This unit is part of the special topic “Bringing the Real World into Algebra”. Beginning with the context of cages at a poultry show, students explore how the number of walls used increases as the number of cages increases, making tables and graphs and writing rules. They discuss the equivalence of different rules. Later, they design and construct some different cages, observing the changes in the relationships between variables.

### Lesson 1: A Single Row of Bird Boxes

Using a toothpick model, students develop and describe rules for the number of ‘flat pack’ panels needed to build a row of temporary bird boxes for a poultry show. Following typical student thinking reported in the research, students are guided to move from recursive thinking to the relational thinking of functions. Through class discussion, students see that there is more than one correct rule for describing a particular pattern.

### Lesson 2: Box Designs with Other Shapes

This lesson follows on from Lesson 1 where students mathematically modelled the function that describes the relationship between the total number of cubic bird boxes in a row and the number of panels required to make them. In this lesson, students find similar relations for rows of triangular and hexagonal prism based bird boxes.

### Lesson 3: Modelling an Array of Chicken Boxes

Students move from considering patterns arising from the number of components in one row of chicken boxes to considering patterns in an array of boxes. Students first look at patterns in the subsequent rows, and then combine these rules with the rules for the first row to calculate quantities of components for the entire array. Students are then challenged to find other patterns in the whole array.

### Lesson 4: Modelling Chicken Boxes in 3D

Students are set the challenging task of finding the number of toothpicks to make a three dimensional model of an array of chicken boxes of any size. They build a 4 x 4 array to test their ideas. A worksheet is provided for students who require a structured approach. The lesson concludes with a class reflection on all the learning intentions of the unit.

Last updated December 11 2018.

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