Authentic Problems: Bunches of Balloons


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What is the best number of balloons to evenly decorate the room?

A purposeful context for division and multiplication. Students explore and present groupings of a bag of 29 balloons to decorate the classroom for an upcoming event. The class decides which grouping is best and the room is decorated. Arrays, commutative properties, repeated addition and skip counting are encountered. There are opportunities for diagnostic interactions. This inquiry unit could be placed before any formal introduction to division and multiplication as it explores the concept of dividing a number into equal parts and grouping into equal sets, and the ‘x’ sign and equations are not used.

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Lesson 1: Discover

Students are presented with the real-life context of decorating the classroom with 29 balloons. Students use counters to represent the balloons, as they collaboratively work to divide the balloons into equal groups. They record each attempt (draw or photograph) as evidence of their findings and clearly label their representations. They discover that 29 cannot be divided into equal-sized groups.

Lesson 2: Devise

Students confirm that 29 balloons cannot be divided into equal groups, so will not evenly decorate the room. They do this by making arrays to show the counters in groups with left overs. Students refer to the arrays and consider the potential attractiveness of the decoration to choose a good bunch size. Using arrays or otherwise, students record some total numbers of balloons that allow for bunches of that size.

Lesson 3: Develop and Defend

In the Develop phase (first session), students test different room arrangements using counters with chosen bunch size. They analyse arrays to decide on the best number of balloons to use. They represent their arrangement using a diagram, array, number sentence and written justification. In the Defend phase (second session), students present their representations to the class and justify why their arrangement is best. They actively listen to others, ask clarifying questions and provide feedback. The class chooses the best option and then decorates the room.

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