# Solubility

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Purpose

In this unit students will investigate the solubility of sugar in water. They will design and carry out experiments which involve making accurate measurements of volume, mass, and temperature.

Achievement Objectives
GM4-1: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
Specific Learning Outcomes
• Make accurate measurements using a variety of measuring equipment.
• Design an experiment to investigate a factor affecting solubility of sugar.
Description of Mathematics

This unit is designed to give students a practical experience in which they can apply a variety of measuring techniques. Students will measure volume, mass, and temperature using a variety of measuring instruments, and will be asked to consider the accuracy of their measurements and ways to improve accuracy. Hopefully students will see that there is always at least slight inaccuracy when measuring and that in practical experiments such as those in this unit the goal is to reduce the error as much as possible.

Associated Achievement Objective

Science, Material World - Properties and changes of matter AO2: compare chemical and physical changes.

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:

• providing teacher support and modelling with measuring and calculating processes
• providing opportunities for students to work in collaborative groupings, pairs, and independently to foster students scaffolding and learning from each other, and the sharing and justification of ideas
• providing benchmarks (e.g. containers holding different amounts of sugar) to support students in making accurate estimations

The context for this unit can be adapted to suit the interests, experiences, and cultural makeup of your students. Although the unit is focussed around the solubility of sugar in water, it could be linked to a broader idea, such as making accurate measurements of volume, mass, and temperature. This could be framed within the context of planning the catering for a school gathering (e.g. fiefia night, hāngi), fair, or camp; or within the context of looking how much sugar (and/or salt) is in the food and drink products we consume.

Te reo Māori kupu such as ine (measure), rita (litre), ritamano (millilitre), karamu (gram), and karamumano (milligram) could be introduced in this unit and used throughout other mathematical learning

Required Resource Materials
• Measuring jug
• LOTS of sugar! (including some icing sugar, caster sugar, and brown sugar)
• Measuring cylinder
• Powdered drink sachet
• Soft drink
• Electronic scales
• Containers
• Thermometer (electronic if possible)
Activity

#### Getting Started (Session 1)

In this session dissolving and solubility are discussed and students make estimates of how much sugar can be dissolved in 100ml of tap water.

1. Present students with a bottle of soft drink.  Ask them what they think are the main ingredients.
What is there most of?  (Students should identify that the drink is primarily made up of water.)
What is in the water to make it taste the way it does?  (As well as flavours, hopefully sugar will be mentioned.)
2. Investigate by reading the ingredients and nutritional information.  You will find that soft drinks have around 10g of sugar per 100ml, and very little of anything else.  A discussion of the difference between mg and g may be necessary for students to understand how small the amounts of other ingredients (e.g. sodium) are.  A good way to illustrate just how big the difference is, is to compare a 1g mass with a 1kg mass.  Just as there are 1000 grams in a kilogram, there are 1000 milligrams in a gram.
3. Discuss why the amounts are given per 100ml.  (A standard volume so comparisons can be made between products.)
4. Ask students to describe how much 100ml is.  (A standard metric cup is 250ml, so just less than half a cup is a reasonable approximation.)
5. Ask students to describe how much 10g is.  (Two teaspoons.)  A 10 g mass might be a useful resource to give students a real feel for the mass.
6. Show students a sachet of Raro (or similar).  Ask them what they think it is made from.
7. Investigate by reading the ingredients and nutritional information.   Powdered drink sachets are almost pure sugar.
8. Discuss how much sugar there would be in the drink if it were made up following the instructions on the packet.
Is this more or less sugar than in the soft drink? (The total volumes will be different so conversion will be required.)
9. Ask students to estimate how much sugar they think is the most that could be dissolved in 100ml of water.  Discuss and record estimates to refer back to later.
10. Investigate by allowing groups to measure 100ml of water (using a measuring jug), before adding one measured teaspoon (5g) of sugar at a time, stirring until it dissolves.  You may find results vary from around 50g to 65g depending on room temperature.  Ensure that students keep the measuring jug level when they are measuring and that the teaspoons of sugar are level teaspoons, otherwise their measurements, and hence their results will be incorrect.
11. Record each group’s results in grams per litre (using correct units – g/l, or gl-1) and discuss whether the estimates made were accurate.
Are you surprised at how much dissolved?
12. As an at home task this week students are to investigate the amounts of sugar in various drinks that they can find in the supermarket or at home.  See who can find the drink with the most sugar in it.

#### Exploring (Sessions 2-4)

In these sessions we elaborate on the work of the previous session by making our measurements more accurate and by investigating different types of sugar (White sugar/brown sugar/icing sugar/castor sugar), different temperatures, and using salt instead of sugar. Introduce and model the processes and thinking involved in each step of the investigation before letting students investigate. Consider grouping your students to encourage tuakana-teina (peer learning).

1. Remind students of the results of the previous day’s experiment.  Ask:
What are some problems with the way we carried out the experiment?
How could we make the experiment more accurate?
Hopefully your students will realise that the measuring equipment used was not very accurate and that this could be improved on.
2. Introduce the equipment that will be available to students for measuring.  If possible, provide a range of scales for students to use, including an accurate electronic set (you should be able to borrow one from a local high school or students may be able to bring one from home), and a range of measuring cylinders and cups.  Ensure that students are familiar with how to use each, for example, some types of scales need to be ‘zeroed’, or calibrated to a start point, before measuring. Model the processes involved.
3. Discuss how accurate each piece of equipment is:
Why are some more accurate than others?
What kind of thing would you be likely to measure with each?
Are any of these measurements exact?
How close are they?
Some measuring equipment gives a level of accuracy, otherwise it is normally assumed that you can measure to within half of the smallest unit on the scale.  So, for example if the electronic scales say 0.125kg you can say that the mass is more than 124.5g and less than 125.5g.
4. Repeat the previous experiment with a higher degree of accuracy.  Students should use a measuring cylinder to measure the water, and if possible use an electronic scale to measure the sugar.  You can avoid inaccuracy by making fewer measurements, meaning you should measure a larger amount of sugar (but one that you know will dissolve) first, before adding 5g amounts until no more will dissolve.  As students work, circulate, ensuring that they are using the measuring equipment accurately.
5. Compare the results obtained with those from the previous session.  Discuss any differences.
6. Discuss the accuracy of the new results.
Are there any sources of error?
Is there anything that could be affecting the results?
Could we have controlled them?
Students should realise that there will always be small errors in this kind of experiment, but that it is important to think about ways to reduce them as much as possible.
7. Discuss what else might influence the amount that dissolves.
What might affect the amount that dissolves? (Students might suggest the different types of sugar used or temperature - if not, you should suggest them.)
Would using salt instead of sugar affect the result?
Could we test to see if these factors make a difference?
How?  (Students must realise that to carry out an experiment like this, everything must be kept constant, except the factor being tested.)
8. Students should work in groups to investigate whether using different types of sugar affects the amount that dissolves, and whether changing the temperature makes a difference to the amount that dissolves.
9. Students should first write a hypothesis (prediction), and then write a detailed design of the method they will use to investigate their hypothesis. Provide support and feedback to ensure students are successful in this task.
10. The teacher should check and, where necessary, amend the students’ experiment designs.  Ensure that they consider how to control as many factors as possible in their experiment, and that all methods of measurement are as kept accurate as possible.
 Notes on experimental design: 1.    Effect of type of sugarStudents investigating the effect of using different types of sugar must realise the importance of keeping all other factors (such as volume of water, and temperature) constant.  They should realise that the weight of a teaspoon of icing sugar might not be the same as the weight of a teaspoon of caster sugar. 2.    Effect of temperatureIf students are investigating the effect of temperature it is probably best that they don’t use elements, as there is a risk of burns.  It should be sufficient to place one container of water in a tub of ice to lower its temperature and place another in hot tap water to raise its temperature.  Students should monitor the temperature of their water with a thermometer (a digital thermometer would be ideal, but a mercury thermometer should suffice.) 3.    Using salt instead of sugarIf comparing the solubility of salt to that of sugar students must ensure that they keep all factors not being tested consistent between the test on sugar and that on salt.
1. As students carry out their investigations, circulate to check, support, and correct students’ measuring techniques as required.
2. Any groups exploring the effect of temperature will undoubtedly notice that significantly more sugar dissolves at higher temperatures.  Possibly a group could work with the teacher to see how much sugar will dissolve at even higher temperatures.  With supervision students could try dissolving sugar in boiling water.
How much will dissolve now?
Are there extra factors to consider in this experiment?  (Water is lost as steam/sugar melting rather than dissolving.)
How can we avoid/compensate for the water loss?
How can we tell whether the sugar has melted or dissolved?
Will the thermometer you are using still be accurate at these temperatures?

EXTENSION 1

Students could be asked to investigate whether dissolving some salt in the water affects the amount of sugar that can be dissolved.  They could try dissolving different amounts of salt in water and then testing how much more or less sugar will dissolve.

EXTENSION 2

Challenge students to calculate how much sugar (or salt) could be dissolved in larger volumes of water, such as the school swimming pool (dimensions could be measured and volume calculated), or even the world’s oceans.  Estimates of the volume of water in the world’s oceans can be found online.

#### Reflection (Session 5)

In this session students are given time to write up their results, and report back to the class.

1. Students should be given time here to write up their results for presentation, using a method that allows them to express their mathematical thinking in a relevant and meaningful way (e.g. using digital tools, making a movie, making a poster, written or verbal presentation).
2. Results should include; hypothesis, experimental design, results, and conclusion.
3. Students should be encouraged to think about what they could have done better or what they might have done differently knowing what they do now:
1. How could measurements have been more accurate?
2. How could other inconsistencies have been avoided?
3. What else could they have considered/tested?
4. Groups should present their reports to the class. Provide groups time to give other groups feedback. Ensure you set clear standards and expectations for the type and amount of feedback to be given.