7 th Grade Pre-Algebra Focus 1: Proportional Reasoning
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Transcript of 7 th Grade Pre-Algebra Focus 1: Proportional Reasoning
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7th Grade Pre-Algebra
Focus 1: Proportional Reasoning
Standards: 7.RP.1, 7.RP2a, 7.RP.2d
Resource: Connected Math Program 2
Common Core Investigation 1
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Common Core Investigation 1: Graphing ProportionsMathematical Learning Goals
Compute unit rates associated with ratios of fractions, including quantities measured in like or different units
Decide whether two quantities are in a proportional relationship
Explain what any point (x,y), including (0,0) and (1,r) where r is a unit rate, on a graph of a proportional relationship means in terms of the situation
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Problem 1.2: Learning TargetStudents will extend their understanding of ratios and develop understanding of proportionality to solve problems by:
Converting rates to unit rates
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Key Vocabulary Terms• RATE
A rate is a ratio that compares quantities in different units such as miles to hours.
An example of a rate is
• UNIT RATE A unit rate is a rate for which one of the numbers being compared is 1 unit.
An example:
is 140 miles 3.5 hours, or 40 miles per 1 hour is
The rate of miles to hours becomes miles PER hour, which is written mi/h.
The word “per” can be replaced with “for one.”
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Getting Ready for Problem 1.2Referring to the Key Vocabulary Terms examples, answer the following:
What two units are being compared in 140 miles in 3.5 hours?
How could you use this rate to find the distance that could be traveled in 7 hours?
Would it be helpful to find out how many miles are traveled in 1 hour? Why?
How can you find the unit rate for the rate ?
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Problem 1.2: Road Trip & Basketballs
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Problem 1.2Have you thought about?
How can converting rates to unit rates make comparing those rates easier?
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Class Discussion & Sharing
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Key Vocabulary Term
• PROPORTIONAL RELATIONSHIP
Two quantities are in a proportional relationship if a change in
one quantities corresponds to a change by the same factor in the
other quantity.
The ratios between the quantities do not change when the
quantities themselves change.
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Problem 1.2: Learning TargetReview & Recap
Students will extend their understanding of ratios and develop understanding of proportionality to solve problems by:
Converting rates to unit rates
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Pre-Algebra Homework
Exercises
#3, 5, 7, 9Work & answers in your math workbook