Mini Minds Hub · Free printable
Density, Mass and Volume: Free Printable Worksheet for Year 9
- ForYear 9
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Density, Mass and Volume is a free printable maths worksheet for Year 9 (ages 13 to 14), in Key Stage 3. Students use the formula density = mass ÷ volume, with a formula triangle, to find a missing density, mass or volume. Page 2 gives the grown-up notes, help for students who find it hard, a stretch idea and the answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to the student and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Students work through numbered questions and write each answer in the space provided. Masses are given in grams and volumes in cm³. In some questions the student finds a density from a mass and a volume. In others they find a mass from a density and a volume, or a volume from a mass and a density. The triangle helps them pick the right operation each time.
- Mass 200 g, volume 50 cm3. Find the density.
- Mass 90 g, volume 30 cm3. Find the density.
- Density 2, volume 40 cm3. Find the mass.
- Density 5, volume 12 cm3. Find the mass.
- Mass 150 g, density 3. Find the volume.
- Mass 84 g, density 7. Find the volume.
- Mass 360 g, volume 90 cm3. Find the density.
Worked example: finding a volume
Mass 135 g, density 9. Find the volume.
This question uses different numbers from the sheet. It shows two ways to work.
Method 1: the formula triangle- Draw a triangle with mass on top, and density and volume along the bottom.
- Cover the volume. What is left is mass over density.
- So volume = mass ÷ density.
- Work it out: 135 ÷ 9 = 15.
- Start with density = mass ÷ volume.
- Multiply both sides by volume to get density × volume = mass.
- Divide both sides by density to get volume = mass ÷ density.
- Work it out: 135 ÷ 9 = 15. Check by multiplying back: 9 × 15 = 135.
Build and use the formula triangle
Draw it
Draw a large triangle. Split it with a line across the middle. Write mass in the top part. Write density and volume side by side in the bottom part.
Cover to find
Put a finger over the quantity you want to find. If the two left are side by side, multiply them. If one is above the other, divide the top by the bottom.
Write the formula
Before any numbers, write the formula in words, such as density = mass ÷ volume. This stops the numbers going in the wrong places.
Check by multiplying back
Put your answer into a different version of the formula. If mass = density × volume still works, your answer is very likely right.
What density tells us
Density describes how much mass is packed into a given volume. Two objects can be exactly the same size but have different masses, because one is made of a more tightly packed material. For solids, density is often written in grams per cubic centimetre, or g/cm³. The same idea works with other units, as long as they match.
The formula triangle is a memory aid. It does not replace understanding. Students who see that density = mass ÷ volume is a rate, mass for each unit of volume, can rearrange it with confidence. This links to the Key Stage 3 strand on ratio, proportion and rates of change, which also includes speed.
Quick facts about density
- Mass is the amount of matter in an object. It is measured in grams or kilograms.
- Volume is the space an object takes up. For solids it is often measured in cm³.
- 1 cm³ is the same volume as 1 millilitre.
- Water has a density of about 1 g/cm³.
- An object floats in water if its density is less than the density of water.
Skills and curriculum link
- Using formulas
- Rearranging
- Ratio and rates
- Units
- Multiplying and dividing
This sheet supports the area below. It is matched to the published England framework. Please check it against your own school plan.
| Framework | Subject or area | Strand | Year |
|---|---|---|---|
| National Curriculum (England) | Maths | Ratio, proportion and rates of change | Year 9 |
What children will be able to do
- I can use density = mass ÷ volume.
- I can find a missing mass or volume by rearranging the formula.
- I can check that my units match.
Ideas that help with density
- Density is a rateDensity tells you the mass for each 1 cm³. Thinking of it as mass per unit of volume makes the division feel sensible.
- Same size, different massTwo objects of equal volume can have different masses. The one with the greater mass is the denser one.
- Units must matchIf mass is in grams and volume is in cm³, then density is in g/cm³. Mixing units, such as kilograms with cm³, gives wrong answers.
- Inverse operationsMultiplying and dividing undo each other. That is why mass = density × volume and volume = mass ÷ density both follow from the same formula.
Key words
- MassThe amount of matter in an object. It is measured in grams or kilograms.
- VolumeThe amount of space an object takes up. It is measured in units such as cm³.
- DensityHow much mass there is in each unit of volume. It is found by mass ÷ volume.
- FormulaA rule written with letters or words that shows how quantities are linked.
- RearrangeChange a formula so a different quantity is on its own. The formula stays true.
- UnitWhat a quantity is measured in, such as grams or cm³.
How to use it
- Print both pages. Page 1 is for the student. Keep page 2, which has the notes and answers.
- Draw the triangle with mass on top, and density and volume at the bottom. Cover the one you need.
- Work through the first two questions together the first time. Write the formula before using any numbers.
- Let the student try the rest alone. Ask them to write the unit next to each answer.
- Check against page 2. Ask, "How did you choose whether to multiply or divide?" Come back another day to repeat the sheet.
Help, stretch and game ideas
If it feels too hard
Work through the first two questions together. Write the formula each time, then cover the unknown in the triangle. Say out loud whether you multiply or divide. Add units to every number as you go, so mass in grams and volume in cm³ stay clear.
To stretch confident children
Make up two more questions and swap them with a friend. Write one that finds a density, one that finds a mass and one that finds a volume if you can. Solve each other's, then check by multiplying back.
Make it a game
Take two objects of about the same size, such as two similar blocks made of different materials. Weigh each one and compare the results. Say which is denser and explain how you know, using mass and volume.
Mistakes to watch for
Watch forA student multiplies mass and density when asked for a volume.
Try thisCover volume in the triangle. Mass is over density, so divide. Then multiply the answer by the density to check it gives back the mass.
Watch forA student divides volume by mass to find a density, for example 10 ÷ 60 instead of 60 ÷ 10.
Try thisWrite density = mass ÷ volume first. Mass is the top number in the triangle, so it goes first in the division.
Watch forA student writes only a number with no unit, or mixes kilograms with cm³.
Try thisWrite the unit beside every value. Grams with cm³ give g/cm³. Convert first if the units do not match.
Talk about it
- How does the formula triangle help you decide whether to multiply or divide?
- Two objects are the same size but one has a bigger mass. Which is denser, and why?
- What units does your answer have, and why?
- How can you check an answer by using a different version of the formula?
- Why is density called a rate?
- Where might you meet density in science lessons or in everyday life?
Take it off the page
Same size, different mass
Find two objects of similar size, such as a toy brick and a small stone. Hold one in each hand. Predict which has the greater mass, then weigh them to check.
Sink or float
Ask an adult to help you fill a bowl with water. Gently test small safe objects and sort them into those that sink and those that float. Talk about what that suggests about their density.
Triangle poster
Make a poster of the formula triangle with an example for each of the three versions. Use your own numbers. Pin it where you do homework.
Who it is for
Parents
Sit beside your student for the first two questions and let them explain each choice. Ask them to write the formula before every calculation. Praise careful thinking and tidy working, not just right answers.
Teachers
Use it as a starter after teaching rates, as a plenary on formulas and units, or as a homework or cover task. Page 2 has support and stretch ideas, so it suits mixed ability groups. Ask students to explain their rearranging.
Home educators
This fits alongside science and everyday measuring. Pair it with weighing objects at home, comparing similar sized items. You can print it again for revision or for brothers and sisters.
Where this fits in maths
Before this sheet, students need confident multiplying and dividing, and a sense of ratio and rates. They should also be comfortable with measuring in grams and cm³ and with simple rearranging.
After it, students can meet other compound measures, such as speed and pressure, which also link quantities with a multiplication or division. At Key Stage 4 they use the same skills in more complex formula and proportion problems, and in science.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- How do you rearrange the formula to find mass?
- What units does your answer have, and why?
- Which of two objects is denser, and how do you know?
Questions parents and teachers ask
- What age is Density, Mass and Volume for?
It is written for Year 9 (ages 13 to 14), in Key Stage 3. It suits students who know how to multiply and divide and are ready to apply formulas.
- What will students practise?
They practise using density = mass ÷ volume to find a missing density, mass or volume. They also work with units and ratio ideas, and meet the formula triangle as a memory aid.
- How do I use the formula triangle?
Draw a triangle with mass on top, and density and volume at the bottom. Cover the quantity you want. If the other two are side by side, multiply. If one is above the other, divide.
- What if it feels too hard?
Work through the first two questions together and write the formula each time. Use the triangle, say whether you multiply or divide, and write the unit beside every number. Then let the student try again alone.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for revision or for other students.
- Can teachers use it in class?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 has support, stretch and answers.
- Is this a screen free activity, and do I need colour?
Yes, it is screen free and needs only paper and a pencil. No colour is needed. It prints well in black and white on plain A4 paper.
More like this
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.