Basketball Formulas: Solve for the Quantity You Need
Materials Needed
- Pencil and paper or whiteboard
- Calculator
- Basketball court diagram or basketball hoop image
- Optional: basketball, measuring tape, or access to a basketball court
Learning Target
I can rearrange formulas to solve for a specific variable and use the formulas to solve geometry problems about basketball.
Objectives
By the end of this 15-minute lesson, the learner will be able to:
- Identify the quantity a problem asks for.
- Rearrange a geometry formula to isolate a chosen variable.
- Substitute measurements into a rearranged formula and solve a basketball-related problem.
- Check whether the answer is reasonable and includes appropriate units.
Success Criteria
- I identify the variable I need to find.
- I use inverse operations to isolate that variable.
- I substitute values accurately.
- I label my answer and explain what it means in the basketball situation.
Introduction: Bell Work and Hook — 3 Minutes
Bell Work: Reinforce Prior Knowledge
Complete these questions without looking at the lesson examples:
- Solve for x: x + 7 = 15.
- Solve for r: 2r = 18.
- The area of a rectangle is found using A = lw. If A = 48 and w = 6, what is l?
Quick check: Answers are 8, 9, and 8. Connect the skill to today’s lesson: “To solve for a variable in a formula, we use the same inverse operations we use to solve an equation.”
Basketball Hook
Ask: “If you know the area of a rectangular basketball court and its length, how could you find its width? What if you know the circumference of a basketball and need to find its radius?”
Body: I Do, We Do, You Do — 10 Minutes
I Do: Teacher or Parent Modeling — 3 Minutes
Example 1: Finding the Width of a Basketball Court
The area formula for a rectangle is:
A = lw
Suppose a basketball court has an area of 4,700 square feet and a length of 94 feet. Find the width.
- Identify the variable needed: w.
- Start with the formula: A = lw.
- Divide both sides by l to isolate w:
w = A ÷ l - Substitute the values:
w = 4,700 ÷ 94 - Solve:
w = 50 feet
Think aloud: “Because length and width are multiplied, I divide by the known length to undo multiplication. The answer is reasonable because a basketball court is much wider than a few feet but much shorter than 100 feet.”
Example 2: Finding the Radius of a Basketball
The circumference formula is:
C = 2πr
Rearrange the formula to solve for r:
r = C ÷ 2π
If a basketball has a circumference of approximately 29.5 inches:
r = 29.5 ÷ 2π ≈ 4.7 inches
We Do: Solve Together — 4 Minutes
Work through each problem together. The learner should explain which operation is used and why.
Problem 1: Finding Court Length
A rectangular practice court has an area of 2,400 square feet and a width of 40 feet. Find the length.
- Start with: A = lw.
- Isolate l: l = A ÷ w.
- Substitute: l = 2,400 ÷ 40.
- Answer: l = 60 feet.
Check for understanding:
- Which variable were we solving for?
- Why did we divide by the width?
- What units should the answer have?
Problem 2: Finding Diameter
The circumference of a circular shooting target is approximately 18.84 feet. Use C = πd to find its diameter.
- Start with: C = πd.
- Isolate d: d = C ÷ π.
- Substitute: d = 18.84 ÷ 3.14.
- Answer: d ≈ 6 feet.
Think-Pair-Share option: The learner explains the steps aloud to a parent, tutor, stuffed animal, or imaginary teammate.
You Do: Independent Basketball Challenge — 3 Minutes
Choose one challenge. Show the formula, rearrange it, substitute values, and include units.
Challenge A: Court Width
A rectangular basketball court has an area of 4,700 square feet and a length of 94 feet. Use A = lw to find the width.
Challenge B: Three-Point Arc Radius
A circular practice arc has a circumference of approximately 59.7 feet. Use C = 2πr to find its radius. Round to the nearest tenth.
Challenge C: Design Your Own
Create a basketball geometry problem using one of these formulas:
- A = lw
- C = 2πr
- C = πd
Give two measurements, ask a partner to find the missing quantity, and solve the problem yourself.
Conclusion: Closure and Assessment — 2 Minutes
Exit Ticket
Solve this problem independently:
A rectangular basketball training area has an area of 3,600 square feet and a width of 40 feet. Rearrange A = lw to solve for the length, then find the length.
Expected response:
l = A ÷ w
l = 3,600 ÷ 40 = 90 feet
Recap
Ask the learner to complete this sentence:
“To isolate a variable in a formula, I use __________ operations. In today’s basketball problems, I isolated the missing variable by __________.”
Key takeaway: Rearranging a formula means using inverse operations to get the variable you need by itself. Then substitute the known values, solve carefully, check that the answer is reasonable, and include units.
Assessment
- Formative: Bell work, verbal explanations, guided practice, and checks for understanding.
- Summative: Independent basketball challenge and exit ticket.
- Feedback: Give specific feedback such as, “You correctly isolated the variable. Now check that your substitution and units match the question.”
Differentiation and Adaptations
- Support: Provide a formula chart, highlight the target variable, and use the sentence frame: “Because the variable is multiplied by ___, I will divide both sides by ___.”
- Visual support: Draw a rectangle for the court or a circle for the basketball target and label each measurement.
- Hands-on option: Measure a basketball, hoop area, room, or driveway and use a formula to find a missing measurement.
- Digital option: Use a calculator or spreadsheet to test different court dimensions.
- Extension: Rearrange a more complex formula, such as A = 1/2bh, to solve for h, then create a triangular basketball passing-zone problem.
- Challenge: Compare two courts by calculating an unknown dimension and explaining which court provides more playing area.