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*How many [sandwiches] does our class eat at school in a year?*

Students examine their lunchbox contents and decide on a popular food item to focus on for the investigation – how many of the item would a class eat in a year? Collaboratively, groups of students devise plans for finding out the total number of items eaten. The sequence of four lessons provides opportunities for students to invent, implement and refine strategies for repeated addition with larger numbers.

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Lesson 1: Discover Phase

This lesson poses the inquiry question, ‘How many [sandwiches] does our class eat at school in a year?’ Students examine what is in their lunch boxes on one day. With a focus on data, students list the items in their lunch box, compare their lists within a small group and categorise the items. Each group orders their items from most to least common and selects an item common in their group to be the focus of their inquiry for the unit.

Lesson 2: Devise Phase

Students identify the mathematical knowledge they need to find how many of the selected items they eat in a school year (e.g. number of days in a school week, weeks in one term and terms in a year). Students devise a plan to calculate or otherwise demonstrate the total number, using grouping, partitioning and repeated addition strategies. They refine their plans with ideas from a Checkpoint where they share strategies and methods.

Lesson 3: Develop Phase

Students implement a range of known and invented strategies to work out how many of their selected item they eat in a year. Through sharing, discussion and feedback, students refine the calculation process. They consider and develop more flexible and efficient counting, grouping and adding methods. They reach consensus about the most efficient strategies to use. Groups begin to use a grid paper representation, to explain their chosen strategy and mathematics used.

Lesson 4: Defend Phase

The lesson begins with evaluating strategies for finding the yearly total number of [sandwiches] using the grid paper representation. These representations show the steps that students followed to calculate their answer and help them find more efficient ways to calculate totals. Students answer the inquiry question, demonstrating their mathematical evidence. They reflect on the feedback given to determine what they did well and how they could improve their presentation and models.