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.• 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

MALE FEMALEUsing the radius bone h = 3.65 r + 80.41 h = 3.88 r + 73.50Using the femur bone h = 2.24 f + 69.09 h = 2.32 f + 61.41

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.

MALE FEMALEUsing the radius bone h = 3.65 r + 80.41 h = 3.88 r + 73.50Using the femur bone h = 2.24 f + 69.09 h = 2.32 f + 61.41

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?

MALE FEMALEUsing the radius bone h = 3.65 r + 80.41 h = 3.88 r + 73.50Using the femur bone h = 2.24 f + 69.09 h = 2.32 f + 61.41

Length of yours Calculation of your height Actual height

Radius

Femur

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?

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?

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:

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)

REARRANGING FORMULAS

LG: I can rearrange a formula by “undoing” each operation

LG: I can solve problems using rearranged formulas

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.

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.

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.

Example 1b – Isolating a Variable • The volume, V cubic metres, of a rectangular prism with

length l metres, width w metres, and height h metres, is given by the formula

• Isolate h.

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.

Example 2

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

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

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.

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.

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.