect the graph. Encourage them to explore the game using the tracking controls and noting the relationship between the horizontal and vertical components of the graph between the points. Be clear that in this case, the x and y axis are representing the horizontal and vertical position of graphs in this game.
2. Students may rely on procedure to determine the slope and y-intercept of the equations. Ask the student questions that will lead them back to focusing on the relationships between points. For instance, you can ask them how to get from one point/Zog to the next and whether the same is true when a third Zog is entered into the mix.
Resources
The purpose of this activity is for students to develop procedural fluency with graphing and writing linear equations. The game provides many examples of linear equations for students to consider, and the handout keeps the focus on relationships between the position variables. The dynamic environment of the game will allow for some exploration of the effect the m and b have on the equation y=mx+b. The purpose of including this lesson in the unit is to familiarize students with linear equations and their corresponding graphs so that the students are able to think critically when proceeding to considering linear relationships that are not based on position variables. The specific standards can be found covered can be seen in the next section.
Standards
The activity covers Common Core Georgia Performance Standards (CCGPS) for 8th Grade. The detail of standards could be found here.
Activity Links
Save the Zogs
Materials Needed
Access to website (http://www.mathplayground.com/SaveTheZogs/SaveTheZogs.html), computer lab, student handout (see attached file), paper, pencil.
Formative Question
See the handout attached below.
Sequence of Lesson
Warm-up: Introduce the unit to the class. Discuss how the class will be exploring linear and quadratic relationships. Give some examples of linear relationships (e.g. price of vegetables and weight of vegetables, price of house and square footage of house, time and plant growth, distance and time for a car traveling at 50 mph). Ask students to think of some other examples of quantities that they think might have a linear relationship. The discussion does not need to go into specifically whether the students are describing linear relationships or not. Rather, the idea is for students to understand that the goal of this unit is to use mathematics to describe the relationship between two variables.
Lecture: The lecture should cover the ideas needed for students to be able to graph and interpret linear equations. This section is specifically for obtaining a procedural understanding of writing an equation in y=mx+b form.
Description: The purpose of this activity is for students to practice graphing linear equations. The game provides a way for students to graph given linear equations and to find the linear equations for given graphs. At this point, students should be developing procedural fluency of linear equations. The purpose of the handout is for the students to maintain a sense of understanding the relationships between the variables instead of solely relying on memorized techniques (e.g. rise over run).
1. Allow the students to go to the website and to play the game for 10 minutes or so before handing out the handout.
Note: You can also assign the students to play the game for homework and come to class so they are immediately ready to jump into answering the questions.
2. Pass out the handouts.
3. Ask the students to answer the questions in the handout (in groups or individually) on a piece of paper.
Note: You can also project the questions on the screen.
4. After the students have completed their handouts, bring the class back together and have students share their linear/non-linear graphs with the class (Students can redraw them on the board or hold up their paper if their graphs were drawn big enough). Facilitate a discussion that centers around how students determined the values for their equations. This includes a discussion on the justification questions on the handout. Some possible questions include
- What are some similarities and differences between the non-linear equations each group drew?
- What would happen if we changed this point on the graph to this one?
- How can we think about finding the slope of an equation without using rise over run?
- What has to be true for three points to have a linear relationship?
- Can you give an example of some other linear relationships?
Post-Activity: After the students complete the “Save the Zogs” activity, ask each of the students to write down what they learned and what they had trouble understanding during the lecture. Collect the responses from the students and be sure to address the troubling concepts in the following days.
Common Misconceptions and Difficulties
1. Students may have difficulty understanding how the m and b in y=mx+b affect the graph. Encourage them to explore the game using the tracking controls and noting the relationship between the horizontal and vertical components of the graph between the points. Be clear that in this case, the x and y axis are representing the horizontal and vertical position of graphs in this game.
2. Students may rely on procedure to determine the slope and y-intercept of the equations. Ask the student questions that will lead them back to focusing on the relationships between points. For instance, you can ask them how to get from one point/Zog to the next and whether the same is true when a third Zog is entered into the mix.
Resources