By Nicole Brent (S00103122) and Emma Buis (S00117027) Our Journey to Maths in the Workplace Bricklaying Step Two: Initial Brainstorm Maths Within

Bricklaying Leveling Angles Ensure walls are straight -

both

horizontally and vertically Calculating how

many bricks will

be needed How? Time - The time the job will take

- The time the cement takes to dry How would you

use area to calculate

the number of bricks needed? Measurement -Calculating the number of bricks needed given the length of a wall/ building.

-Calculating the number of bricks needed given the height of a wall/ building.

-Cutting bricks to right length How much cement

should you make

without risk of it

drying before use? Ratio -Cement to water

-Cement to brick Cost -Labour

-Material Step One: Choosing a Work place Hover cursor

over video and

press play

Hover cursor over video and press play

Hover cursor over video and press play Please wait for audio Step Four: The Interview (Part 1) Step Four: The Interview (Part 2) Step 6: Make Our Own Maths Problems Question one: A bricklayer is told he has two options for how he is to be paid for his work. He can either be paid a standard $15 an hour or paid $400 per thousand bricks he lays. The average amount of bricks he can lay in one day is 300. He works for seven hours a day. Which option should he choose?

Option one:15 X 7 = $105

Option two:300/1000 = 3/10 = 0.3X400=$120

Solution: the bricklayer is better off getting paid $400 per thousand bricks he lays. Research Idea One Patterning and Symmetry Research Idea Two Weather Research Idea Three Pythagoras Theorem Research Idea Four Time - Counting Bricks Acknowledgements:

Jack Buis, for the audio interview and video

Dianne Buis, for lending the photos she took in 1985-1986 From our research, we learnt that there are different patterns that bricklayers use called bonds (Reid, 2008). For example: English bond. We are hoping to expand on this research in our interview and discover why there are different patterns used in bricklaying. Could it be for decorative purposes only or do different bonds alter the strength of a structure? From our research, we also noticed that symmetry is very important in these patterns. It would be good to find out how bricklayers achieve such precise results. From our research we were reminded about the difference weather can make. For example, the amount of cement a bricklayer makes on a cold day will be more on a hot day because cement dries quicker in hot weather. Pythagoras Theorem states

C^2= A^2+B^2. A, B and C represent different sides of a triangle. This is relevant to bricklayers as they can use this formula to ensure the sides of a wall are at right angles to each other. Our research has also taught us that often bricklayers will try and calculate an average of how many bricks they can lay in one day (Noble, 2012). This can help them when estimating how long it takes to complete a job. Step Five: Final Brainstorm Maths Within

Bricklaying Leveling Angles Time

The time the cement takes to dry Measurement Cutting bricks to right length. This needs to be exact and is done by calculating length and height of the brick. Any slight miscalculations in the measurement can be changed by adjusting the vertical joints called perbs. Ratio Cost Labour. There are two ways labour cost can be accounted for. Either bricklayers are paid at an hourly rate or paid a certain amount per 1000 bricks laid. Plumb= straight vertically

Level= straight horizontally Pythagorus Theorem or

in bricklaying terms: 3,4,5 method.

Ensures two walls meet at a right angle. This measure works with 3 and 4 measuring along two joining walls and 5 being the diagonal between these points. The diagonal measurement is always the bigger number eg. 5. Sand, cement, limil and water are used in the making of mortar. The ratio of these are 6:1:1:1.

There are approx. 100 bricks to a wheelbarrow of mortar. Important for other add-ins such as windows and doors as the whole space must be plumb for a door or window to fit. Leveling affects other trades who are unable to complete their work if the brickwork is not level. Important for measurements such as those used in constructing bay windows. The first angle of a bay window comes out at 45 degrees. Bricklayers need to ensure they take these angles into account. In order to correctly construct an arch way (or any design requiring multiple angles) a template must first be made out of chipboard. This reflects the relevant angels. This template is then propped up vertically and the bricks are laid around the top of it, this ensuring measurements and angles are correct. Gauge. This is a measuring device which has the measurements of bricks marked along it. A gauge is propped up where a wall is being built and shows the bricklayer how many bricks high the wall will be. There is approx. 35 bricks per square metre. Measure length and height to get area or work out how many bricks high by how many bricks long are needed for a particular structure using the measurements of a brick. Weather affects the timing of mortar drying. In summer, mortar will dry out after two hours, in winter after four hours. Additives, however, stop mortar from drying out so this can be taken into consideration when making mortar on hot days. Water can also be added to mortar to stop it from drying out but this affects the strength. The time the job will take Calculated by working out the average number of bricks laid in a day. Eg. 300 in day. In order to ensure brick work is symmetrical, plans of patterns are drawn. Symmetry is also achieved by making sure the edge of the brick work is plumb. If this is plumb, the bricks will automatically line up symmetrically. Materials.

Quotes are obtained from the brick-yard etc and added together.

However, generally this is organised by the client. There are different types of brick patterns. These are called bonds. English bond is the strongest and is mainly used in railways as a double wall. Stack bond is the weakest as the bricks are stacked directly on top of each other.

English bond is stronger because of the overlap between the bricks contact with each other from below and above. This overlap ensures that the bricks join into one single mass, thereby resulting in a stronger whole structure. The type of brick also influences the strength of the wall - the smaller the brick the stronger the wall. This is because the smaller the brick, the more bricks used therefore more overlapping occurs. Symmetry and Patterns Bricks with holes in the centre of them are weaker than "frogs" (solid, pressed bricks) but are cheaper in cost. Step Seven: Reflection In looking at our initial brainstorm it can be seen that our knowledge of the maths within bricklaying was quite limited. Through our research and interview process however, we expanded on our original thoughts and understandings as well as developing entirely new ideas. For example, in our initial brainstorm we had not considered symmetry or patterning as relevant in bricklaying. We discovered, however, that it does play an important role in the strength and structure of a brick building. There were also other certain facts which we found surprising and interesting. For example, we found it curious that although precise measurement plays a very important role when bricklaying, estimation is also important. Ie., although there is a ratio of cement, water, limil and sand that should be followed when making mortar, informal units of measurement (such as measuring in buckets or shovels) is used.

Our final brainstorm allowed us to consolidate and expand on all we had learnt and display this in a detailed format. This final brainstorm challenged us to explain our new found knowledge in a clear and concise way. It also allowed us to see the links between different mathematical ideas such as angles and measurement. The growth of our understandings can clearly be seen when comparing our initial brainstorm with the final brainstorm, as we found the need to explain what we knew in much greater detail.

We found it beneficial to include a range of multi-modal texts in our presentation such as audio, videos, mind-maps and written text because it helped highlight and expand on our ideas in different ways. For example, we decided to include the videos on leveling because when conducting the audio interview we found it hard to visualise what our interviewee was saying. The videos were then a great way of visually demonstrating his explanations.

Overall, we have learnt a significant amount of the maths bricklayers use. Furthermore, we have discovered that bricklayers need to use maths in many different ways including ratios, measurement, symmetry and calculating cost. References Reid, D. A. (2008), Brick Pattern Math. Retrieved from:

http://plato.acadiau.ca/courses/educ/reid/geometry/brick/plane1.html Noble, G. (2012, October 28) Time is Money [Blog Post]. Retrieved from http://becomeabricklayer.com.au/blog/tags/Bricklaying-Skills/ Question two:

A house has a 24m perimeter and 3m high walls. There are 35 bricks per square metre and a bricklayer can lay 300 bricks per day.

a) How many bricks would be used in the total building of the house?

b) How long will it take to lay the entire perimeter?

c) A bricklayer makes up 2 batches of mortar per day. Each batch contains a ratio of 6kg:1kg:1kg:1L of sand, cement, limil and water. He already has 50kg of sand. How much more will he need to order to make enough mortar to complete the house?

a) Walls are 24m long x 3m high= 72m^2

35 bricks per square metre x 72 square metres = 2,520 bricks

b) 2,520 total bricks / 300 bricks per day= 8.4 days.

c) 6kg sand per batch. 12kg sand per day.

12 kg sand x 8.4 days = 100.8kg sand in total

100.8kg - 50kg = 50.8kg sand needs to be ordered. English Bond

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# EDMA309- Maths in the Workplace

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