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

Unit Rates

Unit 4, Day 2

Adapted from the lesson at www.mrhammond.org/math/mathlessons/6-2.ppt

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.

ExamplesRate: 150 heartbeats

2 minutes

Unit Rate (Divide to get it):

150 ÷ 2 = 75 heartbeats per minute.

Food for Thought…

Can you think of any unit rates you may encounter in “the real world”?

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

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

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.

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

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

Time to Shop!

• http://www.brainpop.com/math/dataanalysis/comparingprices/

Conversion Factors

• A conversion factor is a ratio of equivalent measurements.

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

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

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.

Using Conversion Factors

Practice:

Practice:

Homework

• Page 145, #1-6, 9-15

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