Ratios

Ratios, Rates, Unit Rates7th Grade MathNovember, 2012A ___________ is a comparison of two numbers by division.

A ratio must be expressed in __________ .

Example #1:There are approximately 600 students at Lewisburg School. There are 30 teachers. What is the student to teacher ratio at Lewisburg School?RatioSimplestForm600 students/30 teachers or 20 students/1 teacher3 ways to write a ratio!There were 6 chocolate donuts in the box of 12 donuts.

Part to Whole = =

** This can be expressed as: **1:21 to 2 ALL THREE OF THESE MEAN ~ 1 CHOCOLATE DONUT FOR EVERY 2 DONUTS.

__________________ shows 2 ratios have the same value.Reduce to lowest terms.Same methods as Equivalent Fractions

Example Are these two ratios equivalent?:$4 for every 16 ounces$4/16 oz

$10 for every 40 ounces$10/40 oz

These two ratios are equivalent!!Equivalent Ratios2nd Block start hereGrab Bag!!Bag of various items.Create ratios on whiteboards (include units)Time Frame = 15 minutes

Choose a partner and take turns taking your pulse for 2 minutes.Count the number of beats for each of you.Write the ratio beats to minutes as a fraction.

A ___________ is a ratio that compares two different kinds of units.

Example:Heartbeat exampleTwo Units = heartbeats and minutesGasoline exampleTwo Units = miles and gallonsMoney exampleTwo Units = price and poundsRateDifferent Types of RatiosDifferent Types of RatiosDifferent Types of RatiosPart/Whole ExamplesRatioPart/Part ExamplesRatioRate ExamplesRate6 red roses to 24 flowers in bouquet6 red roses to 18 yellow roses12 roses per 3 bouquets5 footballs to 25 balls in gym supply5 footballs to 8 soccer balls5 footballs per class80 points earned to 100 points possible80 points earned to 20 points not earned1400 points earned per 20 students14 girls to 22 students in class14 girls to 8 boys in class110 students per 5 teachersDifferent Types of RatiosPart/Whole ExamplesRatioPart/Part ExamplesRatioRate ExamplesRate6 red roses to 24 flowers in bouquet6/246 red roses to 18 yellow roses6 to 1812 roses per 3 bouquets12:35 footballs to 25 balls in gym supply5/255 footballs to 8 soccer balls5 to 85 footballs per class5:180 points earned to 100 points possible80/10080 points earned to 20 points not earned80 to 201400 points earned per 20 students1400:2014 girls to 22 students in class14/2214 girls to 8 boys in class14 to 8110 students per 5 teachers22:1Lets try together:http://math.rice.edu/~lanius/proportions/rate.html

Take out since we did the grab bag!PracticePractice Problems:Glencoe Rates and RatiosPage 284 - #1-17A ____________ is a ratio that is simplified so that it has a denominator of ONE unit.

Examples:I made $300 for 6 hours of work. Write the unit rate.

We drove 220 miles on 8 gallons of gas. Write the unit rate

Unit Rate$300/6 hours = $50/1 hour220 miles/8 gallons = 27.5 miles/1 gallonHow to calculate unit rate?Easiest way is to divide BOTH the numerator AND the denominator by the denominator.

Example #1:

How to calculate unit rate?Easiest way is to divide BOTH the numerator AND the denominator by the denominator.

Example #2:

Common Unit RatesMy IdeasRateUnit RateClass IdeasRateUnit RateCommon Unit RatesRateUnit RateNumber of Miles 1 hourMiles per hourNumber of Miles 1 gallonMiles per gallonNumber of Dollars 1 poundPrice per poundNumber of Dollars 1 hourDollars per hourPracticePractice Problems:Glencoe Unit RatesPage 290 - #7-18

Grocery Store Comparison UNIT RATE!Four Products:Find the best price!!PracticeSmall Group:Use the grid provided to answer the question on each cardDeck of cardsMUST INCLUDE THE UNITS FOR RATIOS!!LEVEL 1: INDIVIDUALDeal out cards evenly to each playerAnswer that problem on your paperPlace your card in a common pile so partners can find what they needContinue until youve answered all cardsPracticeParent Participation:Using what you know about unit rate, ask your parents/grandparents to give you 3 examples of when they have compared unit rates.Write them down and be prepared to share them with the classExample: Mr. Northern