Students will ask and answer questions about the graphical representations of javelin throws for two competitors at the Olympics. They will challenge preconceived notions about the representation and draw conclusions. Students will explore how scale drastically impacts the audience’s initial notion of the results.

The distance of six javelin throws for two competitors are represented in value-bar graphs. Students will make initial assumptions about the results. However, upon further investigation, students will realize that the interval for the scale selected in each graph differs. This change in the graphical representation will impact the students’ preconceived notions about the results of this event. Students will then represent the results of a third javelin thrower using a graph and scale of their choice. Some of the big ideas that may emerge in this lesson include;  

• There are different types of data;
• Data is often characterized as continuous or discrete;
• Discrete data is often countable and can only take on certain values;
• Continuous data is measurable and can take any value (within a range);
• Scale in graphs are the system of marks at fixed intervals;
• The intervals can be unitized; 
• Changing the interval selected for a scale can impact the audience’s initial notion of the data; and,
• The range of a set of data is the difference between the highest and lowest values in the set.

Show students this video:

Then, ask students:

What do you notice?

What do you wonder?

Give students 60 seconds (or more) to do a rapid write on a piece of paper.

Then, ask students to share with their neighbours for another 60 seconds.

Finally, allow students to share with the entire group.

Some of the noticing and wondering that came up in a class recently included:

• I notice some type of field.
• I notice something being thrown and landing.
• I notice a scale below, it goes up by 10.
• I wonder if this is a sport.
• I wonder if the scale is in feet or metres.
• I wonder where it landed.

At this point, you can answer any notices and wonders that you can cross off the list right away. Share the following information:

This is an animation of a Javelin throw runway and landing sector. Javelin throw is part of the athletics (track-and-field) sport. It is a sport where athletes throw a spear called a javelin for distance. Each throw is measured from the throwing arc to the point of impact. The distance is measured in metres.

Student prompt:

How far was this javelin thrown?

Make an estimate.

We can now ask students to make an estimate (not a guess) as we want them to be as strategic as they can possibly be. This will force them to use reasoning to try and come up with a reasonable distance for this throw. 

Consider asking students to think about a number that would be “too low” and a number that would be “too high” before asking for their best estimate in order to help them come up with a more reasonable estimate.

Let them chat with their neighbours and challenge them to an estimation duel or a math fight.

Also consider asking students:

How might you make your estimate more precise?

Students might recommend moving the scale upwards or zooming in to get a better look.

Student prompt:

Update your estimate.

We can now ask students to update their estimate.

Monitor student thinking by circulating around the room and listening to the mathematical discourse. Encourage students to use precise mathematical language and listen for the use of fractional language. Are students considering the relationship between the point of impact and the scale, noticing that the throw is less than halfway between 88 and 89 metres. How are students describing this distance? 88 and one-fourth of a meter? 88 metres and 25 centimetres? 88.25 metres? 

Allow students to share their estimates with neighbours first, then with the class. Write down their estimates on the chalkboard/whiteboard/chart paper so students feel their voices are being heard and so they feel they have a stake in solving this problem. 

Share the following image with students to reveal the actual distance of this throw.

Share the following graphs with students. 

Explain that the two value-bar graphs represent the six throws of two different male competitors in the javelin throw at the Olympic games.

Student prompt:

Based on your first impression, which thrower was most consistent? Justify your answer.

Allow students some time to discuss and share what they see.

Then, prompt students with:

Now, look more closely. Was your first impression correct? Explain.

Student Prompt:

The data for a third thrower is shown in the table below.

Graph this data.

Justify your choice of interval for the scale.

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Show students the following graphs for all three javelin throwers using the same scale.

Provide students an opportunity to reflect on their learning by offering these consolidation prompts to be completed independently.

Consolidation Prompt #1:

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Consolidation Prompt #2:

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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