# Authentic Problems: Target Ball

ACMNA013; ACMNA019; ACMSP263; ACMSP262;

This unit for Year 1 is one of a set of ten units in the special topic “Mathematical Inquiry into Authentic Problems”. Each of these units is designed around the 4D Guided Inquiry Model, and highlights the importance of students providing mathematical evidence. The lessons adopt a carefully designed pedagogy to help students master content knowledge whilst learning about the process of inquiry.

Students work to recommend how the sports teacher should set up a game of ‘Target Ball’. They investigate the best type of ball to roll, and where to position the target. In groups, they negotiate consistent measurement practices to ensure fair testing (e.g. surface, type of ball, how to roll, who rolls, how to record) and select an appropriate informal, uniform unit of measure to make comparisons. They make sense of the differences in their measurements by organising and displaying them on a number line.  The class then uses a table (categorised data) to display the measurements collected from all groups to predict a fair placement for a target ball.

Read the Teachers' Guide (also included in the download) before using this resource.

### Lesson 1: Discover Phase

Students are presented with the real-life context of having to advise the sports teacher on setting up a game of ‘Target Ball’. They need to investigate how far a ball rolls and the best type of ball to use in the game. They each choose a ball, roll it and mark where it stops. They use direct comparison of distances rolled to propose factors that may influence the distances rolled, including the type of ball. Students review the class results to decide on the best ball for Target Ball, and come to appreciate that they will need to measure the distances rolled.

### Lesson 2: Devise Phase

Students work in groups to gather evidence on how far the chosen type of ball rolls. They measure with an informal unit of their own choice. Groups use sharing opportunities to reduce error when measuring, to improve their recording methods and to address the need to record lengths involving part of the informal unit.

### Lessons 3: Develop Phase

Groups repeat the rolling and measuring of the previous lesson, gathering better data. This time, all groups use the same informal unit (cut-out cardboard foot). Students organise and display their own groups’ measurements on a number line, then interpret their evidence and write mathematical statements to say how far the ball rolls.

### Lessons 4: Defend Phase

Students investigate where to position the target in Target Ball to make the game fair. The previously collected measurements from the whole class are categorised into intervals and displayed in a table. Students then make simple inferences to recommend the position of the target. To convince themselves and others that this position is fair, students play the game and use the results in their justification. They reflect on the whole inquiry.

Last updated May 22 2018.