# IB Physics Standard 2.1.5 (Analyze and calculate the slopes of displacement-time graphs and veloc...

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IB Physics Standard 2.1.5 (Analyze and calculate the slopes of displacement-time graphs and velocity-time graphs, and the areas under velocity-time graphs and acceleration-time graphs

## 1. Objective 1: Analyze and calculate the slopes of displacement-time graphs

### 1.1. Big Idea 1: Calculate the slope of a displacement-time graph

1.1.1. Key Factors about the IB Physics Students: Each student would have taken an algebra course by now and would be familiar with how to calculate slopes.

1.1.1.1. Scaffolding Strategy 1: Show and Tell

1.1.1.1.1. In the first activity we will watch a high speed camera video of several students ice skating across a 5 m section of ice. We will verbally describe their motion and then try to plot their motion using a displacement time graph

1.1.1.2. Scaffolding Strategy 2: Tap into Prior Knowledge

1.1.1.2.1. After plotting the data collected from the video we will then review the concepts of slopes and gradients, from their algebra class, and relate the slope of a displacement time graph to velocity

1.1.1.3. Scaffolding Strategy 3: Give Time to Talk

1.1.1.3.1. Students will now have time to calculate the individual velocities of the students using their graphs. Students will be assigned to groups randomly to do this.

1.1.1.4. Scaffolding Strategy 4: Pre-teach vocabulary

1.1.1.4.1. The terms slope, gradient, displacement, time and velocity will be defined for the students

1.1.1.5. Scaffolding Strategy 5: Use Visual Aids

1.1.1.5.1. I will show the students a video on how to draw displacement-time graphs

1.1.1.5.2. We will also look at creating displacement-time graphs using a PhET simulation

1.1.1.6. Scaffolding Strategy 6: Pause, Ask Questions, Pause, Review

1.1.1.6.1. Students will have the opportunity here to use another PhET simulation to predict the motion of a man moving back and forth with respect to displacement-time graphs. Here students can investigate the motion of the man moving forwards, backwards and accelerating. Students will be able to pause, ask questions and review concepts that we have covered in class that day.

## 2. Objective 2: Analyze and calculate the slopes of velocity time graphs

### 2.1. Big Idea 2: Calculate the slope of a velocity-time graph

2.1.1. Key Factors about the IB Physics Students: Each student would have taken an algebra course by now and would be familiar with how to calculate slopes.

2.1.1.1. Scaffolding Strategy 1: Show and Tell

2.1.1.1.1. In the first activity we will watch a high speed camera video of several students ice skating across a 5 m section of ice. We will verbally describe their motion and then try to plot their motion using a velocity time graph

2.1.1.2. Scaffolding Strategy 2: Tap into Prior Knowledge

2.1.1.2.1. After plotting the data collected from the video we will then review the concepts of slopes and gradients, from their algebra class, and relate the slope of a velocity-time graph to velocity

2.1.1.3. Scaffolding Strategy 3: Give Time to Talk

2.1.1.3.1. Students will now have time to calculate the individual accelerations of the students using their graphs. Students will be assigned to groups randomly to do this.

2.1.1.4. Scaffolding Strategy 4: Pre-teach vocabulary

2.1.1.4.1. The terms slope, gradient, velocity, time and acceleration will be defined for the students

2.1.1.5. Scaffolding Strategy 5: Use Visual Aids

2.1.1.5.1. I will show the students a video on how to draw velocity-time graphs

2.1.1.6. Scaffolding Strategy 6: Pause, Ask Questions, Pause, Review

2.1.1.6.1. Students will have the opportunity here to use another PhET simulation to predict the motion of a man moving back and forth with respect to velocity-time graphs. Here students can investigate the motion of the man moving forwards, backwards' accelerating and decelerating. Students will be able to pause, ask questions and review concepts that we have covered in class that day.

## 3. Objective 3: Calculate the area under a velocity-time graph

### 3.1. Big Idea 3: Determine what the area under a velocity-time graph represents with motion

3.1.1. Key Factors about the IB Physics Students: Each student would have taken a basic geometry course by now and would be familiar with how to calculate the area of different shapes (triangles, circles and rectangles)

3.1.1.1. Scaffolding Strategy 1: Show and Tell

3.1.1.1.1. With this activity we will start by looking at the PhET Moving Man simulation for displacement-time graphs. I will ask the students to use the given motion to create a velocity-time graph

3.1.1.2. Scaffolding Strategy 2: Tap into Prior Knowledge

3.1.1.2.1. With this activity we will collect some data on students walking 25 m, running 25 m and accelerating over 25 m. The students will be expected to graph their data using Excel, Numbers or Loggerpro. Once they have done this they will then use integration to measure the area under the velocity-time graphs they have created.

3.1.1.3. Scaffolding Strategy 3: Give Time to Talk

3.1.1.3.1. Students will then have the opportunity to talk about what they think the area under the curve represents after they have integrated the data.

3.1.1.4. Scaffolding Strategy 4: Pre-teach Vocabulary

3.1.1.4.1. We will review the following vocabulary terms: velocity, time, acceleration, and area

3.1.1.5. Scaffolding Strategy 5: Use Visual Aids

3.1.1.5.1. I will show the students a video on what the area under a curve for a velocity-time graph represents and how it correlates to the integration we did earlier in class.

3.1.1.6. Scaffolding Strategy 6: Pause, Ask Questions, Pause, Review

3.1.1.6.1. At the end I will give students several practice problems to work on in class with velocity-time graphs. Here students will have the opportunity to work in small groups, which have been chosen at random, to solve for the area under the given curves. After solving a few questions students will then collect data of an accelerating cart on an air track. They will then plot this data and use the differentiation tools in Excel, Numbers or Loggerpro to determine the area under their curves. This will allow students to move at their own pace while discussing concepts and reviewing together.

## 4. Objective 4: Calculate the area under an acceleration-time graph

### 4.1. Big Idea 4: Determine what the area under an acceleration-time graph represents with motion

4.1.1. Key Factors about the IB Physics Students: Each student would have taken a basic geometry course by now and would be familiar with how to calculate the area of different shapes (triangles, circles and rectangles)

4.1.1.1. Scaffolding Strategy 1: Show and Tell

4.1.1.1.1. With this activity we will start by looking at the PhET Moving Man simulation for displacement-time graphs. I will ask the students to use the given motion to create a acceleration-time graph

4.1.1.2. Scaffolding Strategy 2: Tap into Prior Knowledge

4.1.1.2.1. With this activity we will collect some data on students walking 25 m, running 25 m and accelerating over 25 m. The students will be expected to graph their data using Excel, Numbers or Loggerpro. Once they have done this they will then use integration to measure the area under the acceleration-time graphs they have created.

4.1.1.3. Scaffolding Strategy 3: Give Time to Talk

4.1.1.3.1. Students will then have the opportunity to talk about what they think the area under the curve represents after they have integrated the data.

4.1.1.4. Scaffolding Strategy 4: Pre-teach Vocabulary

4.1.1.4.1. We will review the following vocabulary terms: time, acceleration, and area

4.1.1.5. Scaffolding Strategy 5: Use Visual Aids

4.1.1.5.1. I will show the students a video on what the area under a curve for a velocity-time graph represents and how it correlates to the integration we did earlier in class.

4.1.1.6. Scaffolding Strategy 6: Pause, Ask Questions, Pause, Review

4.1.1.6.1. At the end I will give students several practice problems to work on in class with acceleration-time graphs. Here students will have the opportunity to work in small groups, which have been chosen at random, to solve for the area under the given curves. After solving a few questions students will then collect data of an accelerating cart on an air track. They will then plot this data and use the differentiation tools in Excel, Numbers or Loggerpro to determine the area under their curves. This will allow students to move at their own pace while discussing concepts and reviewing together.