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Year 4 Maths Mass

Solve mass problems

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Theory

Solving mass problems is a Year 4 skill: working with grams and kilograms, converting between them (\(1\) kg \(=\ 1000\) g), and using addition, subtraction and multiplication to find a total, a difference or a missing mass. This Year 4 maths page shows how to change to the same unit first, then solve mass word problems with bar models and pan balances. Curriculum: VC2M4M01 / AC9M4M01.

Mass is how heavy something is. In Australia we measure mass in grams (g) for light things and kilograms (kg) for heavier things. The key fact that links them is \(1\) kg \(=\ 1000\) g.

To solve a mass problem, first make sure every mass is in the same unit. Change kilograms to grams by multiplying by \(1000\), and change grams to kilograms by dividing by \(1000\). Then add for a total, subtract to find a difference or a missing mass, or multiply for equal groups.

A mass can be written in mixed form using both units. For example, \(1250\) g is the same as \(1\) kg \(250\) g, because \(1000\) g makes \(1\) kg and \(250\) g is left over.

Bar model showing two masses making a total A bar split into two parts, 550 grams and 300 grams, with a bracket above showing the total is 850 grams. Total = 850 g 550 g 300 g 550 + 300 = 850 g
A bar model joins two parts to make the whole.
A level pan balance for finding a missing mass A balance scale with a level beam. The left pan holds 900 grams. The right pan holds 600 grams plus an unknown mass. Because it is level, both pans hold 900 grams. 900 g 600 g + ? Level: both sides = 900 g
A level balance means both pans hold the same mass.

These mass facts are worth remembering. They let you change units before you add or subtract.

\[ 1 \text{ kg} = 1000 \text{ g} \]
1 kg =1000 g
\[ \dfrac{1}{2} \text{ kg} = 500 \text{ g} \]
12 kg =500 g
\[ \dfrac{1}{4} \text{ kg} = 250 \text{ g} \]
14 kg =250 g
\[ \dfrac{3}{4} \text{ kg} = 3 \times 250 = 750 \text{ g} \]
34 kg=3×250=750 g
\[ 3.5 \text{ kg} = 3 \tfrac{1}{2} \text{ kg} = 3500 \text{ g} \]
3.5 kg=3500 g
Kilograms and gramsGrams
1 kg1000 g
1 kg 250 g1250 g
2 kg 750 g2750 g
4 kg4000 g
Same unit first. You cannot add kilograms straight to grams. Change kilograms to grams by multiplying by \(1000\), then add or subtract.
Decimal kilograms. \(.5\text{ kg}\) is half a kilogram, which is \(500\text{ g}\). So \(2.5\text{ kg} = 2000 + 500 = 2500\text{ g}\).

How to solve a mass problem

  1. Same unit. Change every mass to the same unit, usually grams. Multiply kilograms by \(1000\).
  2. Read any scale. Work out what each mark is worth from the labelled numbers, then count on to the pointer before you add or subtract.
  3. Choose the operation. Add for a total, subtract for a difference, a missing mass or how much more fits, multiply for equal groups, and divide to share a mass equally.
  4. Answer with a unit. Work out the number, write \(\text{g}\) or \(\text{kg}\) next to it, and rename to kilograms and grams if the question asks.
Example 1 — Total mass
A shopping bag holds a \(650\) g box of cereal and a \(470\) g jar of jam. What is the total mass?
Bar model adding 650 grams and 470 grams A bar split into 650 grams and 470 grams with a bracket above showing the total of 1120 grams. 1120 g 650 g 470 g
Solution
\(650 + 470\)\(=\)\(1120 \text{ g}\)
\(1120 \text{ g}\)\(=\)\(1 \text{ kg } 120 \text{ g}\)
650+470=1120 g

The total mass is \(1120 \text{ g}\), or \(1 \text{ kg } 120 \text{ g}\).

Example 2 — Missing part
Two books together have a mass of \(1\) kg \(100\) g. One book is \(680\) g. What is the mass of the other book?
Bar model with a known part and a missing part A whole bar of 1100 grams split into a known part of 680 grams and an unknown part marked with a question mark. 1100 g (1 kg 100 g) 680 g ?
Solution
\(1 \text{ kg } 100 \text{ g}\)\(=\)\(1100 \text{ g}\)
\(1100 - 680\)\(=\)\(420 \text{ g}\)

The other book has a mass of \(420 \text{ g}\).

Example 3 — Equal groups
A shelf holds \(3\) bags of pasta. Each bag has a mass of \(800\) g. What is the total mass, in kilograms and grams?
Solution
\(3 \times 800\)\(=\)\(2400 \text{ g}\)
\(2400 \text{ g}\)\(=\)\(2 \text{ kg } 400 \text{ g}\)
3×800=2400 g

The total mass is \(2 \text{ kg } 400 \text{ g}\).

Example 4 — Two steps
A tub holds \(1\) kg \(300\) g of toys. You add \(900\) g more. The tub can hold up to \(4\) kg. How much more can still fit?
Solution
\(1300 + 900\)\(=\)\(2200 \text{ g}\)
\(4 \text{ kg}\)\(=\)\(4000 \text{ g}\)
\(4000 - 2200\)\(=\)\(1800 \text{ g}\)

Another \(1800 \text{ g}\), or \(1 \text{ kg } 800 \text{ g}\), can still fit in the tub.

Example 5 — Share a mass
A farmer shares \(15\) kg of potatoes equally into \(5\) boxes. Then each box is shared equally into \(4\) bags. What is the mass of each bag, in grams?
Solution
\(15 \div 5\)\(=\)\(3 \text{ kg}\)
\(3 \text{ kg}\)\(=\)\(3000 \text{ g}\)
\(3000 \div 4\)\(=\)\(750 \text{ g}\)

Each box holds \(3\) kg and each bag holds \(750 \text{ g}\).

Example 6 — Masses in a table
The table shows the masses of three pets.
PetMass (kg)
Max14
Bella9
Rocky21
How much heavier is Rocky than Bella? What is the total mass of the three pets?
Solution
\(21 - 9\)\(=\)\(12 \text{ kg}\)
\(14 + 9 + 21\)\(=\)\(44 \text{ kg}\)

Rocky is \(12\) kg heavier than Bella. Together the pets have a mass of \(44\) kg.

Common pitfalls

Convert before you add. Watch out for adding kilograms straight to grams. Change both to grams first, so \(1\) kg \(+\ 400\) g means \(1000 + 400 = 1400\) g.
Line up the right amount. Since \(1\) kg \(=\ 1000\) g, a mass of \(1\) kg \(80\) g is \(1080\) g, not \(180\) g. The grams part fills up to \(1000\) before the next kilogram.
Answer with a unit. A number on its own is not a mass. Always write \(\text{g}\) or \(\text{kg}\) next to your answer.
Decimal kilograms. \(2.5\) kg is \(2500\) g, not \(25\) g or \(250\) g. The \(.5\) means half a kilogram, which is \(500\) g.

Frequently asked questions

How many grams are in a kilogram?

There are \(1000\) grams in \(1\) kilogram. To change kilograms to grams you multiply by \(1000\), so \(6\) kg is \(6000\) g.

How do you solve a mass word problem?

First change every mass to the same unit, usually grams. Then decide whether to add, subtract or multiply. Add masses for a total, subtract for a missing mass, and multiply for equal groups. Finish by writing the unit next to the answer.

How do you add kilograms and grams together?

Change the kilograms to grams first by multiplying by \(1000\), then add. For example \(1\) kg \(200\) g is \(1200\) g, and \(1200 + 500 = 1700\) g.

How do you find a missing mass?

Work in the same unit and subtract. If two items together are \(1100\) g and one is \(680\) g, the missing item is \(1100 - 680 = 420\) g.

How do you write grams in kilograms and grams?

Split off each whole \(1000\) g as \(1\) kg. So \(2400\) g is \(2000 + 400\), which is \(2\) kg \(400\) g.

What is half a kilogram in grams?

Half a kilogram is \(500\) g, because half of \(1000\) is \(500\). A quarter of a kilogram is \(250\) g.

How do you change a decimal number of kilograms into grams?

Split it into whole kilograms and the part after the point. \(.5\) kg is half a kilogram, \(500\) g. So \(3.5\) kg is \(3000 + 500 = 3500\) g.

How do you check if something is under a mass limit?

Put both masses in the same unit and compare. A bag limit of \(7\) kg is \(7000\) g, and \(6\) kg \(900\) g is \(6900\) g, so that bag is \(100\) g under the limit.

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