Note: Vocabulary words in bold are defined on the attached Pendulum Vocabulary sheet.

**ENGAGE **(15 - 20 minutes - Choose the option that best meets the needs of your students):

**Option A: Solving a Real-World Problem with Swings**

- Take students onto playground and tell students they are going to have a contest to see who can swing the fastest. Ask students how you will figure out the winner. How can we determine which swing is going the fastest? Students should come up with the idea that the fastest swinger is the person who swings the greatest number of times in a given amount of time. Time students for 15 second intervals to see which student swings the fastest.
- Return to classroom and use playing cards to sort students into groups of 4. Students with the same number will be in the same group; each suit will be assigned a job within the group.
*Hearts*= recorder / counter, *Clubs* = timer, *Spades* = Starter, *Diamonds* = counter. You may choose to assign these jobs strategically or rotate the jobs to each student in the group once the exploration starts.
- Ask students why they think the person who won the contest did so. As students discuss this in small groups, circulate to listen to their ideas. Possible responses may be that he/she is the strongest, has the longest legs, is the lightest, is the heaviest, etc. Then have students brainstorm all the things they might change about the swing to give themselves a better chance of winning. The recorder for the group should record the group’s responses. Collect all responses on a class chart.

**Option B: Solving a Real-World Problem about a Grandfather Clock**

- Show students a real grandfather clock or use a clock animation to demonstrate the pendulum on a grandfather clock.
- Read "Grandfather's Clock" story aloud to students to present the problem of a grandfather clock that is running too slowly. (You may also choose to print copies of this story for each student to make this part into a guided reading lesson.)
- Use playing cards to sort students into groups of 4. Students with the same number will be in the same group; each suit will be assigned a job within the group.
*Hearts*= recorder / counter, *Clubs* = timer, *Spades* = Starter, *Diamonds* = counter. You may choose to assign these jobs strategically or rotate the jobs to each student in the group once the exploration starts.
- Ask students what they think they could change about the pendulum to speed up the grandfather clock. As students discuss this in small groups, circulate to listen to their ideas. Possible responses may be the weight on the pendulum, the length of the pendulum, etc. Some students may focus on the interior clock mechanisms, so assure students that the pendulum swing controls the speed of the clock. The recorder for the group should record the group’s responses. Collect all responses on a class chart.

**EXPLORE** (20 - 30 minutes if each group only tests one variable, up to 2 hours if each group tests each variable at stations):

For the exploration, you can either let each group decide on one variable to test *or* have all groups rotate through four stations to test each of the variables. The plan below is written assuming that each group will only test one variable, but your data will be more accurate if all groups test each variable in stations. Students will have a better understanding of variables and the experimental process if they test each variable, but you can “divide and conquer” for the sake of time if necessary!

- Tell students they will be making a pendulum to simulate a swing. To help students identify the parts of the pendulum system, have them use the "Make a Swinger" handout to construct a standard pendulum. For the pendulum weight, students may either attach a penny or a washer. (The benefit of using washers is that they are easier to attach, but you must have washers of three different sizes for students to use. Pennies are more readily available, but students may need to tape them in place to keep them from flying off the pendulum when it is swung.)
- Once all students have constructed a pendulum, discuss how you will count the number of swings a pendulum makes. Decide on a standard of counting full
**cycles**. As you time the students for 15 seconds, have them count the number of cycles. Ask students is every group should have counted the same number, which they should have. Explain that this is the **standard** swinger, meaning that every group made it the same way and therefore should have gotten the same **result**. Ask them to brainstorm a list of parts of the pendulum system, putting a star by the ones that they think will affect the number of swings the pendulum makes in 15 seconds. Students will probably come up with changing the weight, changing the length of the string, type or thickness of string, force pushing the pendulum, and release position. Explain that since the students are using the pendulum as a model for a swing, they are trying to figure out how to modify *the swinger or pendulum*, not the *force* with which the swing is pushed. The pendulum should simply be dropped and allowed to swing using the forces of gravity and momentum. However, students should consider anything they could change about the pendulum other than the force to change the number of swings. Have groups share their findings and post on class chart.
- Discuss how to gather accurate data (attend to precision, have more than one person count and retry if students do not get the same number, make sure recorder writes down number as soon as the data is collected, count silently so you do not get your count mixed up with another group’s, etc.).
- For groups that are selecting a variable to test, have each group fill out the project planning sheet (included in the uploaded documents section). If you prefer to set up four stations where each group tests each of the four variables, use the pendulums stations sheet instead. The stations sheet already has most of the planning done for the students. If each group is going to plan its own experiment, walk them through the planning sheet using the attached digital presentation.
- Have groups experiment and collect data on recording sheets. You can let a student be the timer in each group, or you can be the timer and assign the timer a counting job instead. Each group tests the variable 3 times and records the number of cycles in 15 seconds. Since students at this grade level have not yet learned to compute the mean, have them use the median as the average for their three trials.
- After collecting the data, have groups discuss the differences in the medians (if any) and write a conclusion that answers the original question about whether their variable affected the number of swings.
- Have each group report back to the whole class and discuss which variable actually affected the number of swings in 15 seconds (the length of the string).

**EXPLAIN **(30 - 40 minutes):

- Have students turn and talk to a partner about why they think the length of the string affected the number of swings when the other variables did not make a difference in the results.
- Use PHet virtual pendulum to show two pendulums at the same time. Ask students what they could do to win the swinging contest (“Have the shortest swing!”)
- But what if we wanted to be able to tell how many times ANY pendulum would swing in 15 seconds? How could we figure it out without having to test every length pendulum in the world? Give students time to discuss this question. They will probably say that they need more data.
- Hang a number line on the board with numbers from 1-30. Tell students that they need to collect more data to be able to predict the motion of any possible pendulum, so they are going to do more tests. Hang the standard pendulum under the number of swings it made in 15 seconds. Students who tested other lengths may also hang those pendulums under the number of swings those pendulums made.
- Distribute length cards to each group so each group can test 1 – 3 more pendulums. Very long pendulums will need to be hung from a door frame or other high structure. These groups may take longer to test their pendulums. Groups will continue testing pendulums and hanging pendulums on the number line until all the length cards are used. Make sure each group tapes the length to the pendulum so they can tell which length made each number of swings.
- Have students look at number line and pendulums to notice the general trend. Does it match their original conclusion that shorter pendulums swing faster and longer pendulums swing slower? Is there any data that appears inconsistent? Retest individual pendulums that do not follow the pattern to make sure that data is accurate.
- Give each student a Swingers Picture Graph sheet (p. 5 of FOSSWeb resource). Fill in the chart at the bottom of the page together, making sure the students can see the length of each pendulum and the number of swings it made. After students have filled in chart, have them draw each pendulum under the appropriate number.

**ELABORATE** (15 – 20 minutes):

- Have students take the data from the Swingers Picture Graph and transfer it into a bar graph.
- Model how to use this graph to predict the movement of pendulums not tested. Ask probing questions, such as “Why don’t we have any pendulums under the numbers 1 – 4? Why doesn’t our number line need to go above 30?”
- Return to original problem posed in ENGAGE portion of lesson. If your students are figuring out how to win the swinging contest, go back outside and shorten some of the swings for second contest. (For safety considerations and to eliminate differences in students pushing the swings, have students release the swings without passengers to observe the shortest swing swinging faster than the others.) If your students are solving the grandfather clock problem, tell them that the pendulum needs to swing 8 times in 15 seconds to keep accurate time. Students need to use their graphs to predict the length of a pendulum that meets this criteria. Then they will test their predictions and make modifications as needed to make a successful pendulum.

Note: Vocabulary words in bold are defined on the attached Pendulum Vocabulary sheet.

**ENGAGE **(15 - 20 minutes - Choose the option that best meets the needs of your students):

**Option A: Solving a Real-World Problem with Swings**

- Take students onto playground and tell students they are going to have a contest to see who can swing the fastest. Ask students how you will figure out the winner. How can we determine which swing is going the fastest? Students should come up with the idea that the fastest swinger is the person who swings the greatest number of times in a given amount of time. Time students for 15 second intervals to see which student swings the fastest.
- Return to classroom and use playing cards to sort students into groups of 4. Students with the same number will be in the same group; each suit will be assigned a job within the group.
*Hearts*= recorder / counter, *Clubs* = timer, *Spades* = Starter, *Diamonds* = counter. You may choose to assign these jobs strategically or rotate the jobs to each student in the group once the exploration starts.
- Ask students why they think the person who won the contest did so. As students discuss this in small groups, circulate to listen to their ideas. Possible responses may be that he/she is the strongest, has the longest legs, is the lightest, is the heaviest, etc. Then have students brainstorm all the things they might change about the swing to give themselves a better chance of winning. The recorder for the group should record the group’s responses. Collect all responses on a class chart.

**Option B: Solving a Real-World Problem about a Grandfather Clock**

- Show students a real grandfather clock or use a clock animation to demonstrate the pendulum on a grandfather clock.
- Read "Grandfather's Clock" story aloud to students to present the problem of a grandfather clock that is running too slowly. (You may also choose to print copies of this story for each student to make this part into a guided reading lesson.)
- Use playing cards to sort students into groups of 4. Students with the same number will be in the same group; each suit will be assigned a job within the group.
*Hearts*= recorder / counter, *Clubs* = timer, *Spades* = Starter, *Diamonds* = counter. You may choose to assign these jobs strategically or rotate the jobs to each student in the group once the exploration starts.
- Ask students what they think they could change about the pendulum to speed up the grandfather clock. As students discuss this in small groups, circulate to listen to their ideas. Possible responses may be the weight on the pendulum, the length of the pendulum, etc. Some students may focus on the interior clock mechanisms, so assure students that the pendulum swing controls the speed of the clock. The recorder for the group should record the group’s responses. Collect all responses on a class chart.

**EXPLORE** (20 - 30 minutes if each group only tests one variable, up to 2 hours if each group tests each variable at stations):

For the exploration, you can either let each group decide on one variable to test *or* have all groups rotate through four stations to test each of the variables. The plan below is written assuming that each group will only test one variable, but your data will be more accurate if all groups test each variable in stations. Students will have a better understanding of variables and the experimental process if they test each variable, but you can “divide and conquer” for the sake of time if necessary!

- Tell students they will be making a pendulum to simulate a swing. To help students identify the parts of the pendulum system, have them use the "Make a Swinger" handout to construct a standard pendulum. For the pendulum weight, students may either attach a penny or a washer. (The benefit of using washers is that they are easier to attach, but you must have washers of three different sizes for students to use. Pennies are more readily available, but students may need to tape them in place to keep them from flying off the pendulum when it is swung.)
- Once all students have constructed a pendulum, discuss how you will count the number of swings a pendulum makes. Decide on a standard of counting full
**cycles**. As you time the students for 15 seconds, have them count the number of cycles. Ask students is every group should have counted the same number, which they should have. Explain that this is the **standard** swinger, meaning that every group made it the same way and therefore should have gotten the same **result**. Ask them to brainstorm a list of parts of the pendulum system, putting a star by the ones that they think will affect the number of swings the pendulum makes in 15 seconds. Students will probably come up with changing the weight, changing the length of the string, type or thickness of string, force pushing the pendulum, and release position. Explain that since the students are using the pendulum as a model for a swing, they are trying to figure out how to modify *the swinger or pendulum*, not the *force* with which the swing is pushed. The pendulum should simply be dropped and allowed to swing using the forces of gravity and momentum. However, students should consider anything they could change about the pendulum other than the force to change the number of swings. Have groups share their findings and post on class chart.
- Discuss how to gather accurate data (attend to precision, have more than one person count and retry if students do not get the same number, make sure recorder writes down number as soon as the data is collected, count silently so you do not get your count mixed up with another group’s, etc.).
- For groups that are selecting a variable to test, have each group fill out the project planning sheet (included in the uploaded documents section). If you prefer to set up four stations where each group tests each of the four variables, use the pendulums stations sheet instead. The stations sheet already has most of the planning done for the students. If each group is going to plan its own experiment, walk them through the planning sheet using the attached digital presentation.
- Have groups experiment and collect data on recording sheets. You can let a student be the timer in each group, or you can be the timer and assign the timer a counting job instead. Each group tests the variable 3 times and records the number of cycles in 15 seconds. Since students at this grade level have not yet learned to compute the mean, have them use the median as the average for their three trials.
- After collecting the data, have groups discuss the differences in the medians (if any) and write a conclusion that answers the original question about whether their variable affected the number of swings.
- Have each group report back to the whole class and discuss which variable actually affected the number of swings in 15 seconds (the length of the string).

**EXPLAIN **(30 - 40 minutes):

- Have students turn and talk to a partner about why they think the length of the string affected the number of swings when the other variables did not make a difference in the results.
- Use PHet virtual pendulum to show two pendulums at the same time. Ask students what they could do to win the swinging contest (“Have the shortest swing!”)
- But what if we wanted to be able to tell how many times ANY pendulum would swing in 15 seconds? How could we figure it out without having to test every length pendulum in the world? Give students time to discuss this question. They will probably say that they need more data.
- Hang a number line on the board with numbers from 1-30. Tell students that they need to collect more data to be able to predict the motion of any possible pendulum, so they are going to do more tests. Hang the standard pendulum under the number of swings it made in 15 seconds. Students who tested other lengths may also hang those pendulums under the number of swings those pendulums made.
- Distribute length cards to each group so each group can test 1 – 3 more pendulums. Very long pendulums will need to be hung from a door frame or other high structure. These groups may take longer to test their pendulums. Groups will continue testing pendulums and hanging pendulums on the number line until all the length cards are used. Make sure each group tapes the length to the pendulum so they can tell which length made each number of swings.
- Have students look at number line and pendulums to notice the general trend. Does it match their original conclusion that shorter pendulums swing faster and longer pendulums swing slower? Is there any data that appears inconsistent? Retest individual pendulums that do not follow the pattern to make sure that data is accurate.
- Give each student a Swingers Picture Graph sheet (p. 5 of FOSSWeb resource). Fill in the chart at the bottom of the page together, making sure the students can see the length of each pendulum and the number of swings it made. After students have filled in chart, have them draw each pendulum under the appropriate number.

**ELABORATE** (15 – 20 minutes):

- Have students take the data from the Swingers Picture Graph and transfer it into a bar graph.
- Model how to use this graph to predict the movement of pendulums not tested. Ask probing questions, such as “Why don’t we have any pendulums under the numbers 1 – 4? Why doesn’t our number line need to go above 30?”
- Return to original problem posed in ENGAGE portion of lesson. If your students are figuring out how to win the swinging contest, go back outside and shorten some of the swings for second contest. (For safety considerations and to eliminate differences in students pushing the swings, have students release the swings without passengers to observe the shortest swing swinging faster than the others.) If your students are solving the grandfather clock problem, tell them that the pendulum needs to swing 8 times in 15 seconds to keep accurate time. Students need to use their graphs to predict the length of a pendulum that meets this criteria. Then they will test their predictions and make modifications as needed to make a successful pendulum.