In this unit the kilogram is introduced as a standard unit of measurement using the context of supermarket shopping. We develop our understanding of the "feel" of a kilogram by making our own kilogram weights.
- Recognise the need for a standard unit of mass.
- Recognises a kilogram mass.
- Relates the kilogram to everyday containers and familiar non-standard units.
When students can measure objects 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 to measure the same mass and have recognised that consistency in these units would allow for easier and more accurate communication of mass measures.
Students’ measurement experiences must enable them to:
- develop an understanding of the size of the standard unit
- estimate and measure using the unit
It is sensible to begin with the kilogram as the gram is too small to "feel". An appreciation for the feel of a kilogram needs to be built up with lots of examples of 1 kilogram mass, for example, 1 kilogram bags of stones, polystyrene, sand, butter and nails. The students should compare a standard 1 kilogram mass with other objects first by holding and then by using a balance scale.
The usual sequence is then to divide the kilogram into smaller parts, for example, 1/2 a kilogram (500 grams), 1/4 of a kilogram (250 grams) and 1/10 of a kilogram (100 grams).
Students should also be introduced to the use of spring balances to measure the mass of objects.
As the students become familiar with the size of the kilogram and gram they should be given many opportunities to estimate before measuring.
The learning opportunities in this unit can be differentiated by providing support to students and by varying the task requirements. Ways to support students include:
- letting students attempt problems using physical materials as much as possible, so they develop a ‘feel’ for the benchmark units
- directly modelling measurement with tools, such as digital scales for mass
- providing opportunities for students to copy the correct usage of tools
- clarifying the language of measurement units, such as “kilogram” as a mass that is made up of 1000 grams
- pairing students up (tuakana/teina relationship) or letting them work in flexible groups of different levels (mahi tahi relationship), and encouraging them to share their learning.
The context for this unit is a supermarket. It can easily be adapted to another context that may be more familiar or relevant to your students. For example:
- packing grocery items into a kete at a local market, community garden or pataka kai for a whānau gathering.
Te reo Māori vocabulary terms such as ine (measure), maihea (weight), manokaramu (kilogram), papatipu (mass), taumaha (heavy), karamu (gram), and taimāmā (light) could be introduced in this unit and used throughout other mathematical learning. Other te reo Māori that could be useful in this unit are the names of some fruit and vegetables. For example; aporo (apple), riki (onion), kumara (sweet potato).
- An assortment of grocery items
- Bucket balances and weights
- Material suitable for packaging into 1kg (gravel, nuts and bolts, stones, wet sand, marbles, water)
- Fruit and vegetables suitable for bagging (oranges, lemons, onions, potatoes, carrots)
- Pose the problem:
I want to pack my supermarket bag carefully and make sure the heavier things are at the bottom so that they don’t squash the lighter objects. I am going to weigh them to find out which is heavier. What could I use?
The concept of packing a kete at the local market, or patata kai (community garden) could be used here, for the same purpose.
- Have the students help with the weighing and talk about the use of balance scales.
Make sure the scales are balanced at the start. Place objects carefully into the middle of the buckets to avoid them tipping or jumping off hooks.
Weigh the packages using different non-standard units of measurement each time and record the results.
Objects Non-standard Packet of tea bags
Packet of cereal
Tin of fruit
…..Flats (one hundred blocks)
Can I tell from this which one is heavier?
What do I need to do? (Emphasise the need for a standard measure - e.g. if we could measure all of these items in the same way, it would make it easier to find out which items are heavier).
Do you know of a measure that a lot of people use when they are trying to find out how heavy something is?
- Discuss objects that are measured in kilograms and grams. Students might contribute ideas such as baking (e.g. the measurement of ingredients), travelling (e.g. the weighing of luggage), or farming (e.g. weighing stock).
- Pass kilogram weights around so that the students can feel the mass. Can you think of other items that weigh the same as this object? How do you know they all weigh 1 kilogram?
- To conclude the session, you could pose the following question to students: what is heavier, a kilogram of steel, or a kilogram of feathers? There is a popular video on YouTube which demonstrates the importance of using a scale to confirm the mass of a kilogram of steel and a kilogram of feathers. Your students may find this video engaging, and may think of other similar situations in which the video could be applied.
For the next 3-4 days the students will spend time making a kilogram and finding containers and objects that have an equal mass to it. The activities could be worked through with a group of students if there are not sufficient balances and scales.
- Have the students make their own kilogram weights using a range of materials, for example, nuts and bolts, wet sand, gravel, stones, marbles. Using balance scales and a 1 kilogram weight the students can make their own 1 kg weights. The kilogram weights can be readily "sealed" in resealable plastic bags.
When the kilogram mass has been made, provide the students with opportunities to find objects and containers that they can compare their kilogram weight (mass) to and record their findings in a table. Encourage students to estimate through handling the objects first. Suitable objects include soap powder, sugar, two litres of water, cans of food, boxes of cereal.
Heavier than 1kg About 1 kg Lighter than 1kg
- Share their findings:
Were you surprised at how heavy any of the packages were?
How did you decide that a package was about 1kg?
- Discuss with the students how fruit and vegetables are weighed in the supermarket.
- Show them three bags of potatoes of varying size, for example, 1kg, 500g, 1.5kg and ask them to decide which one weighs 1kg.
Is it possible to decide how heavy something is just by looking at it?
Are all big things heavy?
Are all small things light?
- Explain to the students that they are going to do the fruit and vegetable shopping today. Consider linking to a context that is more relevant to your learners (e.g. doing the shopping for a small hui at school, shopping for kai to be brought to the marae). They will need to write a shopping list and estimate how many pieces would be close to 1 kilogram. Explain to the students it would be difficult getting exactly a kilogram and usually an amount that is just over or under is acceptable.
- Provide the students with potatoes, onions, oranges, lemons, and carrots and have them bag them into 1kg amounts. Discuss their results with them. Were they close to their estimations? Was there a particular fruit or vegetable that was lighter or heavier than they thought?
- We now explore 1/2 and 1/4 of a kilogram. Begin by passing a bag of lollies (with label covered) around.
Is the bag heavier or lighter than a kilogram?
Why do you think that?
How much lighter?
What do we use when we want to weigh something that is lighter than a kilogram?
- How could we make our kilogram weight into smaller weights?
If we divided it into 2 equal parts how much would each one weigh?
Have the students create 1/2 kg or 500 gram weight.
- Pose the problem of creating a 1/4 kg or 250grams. How many equal parts would they need to divide the clay into?
- Finish by finding objects in the room that are close to 500grams and 250 grams.
The final session provides the students with the opportunity to put their practical skills of weighing to use and to extend their knowledge of units of mass through baking a chocolate cake. Non-bake alternatives could be making jelly or lolly-cake. The key learning to be experienced is using standard units of mass, everyday measuring containers (e.g. which bowl is most suitable to hold the 175g of flour needed to bake the cake). If you feel the food context is inappropriate to your students, then consider other contexts such as building a lego sculpture and estimating its weight.
- 175g flour
- 20g cocoa
- 150g sugar
- 1tsp baking powder
- 1 egg
- 200mL milk
- 75g melted butter
- 1/2 tsp. vanilla essence
Put the flour, cocoa, sugar, and baking powder in a bowl.
Beat the egg and put it in the bowl.
Add the milk, melted butter, and vanilla essence.
Pour into a 2 litre round plastic container lined with waxed paper.
Place in the microwave for 8 minutes on high.
Remove from the container immediately.
The students could work with an adult helper. Either balance or spring scales can be used. Using balance scales gives students the opportunity to make up the weights.
Prior to placing the cake in the microwave, have the students estimate the mass of the cake and container.