## Bunches of Balloons: Where to next?

Written by Kris Westcott

One of my favourite (there are so many) reSolve classroom resources is the Bunches of Balloons authentic problem for Year 2. I have used this task in quite a few classrooms now through a team teaching model and have always found the level of student engagement, and achievement, to be high.

Bunches of Balloons employs the 4D guided inquiry model which sees students explore a relevant problem within a familiar context, investigate and determine the most effective approach, implement and refine their ideas and then present their findings to an audience.

From the Authentic Problems: Bunches of Balloons page:

### 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.

I recently presented this experience at the Mathematics Association of NSW conference. I began with the reSolve Professional Learning Module Consolidating Learning. This module specifically addresses the third aspect of the protocol, in that tasks promote a knowledge-building culture, including through:

• Sustained higher order thinking
• Valuing mistakes as part of the learning process
• Building understanding through collaborative inquiry and reflection.

The assertion is that to consolidate the new understandings, students should be presented with similar problems in a different context. Similarly, by maintaining the context of the investigation and varying the content, students are able to work on the new, through the familiar, thus reducing the cognitive load.

Following an introduction to the original task, conference attendees were challenged to determine: where to next? Their responses, shown below, maintain the party context. In some instances, the content of arrays and multiplication are kept for consolidation, with an added level of sophistication which would require enabling prompts for some students. The content areas of measurement, position and statistics have also been brought into the context. The suggested use of manipulatives recognises that the complexity of some aspects goes well beyond that usually expected by Year 2 students.

 Where to next?Following “Bunches of Balloons” We would keep the successful party context to develop the students’ exploration of arrays…. to promote ‘trusting the count’, repeated addition and language of grapple – see and say. Party bag distribution  (student choice) e.g. whistles –15 to a packet Lollipops – 48 to a packet Groovy glasses – 6 to a packet This aspect could become more complex by displaying a mixed bag of party favours. How many are there? How best to display – array or graph? Which represents the best value for money? 31 guests...where shall we seat them? Thinking of multiplication as area: Floor plan, wooden blocks, pattern blocks etc. Table for cake, gift table, food and drinks, seating How much play space will there be? “What do you see? Can you see it another way? What did your buddy do?” Cupcakes are bought in trays of 12. What dimensions could the box be? What might the cakes look like? Party planning – time catering, seating

Many of these suggestions were similar to those which my Year 2 classes used in Term 2. An extract from that unit is shown below. The students were promised an actual party based on their findings, so the motivation to solve each inquiry question was high and extending prompts which suggested they may get more ‘booty’ at the party were enthusiastically approached.

When my Year 2 classes went through this investigation, each of the original three lessons was preceded by a number talk where students supported each other in the use of vocabulary and strategies. Images for these talks could be taken by the teacher but I used some of my favourite sites and Google image search for convenience, as well as being able to generate a variety of engaging stimuli:

### Investigation 1: Lollipops

• Jointly view and discuss the image above.
• How many packets of lollipops would we need for fair shares at our party? How many would each student get? What information do we need to work this out?
• Allow students to begin investigation based on their own ideas and the information provided.
• Interrupt students and have them report in their progress so far. Is one bag enough? Are there left overs? What about using multiple bags?
• Students should record their working using diagrams and words.
• How much will it cost to buy enough bags of lollipops – this information will be added to throughout the week.

Enabling Prompt: Use counters to represent lollipops. Are there enough in the bag for everyone to get one lollipop? Two lollipops?

Extending Prompt: How many bags would be needed for each student in the class to get three lollipops?

### Investigation 2: Cupcakes

• Review actions in previous activity. What worked? What information was needed? What equipment (if any) assisted in the investigation?
• Display above cupcakes picture and discuss arrangement in arrays – remind about directions of rows and columns.
• Ask students to label the diagram using groups, rows and repeated addition.
• Partner talk - How will this structure help in working out how many cupcakes each child will get from one packet? (You may like to give each student a smaller version of the picture)
• If each student is to get 2 cupcakes, how many packets will be needed and how many cupcakes will be left over?
• Students share back their strategies and findings.
• Add cost of cupcakes to chart begun during the last lesson.

Enabling prompt: Think about how you approached the lollipop problem. How could that help today?

Extending prompt: How many packets of cupcakes would we need to buy so that there were none left over?

### Investigation 3: Chips

See previous activities.

Once the price of the chips has been added to the chart, ask students to estimate how much it will cost to have our party? Challenge students to work out how much.

Jointly decide when to hold the party and whether students will contribute items as well. I recommend holding this over until after Ramadan if you have any students who are fasting.