math on the mind how many inches are in 1 foot? how many cups are in 1 pint? how many feet are in 1...
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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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ExamplesRate: 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 $1.56ounces 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?
$2.0748 fl.oz.
0.043125 $0.04 per fl.oz.
$1.6432 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:&imgrefurl=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=220&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=1R2ADSA_enUS405&biw=1024&bih=543&tbm=isch&tbnid=xKYVR4LLoePzyM:&imgrefurl=http://www.extension.org/pages/19896/using-unit-pricing&docid=XV6loYpkUOojcM&imgurl=http://www.extension.org/mediawiki/files/b/be/10oz_cheerios.jpg&w=250&h=87&ei=J5awTreUJ6TY0QGZmv3qAQ&zoom=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&biw=1024&bih=543&tbm=isch&tbnid=9L1KK3GsGn_URM:&imgrefurl=http://pvhs.fms.k12.nm.us/teachers/jlong/Algebra%2520Lesson%2520Plans%2520Fall%25202010&docid=nw59zIOy6HOIAM&imgurl=http://pvhs.fms.k12.nm.us/teachers/jlong/04F384E3-00757F35.37/10610_22630_0.gif%253Fsrc%253D.PNG&w=162&h=92&ei=J5awTreUJ6TY0QGZmv3qAQ&zoom=1&iact=rc&dur=47&sig=101549648530835685433&page=10&tbnh=73&tbnw=129&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/dataanalysis/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 meter2.725 yardsYou can see that the unit meters will cancel.
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Using Conversion Factors
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Practice:
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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/numbersandoperations/customaryunits/preview.weml
http://www.hillsboroschools.net/team6a/connor/math/Ch3%20--%20Decimals%20and%20Metrics/MeasurementPics/units_of_measure.gif