Compare & order mass
Comparing mass means working out which object is heavier or lighter, and ordering lines masses up from lightest to heaviest. In South Australian Year 3 maths students do this on a pan balance and with masses written in grams and kilograms (Australian Curriculum AC9M3M02).
Students read which side of a balance is heavier, change kilograms to grams so mixed masses can be compared, and use \(>\), \(<\) and \(=\). They order three or four masses, including close ones such as 806 g and 860 g, find how much heavier one thing is, for example \(1\text{ kg} - 650\text{ g} = 350\text{ g}\), and work out the mass needed to make a balance level. Parcels, melons, school bags and dogs are the settings. It is part of Year 3 Mass.
Theory
Comparing and ordering mass is a Year 3 measurement skill: deciding which object is heavier or lighter, reading a pan balance, and putting masses in order. This Year 3 maths page shows how to use the same unit, convert with 1 kg = 1000 g, and find how much heavier one mass is than another in grams and kilograms.
Mass tells you how heavy something is. We measure mass in grams (g) for light things like an apple, and kilograms (kg) for heavy things like a school bag. A kilogram is bigger: \(1\text{ kg} = 1000\text{ g}\).
To compare two masses, put them in the same unit and look at the numbers. The heavier mass has the larger number and the lighter mass has the smaller number. To order a set of masses, line them up from lightest to heaviest (smallest to largest).
A pan balance compares two masses at once. The heavier object pulls its pan down, so the lower pan holds the heavier mass. If the pans are level, the two masses are equal.
Mass has no formula, but these facts let you change kilograms into grams so you can compare and order any masses.
How to compare and order masses
- Use the same unit. Change every mass to grams. Remember \(1\text{ kg} = 1000\text{ g}\), so \(1\text{ kg } 400\text{ g} = 1400\text{ g}\).
- Compare the numbers. The larger number is heavier and the smaller number is lighter. Equal numbers mean equal masses.
- Order or subtract. Line the numbers up smallest to largest to order them (or largest to smallest for heaviest first), or subtract to find how much heavier one mass is.
- Balance problems. To make a balance level, find the difference between the two pans and add it to the lighter pan.
- Compare digits. If the masses in grams have different numbers of digits, the longer number is heavier. If not, compare the thousands, then the hundreds, then the tens.
The masses share a unit (grams), so compare the numbers.
| \(640\) | \(>\) | \(590 > 470 > 380\) |
The heaviest is \(640\text{ g}\).
Change to grams first, then compare.
| \(1\text{ kg } 300\text{ g}\) | \(=\) | \(1300\text{ g}\) |
| \(1300\) | \(>\) | \(1250\) |
So \(1\text{ kg } 300\text{ g}\) is heavier.
Change each mass to grams, then order smallest to largest.
| \(1\text{ kg}\) | \(=\) | \(1000\text{ g}\) |
| \(1\text{ kg } 250\text{ g}\) | \(=\) | \(1250\text{ g}\) |
| \(900\) | \(<\) | \(1000 < 1250\) |
In order: \(900\text{ g}\), \(1\text{ kg}\), \(1\text{ kg } 250\text{ g}\).
Change both to grams, then subtract.
| \(2\text{ kg}\) | \(=\) | \(2000\text{ g}\) |
| \(1\text{ kg } 200\text{ g}\) | \(=\) | \(1200\text{ g}\) |
| \(2000 - 1200\) | \(=\) | \(800\text{ g}\) |
The pumpkin is \(800\text{ g}\) heavier.
| \(900 - 350\) | \(=\) | \(550\text{ g}\) |
| \(350 + 550\) | \(=\) | \(900\text{ g}\) |
Add \(550\text{ g}\) to the right pan. Then both pans hold \(900\text{ g}\).
| \(4\text{ kg}\) | \(=\) | \(4000\text{ g}\) |
| \(2\text{ kg } 700\text{ g}\) | \(=\) | \(2700\text{ g}\) |
| \(4000 - 2700\) | \(=\) | \(1300\text{ g}\) |
| \(1300\text{ g}\) | \(=\) | \(1\text{ kg } 300\text{ g}\) |
The box of books is \(1\text{ kg } 300\text{ g}\) heavier.
\(985\) has only three digits, so it is the lightest. The other three each have \(1\) thousand.
Hundreds: \(1035\) has \(0\) hundreds, so it comes next. \(1305\) and \(1350\) both have \(3\) hundreds, so compare the tens: \(0 < 5\).
| \(\text{order}\) | \(:\) | \(985 < 1035 < 1305 < 1350\) |
| \(1350 - 985\) | \(=\) | \(365\text{ g}\) |
Lightest to heaviest: \(985\text{ g}\), \(1035\text{ g}\), \(1305\text{ g}\), \(1350\text{ g}\). The heaviest is \(365\text{ g}\) heavier.
Common pitfalls
Frequently asked questions
What does mass mean?
Mass tells you how heavy something is. We measure light things in grams and heavy things in kilograms.
How do you compare two masses?
Put both masses in the same unit first, usually grams. Then compare the numbers. The larger number is the heavier mass.
How many grams are in a kilogram?
There are \(1000\) grams in \(1\) kilogram. So \(1\text{ kg} = 1000\text{ g}\), \(5\text{ kg} = 5000\text{ g}\), and \(1\text{ kg } 500\text{ g} = 1500\text{ g}\).
Which side of a balance scale is heavier?
The heavier side sinks down and the lighter side lifts up. If the two pans sit level, the masses are equal.
How do you put masses in order?
Change every mass to the same unit, then line the numbers up from smallest to largest for lightest to heaviest, or largest to smallest for heaviest to lightest.
Is a bigger number always heavier?
No. A number is only bigger if the units match. \(950\text{ g}\) looks large, but \(1\text{ kg} = 1000\text{ g}\), so \(1\text{ kg}\) is heavier than \(950\text{ g}\).
How do you find what to add to make a balance level?
Find the difference between the two pans and add it to the lighter pan. With \(900\text{ g}\) on one side and \(350\text{ g}\) on the other, add \(900 - 350 = 550\text{ g}\).
Can two masses with different numbers be the same?
Yes. \(2\text{ kg } 50\text{ g}\) and \(2050\text{ g}\) are the same mass, because \(2\text{ kg} = 2000\text{ g}\) and \(2000 + 50 = 2050\).