Planning a Middle School Lesson Sequence on Newton’s Second Law.
The resource we will use for this lesson is found in Prentice-Hall’s Science Explorer -- Focus on Physical Science (California Edition), published in 2001. This textbook series is widely used across the nation and a special edition has been made to meet California’s educational standards. The material for this topic is found on pages 42 - 46 of this eighth grade science text. These pages of the text and teacher’s guide pages are reproduced here for your convenience. Take time to review these pages carefully. You will need to study the pages in this resource, including both the student pages and the notes to teachers, which surround the student pages in this copy. As you examine the textbook material, reflect on the content that is included, how it is presented, the meanings that can be derived from the diagrams, and the instructional approach that is implied in these pages.
Selected Textbook Pages
Figure 10.1. INSERT PP 42 – 46 including both student and teacher pages HERE –
Questions for Reflection and Discussion: As you examined the materials, what did you learn about (1) the content that is included, (2) how the content is presented, (3) representations of content are included that aid learning, (4) resources that are valuable for you as a teacher, (5) the instructional approach that is implicit?
Identifying and Clarifying Goals and Purposes for the Lesson Sequence
Now, let’s begin with thinking about the goals and purposes that are appropriate for students of this age (grade 8) to accomplish with this particular sequence of lessons.
Figure 10.2 is inserted here to provide you with a reminder of the Criteria in Categories I and VII that are useful in defining purposes of this lesson sequence.
Insert Figure 10.2 about here
At the outset, you should identify the appropriate standards and benchmarks for your school. Since I have chosen the California version of this text, I will begin by examining the Benchmarks from Project 2061, and the California Standards for Grade 8 Science (
Project 2061 Benchmarks relevant to this topic come from three levels. Benchmarks from Grades 3 – 5 show what may be expected as pre-requisite knowledge that students may have as you begin the topic. One benchmark is stated for this topic from the grade 3 – 5 list:
Something that is moving may move steadily or change its direction. The greater the force is, the greater the change in motion will be. The more massive the object is, the less effect a given force will have (Project 2061, 1993, p89).
A single benchmark is given for each the two higher levels. For Grades 6 – 8 the benchmarks is as follows:
In the absence of retarding forces, such as friction, an object will keep its direction of motion and its speed. Whenever an object is seen to speed up, slow down, or change direction, it can be assumed that an unbalanced force is acting on it (Project 2061, 1993, p90).
For Grades 10 – 12, the benchmark listed is a statement of Newton’s second law:
The change in motion of an object is proportional to the force applied and inversely proportional to the mass (Project 2061, 1993, p91).
The California Standards for Grade 8 Science on the topic of Force (which is the relevant set that follows standards for Motion) follow. The full set of standards are included to provide context; the most relevant standards are highlighted:
Forces
2. Unbalanced forces cause changes in velocity. As a basis for understanding this concept:
a. Students know a force has both direction and magnitude.
b. Students know when an object is subject to two or more forces at once, the result is the cumulative effect of all the forces.
c. Students know when the forces on an object are balanced, the motion of the object does not change.
d. Students know how to identify separately the two or more forces that are acting on a single static object, including gravity, elastic forces due to tension or compression in matter, and friction.
e. Students know that when the forces on an object are unbalanced, the object will change its velocity (that is, it will speed up, slow down, or change direction).
f. Students know the greater the mass of an object, the more force is needed to achieve the same rate of change in motion.
g. Students know the role of gravity in forming and maintaining the shapes of planets, stars, and the solar system.(Author’s note: This part of the standard appears to go beyond the scope of the lessons being planned.)
9. Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Students will:
a. Plan and conduct a scientific investigation to test a hypothesis.
b. Evaluate the accuracy and reproducibility of data.
c. Distinguish between variable and controlled parameters in a test.
d. Recognize the slope of the linear graph as the constant in the relationship y = kx and apply this principle in interpreting graphs constructed from data.
e. Construct appropriate graphs from data and develop quantitative statements about the relationships between variables.
f. Apply simple mathematic relationships to determine a missing quantity in a mathematic expression, given the two remaining terms (including speed = distance/time, density = mass/volume, force = pressure x area, volume = area x height).
g. Distinguish between linear and nonlinear relationships on a graph of data.
What will be the purposes and objectives of this lesson sequence? The authors of the textbook indicate that this topic addresses three benchmarks 2e, 2f and 9f, which are highlighted above. Drawing on the two sets of benchmarks, it appears that students should know and be able to do the following when they complete this set of lessons:
- Describe what is meant by change of motion, using terms such as velocity, speed, acceleration, speeding up, deceleration, slowing down, and changing direction.
- When examining a system in which a change in motion is noted, describe the change in speed and/or direction and identify the unbalanced force(s) acting on the object that change the object’s motion to demonstrate a sound understanding of the concept of acceleration.
- When examining a system in which motion is occurring describe, demonstrate and give examples of the following: a. different changes in motion including changes in speed and changes in direction; b. the effect of an unbalanced force in increasing, decreasing speed, or changing direction; c. the effect of different strength of forces on change in motion for a particular mass; d. the effect of a particular strength of force in changing the motion of different masses. (This can also be stated as follows: The change in motion of an object is proportional to the force applied and inversely proportional to the mass.)
- Identify and use newton as a unit of force that is consistent with the metric system.
- Evaluate the accuracy and reproducibility of data from empirical investigations.
Let’s reflect on these objectives. First, what do we want students to know about Newton’s second law? The textbook uses terms including force, mass and acceleration and it also shows the mathematical relationship among these, that is
Force = Mass x Acceleration and Acceleration = Force/Mass
By introducing the term “inversely proportional” in Objective 3 above, we have included understanding the mathematical relationships in Newton’s second law as part of the purposes of this lesson sequence. Also, since the textbook uses language that is commonplace, the terms in objective 1 are appropriate. Moreover, precise the distinctions between terms such as velocity and speed that are part of a physics course are not made in these lessons and would only add unnecessary complications at this point. Moreover, velocity is not used in the on the textbook pages for this lesson sequence.
Another aspect of the purposes of this lesson sequence is to allow students to both develop understanding of Newton’s second law and to learn how and when to use it. Therefore, the objectives include the terms demonstrate and give examples.
One complicating factor in the presentation of the material in the textbook is the use of newtons as the force unit, which this has not been introduced earlier in the text. This is not a familiar unit for students. Another complication is that the distinction between mass and weight does not appear to have been made as yet in this textbook, so students probably will not be familiar with this aspect of the topic. Benchmark 9f from the California Standards also adds a complication in that it requires that students can use a formula to calculate the missing term such as finding a numeric value for acceleration when the mass of an object and the force applied to it are known. Therefore, Objective 4 was added to account for these points.
How do the indicators, shown in Figure 10.3, help you in expressing purposes in a clear and comprehensible manner? All of the indicators are important.
Insert Figure 10.3 about here
Questions for Reflection and Discussion: Why has so much time and space been devoted to objectives for this short lesson sequence? Why is this an essential part of planning? How has each of the resources presented above been useful in identifying the objectives? Why is each of the resources necessary? What important resource should be included as you plan the lesson for your students that was not present if you teach somewhere other than California?
Creating a Supportive, Motivating Environment for Students
You must admit, that the set of five objectives above don’t seem too exciting for grade 8 students. So how can we make it more appealing to our students? I suggest that there are two aspects of making this topic more appealing: one is to address something of interest and the other is to address an aspect of science that may be intriguing to students’ developing view of the world. For the first, I suggest that the favorite sports of your students may be an important vehicle for incorporating some “life” into your purposes. Let’s assume that soccer is popular with your students, as it is with both male and female students at middle school level in many parts of the country. A soccer ball goes through many changes in motion during each minute of play. All of these involve acceleration resulting from unbalanced forces acting on the ball. Most people have observed hard kicks that have sent the ball through long distances at high rates of speed. Most people have seen the ball change direction and noted that the force causing the change has been a person’s feet or head or body. Therefore this is a good topic to use to enhance interest in the topic. If you add softball, or baseball, you can further enrich interest if your students are engaged in it.
This leads us to the formation of a central or driving question for this topic. Here is one suggestion; perhaps you can identify one, such as extreme skateboarding, for your class that is more appealing:
How can we understand the motion of a soccer ball during play?
The intention here is to use the motion and changes in motion of a soccer ball to develop understanding of motion in general. When kicked, stopped, headed, soccer balls change their motion. How does this relate to the forces applied to them? What if a soccer ball became water-soaked? How does this change its mass, and what affect does this have on its change in motion? What if soccer were played with a heavier or lighter ball? What if it were played with a larger ball with more air resistance?
Choosing a central question that allows you to transform your study of science into a topic that connects with students’ lives is an important part of instructional design. It needs thoughtful attention from teachers who are aware of, and capitalize on, their students’ interests and motivations. This thoughtful approach to making the subject matter more appealing to students is an example of Category VII, especially Criterion VII.B, Encouraging Curiosity and Questioning.
The second aspect of bringing “life” to the purposes is to give attention to how scientists think about, talk about, and understand motion. This will help students to understand the scientific habits of mind that have enabled scientists to give meaning to experiences and investigations with natural phenomena. It will help them understand what underlies the terms and rules that scientists use. Therefore, I recommend a second driving question as follows:
How do scientists think about and describe motion of objects?
I also suggest that these two questions be displayed in a prominent place in your classroom and remain there for the duration of this lesson sequence, and perhaps longer, as they may also be useful during subsequent lesson sequences in this unit including the study of friction and motion.
A Missing Element that You Must Provide
An essential component for understanding this topic is missing from both of these sets of statements about educational goals, and it is only implicit in the textbook. That component is a deep understanding of acceleration – that it is a change in either speed or direction of motion that occurs over some period of time. What makes it difficult to grasp is the fact that in many familiar instances the period of time is very short. Kicking a ball is a good example. How and when does acceleration occur? It is only in the fraction of a second that the kicker’s foot is in contact with the ball. In that short time, the foot compresses the ball’s motion changes from no motion, to motion at a high speed. If you think about throwing a ball, your arm swings through an arc, moving the ball from zero speed to a speed of many miles per hour in the fraction of a second it takes to complete the movement of your arm and release the ball. Acceleration of the ball occurs in that fraction of a second. The force on the ball that causes acceleration is from your hand. The speed of the ball after it leaves your hand is only as great as you, the thrower, impart to it.
It will be easier for students to observe negative acceleration, or deceleration, as soccer balls slow down when rolling across the grass. The retarding force is friction with the grass and air. Deceleration of a rolling soccer ball occurs over a longer duration and therefore is easier to study. Deceleration also can occur in an extremely short time duration when a moving ball is blocked. In such instances, the ball will go through a very rapid deceleration, from a high speed to a stop and then often rebound at a high speed. In less than a second, the ball will decelerate to zero speed and then accelerate to a high speed in a different direction. The forces involved in these changes are often quite large, as you know if you are the blocker! The forces on the rolling ball, which has a smaller deceleration are also smaller. These differences can be understood in terms of Newton’s Second Law – a = f/m.
In this lesson sequence, one important objective will be to help students understand acceleration deeply. Many different examples will be needed to help students attain this understanding. It also will require many different activities including hands-on experiences, reflection on those experiences, talking about them, writing about them, and representing them and the meaning behind them, in various ways. One difficulty is that most students will have a naïve concept about acceleration “as something related to speed.” Enhancing and clarifying that concept will be a critical, foundational part of your work in this unit. Unless you assure that this understanding emerges, many of your students will miss the importance and meaning of this lesson sequence.
Questions for Reflection and Discussion: How has the emphasis on Category VII helped you to think differently about this topic? In what ways do the two guiding questions about soccer and how scientists think improve the lesson sequence? What alternative would you recommend as guiding questions?
Questions for Reflection and Discussion: Return Figure 10.2 and rate the development on Objectives and Purposes according to the plan outlined in Chapter 9. Rate each item as S, P, or N, based on your interpretation of the adequacy of the development up to this point. Be reflective in assigning your ratings. It may be useful to have a group or whole-class discussion based on this task.
Students’ Ideas and Assessment
Looking next at Categories II and VI we will begin to examine how to build on students’ ideas and to consider assessment as part of backward design. These are summarized in Table 10.4 and 10.6 for your convenience.
Insert Figure 10.4 about here
What are the common misconceptions that students have on this topic of changing motion? Figure 10.5 contains one set I found on the internet at the following site that deals with force and motion: While all of these misconceptions relate in some way to Newton’s Second Law, the three that are highlighted are the most closely related.