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.
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, this is 1/2 a cup. The students will use non-standard units and the discussion and recording of results will be based around the difference between results and how we could come up with a standard answer.
- Present the students with a small container (about 1/2 cup size). Let the students measure using spoonfuls of kernels to see how many will fit into the container. Provide a variety of spoons from teaspoons to large salad and serving spoons.
- Record the volume of the container on a chart with illustrations of the spoons used and how many it took to fill the container. Ask ‘Why do we all have different results?’ and chart the answer encouraging the students to make comparisons between 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 get the students to make predictions about how much popcorn there will be. Explore some containers including ice-cream containers, bowls and boxes and get the students to decide the container that will be right for 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 check the students’ predictions by using the containers to see which is the best fit. 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 containers would be filled by the popped corn. Let the students measure the popped corn with the non-standard measure (it is good to have extra batches of popcorn so that all students can be involved in measuring).
In this investigation the students revisit the results from the previous investigation, the idea of measuring the popcorn using a litre measure is explored.
- Revisit the results of the volume investigation and talk about how much popcorn was made. Introduce some litre containers to the class (soft drink bottles could be cut down to a litre or half litre quite easily).
- Let the students measure the volume of the container which the popcorn 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 filling the litre container and counting how many fit into each bowl, ice cream container and box. Get the students to label and order the containers and to 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 a fair share.
- Pose the question: How much popcorn do you like to eat when you go to the movies?
- Get the students to discuss the statement. Have lots of small containers available so that they 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. Let the students make some considerations such as making some for the principal or neighbouring teachers. 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 let 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 the serving of popcorn into. The batches of popcorn will be made and the students will be able to measure out their serving to eat or to take home and share.
- Provide the students with materials to make cones to hold the popcorn. Make sure that the paper or cardboard will be big enough to make a cone to hold the serving size. Let the students construct and adjust the cones so that they will hold the serving size of popcorn. The students will need to measure their cones to make sure they will be the right size. They should be able to adjust them 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. Get the students to fill their cone using the serving size container as the measure. Provide plastic bags for those who wish to take their popcorn home to share.
- When all the containers are filled discuss how many batches of popcorn were made, how many litres it would have been and how much is left over.
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.