Everyday Mathematics
This curriculum is a single, unified project that puts students in the role of a Construction Project Manager. It is designed to be completed over two lessons, with each phase corresponding to a specific WorkKeys skill. The activities are hands-on, practical, and directly tied to the skills measured on the test. Use your workbook to source additional practice problems for each section.
The Construction Manager's Toolkit: The Complete Supply List 🧰
For all lessons: Whiteboard or chalkboard, markers or chalk, student worksheets (from your provided workbook), one dry-erase board with a marker per student or group, and a simple calculator.
For Scale Drawings: Rulers, tape measures, graph paper.
For Area and Volume: A cylindrical object (like an empty soda can or a small coffee can), a rectangular prism object (like an empty box or a small building block), scissors, and cardboard.
For Series of Proportions and Mean from Subgroup Averages: Colored blocks or linking cubes, and play money or counters.
For Percentage of a Percentage: A 100-square-inch piece of paper or cardstock (e.g., 10" x 10"), scissors, and a marker.
Lesson 1: The Blueprint and Building Plans 📐
Estimated Time: 50-60 minutes
Concepts: Scale Drawings, Area of a Circle, Volume of Rectangular Solids, and Volume of Circular Cylinders.
Objective: Teach students to find a missing dimension from a scale drawing.
Activity: "Scaling the Blueprint." Give students a simple drawing of a room or a piece of equipment on graph paper with a given scale (e.g., 1 square = 2 feet). The blueprint will have some dimensions labeled and some missing. Students will use a ruler to measure the missing dimension on the drawing and then use the scale to find the real-world dimension. For example, if a wall measures 3 squares long, they would calculate the real-world length is 6 feet.
Hands-On Application: "Let's bring this to life." Have students use a large piece of cardboard and a tape measure to physically draw a scaled-up version of one of the walls from their blueprint.
The "How-To":
a. Tell students: "Our blueprint says this wall is 6 feet. Let's create our own scale to draw it on the cardboard. Let's use a scale where 1 foot = 1 inch."
b. Have a student use the tape measure to measure 6 inches on the cardboard and draw a straight line.
c. Tell them: "We've just created a real-world representation of the wall's length based on our blueprint, just like a construction crew would on a building site."
Practice Problems:
Problem A: A drawing of a building is at a scale of 1 inch = 10 feet. A room measures 3 inches by 5 inches on the drawing. What are the actual dimensions of the room?
Problem B: On a blueprint, a hallway is shown as 2 centimeters wide. If the scale is 1 cm = 5 meters, what is the actual width of the hallway in meters?
Solutions:
Problem A Solution:
Length = 3 inches x 10 feet/inch = 30 feet.
Width = 5 inches x 10 feet/inch = 50 feet.
Problem B Solution:
Width = 2 cm x 5 meters/cm = 10 meters.
Objective: Teach students to calculate the area of a circle.
Activity: "The Circular Pad." Present a scenario where they need to calculate the area of a circular cement pad. Give each student a cylindrical object (e.g., an empty can). Have them use a tape measure to find the diameter or radius of the can's base. Students will then use the formula for the area of a circle (Area = πr²) to find the area of the base.
Hands-On Application: "Let's get a feel for the area."
The "How-To":
a. Have students trace the base of the cylindrical object onto a piece of cardboard.
b. Tell them: "This is the area of the cement pad we just calculated. Now, let's cut out a square that takes up about the same amount of space."
c. Have them use their ruler and scissors to cut out a square or rectangle of cardboard that has a roughly equivalent area. This gives them a tangible feel for the space the circle occupies.
Practice Problems:
Problem A: A circular sprinkler waters an area with a 15-foot radius. What is the total area watered?
Problem B: A circular tabletop has a diameter of 3 feet. What is the area of the tabletop?
Solutions:
Problem A Solution:
Area = πr² = π(15)² = 225π ≈ 706.86 square feet.
Problem B Solution:
Radius = Diameter / 2 = 3 / 2 = 1.5 feet.
Area = πr² = π(1.5)² = 2.25π ≈ 7.07 square feet.
Objective: Teach students to calculate the volume of a rectangular solid and a circular cylinder.
Activity: "The Foundation." Present a scenario where a contractor needs to know the volume of concrete required for a foundation. Give each student a small rectangular box. Have them use a ruler to measure the length, width, and height of the box. They will then calculate the volume using the formula (Volume = L x W x H). After this, they will calculate the volume of their cylindrical object using the formula (Volume = πr²h).
Hands-On Application: "Let's see what volume really means."
The "How-To":
a. After students calculate the volume of the box, give them a container of colored blocks.
b. Tell them: "Now, fill the box with the blocks. The number of blocks that fit in the box represents the volume we just calculated."
c. Have them count the blocks to see how close their estimate was to their calculated volume. This makes the concept of volume a tangible amount, showing that the formula represents a real, physical space.
Practice Problems:
Problem A: A rectangular pool is 10 feet long, 5 feet wide, and 3 feet deep. What is the volume of water the pool can hold?
Problem B: A cylindrical water tank has a radius of 2 meters and a height of 5 meters. What is its volume?
Solutions:
Problem A Solution:
Volume = L x W x H = 10 ft x 5 ft x 3 ft = 150 cubic feet.
Problem B Solution:
Volume = πr²h = π(2)²(5) = 20π ≈ 62.83 cubic meters.
Lesson 2: Project Management and Financials 📈
Estimated Time: 40-50 minutes
Concepts: Series of Proportions, Percentage of a Percentage, and Mean from Subgroup Averages.
Objective: Teach students to set up and calculate a series of proportions.
Activity: "The Supply Chain." This activity will use colored blocks or linking cubes to model a supply chain. For example, "For every 2 blue blocks (concrete), you need 3 red blocks (gravel), and for every 1 red block, you need 4 green blocks (sand)." Students will model this with the blocks. Then, present a series of proportions problem: "If you have 10 blue blocks, how many green blocks do you need?" This requires them to solve for the red blocks first, then the green blocks.
The "How-To": The physical model will demonstrate the multi-step nature of the ratio problem.
a. Tell students: "Our first ratio is 2 blue blocks for every 3 red blocks. Take out 10 blue blocks."
b. Have them set up groups of 2 blue blocks, noting that they have 5 groups.
c. Tell them: "Now, add 3 red blocks for each group. You should have 5 x 3 = 15 red blocks." This makes the first proportion tangible.
d. Tell them: "Our second ratio is 1 red block for every 4 green blocks. You have 15 red blocks. How many green blocks do you need?"
e. Have them place 4 green blocks for each red block to see the answer: 15 x 4 = 60 green blocks. This reinforces the concept that the result of one proportion becomes the input for the next.
Practice Problems:
Problem A: The ratio of bricks to mortar is 10:1. The ratio of mortar to sand is 1:2. If a project requires 200 bricks, how much sand is needed?
Problem B: For every 3 workers, you need 2 safety vests. For every 1 vest, you need 4 pairs of gloves. If you hire 12 workers, how many pairs of gloves do you need?
Solutions:
Problem A Solution:
Mortar needed = 200 bricks / 10 = 20 mortar.
Sand needed = 20 mortar x 2 = 40 sand.
Problem B Solution:
Vests needed = 12 workers / 3 = 4 vests.
Gloves needed = 4 vests x 4 = 16 pairs of gloves.
Objective: Teach students to calculate a percentage of a percentage.
Activity: "The Project Budget." Present a real-world scenario involving a budget with multiple percentage deductions.
Hands-On Application: You will use a 100-square-inch piece of paper or cardstock (e.g., 10" x 10") to represent 100% of a budget. Explain that each square inch represents 1% of the total.
The "How-To":
a. Tell students: "The initial project budget is $10,000. 30% of the budget is for materials. Use a marker and ruler to measure and cut out a 30-square-inch section of the paper. This piece of paper represents your materials budget."
b. Tell them: "Of the materials budget, 10% is for electrical supplies. Now, take only the 30-square-inch piece you just cut. This is a new whole, representing your materials budget. Use scissors to cut off 10% of this piece. Since 10% of 30 square inches is 3 square inches, you will cut off a 3-square-inch piece."
c. Tell them: "Finally, let's connect this back to the money. If the original 100 square inches represented $10,000, then each square inch represents $100. The 3 square inches you cut off represent 3 x $100 = $300." This makes the abstract calculation of a percentage of a percentage a physical, demonstrable action.
Practice Problems:
Problem A: A company has a profit of $50,000. 20% of the profit goes to taxes. The remaining amount is put into savings, and the company gives 25% of the savings to employees as a bonus. How much is the employee bonus?
Problem B: A contractor's total earnings were $5,000. 15% of the earnings are put into a retirement fund. Of the remaining money, 20% is set aside for future projects. How much is set aside for future projects?
Solutions:
Problem A Solution:
Taxes = $50,000 x 0.20 = $10,000.
Remaining profit = $50,000 - $10,000 = $40,000.
Employee bonus = $40,000 x 0.25 = $10,000.
Problem B Solution:
Retirement fund = $5,000 x 0.15 = $750.
Remaining money = $5,000 - $750 = $4,250.
Future projects = $4,250 x 0.20 = $850.
Objective: Teach students to find the mean of a group of numbers when the average of each subgroup is known.
Activity: "The Team's Performance." Divide the class into two or three subgroups. Give each group a simple, timed task (e.g., assembling a small puzzle or putting together a few LEGO pieces). Have each group find the average time it took to complete the task. Then, present a problem: "Group A has 10 members, and their average time was 3 minutes. Group B has 15 members, and their average time was 4 minutes. What is the average time for the entire class?" Students will have to calculate the total time for each group before finding the overall average.
The "How-To":
a. Tell students: "We can't just average the averages. We need to find the total amount for each group first."
b. Have students use their play money or counters to model this. "Group A has 10 members with an average of 3 minutes. That's a total of 10 x 3 = 30 minutes. Let's model this with 30 counters."
c. "Group B has 15 members with an average of 4 minutes. That's a total of 15 x 4 = 60 minutes. Model this with 60 counters."
d. "To find the overall average, we add the total times for each group (30 + 60 = 90) and divide by the total number of members (10 + 15 = 25). 90 / 25 = 3.6 minutes." This physically demonstrates the reason for finding the total first before calculating the final mean.
Practice Problems:
Problem A: A store has three shifts. The average number of customers on the morning shift is 100 (with 4 workers). The average number of customers on the afternoon shift is 150 (with 5 workers). What is the average number of customers per worker for the two shifts combined?
Problem B: A company has two departments. Department 1 has 5 employees with an average salary of $50,000. Department 2 has 10 employees with an average salary of $60,000. What is the average salary of all employees in both departments?
Solutions:
Problem A Solution:
Morning shift total = 100 customers/worker x 4 workers = 400 customers.
Afternoon shift total = 150 customers/worker x 5 workers = 750 customers.
Overall average = (400 + 750) / (4 + 5) = 1150 / 9 = 127.78 customers per worker.
Problem B Solution:
Total salary, Dept 1 = 5 employees x $50,000/employee = $250,000.
Total salary, Dept 2 = 10 employees x $60,000/employee = $600,000.
Overall average salary = ($250,000 + $600,000) / (5 + 10) = $850,000 / 15 = $56,666.67.