Purpose

In this practical unit students make ramps, roll marbles down them, record the distance the marble travels from different starting positions, graph these distances, predict other distances, and make statements based on the information they find out.

Achievement Objectives

S4-1: Plan and conduct investigations using the statistical enquiry cycle: determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, varia

Specific Learning Outcomes

- construct a stable ramp to meet conditions
- follow and repeat a procedure to replicate exactly the same conditions
- measure and record distances accurately
- graph the starting positions and distances traveled on scatter graphs
- talk about distinctive features of scatter graphs
- make statements, backed up by reference to graphs, about possible actions

Description of Mathematics

Scatter graphs are introduced in this unit. To understand scatter graphs students need to comprehend the relationship between the horizontal and vertical axes, i.e. x-axis and y-axis, and how one mark on the graph displays two variables. Making predictions based on information from graphs and from student’s own experimenting is a feature of this unit. The nature of predicting, the risks of predicting based on a small number of trials, handling unexpected results, looking for patterns and trends and making sense of the results are areas the teacher needs to be aware of, and specifically teach, when needed.

The practical nature of this unit lends itself to teaching concepts in small groups of students, when needed. The teacher’s role throughout the unit is to question and ask students to justify their predictions and way of working. The unit is cross-curricular with achievement objectives from Science in the New Zealand Curriculum Making Sense of the Physical World, Level 4. * process and interpret information to describe or confirm trends and relationships in observable physical phenomena

Required Resource Materials

- material to raise one end of the ramp, e.g. books
- instrument to measure distances, i.e. student made or commercial ruler
- Scatter Graph - Blank, Copymaster 1
- material to make a stable ramp, e.g. wooden metre rulers
- one marble
- Scatter Graph Samples, Copymaster 2 (501KB)
- paper and pencil

Key Vocabulary

experiment, prediction, scatter graph, distinctive feature, horizontal axis, vertical axis, variables, trials, justify, trends, linear trend, outliers,

Activity

During this session students are to make ramps, roll marbles down them and record the distance the marbles travels.

Organise the students into pairs and have them make a stable ramp. The ramp could be made using a single wooden metre ruler with a grove down the middle of it, two metre rulers joined together or other suitable material. The ramp needs to remain the same throughout the session. Place one end of the ramp on books to make a slope and the other end positioned to allow the marble to roll until it stops without hitting anything. Some experimentation will be needed to get an appropriate height and position to allow the marble to roll freely to a stop. The positioning of all the students’ ramps needs thinking through, as it is important that the marbles roll without hitting anything before they stop.

Once a stable ramp has been made and tested, have the students record the features of the ramp so it can be put away and rebuilt in exactly the same way in later sessions.

With the ramps in place, have the students roll their marbles down their ramps, rolling to a stop. The distance from the end of the ramp needs to be recorded each time the marble is rolled. Each pair of students need to roll and record the marble 20 times during this session - see the five tasks below. How the students measure the distance the marble rolls needs to be considered. Students could make their own metre ruler using a strip of paper or card as a way to obtain the number of rulers needed.

Task 1: Roll the marble from the top of the ramp

Start the marble at the top of the ramp and record the distance it travels from the bottom of the ramp. Record the distance travelled by the marble for four rolls.

Task 2: Start 10 cm from the top of the ramp

This time, start the marble 10 centimetres from the top of the ramp and record the distance it travels from the bottom of the ramp. Record the distance travelled by the marble for four rolls.

Task 3: Start 20 cm from the top of the ramp

Roll the marble and measure the distance starting 20 centimetres from the top of the ramp. Record the distance travelled by the marble for four rolls.

Task 4: Start 80 cm from the top of the ramp, i.e. 20 cm from the bottom

Roll and measure four times.

Task 5: Start 90 cm from the top of the ramp, i.e. 10 cm from the bottom

Roll and measure four times.

Once completed, pack the ramp and marbles away, reminding the students that they will need to set up their ramps exactly as they are today in the next session. Make sure they keep the 20 distances they recorded.

Each pair of students is to rebuild their ramp so it is exactly the same as it was in Session One. Once completed, they are to roll the same marble used in Session One, down their ramp once from each of the five starting positions, recording the distance travelled from the end of the ramp. These five distances are to be added to the distances from Session One.

The students are to leave the ramps in place and shift their focus to the recording of the distances onto a scatter graph. Explain to the class what a scatter graph is and how the two axes are used to show the starting distance and the distance rolled using a single cross. Show the students the completed scatter graph below.

Ask the students:

- Could this graph be helpful in predicting other starting positions?
- What distance would the marble travel if started 50 cm from the top of the ramp?

Discuss the distinctive features of the above graph:

- the distances that do not follow the pattern, i.e. outliers
- the clusters or groupings of the distances starting from the same place
- the overall pattern or trend of the data, i.e. a straight line
- other pattern or trends that could be possible
- maximum and minimum distances

Hand out a blank scatter graph for the students to use to display the 25 distances their marble travelled from Session One and today.

Have the students look at their own scatter graphs and predict the distance the marble will travel when started 40 cm, 50 cm and 60 cm from the top of the ramp. Before rolling the marble on their ramps, have each pair explain or write down why they think it will roll the distances they have predicted.

Roll the marble down their ramps to see how close their prediction was. Record the distances, rolling the marble from each starting positions at least three times. Discuss these results in relationship to their predictions. Pack up the ramps and marbles reminding the students they will need to use the ramps again during Session Four.

This session has the students looking at a range of scatter graphs of data from marble rolling, with the task of predicting distances the marble is likely to roll. The discussion about making sense and using information from scatter graphs started in Session Two continues and is developed during this session.

There are five scatter graphs for the students to look at and predict from. The teacher needs to work out the best way to get all the students discussing the graphs, i.e. handed them out all together, one at a time or set up five stations for groups of students to visit. Discussing and explaining their thinking is a very important part of this session. The discussing and predicting allows teachers to assess student understanding and the amount of teaching needed.

Scatter Graph Samples, Copymaster 2, has the five scatter graphs for students to look at, plus graphs with trend lines for the teacher.

The following questions could be used as part of the discussion.

- What distance is the marble likely to roll if it was started from the top of the ramp? 50 cm?
- Is the pattern or trend linear, i.e. a straight line?
- Describe the overall trend of this ramp.
- Is there a starting position that will have the marble stop at 180 cm? 80 cm?
- Why are some distances clustered together closer than others?
- What is the range of distances are you absolutely sure the marble will stop at, given a set starting position?
- What is the range of distances you think the marble will stop at?
- On a scale from 1 to 10, how confident are you in your prediction? Explain why. Scale: 1 = not confident at all, 10 = extremely confident.
- Do scatter graphs with non-linear trends, i.e. curves, result from curved ramps?

During this session the students are to build their ramps again with one aspect of it changed. The students could change the height of the ramp, a golf ball could be used instead of the marble, the surface the marble rolls on could be different, etc.

Once their ramps have been changed they are to roll and record the distance the marble travels. Roll the marble:

- 5 times, starting 30 cm from the top of the ramp
- 5 times, starting 50 cm from the top of the ramp
- 5 times, starting 70 cm from the top of the ramp

Graph the results on a scatter graph, then predict the distance the marble will travel when rolled from the top of the ramp, 10 cm from the top of the ramp and 20 cm from the top of the ramp. Predict the distance and state how accurate they think they are before starting the experiment. Adjustments to predictions are acceptable as the rolling and measuring continues, as long as they are accompanied by explanations.

This activity could be repeated several times with different changes made.

"What if . . ." questions could be posed to challenge students:

- What if the ramps from Session One were two metres long, how long would the marble roll from the top of the ramp?
- What if the ramps were curved?

Students should be asked to choose one of their experiments and produce an A4 poster describing what they did and what they found. Discuss an appropriate layout for the poster:

- Title
- Description of the experiment
- Scatter graph with trend line
- Description of results

At the end of Session Five students could present their posters to the rest of the class

Attachments

ScatterGraphBlank.pdf152.55 KB

Five_graphs.pdf501.91 KB