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Using Formulas to Solve Problems

Using Formulas to Solve Problems. LG: I can solve real-world problems by substituting values into formulas and solving. INVESTIGATION. These formulas give the height, h , of an adult.

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Using Formulas to Solve Problems

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  1. Using Formulas to Solve Problems LG: I can solve real-world problems by substituting values into formulas and solving.

  2. INVESTIGATION • These formulas give the height, h, of an adult. • They rely on the lengths of the radius bone, r, and the femur bone, f. (Note: All measurements are in centimeters) • A) predict the height of a female whose femur is 40.6 cm long

  3. INVESTIGATION • These formulas give the height, h, of an adult. • They rely on the lengths of the radius bone, r, and the femur bone, f. • B) predict the height of a male whose radius is 28.1 cm long.

  4. INVESTIGATION • These formulas give the height, h, of an adult. • They rely on the lengths of the radius bone, r, and the femur bone, f. • C) Complete the chart • D) Which formula gave you the more accurate prediction?

  5. What is a formula? • It’s a mathematical equation that relates two or more variables, which each represent real-world quantities. • Can you think of any examples from work or school?

  6. Example 1 – Substituting into a formula • Pediatric nurses use Young’s formula,to calculate a child’s dose of medicine. • C is the child’s dose in milligrams • A is the adult’s dose in milligrams • g is the child’s age in years. • If the adult dose of a medication is 600 mg, what would be a 3-year-old’s dose?

  7. Example 2 – Choosing Formulas and Converting Measures • A landscaper uses a bucket with radius 18 cm and height 18 cm to pour soil into a rectangular planter that measures 1 m by 40 cm by 20 cm. • How many buckets of soil are needed to fill the planter? • OUR PLAN:

  8. Investigation: How much do I need to eat? • What is a BMR? • Used to determine the amount of energy required by the body at rest. This value can then be adjusted depending on activity level • Use the Harris-Benedict Equation to calculate your BMR • You will need: • Age in years • Weight in kg (pounds x 2.2) • Height in cm (measuring tapes available)

  9. Rearranging Formulas LG: I can rearrange a formula by “undoing” each operation LG: I can solve problems using rearranged formulas

  10. MINDS ON • To change a flat tire, FIRST, you have to take the old tire off, THEN, you have to put the new tire on. • The process of removing the old tire is shown below. • Put the new tire on by undoing each operation you completed to take the old tire off.

  11. Applying this “undoing” to math • If we know a temperature in Fahrenheit, we can find the temperature in Celsius using this formula: • To get from ºF to ºC, we would follow BEDMAS since C is already by itself • So… • To get from ºC to ºF, we would follow BEDMAS BACKWARDS to UNDO each operation to get F by itself.

  12. Example 1a – Isolating a Variable • The amount, A dollars, of an investment is given by the formula , where P dollars if the principal and I dollars is the interest earned. • Isolate P.

  13. Example 1b – Isolating a Variable • The volume, Vcubic metres, of a rectangular prism with length lmetres, width w metres, and height hmetres, is given by the formula • Isolate h.

  14. Example 1c – Isolating a Variable • Ohm’s Law, relates the current, I amperes, running along an electrical circuit to the voltage, V volts, and the resistance, R ohms. • Isolate V.

  15. Example 2 • Convert 30ºC to degrees Fahrenheit using • 2 ways to do this: You try first, then we’ll see both come out

  16. When should we do what? • ISOLATE the variable THEN SUBSTITUTE in given values • If you have to solve for the variable several times • SUBSTITUTE in given values THEN SOLVE for the variable • If the numbers are simple • If rearranging the formula is really difficult

  17. Example 3a – Solving problems with Powers • The area of a circle is . • Use this formula to determine the radius of a circular oil spill that covers an area of 5 km2.

  18. Example 3a – Solving problems with Powers • The volume of a sphere is . • Use this formula to determine the radius of a Nerf ball with volume 1 m3.

  19. Quiz tomorrow! • On these learning goals: • I can solve real-world problems by substituting values into formulas and solving. • I can rearrange a formula by “undoing” each operation. • I can solve problems using rearranged formulas.

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