# Architecture and Primary Maths

Architecture to the artist is all about design and beauty but through part of those aspects; symmetry, we link into mathematics.  Whilst no one wants an ugly building, the practicality is that without maths and science, we’d never know whether the design of beautiful buildings would work until it was too late.

Activity One – House of Cards

LO: Understand how different shapes have different properties relating to strength and stability Be able to state how a shape can be strengthened by introducing triangles into it
This activity helps children to understand the strength of shapes and how they can be used in buildings
Divide the children into groups of four and give them a pack of playing cards. Ask them to build a structure as tall as they can using the cards. Don’t give them any clues as to how they should do it. Some will begin with standard square shapes but find that they are unstable whilst others will use a triangle shape which they’ll find more stable.

Ask the children to tape four cards together to make a square and another three to make a triangle. Place each on the desk and get them to press gently on the top of each, what do they notice happening?

Talking Point: If they have completed a science module on forces ask them to describe what is happening at the places where the cards join and to the cards themselves. They should notice that the square simply collapses as the angles change from 90 degrees at each adjoining edge. With a lot of force placed centrally, the top will bend inwards causing the sides to fold in also. With the triangle they should feel more resistance and whilst the sides may flex inwards, the shape should remain more stable. Ask them how they could stabilise the square shape and they may suggest adding a brace so it forms a triangle.

Extension: Get a tray of 36 eggs and ask the children what they think would happen if they stood on them. Tell the children that one of them is going to try. Place a piece of board on top of the eggs and ask a child to slowly and carefully stand on the centre of the board. The eggs will not break. Now show the children the cross section of the eggs, the tray and the board and ask them to say why they think the eggs supported their weight.

At Home: Find pictures of objects which are strengthened using triangles e.g. cranes, bridges, greenhouses etc.

Activity Two: Density and Weight

LO: Understand how the force exerted by an object is determined by the weight of the object and the area of the base where the force is being applied
Understand that the force can be reduced by increasing the surface area of its point of contact or by reducing its mass

Ask the children to research why New York has many skyscrapers and why London has so few. They should discover that it’s because of the type of ground the building is constructed on. London is mainly built on soft soil whilst New York has a rock base. If London had the same size buildings as New York, they would sink into the soil. Demonstrate this to children with a tray of wet soil and a block of wood. Stood on its end, it sinks into the wet soil. Placed on its side, it sinks in much less.

Talking Point: Why does the horizontal building sink less than the vertical one? This is a difficult question but many children answer it by saying there’s more of the building touching the soil without going on to explain why this helps.
You can demonstrate why it works by getting two or more bathroom scales and a plank of wood. Place the plank of wood on one of the scales and ask a child to stand on it, noting their weight. Now try the same with the wood placed across two scales and again across three if you have another. The children will find that the two scales each show half the weight whilst three will show a third of the weight.
Explain to them that it’s forces at work again and that the building presses down over its base area and that the force is calculated by the weight divided by the base area in each case so with the horizontal building having a bigger base, the force is less.

Talking Point: Ask the children if they can think of another way in which the force could be reduced. Remind them that the key elements are the surface area of the point of contact, the mass and gravity. They should suggest reducing the mass by using lighter materials.

At Home: Ask the children to investigate pressure around the home. With parents’ help, move some of the furniture and see the marks left by it in carpet or lino. Which has the deepest marks? What can be done to reduce damage to the floor coverings?

Activity Three: Plans and Scale Drawings

LO: Understand how scales are used to represent buildings or locations in real life
Use scales to calculate actual sizes or to reduce actual size to be able to represent an object on a piece of paper

Architects and builders work from plans drawn to scale to ensure that the finished building is as the architect designed it. It would be very difficult to work from a full size drawing so the plans are reduced in size and drawn to scale.
Show the children various maps and plans drawn to scale. Ask them to identify how they would know what size it represents. They should notice two kinds of scale; one where it simply gives a ratio so 1: 100,000 where 1cm on the plan or map represents a kilometre or it may have the scale as a bar with the relevant distance marked off on it.

This activity needs a big space such as the school hall or playground if the weather is good.

Put the children in groups of four and ask them to bring in up to ten cardboard boxes of the same size if possible. Ask them to construct a ‘building’ from them and then draw it to scale from various aspects. They will need to think very carefully which scale to use so that it fits on a sheet of A3 paper. Remind them that they need to mark the scale on their plan.

Extension: Once everyone has completed their plan, place all the boxes in the middle of the hall or playground, jumbled up, and pass the plans to different groups. Ask them to decide what size the ‘building’ is in real life using the scale and get them to find the correct size boxes to build it.

At Home: Ask the children to draw the floor plan of their home to scale so it fits on a piece of A3 paper.

Dave Lewis
Primary Teacher

For even more inspiring activities based on architecture take a look at Projects Inspired by Architecture, a brand new addition to the Belair On Display series.

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