STILLWATER CROSSING · THE COURSE NOTES · BRIDGE MATH 5/6

Week 31 · Ratio and Proportion

This week

Lessons 146, 147, 148, 149 & 150

Papers

Test 15 to do at home

Method

No calculators, ever · show every step

Instructional notes

Proportion • 2 ratios joined by an equal sign 3 15 • Ex: = 4 20

To solve a proportion with an unknown value: • Determine what number the known values were

multiplied or divided by • Do the same to calculate the unknown value

• Cross-multiply to check

The first and last terms are called the extremes and the second and third terms are called the means.

Example

Find the unknown value and label the means and extremes. Cross- multiply to check your answer.

Extreme Mean 2 10 = think: 2 x ? = 10 3 15 Mean Extreme

Other ways to represent the above:

2:3 = 10:15 or 2 is to 3 as 10 is to 15

Practice

Solve and check each proportion.

15 5 = __14_: 36 = 7:18 1 is to 2 as 15 is to _30_ 27 9

21 3 = 6:2_ = 54: 18 8 is to 32 as _1_ is to 4 56 8

Instructional notes

Scale Drawings

Scale drawings picture an object that is either much larger or much smaller than the object drawn. Examples are maps of the world or drawings of an atom.

To find the actual size using a scale drawing, set up a proportion.

Scale Measured

ddddddd ddddddd = aaaaaa aaaaaa

Example

Use the scale to find the real distance.

Karlo hiked from the Oasis to the Waterfall on Tuesday. The distance between the two spots on the map measures 4 cm. What is the actual distance Karlo walked?

Scale Measured Scale Measured ddddddd ddddddd 1 4 = = aaaaaa aaaaaa 50 200

Practice

1. The length of the kitchen on the floor plan measures 3 inches. What is the actual length of the kitchen? 18 ft

2. The width of the bedroom on the floor plan measures 1.5 inches. What is the actual width of the bedroom? 9 ft

3. The study measures 2 inches by 1.5 inches on the floor plan. What is the actual area of the study? 108 ff 2

Instructional notes

Temperature

Temperature is: • Measured with a thermometer • Measured in degrees

• Fahrenheit used in United States

• Celsius used around the world

Reference Temperatures Fahrenheit Celsius Normal Body Temperature 98.6°F 37°C Boiling Point of Water 212°F 100°C Freezing Point of Water 32°F 0°C

Example

Write the correct temperature.

35°C -8°C

Practice

Solve each problem.

1) This morning at 6 a.m. the temperature was 23°C. Each hour the temperature increased 2°C. What was the temperature at 3 p.m.? 41°C

2) Terrell left water in a bottle outside to make ice. The current temperature is 45°F? How many °F must the temperature drop for the water to become ice? 13°F

3) The temperature this morning was 0°C. What is the temperature in Fahrenheit? 32°F

4) This morning the temperature was 76°F. By 3pm the temperature had risen 25 degrees. What is the temperature at 3pm? 101°F

✍ In your own words

Why are scale drawings useful? Give a real-life example of when you would use one. Suggested Answer: Scale drawings let us represent large things (like buildings, maps, or rooms) on a small piece of paper. Architects use them for building plans, and maps use them so we can measure distances without traveling there first. Quick Review 0.032⟌5 0.12 × 0.03 = 34.03 - 4.287 = 156.25 0.0036 29.743 5 5 3 8 1 4 + = 7 -2 = x = 8 6 4 9 2 7 11 31 2 1 4 24 36 7 C B 3 30 1 ÷ = 5 × 16 = 7 70 4 E A 1 84 If m∠AEC = 140° and m∠BEC = 105° What is the m∠AEB? 35°

Homework this week

Work-text	Lesson 146	Lesson 147	Lesson 148	Lesson 149	Lesson 150
Speed drill	146	147	148	150

Terms on the record

Term	Meaning
extremes	The first and last terms are called the extremes and the second and
means	third terms are called the means.
scale drawings	Scale drawings picture an object that is either much larger or much
larger	Scale drawings picture an object that is either much larger or much
smaller	smaller than the object drawn. Examples are maps of the world or
temperature	Temperature is:
reference temperatures	Fahrenheit Celsius

STILLWATER CROSSING // BRIDGE MATH // PENUMBRA · steady on