Shooting 3-pointers: Part 1

Introduction

Display the teacher’s slides and the teaching notes that complement the lesson. The slides could also be printed for students if needed.

• Introduce the activity to the class and provide prompting questions in the teaching notes, designed to immerse students in the world of professional basketball; that is, types of basketball scoring shots, what shots students like to practise, and considering the types and number of shots professional basketballers take. Ask students the following investigative question: why do basketball players shoot so many 3-pointers? (slides 1 and 2)
• Inform students that professional sports team (like in the NBA) employ mathematicians. They use mathematical modelling to analyse data (game stats) to inform teams on how to win games, for example, what players need to score to win games.
• Tip: hook students in by showing short videos of professional players scoring 3-pointers in NBA/WNBA.

Learning intention/success criteria

• Discuss the learning intentions and success criteria for this lesson sequence. Inform students that they are learning how to think mathematically when constructing and testing a problem that exists in the real world. Explain that the activity is designed to guide students through the formulation of a mathematical model to investigate a real-life question, to collect and use data, to analyse the data, to communicate the results back to the class, and to suggest revisions to the model when considering feedback (slide 3).

Skills check

• This lesson gives teachers the opportunity to guide students through the mathematical modelling process. The problem and investigation into the problem is predetermined in this activity; however, students are guided along the path step by step. Teachers are encouraged to use classroom dialogue and questioning to have students use critical thinking skills to uncover the reasons for the approach taken. Use the ‘wh’ and how’ questions to help students suggest the next step and answer why they are taking this step, whether it be construction of the problem or performing a calculation.
• Slides 4 and 5 are designed to test prerequisite knowledge, specifically percentages, decimals and proportional reasoning. These are skills taught in Year 7; however, they are important arithmetic skills to consolidate. Ensure you can connect the arithmetic to the investigation, so that students can access deeper mathematical thinking skills.
• Go through the slide questions as a class. Students are expected to provide full sentences within the basketball context in their notes. An extension question is also provided. Answers are provided in the teaching notes in the teacher’s slides, including a fist-to-5 temperature test to identify those students requiring support or extension.

Data collection

• Circulate the Mathematical modelling assessment and Data collection notes handouts to students (slide 6). Inform the class they will be working in groups. It is suggested to predetermine groups for this task, given there is a physical and sporting aspect to it, but also to have students collaborate and support their peers who are at different levels of mathematical achievement.
• Introduce the set-up to the task:

‘As a budding young mathematician and fan, you decide to send a basketball coach an email with a suggested winning strategy. You’ve noticed recently that the team doesn’t shoot many 3-pointers, even though most of the players shoot two-pointers with a high degree of accuracy.

Write a convincing email to the coach to persuade him that shooting 3-pointers is a good idea. The coach is notoriously sceptical and can only be swayed by strong evidence. Therefore, your email must include data, calculations and graphs, and relevant analysis of them. To submit, send this email to your teacher.’

• Explain that this task is an investigation and one in which they will (with guidance) break down the investigative question to formulate a mathematical model to test the conjecture proposed. Students will produce and collect their own data, present the data in an organised way, correctly use calculations (involving percentages), plot data effectively, provide written analysis that is relevant and accurate, communicate results as a group in a logical manner, support logic with mathematical evidence, consider feedback, and compose a persuasive email that identifies both the strengths and weaknesses of the model used.

To begin the task

It’s important to use a questioning technique to have students create their own ideas for collecting and analysing data. While the steps suggested in the slides are to progress the investigation and are designed to scaffold all abilities, feel free to edit the slide show or investigation to suit the way students drive the discussion. Your class may decide to run the investigation slightly differently according to their own great ideas. Otherwise, use the slides as a guide or follow them explicitly.

Refer to slide 7 and the teaching notes. The slides are animated so that the teacher has time to prompt the class before the steps are explicitly given on the slide by clicking the mouse.

• Students will produce scoring data based on six locations on a basketball court where players can take legal shots. If you can, use the language of basketball as shown in the diagram for those students unfamiliar with the game, to increase engagement.
• Talk about data: question students on sampling and the type of data collection that best suits this task (random, non-random, qualitative, quantitative); discuss the implications and advantages of different ways of collecting data for this scenario; discuss how a team should organise the data so that it is collected meaningfully (should they use a table, spreadsheet, tally); could they use digital tech to collect data?
• Allow students to confer with their groups and decide exactly on their chosen six locations, with each member of the team having 10 attempts to score shots from each of the six locations.
• Introduce the excel spreadsheet (slide 8) and show students how they will collect data. Demonstrate where they will enter data for their team members and reiterate the language of maths: number of shots will be recorded as the equivalent decimal (since they are taking ten shots). Ensure students understand this point.
• Share the spreadsheet with each group, and have the group set up their spreadsheets, typing in names of the group members in the relevant row. Ensure students save the spreadsheet to their device to quickly access it the following lesson.
• An iteration on data collection is given in Shooting 3-pointers: Part 2.

End of Part 1

This is a natural end to Part 1 of the investigation. Shooting 3-pointers: Part 2 requires set up, time on the court and time for analysis. Feel free to iterate where you end Part 1 to suit your timetable and maths lesson sequence.

• Summarise the task to ensure students are free to ask questions using this time.
• Prepare to set up the iteration of the collection of data ready to begin when the bell goes.