Year level: 8

Strand: Number

Lesson length: 60 min

This lesson, split into two parts, gives students the opportunity to participate in a real-life problem both in and out of the classroom. Students are guided through the process of formulating a problem that can be solved using a mathematical modelling approach. A professional sporting context allows students to engage in a common basketball scoring move: shooting 3-pointers. In Shooting 3-pointers: Part 2, students conduct a statistical investigation, collecting and analysing data using percentages and equivalent decimals, and choosing efficient calculations and strategies.

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

They 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

They 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 (P5)
• Multiplicative strategies (P10)
• Statistics and probability: Interpreting and representing data (P7)

Critical thinking:

• Analysing: Interpret concepts and problems (P5); draw conclusions and provide reasons (P5)
• Inquiring: Develop questions (P5); identify, process and evaluate information (P5)

Digital literacy:

• Managing and operating: select and operate tools (P5)

Related content

Health and Physical Education

Science

AC9S8I04

The following opportunity for continual assessment for the halfway point of this investigation is suggested below.

Have students reflect on percentages and decimals. Use the Summary and reflection time to consolidate further explanation and learning, to be able to continue with Shooting 3-pointers: Part 2.

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.

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
• sampling and data collection
• approaching real-life problems mathematically
• using simple data displays: line graph.

What you need:

• Lesson plan (Word)

• Teacher's slides (PowerPoint)

• Data collection spreadsheet template (Excel)

• Data collection notes (Word)

• Shooting 3-pointers assessment (Word)