This unit is made of a number of popcorn investigations, which provide both a purposeful and enjoyable measuring context. The focus of the unit is introducing the students to the need for a standard unit for measuring volume.
Specific Learning Outcomes
- Use non-standard volume units (cups, spoons, bowls) to fill a container and count the number used.
- Recognise the need for a standard unit of volume.
- Measure to the nearest litre and half litre by using litre containers to fill and count.
Description of Mathematics
When students can measure effectively using non-standard units, they are ready to move to the use of standard units. The motivation for moving to this stage, often follows from experiences where the students have used different non-standard units for the same volume. This allows them to appreciate that consistency in the units used allows for easier and more accurate communication.
The usual sequence used in primary school is to introduce the litre as a measurement of volume before using cubic centimetres and cubic metres.
Students’ measurement experiences must enable them to:
- develop an understanding of the size of a litre and 10 millilitres. (1 millilitre is very small and difficult to appreciate however it can be demonstrated with an eyedropper)
- estimate and measure using litres and millilitres
- develop an understanding of the size of a cubic metre and a cubic centimetre
- estimate and measure using cubic metres and cubic centimetres.
The standard units can be made meaningful by looking at the volumes of everyday objects. For example, the litre milk carton, the 2-litre ice-cream container and the 100-millilitre yoghurt pottle. Students should be able to use measuring jugs and to say what the measuring intervals on the scale represent.
Opportunities for Adaptation and Differentiation
This unit can be differentiated by varying the scaffolding provided or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:
- have students use non-standard units to measure, as needed
- provide additional activities for students to practice measuring volume. For example, set up a measuring station with a variety of containers, material which can be used to measure (sand, beads, cotton balls), and both non-standard and standard measures (a variety of spoons, cups, and smaller containers). Challenge students to find the container with the greatest/smallest volume, or to find a set of 3/5 containers and place them in order of increasing volume, recording their results with diagrams and descriptions
- work in small groups with students who need additional support, measuring and recording together.
Including the process of making popcorn in a broader context within the class or school will encourage engagement. For example, the popcorn could be part of a shared lunch for the class, a popcorn stall could be set up as a fund-raiser or as part of a school fair, or the popcorn could be shared at a community event.
Required Resource Materials
- Popcorn kernels (1kg of popcorn makes 10, 1/2 cup batches).
- A popcorn maker (or pot with a lid or microwave and dish)
- Cardboard containers of varying sizes and shapes
- Plastic bowls, ice cream containers and cups
- Spoons of varying sizes
- Standard cups and measuring spoons
- Various containers, which hold a litre or have a litre and half litre marked on them
In these sessions we investigate the volume of corn kernels before and after popping. The amount of popcorn to be made is based on the batch size using a popcorn maker, which is usually about 1/2 a cup of kernels. We use non-standard units to measure the volume of both kernels and popped corn, and think about why the measurements vary (because the units being used vary) and what could be done to improve the consistency of the measurements (use a standard unit).
- Present the students with a small container (about 1/2 cup size). Have the students measure the volume of the container using spoonfuls of kernels. Use a variety of spoons from teaspoons to large salad and serving spoons.
- Record the different measurements of volume on a chart with illustrations of the spoons used.
Ask: Why are we coming up with different numbers of spoonfuls needed to fill the container?
Record students’ responses, encouraging them to compare the sizes of spoons.
- Make the popcorn – popcorn makers are the easiest to use in the classroom setting, but other methods provide the same results.
- As the popcorn pops ask students to make predictions about how much popcorn there will be. Explore some containers including ice-cream containers, bowls and boxes and ask the students to identify a container that they think will be the same volume as the popped corn. (Note that 1/2 cup of kernels makes about 4 litres of popcorn in a popcorn maker.)
- Once the popcorn is popped tip it into the selected container to check the students’ prediction, then find a container that is a good fit for all of the popped corn.
- Get the students to consider the original measure used for the kernels, i.e. 1/2 cup, and to think about how many of these would be filled by the popped corn. Have the students measure the popped corn with the measure used for the kernels. For example, they might find that a half-cup scoop of corn kernels produces 32 half-cup scoops of popped corn.
In this investigation the students revisit the results from the previous investigation, and the idea of measuring the popcorn using a litre measure is explored.
- Revisit the results of the previous volume investigations and talk about the volume of kernels used, and how much popcorn was made. Focus on the fact that the volume of kernels used was different when measured with different sized spoons, and introduce the idea of a standard measure. Note that standard measures are useful because they enable accurate communication, suggesting that if you were going to send instructions for making popcorn to another class spoonfuls of corn kernels would not be a useful way to measure, because they might be using different sized spoons than you.
- Introduce the litre as a standard measure of volume, and ask students to identify things they know that use litres (for example, 2L milk bottles, 2L ice-cream tubs, 1L bottles of juice). Show some litre containers to the class (soft drink bottles could be cut down to a litre or half litre quite easily).
- Have the students measure the volume of the container which the popped corn fitted into using the litre measure (water, rice, wheat or sand could be used for this task, it doesn’t have to be popcorn.)
- Get the students to explore the other containers available and measure them in the same way using the litre container and counting how many fit into each bowl, ice cream container and box. Have the students label and order the containers and identify any that would have fitted the batch of popcorn.
In this investigation the students think about a standard serving size for the popcorn. The students will find out how many litres of popcorn will be needed for everyone in the class to get one serving.
- Pose the question: How much popcorn do you like to eat when you go to the movies? and discuss.
- Have lots of small containers available so that students can choose the size of container which represents the amount of popcorn they would like. Try to come to a consensus about the size of a share of popcorn.
- Choose one container, which represents the size of a serving of popcorn (having some containers which are 1/2 or 1/4 litre size and directing towards those will make the measurement easier, but this isn’t necessary).
- Use the serving size container and talk about how many servings you would need for the class. Students may like to consider making some popcorn for the principal, or a neighbouring class. Use rice, water, sand or wheat to measure out the right number of serves – a large plastic bucket or container will be needed.
- Use the litre containers to find out how many litres of popcorn will be needed for everyone to get a serving. Measure by filling the litre container and counting.
- Look back at the results of Session 3 and have the students work out how many batches of popcorn the class will need to make. Some students may be able to calculate this easily, others will have to use the container that the popped corn fitted into to help them work it out.
In the final day of the unit the students make cones to fit one serving of popcorn into. The batches of popcorn will be made and the students will be able to measure out their serving to eat.
- Provide materials to make cones to hold the popcorn. Ask the students to construct a cone that will hold the agreed serving size of popcorn, then check the volume of their cone by measuring. The volume of the cone can easily be adjusted by making the cone wider or narrower or by cutting from the top.
- Make the batches of popcorn as the students work on the containers. Have the students fill their cone using the serving size container as the measure.
- When all the containers are filled, ask the students to record some facts about making the popcorn to share. What volume of corn kernels have been used? How many batches of popcorn have been made? How many servings were made? How many litres of popcorn have been made? How much is left over?
- Discuss responses together.
Family and whānau,
This week we have been investigating the volume of popcorn. Do you know how many litres half a cup of corn makes when it is popped?
We designed containers at school to hold our popcorn. Ask your child to tell you about the one that they made. Together you could design another shaped container to hold the popcorn and make some at home.