WRITE AND SOLVE EQUATIONS

Learning Goal for Focus 2(HS.A-CED.A.1, 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3):The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step.

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In addition to level 3.0 and above and beyond what was taught in class,  the student may:- Make connection with other concepts in math- Make connection with other content areas.

The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step. - rearrange formulas to highlight a quantity of interest.-Graph created equations on a coordinate graph.

The student will be able to solve linear equations and inequalities in one variable and explain the logic in each step.- Use

equations and inequalities in one variable to solve problems.

With help from theteacher, the student haspartial success with solving linear equations and inequalities in one variable.

Even with help, the student has no success with solving linear equations and inequalities in one variable.

USE ALGEBRA TO SOLVE PROBLEMS

• There are many ways to solve story problems:• Guess & check

• Make a table

• Look for a pattern

• Draw a picture

• Today you will write algebraic equations to solve problems.

Images from http://schools.iclipart.com

GETTING A SPEEDING TICKET

Greg lives in a state in which speeders are fined $15 for each mile per hour over the speed limit. Greg was given a ticket for $180 for speeding where the speed limit is 45 miles per hour. How fast was Greg driving?

• Label what you know:• Speeding ticket =

$180• $15 per mile over limit• “x” how many miles

over speed limit.

• Write an equation.• 15x = 180

• Solve• x = 12

• Answer the question:• Greg was driving 57

miles per hour.Image from http://schools.iclipart.com

THE GAZELLE AND THE CHEETAH

The gazelle can run 73 feet per second for several minutes. A cheetah can run faster (88 feet per second), but can only sustain its top speed for about 20 seconds. Gazelles seem to have an instinct for this difference because they will not run from a prowling cheetah until it enters their “safety zone.” This is the distance the cheetah would need to run to overtake the gazelle in 20 seconds if both are running at top speed. How close should the gazelle let the cheetah come before it runs? (Remember: d=rt)

• Label what you know:• Gazelle’s distance = 73(20)• Cheetah’s distance =

88(20)• “x” buffer distance

• Write an equation.• 73(20) + x = 88(20)

• Solve• 1460 + X = 1760• x = 300

• Answer the question:• The gazelle should not

let the cheetah get closer than 300 feet.

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MONEY!

Currently, you have $60 and your sister has $135. You decide to save $5 of your allowance each week, whereas your sister decides to spend her whole allowance plus $10 per week. How long will it be before you have as much as your sister?

• Label what you know:• My starting amount= $60• My savings each week= $5• Her starting amount = $135• Her spending each week =

$10• “w” number of weeks.

• Write an equation.• 60 + 5w = 135 - 10w

• Solve• 15w = 75• w = 5

• Answer the question:• I will have as much as my

sister in 5 weeks.Image from http://schools.iclipart.com