This unit comprises six problems for students to apply and interpret measurement of mass. Students are also introduced to the concepts of net and gross mass.
Mass is the force created by gravity acting of on an object. Mass is felt as weight, a force that pulls the object towards the centre of the Earth. Mass is measured in units based on grams, and tonnes. Larger or smaller units are created by combining or equally partitioning these units. One kilogram is a combination of 1000 grams (kilo means 1000). One milligram is 1/1000 of a gram and one microgram is 1/ 1 000 000 of a gram. The units for mass come from the mass of water. One cubic metre of water has a mass of 1 tonne, or 1000 kilograms. One millilitre of water has a mass of one gram.
Note that in the New Zealand Curriculum document, “weight” and “mass” are used interchangeably. In a science context, the definition of “force created by gravity acting on an object” would often be equated with weight, not mass. Consider the scientific knowledge of your students (e.g. are they studying forces in science). It may be more appropriate to define mass as the amount of matter in an object (measured in kilograms) and weight using the adorementioned definition (measured in Newtons, N).
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
Tasks can be varied in many ways including:
The context for this unit can be adapted to suit the interests and cultural backgrounds of your students. Use the interests of your students to create contexts that will engage them. Students may be interested in the mass of rugby players. Students from large whānau, or who prepare food for large numbers of people, may relate to measuring quantities to scale up recipes. Carrying heavy objects was a major problem for pre-European Māori. How did they carry heavy loads, or move waka? Counting on Frank by Rod Clement may inspire some students to look for eccentric ways to apply measurement to their daily lives. For example, the human body is 60% water, by mass. How much water is in their body?
Te reo Māori vocabulary terms such as maihea (weight / mass), karamu (gram), manokaramu (kilogram), and tana (tonne) could be introduced in this unit and used throughout other mathematical learning.
The following six stations provide a range of problems for students to apply and interpret measurement of mass. Consider what would be the most effective method for introducing these to your class. You could work on them as a whole class and provide support to groups of students. Alternatively, you could use another relevant igniting activity to introduce the context for learning, before directing students to work on one or more of these stations independently, or in small groups. These stations could serve as the basis for learning in different sessions, or could be used as one session. At the conclusion of these stations, students draw on the problems presented and create their own stations to be used in other lessons.
You have won a prize which can be just one of the following:
What is your choice?
Answers:
1 kg of $1 coins (1000 ÷ 8 = 125 coins, so $125)
1.5 metre of $2 coins (1500 ÷ 26.5 = 57 coins, so $114)
0.5 metre stack of 50c coins (500 ÷ 1.7 = 294 coins, so $147)
This problem could be adapted to reflect food that is meaningful to your students (e.g. the largest tray of pani popo).
The world’s largest lasagne was made in 2012 at a restaurant in Wieliczka, Poland.
It weighed 4865 kg and measured 25 m x 2.5 m.
The ingredients were:
2500kg of pasta, 800kg of mince, 400kg of mozzarella cheese, 100kg of peas, 100kg of carrots, and equal amounts of white sauce and tomato sauce.
Answers:
Konsihiki was the largest active sumo wrestler in the world with a mass of 287 kg. Now he is retired.
How many Konishikis weigh as much as 1 tonne?
Make a table of tonne weights using objects in the classroom. Remember that 1000 kg is a tonne.
Object | Mass | Number in a tonne |
Konsihiki | 287 kg | |
School bag | 5 kg | 200 |
Answers:
The number of Konshihikis in 1 tonne equals 3.48, about 3 and ½ of him.
To find how many of any object make 1 tonne, divided 1 000 by the weight of the object in kilograms. For example, if a schoolbag weighs 5kg then 1 000 ÷ 5 = 200 make 1 tonne.
Find out facts about the mass of very large animals and make a report about these animals for the class. To get you started here are some facts about the Blue Whale, which can be seen in New Zealand waters.
The blue whale is the largest animal living on Earth. It can reach up to nearly 30 metres in length and weigh up to 180 tonnes (t). Their tongues alone can weigh as much as some elephants and their hearts are huge, weighing a whopping 180kg. They have the largest babies on Earth. When they are first born they can be 8 metres (m) in length and weigh 4000kg. Imagine a jet engine that registers at 140 decibels. A blue whale, when it calls, registers at 188 decibels. Compare the facts about the Blue Whale with the large African elephant
The African elephant is the biggest animal on land. Fully grown the male can be 7 metres long, 3.2 metres tall at the shoulder and have a mass of 6500kg. Its tusks can weigh as much as 100kg each. The largest pair of tusks on record are in the British Museum and weigh 133kg each.
What combination of animals could be equal to the elephant's weight?
For example, it takes 6500 ÷ 5 = 1300 big domestic cats to weigh 1 elephant or 130 big dogs.
How many rhinoceroses, lions, giraffes, or hippopotamuses weigh the same as an elephant?
Answers:
Answers will vary depending on what other animals your students research.
Measure out one litre (l) of water.
For each container, estimate the capacity of the container, measure it to check, estimate the mass of water when the container is full, and find the mass of the water using scales.
Record your results like this:
Container | Estimate capacity | Measure actual capacity | Estimate mass of water | Measure actual mass |
A | ||||
B | ||||
C | ||||
D | ||||
E |
Answers:
Answers depend on the size of the containers. Here is an example:
Container | Estimate capacity | Measure actual capacity | Estimate mass of water | Measure actual mass |
A | 400 mL | 450 mL | 390 g | 450g |
Counting on Frank by Rod Clement (1990; Harper Collins Publishers: Sydney) has some great ideas for measurement investigations. You can view readings of the book on YouTube if you cannot source a copy of the book. One of the ideas introduced in the story is about Frank carrying a trolley load of cans to the supermarket.
How did you work that out?
Here is another task based on Counting on Frank that you may choose to use.
Answers:
Dear family and whānau,
In class we have talked a lot about weight this week. In particular, we discovered that Konshiki, the largest Sumo wrestler, weighs 226kg, a Blue Whale weighs 180 tonnes and an elephant weighs 6500kg. What do you think the Blue Whale weighs in kg?
Your child has been asked to look for other facts associated with weight by reading the newspaper or doing some reading on the internet. They should record what they find out. Please encourage them to discuss their findings with you.
You could support them further by weighing items at home or cooking with them.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/weighty-problems at 8:45pm on the 26th February 2024