Grade: 8 Subject: SAT/ACT Skills Unit: Calculator Strategy Lesson: 6 of 6 SAT: Algebra ACT: Math

Mixed Calculator Set

Learn

This lesson puts together everything you've learned about calculator strategy. You'll practice making quick decisions about when to use mental math, paper/pencil, or your calculator for various problem types.

Unit Summary: Key Takeaways

  • Mental math first: Simple operations, perfect squares/cubes, and basic percentages
  • Paper/pencil: Setting up equations, showing algebraic steps
  • Calculator: Complex decimals, roots of non-perfect squares, multi-step calculations
  • Graphing features: Systems of equations, finding zeros, intersections, max/min
  • Error prevention: Double-check inputs, use parentheses, verify with estimation

Quick Reference: Method Selection

Problem Type Best Method Time Estimate
Basic arithmetic (single digits) Mental math Under 5 seconds
Percentages of round numbers Mental math 5-10 seconds
Linear equations Paper/pencil or mental 15-30 seconds
Multi-digit multiplication/division Calculator 10-15 seconds
Systems of equations Graphing calculator 30-45 seconds
Square roots of non-perfect squares Calculator 5-10 seconds

Test Day Checklist

  1. Fresh batteries in calculator (or bring backup)
  2. Calculator in correct mode (degrees for most problems)
  3. Practice the decision framework before test day
  4. Know your calculator's specific button locations
  5. Have a backup strategy if calculator fails

Examples

Example 1: Mixed Method Problem

Problem: A store offers 15% off a $240 item. What is the sale price?

Best approach: Combine mental math and simple calculation

  1. 10% of $240 = $24 (mental math)
  2. 5% of $240 = $12 (half of 10%, mental math)
  3. 15% discount = $24 + $12 = $36 (mental math)
  4. Sale price = $240 - $36 = $204 (mental math)

Calculator alternative: 240 x 0.85 = 204 (also fast, choose what's comfortable)

Example 2: Graphing Calculator Efficiency

Problem: Solve x^2 - 5x + 6 = 0

Method comparison:

  • Factoring (paper): (x-2)(x-3) = 0, so x = 2 or x = 3. Time: ~20 seconds
  • Graphing calculator: Graph Y1 = X^2 - 5X + 6, find zeros. Time: ~30 seconds
  • Best choice: Paper is faster IF you recognize the factoring quickly

Tip: For easy-to-factor quadratics, paper is faster. For complex ones, use graphing.

Practice Quiz

For each problem, decide the best method AND solve it. Click to reveal the answer and recommended approach.

1. Calculate 144 / 12

Method: Mental math

Answer: 12. This is a basic division fact. 144 is a perfect square (12 x 12), so 144/12 = 12.

2. Find the value of 3.7 x 8.2 x 1.5

Method: Calculator

Answer: 45.51. Multiple decimal multiplications are error-prone by hand and time-consuming.

3. Solve 4x - 7 = 21

Method: Mental math or paper

Answer: x = 7. Add 7 to both sides: 4x = 28. Divide by 4: x = 7. Simple enough for mental math.

4. What is the square root of 289?

Method: Mental math (if you know it) or calculator

Answer: 17. If you know 17^2 = 289, use mental math. If not, calculator is fine. Learning perfect squares up to 20 saves time.

5. Find where y = 2x - 3 and y = -x + 6 intersect

Method: Paper (quick algebra) or graphing calculator

Answer: (3, 3). Setting 2x - 3 = -x + 6 gives 3x = 9, so x = 3 and y = 3. Paper is slightly faster for simple systems.

6. Calculate 40% of 75

Method: Mental math

Answer: 30. Think: 10% of 75 = 7.5, so 40% = 4 x 7.5 = 30. Or: 40% = 2/5, and 75/5 = 15, so 2 x 15 = 30.

7. Find the square root of 73

Method: Calculator

Answer: Approximately 8.544. 73 is not a perfect square, so calculator is necessary. Know that 8^2 = 64 and 9^2 = 81 for estimation.

8. What is 6^4?

Method: Calculator (or mental with steps)

Answer: 1296. You could calculate: 6^2 = 36, then 36^2 = 1296. But calculator is reliable for powers.

9. Find the zeros of f(x) = x^2 - 9

Method: Mental math (difference of squares)

Answer: x = 3 and x = -3. Recognize x^2 - 9 = (x+3)(x-3). Faster than graphing for this simple case.

10. Calculate the mean of: 23, 45, 67, 89, 31

Method: Calculator (STAT function)

Answer: 51. Sum = 255, divided by 5 = 51. For larger data sets, STAT > 1-Var Stats is essential. For 5 numbers, either method works.

Check Your Understanding

You should now be able to:

  • Quickly assess which calculation method is most efficient
  • Apply mental math strategies for simple problems
  • Use calculator features appropriately for complex calculations
  • Combine methods when problems have multiple steps
  • Prepare effectively for test day calculator use

Next Steps

  • Review any concepts that felt challenging
  • Practice mixed problem sets regularly
  • Time yourself to build speed and accuracy
  • Continue to the next unit when ready