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[pic] Math for the Workplace 12 [pic]

Masonry Information Sheet

Number Sense

Masons work with integers, decimals, fractions, ratios, proportions, and percentages. Fractions are mostly associated with reading a measuring tape; therefore, common fractions to [pic] are the most important. When working in metric, values to the 1000th place are required.

Operation Sense

Calculations performed by masons include, but are not limited to, calculating the amount of materials being used, such as, bricks, sand, or mortar. They must also calculate the cost price and in turn the retail price charged to the consumer to obtain a profit. The business calculation of

Profit = Retail Price – Cost Price is critical to the viability of a mason’s business.

A well developed sense of estimation is also important. Estimating the amount of water that might already be in sand on a wet day, in order to adjust water when preparing mortar; estimating the amount of mortar required to do a job; or the length of time to complete a job are all important to being a successful mason.

Masons must be very comfortable using technology such as calculators. They also need well developed problem solving skills. Problem solving through obstacles such as changes in the weather, design changes, or availability of resources all require problem solving skills.

Patterns

Masons are often working with patterns as they lay brick.

Measurement

Measurement for reading blueprints and using scales requires proportional thinking. Masons must measure lengths, heights, and widths of walls, fireplaces and other structures being built. They must weigh epoxies and other materials. They must also be able to measure the angles around doorways, windows and other openings. It is essential that all of these measurements be done with both precision and accuracy.

Masons must be able to use tape measures and architectural scales skillfully. They need to find volumes of cubes, and the area of squares, circles, and triangles.

Geometry

Well developed spatial sense is essential for a mason. Understanding angles, symmetry and other geometric properties cannot be understated. Understanding the relationship between squares and cubes or circles and arches is essential.

In order to construct an arch properly, students need to know how to bisect lines and find the starting point for the bisection. The application of circle properties and calculations are essential for doing this accurately.

Possible Project Idea

Front Steps - Construct a set of steps for the front door of a residence. The door is 3 feet 4 inches above the ground and the door is 3 feet wide. Show the planning and the material estimates involved in the construction of this project. Describe the math needed to complete each part of the process.

Note to teacher:

This seems like an easy task but there is a lot going on. Steps involve lots of math.

← The pad that the masonry sits on needs to be 1200mm below finished grade to satisfy the building code and it has to be 100mm wider than the steps, all of the way around.

← The pad also has to be 200mm deep.

← The pad length is determined by the relationship of rise to run and again this is limited by the building code.

← No stair tread can be smaller than 250mm and no riser can be higher than 200mm. One of the problems is to get the treads and the risers to all be the same in the space given and to have them work out so that there is a minimum amount of cuts involved. We need to figure cement volume for the concrete pad and also at ground level there is another pad for the steps themselves to sit on.

← The buried part of the steps can be cement blocks so we have to estimate the blocks involved and the masonry cement and the sand which is used at a ratio of 1:3. These blocks need to be parged, which is a coating of cement used for damproofing below grade. This coat of cement is ¼ of an inch thick and has to be included in the estimating for masonry cement.

← Then there are the steps themselves and the landing at the top. The landing has to be 300mm larger than the door swing. This is why we include the width of the door in the problem.

← The steps themselves are a triangle so we need to know how to figure the area of a triangle to estimate the brick in the sides but the tops are different and then the area below the landing is a rectangle.

← Steps have to be wider than the doorway in order to get railings installed and they are solid masonry from the ground up so the material requirements are huge.

← The top has to have a slope to drain water of 1/8 inch to the foot.

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