1. 2 mathematical reasoning institute lesson goals 3 a.1.c – write linear expressions as part of...

MATHEMATICAL REASONING INSTITUTE

LESSON GOALSLESSON GOALS

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A.1.c – Write linear expressions as part of word-to-symbol translations or to represent common settings.

A.2.c – Write one-variable and multi-variable linear equations to represent context.

A.3.a – Solve linear inequalities in one variable with rational number coefficients.

A.3.d – Write linear inequalities in one variable to represent context.

A.6.c – Use slope to identify parallel and perpendicular lines and to solve geometric problems.

MATHEMATICAL REASONING INSTITUTE 4

WORKING WITH WORKING WITH THE CONTENTTHE CONTENT

Think & Work AloneThink, Pair, Share

Cooperative Learning In Small Groups


Symbols to Words Symbols to Words

Key Phrase

Sum, Increase, Add, All together, Total

Subtract, Decrease, Difference Minus, Fewer

Times, Multiply, Product

Divide, Per, Quotient

Math Symbols

+ (Addition)

- (Subtraction)

x (Multiplication)

÷ (Division)

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Process:Five posters numbered 1 to 5 with

linear expressions written on themNumber off 1 to 5Start at the poster numbered with

your number15 seconds at each poster to write

as many word phrases as you can

Symbols to Words ActivitySymbols to Words Activity

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Process:Index card with a word phrase Write the word phrase on your

posterReach consensus on the correct

translation to an algebraic expression

Record translation on poster

Words to algebraic Words to algebraic expressionsexpressions

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For each of the following, write an expression in terms of the given variable that represents the indicated quantity.

The total cost of a mechanic to repair your car if he spends h hours on the job and charges $39 for parts and $45 per hour for labor.

The sum of three consecutive numbers if the first number is n.

Try These with a Partner!Try These with a Partner!

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For each of the following, write an expression in terms of the given variable that represents the indicated quantity.

The amount of money in Steve’s bank account if he put in d dollars the first year, $600 more the second year than the first year, and twice as much the third year as the second year.

The first side of a triangle is s yards long. The second side is 3 yards longer than the first side. The third side is three times as long as the second side. What is the perimeter of the triangle in feet?

Try These with a Partner!Try These with a Partner!

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Translating Words to Translating Words to Linear EquationsLinear Equations

Equations

n + 32 = 40

4x = 36

K - 7 = 15

3w = -15

6/x = 2

Words

A number increased by 32 is equal to 40.

Four times a number is 36.

Seven less than a number is 15.

The product of a number and 3 is -15.

Six divided by a number is equal to 2.

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Context to Context to Linear EquationsLinear Equations

Context

John called a plumber to fix his broken toilet. In addition to a $50 fee for the visit, the plumber charges $22 per hour. Write an equation that models this situation to determine how many hours the plumber took if John’s total bill was $116.

Equation

h = hours the plumber worked

50 +

50 + 22h

50 + 22h = 116

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Context to Context to Linear EquationsLinear Equations

Context

Jane needs $2100 for a vacation for spring break. She plans to save $350 per month for the trip. Write an equation that represents this situation to help Jane determine how many months it will take her to save for the trip at this rate.

Equation

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m = number of months to save for trip

350m

350m = 2100


Context to Multi-variableContext to Multi-variableLinear EquationsLinear Equations

Context

A line on a graph represents a ramp that extends from the back of a moving truck to the ground. The line has a slope of -.5 and passes through (8, 0). The y-intercept represents the height of the back of the moving truck. Write an equation with two variables that represents this situation.

Equation

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y = mx + b

y = -.5x + b

0 = -.5(8) + b

0 = -4 + b

4 = b

y = -.5x + 4

Linear Inequalities Linear Inequalities

https://www.youtube.com/watch?v=8hhewFQ_K0w

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Inequalities vs. Equations Inequalities vs. Equations ActivityActivity

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Slopes of Parallel & Perpendicular Lines

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/v/equations-of-parallel-and-perpendicular-lines

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• Describe in your own words the relationship of the slopes of parallel lines.

• Describe in your own words the relationship of the slopes of perpendicular lines.

Try with a partner!Try with a partner!

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Using what you know about parallel and perpendicular lines and the relationships of their slopes and what you know about writing the equations of lines do the following:

• Find the equation of the line that is perpendicular to

y = -4x + 10 and passes through the point (7, 2). Leave your answer in standard form.

• Find the equation of the line that is parallel to y = -4x + 10 and passes through the point (7, 2). Leave your answer in standard form.

Try with a partner!Try with a partner!

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Lunch Time! Lunch Time!

Please come back on time.

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1. 2 mathematical reasoning institute lesson goals 3 a.1.c – write linear expressions as part of...

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variable linear equations

linear expressions

linear equations context

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rational number coefficients