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Year 3 Maths Mass

Compare & order mass

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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. Curriculum: VC2M3M02 / AC9M3M02.

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.

Pan balance tipped to the heavier side A pan balance with the left pan lower holding 500 g and the right pan higher holding 300 g. The lower pan is labelled heavier and the higher pan is labelled lighter, because the heavier mass sinks down. 500 g heavier 300 g lighter
The lower pan holds the heavier mass: 500 g is heavier than 300 g.
Number line ordering three masses from lightest to heaviest A number line from 0 to 2000 grams in steps of 250. Three masses are marked with red arrows: 750 g, 1 kg at 1000 g, and 1 kg 500 g at 1500 g, in order from lightest to heaviest. 0250500 75010001250 150017502000 750 g1 kg1 kg 500 g
Ordered lightest to heaviest: 750 g, 1 kg, 1 kg 500 g.

Mass has no formula, but these facts let you change kilograms into grams so you can compare and order any masses.

\[ 1 \text{ kg} = 1000 \text{ g} \]
1 kg =1000 g
\[ 5 \text{ kg} = 5000 \text{ g} \]
5 kg =5000 g
\[ 1 \text{ kg } 500 \text{ g} = 1500 \text{ g} \]
1 kg 500 g =1500 g
Same unit rule. Change every mass to grams before you compare. For whole kilograms, times by \(1000\): \(4\text{ kg} = 4000\text{ g}\). For kilograms and grams, add the grams on: \(2\text{ kg } 250\text{ g} = 2000 + 250 = 2250\text{ g}\).
Same mass, different names. \(2\text{ kg } 50\text{ g}\) and \(2050\text{ g}\) are the same mass. Watch the zero: \(2\text{ kg } 50\text{ g}\) is not \(2500\text{ g}\).
Compare the digits. When every mass is in grams, a number with more digits is heavier, so \(1035\text{ g}\) is heavier than \(985\text{ g}\). If the masses have the same number of digits, compare from the left: thousands first, then hundreds, then tens. So \(306\text{ g} < 360\text{ g} < 603\text{ g}\).
Scales marked in kilograms. Some scales count in whole kilograms. Read the number the pointer is on and keep the answer in kilograms. A \(6\text{ kg}\) bag is \(6 - 4 = 2\text{ kg}\) heavier than a \(4\text{ kg}\) bag.

How to compare and order masses

  1. Use the same unit. Change every mass to grams. Remember \(1\text{ kg} = 1000\text{ g}\), so \(1\text{ kg } 400\text{ g} = 1400\text{ g}\).
  2. Compare the numbers. The larger number is heavier and the smaller number is lighter. Equal numbers mean equal masses.
  3. 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.
  4. Balance problems. To make a balance level, find the difference between the two pans and add it to the lighter pan.
  5. 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.
Example 1 — Find the heaviest
Which is heaviest: \(640\text{ g}\), \(470\text{ g}\), \(590\text{ g}\) or \(380\text{ g}\)?
Solution

The masses share a unit (grams), so compare the numbers.

\(640\)\(>\)\(590 > 470 > 380\)
640>590>470>380

The heaviest is \(640\text{ g}\).

Example 2 — Compare across units
Which is heavier: \(1\text{ kg } 300\text{ g}\) or \(1250\text{ g}\)?
Solution

Change to grams first, then compare.

\(1\text{ kg } 300\text{ g}\)\(=\)\(1300\text{ g}\)
\(1300\)\(>\)\(1250\)
1300>1250

So \(1\text{ kg } 300\text{ g}\) is heavier.

Example 3 — Order the masses
Put \(900\text{ g}\), \(1\text{ kg}\) and \(1\text{ kg } 250\text{ g}\) in order from lightest to heaviest.
Solution

Change each mass to grams, then order smallest to largest.

\(1\text{ kg}\)\(=\)\(1000\text{ g}\)
\(1\text{ kg } 250\text{ g}\)\(=\)\(1250\text{ g}\)
\(900\)\(<\)\(1000 < 1250\)
900<1000<1250

In order: \(900\text{ g}\), \(1\text{ kg}\), \(1\text{ kg } 250\text{ g}\).

Example 4 — How much heavier
The balance shows a pumpkin and a cabbage. How much heavier is the pumpkin?
Pan balance comparing a pumpkin and a cabbage A pan balance with the left pan lower holding a pumpkin of 2 kg and the right pan higher holding a cabbage of 1 kg 200 g. The pumpkin sinks lower because it is heavier. 2 kg pumpkin 1 kg 200 g cabbage
Solution

Change both to grams, then subtract.

\(2\text{ kg}\)\(=\)\(2000\text{ g}\)
\(1\text{ kg } 200\text{ g}\)\(=\)\(1200\text{ g}\)
\(2000 - 1200\)\(=\)\(800\text{ g}\)
2000-1200=800

The pumpkin is \(800\text{ g}\) heavier.

Example 5 — Make it balance
The left pan holds \(900\text{ g}\) of flour. The right pan holds a \(350\text{ g}\) bag of nuts. How many grams must be added to the right pan to make the scale level?
Pan balance with 900 grams of flour and 350 grams of nuts A pan balance tilted down on the left. The left pan holds 900 grams of flour and the right pan holds a 350 gram bag of nuts. flour 900 g nuts 350 g
Solution
\(900 - 350\)\(=\)\(550\text{ g}\)
\(350 + 550\)\(=\)\(900\text{ g}\)

Add \(550\text{ g}\) to the right pan. Then both pans hold \(900\text{ g}\).

Example 6 — Difference in kg and g
A box of books has a mass of \(4\text{ kg}\). A box of toys has a mass of \(2\text{ kg } 700\text{ g}\). How much heavier is the box of books? Give the answer in kilograms and grams.
Solution
\(4\text{ kg}\)\(=\)\(4000\text{ g}\)
\(2\text{ kg } 700\text{ g}\)\(=\)\(2700\text{ g}\)
\(4000 - 2700\)\(=\)\(1300\text{ g}\)
\(1300\text{ g}\)\(=\)\(1\text{ kg } 300\text{ g}\)

The box of books is \(1\text{ kg } 300\text{ g}\) heavier.

Example 7 — Order by place value
Four parcels have masses of \(1350\text{ g}\), \(1035\text{ g}\), \(1305\text{ g}\) and \(985\text{ g}\). Put them in order from lightest to heaviest. How much heavier is the heaviest parcel than the lightest?
Solution

\(985\) 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

Change to the same unit first. Watch out for comparing \(800\text{ g}\) with \(1\text{ kg}\) straight away. Change \(1\text{ kg}\) to \(1000\text{ g}\), then compare.
A bigger number is not always heavier. \(950\text{ g}\) looks large, but \(1\text{ kg} = 1000\text{ g}\), so \(1\text{ kg}\) is the heavier one.
The heavier pan goes down. On a balance, the lower pan holds the heavier mass. Down means heavier, not lighter.
1 kg is 1000 g, not 100 g. A kilogram is one thousand grams. Adding only two zeros gives the wrong mass.

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 \(2000 + 50 = 2050\).

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