This worksheet helps students to write their own algebraic equations to solve a real-world problem.
Students got a new job in a painting company where their job is to estimate the paint needed for painting the walls excluding the door and window areas. The calculations were done manually, but the student is asked to automate this process by finding formulas that can automatically compute the paint needed when the dimensions of the room, doors, and windows are given.
Students will try to understand the relationship between different variables such as width, and height, and write the formula to find the area of a room using these variables. Then they will write formulas to find the total area of windows and doors and finally write another formula to exclude the window and door area. They also are given the opportunity to validate their formula by running test cases against the formula. In the same way, they will write formulas to find the door trim area and door areas.
This is a good algebra refresher activity and at the same time, it is thought-provoking to create fresh formulas.
Students use this activity to understand a problem and then to form an equation that can solve the problem. Students can validate if their equation is correct by running the test cases.
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. *For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product*.
Write, read, and evaluate expressions in which letters stand for numbers.
Write expressions that record operations with numbers and with letters standing for numbers. *For example, express the calculation "Subtract y from 5" as 5 - y*.
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). *For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2*.
Solve real-world and mathematical problems by writing and solving equations of the form *x* + *p* = *q* and* px* = *q* for cases in which *p*, *q* and *x* are all nonnegative rational numbers.
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. *For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation*.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.