Mathematics builds a strong foundation

Most of us take for granted the homes we live in are well built, with straight walls, windows that open and close smoothly, and a roof able to withstand the weather.

If the architect has done their job, and the tradespeople have carried out the design requirements according to plan, all the various components of a home should work seamlessly together.

And beneath the surface, all of those components have been put together perfectly because everyone working on the house used mathematics.

Architects, and the many tradespeople who are needed to build houses like bricklayers, carpenters, tilers and plumbers, all need to know some maths if they are to achieve perfect angles, corners, volumes and quantity estimates.

Here are just five ways maths is used to build from the ground up.

1. The new house must fit on the piece of land where it will be built. The area the house takes up on the ground is measured in square metres, and so is the block of land it will be built on. Planning the house site is a great example of using fractions. The area of the house is subtracted from the area of the land to work out how much land is left over. The new owner might want the house to only take up half of the land to allow for a vegetable garden, or a swimming pool. So, a lot of adding and subtracting is done to get the right proportion of house to land. If you have a 300 square metre block of land, you might just use half of it, and build a 150 square metre house.
2. Walls must be square to hold up the roof. So, builders need to know how to make perfect right angles. The Pythagoras theorem (a²+ b² = c²⁾ has been used for centuries to measure and make squares. It’s sometimes called the 3:4:5 rule and builders and carpenters can quickly make a “set square” on the building site, cutting and measuring bits of wood to make sure they can measure a perfect right angle. For example, they would have a 30cm length on the straight line, a 40cm length on the perpendicular line, and a 50cm length across. If all three measurements are correct, they have a perfectly square corner. Then they use the set square as a tool to check the angles of the walls are at 90 degrees to the floor and able to support the roof.
3. A bricklayer is likely to be making mortar to hold bricks together to make a wall. Mortar is made from a ratio of sand and cement. If the ratio is 6:1 mix of sand to cement, and a bricklayer knows a bag of cement contains four shovels, they can work out how many shovels of sand they need to go with it.
4. There’s a lot of on-site or off-site cutting and measuring to make doors and window frames. The old saying “measure twice, cut once” is essential in building because the carpenter won’t want to waste expensive building materials. To make frames, they might want to cut four pieces of timber from one long piece of timber, so it would be important to know how to do division and multiplication. Carpenters often use tape measures and calculators to help with the calculations and make sure there are no mistakes.
5. When it comes to putting floor tiles in the kitchen or bathroom, the floor tiler will need to be able to work out how many square metres of tiles are needed. They calculate this by multiplying the length of the walls to work out the area of the room. A 4m X 3m room means they need 12 square metres of tiling. They can even add on more rooms and calculate how many tiles they need all together. Individual tiles can vary in size a lot (some are big square tiles and others could be small mosaics). Tiles are usually sold by the square metre, so being able to work out the square metre area of all the rooms means the owner can compare prices of various tiles, or even compare the cost of tiles with other floor coverings like carpet or wood.

Carpenters work with timber, bricklayers use bricks and mortar, and the plumbers look after the pipes, however, they have an important skill in common – they all need to use the same maths to get their job done.

The activities in ORIGO Education’s Think Tanks Measurement & Geometry help students to learn about length & geometric shape while practicing core visual, spatial, reasoning and thinking skills.