Marshmallows

Purpose

In this unit, students use marshmallows in a range of interesting measurement tasks.  Concepts covered include mass, volume, temperature, time, and area, with the skill of estimation being developed.

Specific Learning Outcomes
  • estimate the volume/mass of one marshmallow using appropriate standard units
  • design an investigation to find the average volume/mass of one marshmallow
  • carry out an investigation to find the average volume/mass of one marshmallow
Description of Mathematics

Here the students engage in a variety of measuring and estimating tasks based on marshmallows. These activities should allow them to develop and extend their concepts of measurement and standard and non-standard units.

Required Resource Materials
Cups

Spoons

Kettle

Hot chocolate powder, for example, Milo or similar, and milk

Scales, for example, kitchen scales or similar

Standard measuring devices up to 500mL - cups and jugs

Stop watches (or a clock that can be used to time minutes and seconds)

Thermometer

Marshmallows

A range of containers suitable to measure volume using marshmallows - jam jars, yoghurt pottles

Water

Ingredients and equipment to make marshmallow (see recipe in Session 4)

Electric mixer with variable speed

Baking trays of varying sizes (4)

Key Vocabulary

 investigation, measurement, estimation, metric units, mass, weight, grams, kilograms, scales, volume, litres, millilitres, temperature, average, net weight, degrees Celcius, variable, dimensions, time

Activity

Session 1

In this session students estimate and measure volume using marshmallows.

  1. Tell students you are planning a party and you are going to be buying marshmallows in bulk at one of the supermarkets that has a special on: 1000 marshmallows for $10.  Explain that you will need somewhere to store them and that you would like the students to calculate the volume of the container you will need to do this. Ask students to estimate the volume of the container required and record some of their estimations. How many 2 litre ice cream containers will you need?
  2. Show students the materials they will have to use in their investigations: a range of containers with volumes less than half a litre (for example, jam jars, yoghurt pottles), marshmallows, water and standard measuring devices up to 500mL. Brainstorm ways to use the equipment and record results.
  3. Place students in groups and allow them time to investigate and record some results.
  4. Encourage students to set up a table to record how many marshmallows will fit in a variety of different containers. This will enable them to calculate the average volume of one marshmallow. For example:

Container

Number of Marshmallows to fill container

Volume of container in mL.

Average volume per marshmallow

       
       
       
       

 

  1. Conclude the session by comparing results.
    What did each group find as the average volume of one marshmallow?
    What will the volume of 1000 marshmallows be?
    How many 2 litre ice cream containers will be needed to store 1000 marshmallows?
    How do the results compare with the estimates made at the start of the session?

Session 2

In this session students investigate the mass (weight) of marshmallows and calculate the mass of one marshmallow.

  1. Tell the students they will be doing more investigations with marshmallows today. Explain that you are interested in finding out the mass of one marshmallow but you are having difficulty as the measuring scales you have will not measure one marshmallow very accurately as it is too light. Ask students to estimate the mass of one marshmallow and record some of their estimations.
  2. Show the students the materials they will have to use in their investigation: marshmallows and measuring scales. Discuss various approaches they might use and ways of recording information.
  3. Place students in groups and allow them time to investigate and record some results.
  4. Encourage students to set up a table to record different numbers of marshmallows and their masses. This will enable them to calculate the average mass of one marshmallow. For example:

Number of marshmallows

Mass of marshmallows

Average mass per marshmallow

 

 

 

     
     
     

 

  1. Conclude the session by comparing results. A comparison could also be obtained by counting the number of marshmallows in a standard sized bag and using the net weight of the bag as given by the manufacturers. How do the results compare with the estimates recorded at the start of the session?

Session 3

In this session students investigate the amount of time taken for a marshmallow to melt in hot chocolate of differing temperatures.

  1. Tell the students that at the party you are having you are going to serve your guests hot chocolate with marshmallows and you are interested in how long the marshmallows will take to melt. Ask students to estimate how long it will take, and identify that the time taken will differ for varying temperatures of hot chocolate.
  2. Set up an investigation. Put the students into groups and have each group time the melting of a marshmallow for a different temperature, for example, 1000C, 900C, 800C. Provide each group with hot chocolate and milk and have them mix up the hot chocolate with approximately the right temperature as their first step.
  3. Set up a table to record the results.

Temperature / 0C

Time for marshmallow to melt / seconds

98

 

89

 

82

 

73

 

57

 

49

 

 

  1. Have students look at the table for a pattern.
    When the temperature is lowered by ten degrees how much longer does it take for the marshmallow to melt?
    Are the changes in temperature and melting time consistent as the temperature drops?
  2. Use this information to estimate the time it will take for a marshmallow to melt at a lower temperature, for example, 400C. Record some of these estimates.
  3. Have the students record the melting time for the estimated temperature and compare actual results with estimated times.

Session 4

In this session students make marshmallow and time how long it takes for the ingredients to be beaten adequately using different beater speeds and volumes of ingredients.

  1. Tell the students that you would like them to experiment with making marshmallow as part of the work they have been doing. Show them the recipe and explain that they are going to time how long it takes for the ingredients to be beaten into stiff peaks. Have students estimate the time it will take and record some of these estimates.
  2. Make the marshmallow as a class and time how long it takes for the ingredients to be beaten. Compare the results with recorded estimates.
Marshmallow 2 dessertspoons gelatin dissolved in 1 cup boiling water (teacher would have to do that bit) 2 cups sugar I tsp vanilla 3 drops food colouring (if required) Beat all ingredients together until thick, approximately 15 minutes. Turn into tray, smooth and refrigerate until set.
  1. Discuss what will happen to the time taken for beating if the speed of the beater is increased. What will happen to the time taken if the quantities in the recipe are doubled? What if the quantities in the recipe are tripled?
  2. Ask each student to estimate these times and record their estimates in a table such as the one below.

 

Time taken for beating

Beater on speed 1

 

Beater on speed 2

 

Beater on speed 3

 

Mixture doubled

 

Mixture tripled

 
  1. Put the students in groups and have each group test a different variable (as in the table above). In preparation for tomorrow's session have each group that is working with a single quantity of ingredients use a tray with a different area to set their marshmallow in.
  2. Hold a reporting session where all groups report the time taken for beating under different conditions. Students can compare the recorded times with their own estimates.

Session 5

In this session students use the trays of marshmallow prepared yesterday to investigate the relationship between the area of the tray and the depth of marshmallow produced. They then use this information to estimate the depth of marshmallow that will be produced when an alternative tray is used.

  1. Show students the three trays of marshmallow made in the previous session. Discuss the different shapes of the trays and ask what effect this will have on the depth of marshmallow produced.
  2. Place students into groups and have each group estimate which tray they think will produce the deepest marshmallow and which will produce the shallowest. Ask them to explain their thinking and record some of their estimates.
  3. As a class, measure, calculate and record the area of each tray and then measure the depth of marshmallow each tray has produced.  Assign each group different tasks and compile the results in a table similar to the one shown below. Compare the results with recorded estimates.
Tray dimensions Tray Area Depth of marshmallow
     
     
     
     
  1. Introduce a new and different tray and ask students to discuss in their groups how deep the marshmallow will be from this tray. Ask them to record their estimate and explain their thinking.
  2. Make the marshmallow for the new tray and compare the depth of marshmallow produced with the estimates. (This final comparison may need to happen at a later time to allow the marshmallow time to set. Alternatively, the marshmallow could be made prior to starting this session.)

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