September 27, 2013

On-Core 2-1Unit Rates with complex fractions!!!!

September 27, 2013

Essential Question:How do you find and compare unit rates????

September 27, 2013

If I pay $4 for 2 lbs of apples, how much per pound am I paying?

What if I pay $4.50 for 1 1/2 lbs of apples?

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$4.50 for 1 1/2 lbs:

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Or...just do a unit rate!

September 27, 2013

Jeff hikes 1/2 mile every 1/4 hour. Lisa hikes 1/3 mile every 1/6 hour. How far do they each hike in 1 hour?

a) How many 1/4 hours are in 1 hour? How far does Jeff hike in 1 hour?

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Complete the table for Jeff's hike

Distance (mi)

Time (hr)

1/2

1/4 1/2 3/4 1 2

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c) Complete the bar diagram to help you determine how far Lisa hikes. How many miles does she hike in one hour?

d) complete the table for Lisa's hike.

Distance (mi)

Time (hr)

1/3

1/6 1/3 1/2 1 2

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Reflect:

1. How did you find Jeff's distance for 3/4 hour?

2. Which hiker walks farther in one hour? What does this tell you about the speeds at which they hike?

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Remember: ratio compares two quantities.

Rate compares two quantities with different units

Unit Rate is a rate with denominator of 1. (divide)

Sometimes rates are expressed with complex fractions (a fractions within a fraction). In other words, you are DIVIDING FRACTIONS AGAIN! YAY!

KEEP, SWITCH, FLIP

September 27, 2013

September 27, 2013

Finding unit rates:

While remodeling his kitchen,. Arthur paints the cabinets. He estimates that he paints 30 square feet every 1/2 hour. How many square feet does Arthur paint per hour?

Step 1: Find his rate 30 square feet1/2 hour

Step 2: Find unit rate

September 27, 2013

Try this:

Paige mows 1/6 acre in 1/4 hour. How many acres does Paige mow per hour?

Reflect:

How could you find the unit rate by using a table?

Acres

Time (hr)

1/6

1/4

September 27, 2013

Two containers filled with water are leaking. Container A leaks at a rate of 2/3 gallon every 1/4 hour. Container B leaks at a rate of 3/4 gallon every 1/3 hour. Determine which one is leaking more rapidly.

(hint: find the unit rates of each container)

September 27, 2013

Two liquid storage containers are being filled. Liquid enters the first container at a rate of 2/3 gallon per 1/4 minute. Liquid pours into the second container at a rate of 3/5 gallon every 1/6 minute. Determine which one is being filled faster.

Reflect: How do you know which units to use as the numerator in this question (or any "rate" question, really)

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Practice:Simplify:

Ms. Crane eats 6/7 box of cookies every 1/3 hour. How many boxes of cookies can she eat per hour?

September 27, 2013

Journal Time:

How do you find and compare unit rates?

Write a complex fraction in your journal, and explain how to simplify it.

September 27, 2013