### Ratios, Proportions, and Unit Rates

#### published on: 9/9/2008

**Contributing Teacher(s):**
Nichole McDaniel

**Subject Area:**
Math/Number Sense- Add, Subtract, Multiply, Divide, Estimate, Algebra

**Grade Range:** Middle Grades (6-8)

**Materials Needed: **

- Computer
- Dry erase boards
- Dry erase markers and erasers

**Objective: ** The learner will solve problems involving rates, ratios, and proportions including scaling and converting area and volume with in the same system of measure.

**Essential Question: **

- Is it important to know how to solve proportions and unit rates?

**Instructional Strategy: **Evaluating Student Understanding

**Process Standards:**

- Goal 1.6 discover and evaluate patterns and relationships in information, ideas and structures

**Content Standards:**

- Mathematics 2. Geometric and spatial sense involving measurement (including length, area, volume), trigonometry, ...
**Time Allowance:**4/50 minute class periods to teach and one for the Are You Smarter Than a Fifth Grader Assessment**Technological Resources:**

Power Point Template**Assessment:**

Students will write their answers on dry erase boards as we complete the Are You Smarter than a Fifth Grader game together as a class.**Description:**Students will solve problems involving rates, ratios and proportions including scaling and converting area and volume with in the same system of measure.**Comments:**

**Classroom Component:**Please click here for 5th Grade Template Powerpoint

**7-1 Ratios and Proportions**

**Objective:**The learner will find equivalent ratios to create proportions.**Vocabulary:**

__Ratio__- A comparison of two quantities by division (usually a fraction).

__Equivalent Ratio-__Ratios that make the same comparison.

__Proportion-__Ratios that are equivalent.***NOTE- As long as you multiply OR divide a fraction by the same number, it is equivalent.

**7-3 Analyze Units**

**Objective:**The learner will use one or more conversion factors to solve rate problems.**Vocabulary:**

To convert units, multiply by one or more ratios of equal quantities called__Conversion Factors.__**Find the unit rate.**__$27.99__

9 ounces

**Find the better buy.**- 54 lbs. for $153.84 OR 48 lbs. for $136.77

**Complete each equation. All answers much be in unit rates with labels.**

__15 students__**.**__42 classes__= _________

1 class 1 school

__3 mi__**.**________ =__7,920 ft__

2 hours 1 hour

__300 cm__. _____ = ________m__

6 hr hr

__180 ft__**.**______**.**______ = ______in__5 sec

**7-4 Solving Proportions****Objective:**The learner will solve proportions.**Vocabulary:**

__Cross Products-__in proportions are equal.

- A mixture of fuel for a certain small engine should be 4 parts gasoline to 1 part oil. If you combine 5 quarts of oil with 15 quarts of gasoline, will the mixture be correct?

**7-4 Solving Proportions**

**Objective:**The learner will solve proportions.**Vocabulary:**

__Cross Products-__in proportions are equal.**NOTE- This is different than Unit rates in that with proportions you MUST compare like units and they are EQUAL.

**Set up each proportion and solve.**- If there are 320 calories in 6 ounces of meat, how many calories are in 2 ounces of meat?

- If it takes 3˝ ounces of concentrate to make 11 ounces of perfume, how much perfume can be made with 7 ounces of concentrate?

- At a certain middle school, the ratio of 7th graders to 8th graders is 4 to 3. If there are 600 8th graders, how many 7th graders are there at the middle school?

*For additional information contact :*niki.mcdaniel@leesummit.k12.mo.us

Nichole McDaniel

Pleasant Lea Middle

Lee's Summit R-VII

(816) 986-1175

EMAIL: