Shooting 3-pointers: Part 2

Curriculum information

Achievement standard

Students use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts. They solve problems involving the four operations with integers and positive rational numbers.

They conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range.

Content descriptions

Students use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model. AC9M8N05

Students use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate. AC9M8N04

Students plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty. AC9M8ST04

Students analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques to select and study samples. AC9M8ST02

students compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation. AC9M8ST03

General capabilities

Numeracy:

Proportional thinking (Level 5)
Additive strategies (Level 10)
Multiplicative strategies (Level 10)
Statistics and probability: Interpreting and representing data (Level 7)

Critical thinking:

Analysing: Interpret concepts and problems (Level 5); draw conclusions and provide reasons (Level 5)
Inquiring: Develop questions (PL5); identify, process and evaluate information (Level 5)

Digital literacy:

Managing and operating: select and operate tools (Level 5)

Assessment

The following formative assessment task suggested to assess how each student understood the investigation.

Refer to the original Shooting 3-pointers assessment given to students last lesson. Explain the individual assessment that finishes this investigation. Students are required to use their statistical ‘evidence’ to make a recommendation to a fictional basketball coach on adopting or not adopting (depending on results) the 3-pointer strategy.

Areas of challenge

Students may:

still be uncomfortable using and understanding percentages and decimals, and how these can be applied in real-world contexts and problems
not connect percentages expressed as decimals from 0 to 1 for 0 to 100%, that is 0.2 = 20/100
not align decimal points correctly when converting decimals to percentages and vice versa
not understand the reason for data being converted to percentages for analysis and statistical displays (visual charts)
not understand that a sample may be too small and not representative of the problem or purpose of the investigation
not understand that two different samples from the same population can show variable results
underestimate bias in samples.

Prerequisite student knowledge and language

Students are:

expressing decimals as a percentage
determining the whole, given a percentage
determining the equivalence ratios in their simplest form
calculating averages using sets of data
using a digital spreadsheet
sampling and data collection
approaching real-life problems mathematically
using simple data displays: line graph.

Suggested strategies

Questioning

Collaborative learning

Concrete, Representational, Abstract

Classroom talks

Mathematical investigation

What you need:

Lesson plan (Word)

Teacher's slides (PowerPoint)

Data collection spreadsheet (Excel)

Data collection notes (Word)

Shooting 3-pointers assessment (Word)

A basketball court, cones and basketballs

Learning goals

Learning intention

We are learning to model a basketball problem and use a mathematical modelling approach to solve the problem.
We will communicate a reasoned solution to an investigative question using supporting mathematical evidence.
We will produce tabular and graphical representations of collected data to effectively communicate the solution and review the model.

Success criteria

By the end of this lesson, students can:

use a mathematical modelling approach to solve a real-life sporting question
collect and analyse data and present it in a tabular and infographic presentation
effectively communicate their modelling approach, justify it and review it.

Why are we learning about this?

Developing reasonable estimates is central in many areas of science, technology, mathematics and engineering. Estimating is used in daily life, whether it be cooking, making judgements about appropriate measurements around the home, or financial calculations. Therefore, fluent application of rounding strategies to develop reasonable estimates that can be justified is an important skill to develop.

Learning hook 30 mins

It’s important to note that students need to work fast here, as the remainder of the lesson is finished in the classroom. Students take their laptops to the courts with their spreadsheets ready to record. However, this could also be done on mini whiteboards or in a notebook.

Data collection at the courts

Optional: print out the data collection notes for students to take to the courts for reference.
This is a physical activity and is designed to be engaging and fun. Ensure students are kept busy to keep them on task. Two groups can begin on one court, and if you have more courts, have groups run the experiment simultaneously.
Have the students set up their cones when it’s their time to shoot from the six locations. Ensure a data collector is at the ready. Verify each spreadsheet as each group finishes to ensure all required data is collected.

Iteration: You could use dynamic software or manipulatives like dice to simulate basketball shots if you cannot physically collect scoring data on a basketball court. Note: though this can introduce probability nicely, it does not allow students to produce authentic data relevant to the learning question itself.

Coin flip simulator – each player uses the simulator or a real coin to flip a yes/no or heads/tails event 10 times for the six locations (total of 60 flips).
Probabilities: coin flipping – this coin flip simulator can be set to be unequally biased. This could nicely simulate a successful or unsuccessful three-pointer.

Explore / Body 20 mins

Data analysis in the classroom

The spreadsheet is designed to help display data collection, aid organisation of data and provide an initial graphical presentation of the data. Reinforce the language of statistics and summarise the dialogue on statistics from Shooting 3-pointers: Part 1.
Use slides 1 to 6 of the teacher’s slides to guide students through statistical analysis in steps but use questioning and classroom dialogue to help students reach each step progressively. Teaching notes and suggestions are included with each slide. Again, the slides are animated. The questioning prompts provided can assist with student feedback to allow you to tailor support or extension to some students.
Clarify to students that taking a step-by-step approach when conducting statistical analysis helps to ensure that the analysis answers the original learning question. It will also help develop the important critical thinking and statistical skills required in life to analyse data. (Remind students they will be living in a data-driven age once they finish school.) To scaffold the analysis, the steps required for this activity are shown on each slide.
Note that this lesson helps students to use digital spreadsheets to conduct statistical analysis, but it can be done just as easily by hand, promoting tabling and graphing skills.

Summary and reflection 10 mins

Go to slide 7 and use the SWOT analysis to reflect on the statistical model derived and undertaken. There are several ways this can be used and iterations are suggested in the teaching notes in the slide.

Given this is a mathematics investigation, reflect on the success and limitations of the lesson for your school and class, so that you may run it successfully again the following year.