# The Three Bears

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Purpose

In this unit we compare the volumes of containers using the context of Goldilocks and the Three Bears.

Achievement Objectives
GM1-1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
Specific Learning Outcomes
• Compare the volume of two containers by packing or pouring.
• Order the volume of three or more containers by packing or pouring.
• Recognise that two matched amounts of liquid remain the same when one amount is poured into a container of a different shape.
Description of Mathematics

In this unit we compare the volumes of a number of different containers by pouring the contents from one to the other. We use this direct comparison to order containers from those that hold the least to the most.

We also explore the conservation of volume by looking at how two different shaped objects can have the same capacity.

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:

• being careful about the amount of difference between the capacity of containers. Containers that are very close in capacity will be harder to order
• modelling the measure of volume using different containers
• representing the volume of containers using diagrams, drawings, and simple sentences
• strategically grouping students in pairs and small groups to encourage peer learning, scaffolding, and extension
• working alongside individual students (or groups of students) who require further support with specific area of knowledge or activities.

The activities in this unit can be adapted to make them more interesting by adding contexts that are familiar to them, for example, you may prefer to use three class toys, three teachers, three characters from a culturally relevant story, three animals etc. Consider what links could be made here to students' interests, cultural backgrounds, and to their learning from other curriculum areas. You might use a story other than Goldilocks and the Three Bears to frame this unit - perhaps one focused around native birds filling their nest with twigs or around a lake or river being filled with water.

Te reo Māori kupu such as rōrahi (volume) could be introduced in this unit and used throughout other mathematical learning.

Required Resource Materials
• Water trays
• Water
• Rubber bands
• Rice bubbles and 3 bowls
• Bottles of different volumes and shapes
• Glasses of different volumes
• Beans or rice to use as filling material
• Paper
• Pencils
Activity

#### Getting Started

We introduce this unit by reading Goldilocks and the Three Bears (or another relevant story). The story provides a good starting point for the comparison of different sized containers.

1. Show the students three different sized bowls and ask them to think which one belongs to Father Bear. In our classroom story the bears are going to eat rice bubbles instead of porridge.
Which bowl do you think has the most rice bubbles in it?
Why do you think that one?
How could we find out which bowl holds the most rice bubbles?
2. Let a volunteer demonstrate their idea for determining which bowl hold the most rice bubbles. Discuss.
3. Ask if anyone has another way for working out which bowl belongs to Father Bear. Pouring from one bowl to another is the likely approach although it is also possible to pack the smaller bowl inside the larger one to demonstrate the difference.
4. Show the class a collection of plastic glasses and cups. Explain that these are for the bears' drinks. In pairs the students are to choose 3 cups for the bears and put them in order for Father Bear, Mother Bear and Baby Bear.
5. Ask students to fill up the cup that they think will hold the most water.
Which cup do you think has the most drink in it?
Why do you think that one?
How could you check?
6. Agree on a method for checking which cup holds the most water. Model this method for students and have them repeat it in their groups. One method might be to fill up the container, which students think is the largest, with water, and then tipping the water into the two, supposedly smaller containers. If students have chosen the largest container correctly, then they should find that the smaller containers do not hold as much water as the largest one does. You could use rubber bands to show how far up the side of the containers the water comes.
7. Ask the students to record what they have done, drawing the cups for each bear and explaining which holds the most.

#### Exploring

In the following days we are going to continue to compare and order volumes of containers that might belong to the Three Bears. Each day question students about what they are doing.

• How are you going to work out which holds the most?
• How do you know that one holds more?
• Which container do you think will hold the most? Why?

During the week, students may find containers that look very different even though they hold the same amount. Question them about this.

• Did you expect the containers to hold the same amount? Why / Why not?
• Those containers are different shapes. How do you know they hold the same amount?

Ideas for exploration:

1. The bears' water bottles.
Today the bears are going for a walk and need to take water with them. Find out which bottle belongs to which bear.
2. The bears' lunch boxes.
Today the bears are going for a picnic and each pack lunch into their lunch box. In groups of three, the students could investigate their own lunch boxes (emptied) and decide which box is the largest and which is the smallest.
3. The bears' "secret treasures".
The students are given a variety of small containers that could hold the bears "secret treasures". They need to work out which holds the most, ordering 3 containers from least to greatest volume.
4. Bears' ice-creams. The students make cones of different sizes for the bears. Each pair needs to make three cones. (Use beans for the comparison)

#### Reflecting

In this session the Bears invite Goldilocks to their house for breakfast. As the students make decisions about the bowl, cup, spoon and bottle reflect on the fact that some containers might hold the same amount even though they are very different shapes (conservation of volume). You may have touched on this concept during the week but this session reinforces it for all students.

1. Begin this session by talking about Goldilocks and deciding that she needs containers which hold the same amount as Baby bear.
2. Display two bottles that are different shapes but hold the same volume. Get the students to estimate, which they think holds the most.
Which bottle do you think will hold the most drink? Why?
How could we find out which holds the most drink?
3. Get one of the students to compare the volumes by pouring directly from one bottle to the other. Question the students about what you have found.
Which bottle holds the most?
Which bottle did you think would hold the most? Why?
What is different about these bottles?
What is the same about these bottles?
4. Ask the students to work in pairs to find two containers that hold the same amount but are different shapes. They then collect one more container, so they have 3 different shaped containers, two of which have the same capacity.
5. As a class, groups present their three bottles and others have to choose which two bottles hold the same amount. Have some students demonstrate that two of the containers hold the same amount.