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Math on the Mind How many inches are in 1 foot? How many cups are in 1 pint? How many feet are in 1 yard? How many seconds in 1 minute? CHALLENGES: How many feet in 1 mile? How many ounces in 1 gallon? 12 2 3 60 5280 8 oz/cup× 2 c/pt× 2 pt/qt× 4 qt/gal= 128 oz/gal

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Unit Rates Unit 4, Day 2 Adapted from the lesson at www.mrhammond.org/math/mathlessons/6-2.ppt

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Vocabulary A rate is a ratio that compares two quantities measured in different units. The unit rate is the rate for one unit of a given quantity. Unit rates have a denominator of 1.

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Examples Rate: 150 heartbeats 2 minutes Unit Rate (Divide to get it): 150 ÷ 2 = 75 heartbeats per minute.

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Food for Thought… Can you think of any unit rates you may encounter in the real world?

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Calculate the Unit Rate Gas mileage: 78 miles using 3 gallons of gas Starting wage: $326 for 40 hours of work Sale price: $2 for 5 cans of soup 26 miles/gallon $8.15/hour $0.40/can

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A brand of apple juice costs $1.56 for 48 oz. Find the unit rate. The unit rate is 3.25¢/oz. cost $1.56 ounces 48 oz = $.0325/oz Unit Rate Example

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Example Grape juice is sold in two different sizes. A 48- fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy? $2.07 48 fl.oz. 0.043125 $0.04 per fl.oz. $1.64 32 fl.oz. 0.05125 $0.05 per fl.oz. The 48 fl.oz. bottle is the better value.

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Where do I EVER see this? http://www.google.com/imgres?q=shelf+labels+wegmans&hl=en&rlz=1R2ADSA_enUS405&biw=1024&bih=543&tbm=isch&tbnid=1zI8Rm7UfSj5iM:&i mgrefurl=http://www.babiesdesignfood.com/2011/04/ya-gotta-go-make-some-groceries- at.html&docid=T76ihBnCg_R2DM&imgurl=http://4.bp.blogspot.com/-EHk2Le-jVY0/TbBRns- 98QI/AAAAAAAABBo/DSSknMoQc2k/s1600/IMG_2993.jpg&w=576&h=432&ei=oZSwTvrOLKLb0QHo75CnAQ&zoom=1&iact=hc&vpx=535&vpy=22 0&dur=78&hovh=194&hovw=259&tx=150&ty=115&sig=101549648530835685433&page=8&tbnh=146&tbnw=201&start=66&ndsp=8&ved=1t:429,r:2, s:66

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http://www.google.com/imgres?q=grocery+store+shelf+labels&hl=en&rlz=1R2A DSA_enUS405&biw=1024&bih=543&tbm=isch&tbnid=xKYVR4LLoePzyM:&imgr efurl=http://www.extension.org/pages/19896/using-unit- pricing&docid=XV6loYpkUOojcM&imgurl=http://www.extension.org/mediawiki/file s/b/be/10oz_cheerios.jpg&w=250&h=87&ei=J5awTreUJ6TY0QGZmv3qAQ&zoo m=1&iact=hc&vpx=775&vpy=221&dur=32&hovh=69&hovw=200&tx=76&ty=62& sig=101549648530835685433&page=1&tbnh=69&tbnw=200&start=0&ndsp=8& ved=1t:429,r:3,s:0 http://www.google.com/imgres?q=grocery+store+shelf+labels&hl=en&rlz=1R2ADSA_enUS405&bi w=1024&bih=543&tbm=isch&tbnid=9L1KK3GsGn_URM:&imgrefurl=http://pvhs.fms.k12.nm.us/tea chers/jlong/Algebra%2520Lesson%2520Plans%2520Fall%25202010&docid=nw59zIOy6HOIAM&i mgurl=http://pvhs.fms.k12.nm.us/teachers/jlong/04F384E3- 00757F35.37/10610_22630_0.gif%253Fsrc%253D.PNG&w=162&h=92&ei=J5awTreUJ6TY0QGZ mv3qAQ&zoom=1&iact=rc&dur=47&sig=101549648530835685433&page=10&tbnh=73&tbnw=12 9&start=81&ndsp=8&ved=1t:429,r:0,s:81&tx=84&ty=76

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Time to Shop! http://www.brainpop.com/math/dataa nalysis/comparingprices/http://www.brainpop.com/math/dataa nalysis/comparingprices/

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Conversion Factors A conversion factor is a ratio of equivalent measurements.

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Example Problem: A roll of Christmas gift wrap contains 2.5 meters of paper. What is the length of the paper in yards? Step 1: Write down the known values and the unknown values. Known : length of paper in meters: 2.5 meters Unknown : length of paper in yards http://www2.franciscan.edu/academic/mathsci/mathscienceintegation/MathScienceIntegation-620.htm

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Example Problem: A roll of Christmas gift wrap contains 2.5 meters of paper. What is the length of the paper in yards? Step 2: Find the conversion factor that gives a ratio between meters and yards. Conversion factor 1 meter = 1.09 yards http://www2.franciscan.edu/academic/mathsci/mathscienceintegation/MathScienceIntegation-620.htm

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Example Problem: A roll of Christmas gift wrap contains 2.5 meters of paper. What is the length of the paper in yards? Step 3: Write the conversion factor as a fraction with the unit you want to convert to on top and set the problem up as an equation. http://www2.franciscan.edu/academic/mathsci/mathscienceintegation/MathScienceIntegation-620.htm 2.5 meters x 1.09 yards = 1 meter 2.725 yards You can see that the unit meters will cancel.

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Using Conversion Factors

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Practice:

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Homework Page 145, #1-6, 9-15

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Customary Units http://www.brainpop.com/math/numb ersandoperations/customaryunits/pre view.wemlhttp://www.brainpop.com/math/numb ersandoperations/customaryunits/pre view.weml http://www.hillsboroschools.net/team6a/connor/math/Ch3%20-- %20Decimals%20and%20Metrics/MeasurementPics/units_of_measure.gif

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