Everyday Mathematics
This curriculum is a single, unified project that puts students in the role of a Manufacturing Plant Manager. They will manage the launch of a new product, tackling real-world problems involving rates, proportions, complex percentages, and conversions. 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 Plant Manager's Toolkit: The Complete Supply List 🧰
For all lessons: Whiteboard or chalkboard, markers or chalk, student worksheets, one dry-erase board with a marker per student or group, and a simple calculator.
For the "New Product": Two different-sized bags of a single, consistent item (e.g., small, uniform LEGO bricks, M&Ms, or dried beans).
For "Machine Rates": Two different-sized funnels, two containers with a spout, and sand or water. A stopwatch.
For "Quality Control": A small digital scale, and a large bag of an item with varying weights (e.g., a bag of random screws and bolts, or small rocks).
For "Shipping": A spring scale, and a wooden block or a small box.
For "The Tank Fill": A large pitcher of water, a large measuring cup (e.g., a 2-cup or 500-milliliter size), and a stopwatch.
Lesson 1: Production and Efficiency 📈
Estimated Time: 50-60 minutes
Concepts: Multi-step problems with rates, proportions, and complex percentages.
Objective: Teach students to solve multi-step problems involving multiple rates.
Activity: "The Packaging Machines." Present a scenario: "Your plant has an order for 5,000 new products. We have two packaging machines. Machine A packages 50 items per minute, and Machine B packages 75 items per minute. How long will it take for them to fill this order if both machines are running at the same time?" Have students solve the problem on their dry-erase boards.
Hands-On Application: "Now, let's test our theory." Using the two different-sized funnels and a container of sand or water, explain that the funnels represent the two machines. Have one student use the smaller funnel to "package" 50 scoops of sand while another student uses the larger funnel to "package" 75 scoops. Use a stopwatch to time how long each takes. This makes the concept of different rates tangible. Then, have them work together to "package" a set amount, combining their rates to see how the total time is reduced.
Practice Problems:
Problem A: A plumber and their assistant can install 15 faucets in a day. The plumber works twice as fast as the assistant. If the assistant works alone, how long would it take them to install 15 faucets?
Problem B: Your factory produces 250 parts per hour. If you operate for 8 hours a day, how many days will it take to fill an order of 15,000 parts?
Solutions:
Problem A Solution:
Let P = the plumber's rate and A = the assistant's rate.
P + A = 15 faucets/day.
P = 2A.
Substitute P in the first equation: (2A) + A = 15.
3A = 15, so A = 5 faucets/day.
To install 15 faucets alone, it would take the assistant 15 faucets / 5 faucets/day = 3 days.
Problem B Solution:
Total parts produced per day = 250 parts/hour x 8 hours/day = 2,000 parts/day.
Days to fill the order = 15,000 parts / 2,000 parts/day = 7.5 days.
Objective: Teach students to calculate complex percentages and proportions.
Activity: "Quality Control." Present a scenario: "Of the 500 new products you produced, the first batch of 100 products has some flaws. Let's say 15% of the products in this batch are rejected for a minor flaw. Of the remaining parts, 20% have a major flaw and cannot be sold. How many sellable parts are left from this batch of 100?"
Hands-On Application: "Let's work through this with a physical sample." Give a student a sealed bag of 100 items (the new product, e.g., M&Ms). "You can't see the flaws, so we'll use our math. First, remove 15% of the products. That's 15 items. Count them out and set them aside." Then, ask the student to open the bag and count the remaining items (85). "Now, from this remaining pile of 85, you need to remove 20%." Have the student calculate that 20% of 85 is 17 and physically count out and set aside 17 items. The items left are the sellable ones. This makes the "percentage of a percentage" concept concrete and easy to follow.
Practice Problems:
Problem A: A company’s total sales were $85,000. 35% of the sales were from overseas. Of the overseas sales, 40% were from a single country. What was the amount of money earned from that country?
Problem B: A store buys a product for $50. They mark up the price by 50%. During a sale, they offer a 20% discount on the new price. What is the final sale price?
Solutions:
Problem A Solution:
Overseas sales = $85,000 x 0.35 = $29,750.
Sales from the single country = $29,750 x 0.40 = $11,900.
Problem B Solution:
Price after markup = $50 x (1 + 0.50) = $75.
Discount amount = $75 x 0.20 = $15.
Final sale price = $75 - $15 = $60.
Lesson 2: Material and Logistics 🏗️
Estimated Time: 40-50 minutes
Concepts: Density, pressure, and force; conversions with multiple steps.
Objective: Teach students to solve problems involving density, pressure, and force.
Activity: "The Shipping Container." Present a scenario: "You have two different materials to ship, both in identical boxes. Material A weighs 12 lbs and has a volume of 2 cubic feet. Material B weighs 18 lbs and has a volume of 3 cubic feet. Which material is denser, and what is its density?"
Hands-On Application: "Let's feel the difference." Give students a small spring scale and two different-sized boxes (or simply two objects with different volumes but similar weights). Have them use the spring scale to find the weight (force) of each. This gives them a sense of the weight. Then, place two identical boxes, one empty and one filled with a dense material, on a balance scale. This helps them visualize that density is a ratio of weight to volume.
Practice Problems:
Problem A: A concrete block weighs 50 lbs and has a volume of 1 cubic foot. What is the density of the block?
Problem B: A hydraulic press exerts 200 lbs of force on a piston with an area of 4 square inches. What is the pressure on the piston in pounds per square inch?
Solutions:
Problem A Solution:
Density = Weight / Volume.
Density = 50 lbs / 1 cubic foot = 50 lbs/cubic foot.
Problem B Solution:
Pressure = Force / Area.
Pressure = 200 lbs / 4 square inches = 50 lbs/square inch.
Objective: Teach students to solve multi-step conversion problems.
Activity: "The Tank Fill." Present a scenario: "A pump moves oil at a rate of 15 gallons per minute. How long will it take to fill a container with a volume of 2 cubic meters? (Note: 1 cubic meter = 264.17 gallons)."
Hands-On Application: "Let's create a small-scale model of this problem." Explain that this is a large-scale problem that we can model with a small, manageable demonstration.
Step 1: The abstract math. First, have students use their calculators to perform the conversion: 2 cubic meters is equal to 528.34 gallons. Then, have them set up the final calculation to find the time: Time = Total Volume / Rate = 528.34 gallons / 15 gallons/minute. The final answer is 35.22 minutes.
Step 2: The physical demonstration. Now, we will demonstrate the concept of conversion and rate using our model. Let's use an easy-to-manage amount. Our pitcher represents the pump, and our measuring cup represents the tank.
Step 3: The "How-To"
a. Tell students: "Our pump has a rate of 15 gallons/minute. To model this, let's find the time it takes to pour just one gallon. Since we don't have a gallon container, we'll use a conversion. 1 gallon = 3.785 liters. This means our pump is filling at a rate of 15 x 3.785 = 56.775 liters/minute."
b. Tell students: "Now, let's make it a small, classroom-friendly version. Our measuring cup can hold 500 milliliters. How many minutes would it take for our pump to fill a single 500-milliliter measuring cup?"
c. The math:
First, convert the rate to milliliters per minute: 56.775 liters/minute x 1000 ml/liter = 56,775 ml/minute.
Now, divide the volume by the rate: 500 ml / 56,775 ml/minute = 0.0088 minutes.
To make this more tangible, convert it to seconds: 0.0088 minutes x 60 seconds/minute = 0.53 seconds.
d. Tell students: "Now, for the hands-on part: have a student try to pour exactly 500 ml of water into the measuring cup and time how long it takes. It will be a fraction of a second, which reinforces how fast the real pump is working."
The Point: This activity directly links the abstract conversion and rate problem to a physical demonstration, making the process of scaling up or down more intuitive. You have the full answer for the problem at the top, and the physical demonstration is a complete, step-by-step process with all the math explicitly laid out.
Practice Problems:
Problem A: A driver travels 250 miles on a tank of gas. The car gets 25 miles per gallon. Gas costs $3.50 per liter. How much did the driver spend on gas? (Note: 1 gallon = 3.785 liters).
Problem B: An engine uses oil at a rate of 1 quart every 500 miles. A barrel of oil contains 42 gallons. How many miles can the engine run on one barrel of oil? (Note: 1 gallon = 4 quarts).
Solutions:
Problem A Solution:
Gallons used = 250 miles / 25 miles/gallon = 10 gallons.
Liters used = 10 gallons x 3.785 liters/gallon = 37.85 liters.
Total cost = 37.85 liters x $3.50/liter = $132.48.
Problem B Solution:
Total quarts in a barrel = 42 gallons x 4 quarts/gallon = 168 quarts.
Total miles = 168 quarts x 500 miles/quart = 84,000 miles.