# Solve It

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```					      SOLVE IT!

SOLVING LINEAR EQUATIONS
WRITING EQUATIONS
DISTRIBUTING
TRACING POINTS ON GRAPHS
MEMORIES OF
YESTERYEAR
BUILDING A FOUNDATION
YOU’RE THE
STORYTELLER
RUNNING ON THE
OVERLAND TRAIL
THE MYSTERY BAGS
GAME
YOU’RE THE JESTER
SUBSTITUTION AND
EVALUATION
LETTERS, NUMBERS, AND
A STORY
CATCHING UP
MORE LETTERS,
NUMBERS, AND MYSTERY
BAGS
BACK TO THE LAKE
LINE IT UP
WHO’S RIGHT?
A LOT OF CHANGING
SIDES
WHY ARE THEY
EQUIVALENT?
ONE EACH WAY
DISTRIBUTING THE AREA
THE DISTRIBUTIVE
PROPERTY AND MYSTERY
LOTS
VIEWS OF THE
DISTRIBUTIVE PROPERTY
TAKING SOME OUT, PART I
SUBTRACTING SOME SUMS
TAKING SOME OUT, PART
II
RANDY, SANDY, AND
DANDY RETURN
EQUATION TIME
MORE SCRAMBLED
EQUATIONS AND
MYSTERY BAGS
OLD FRIENDS AND NEW
FRIENDS
NEW FRIENDS VISIT YOUR
HOME
FROM ONE VARIABLE TO
TWO
GET IT STRAIGHT
A DISTRIBUTIVE
SUMMARY
ALL BY ITSELF
MORE VARIABLE
SOLUTIONS
WHERE’S SPEEDY?
A MIXED BAG
THE GRAPH SOLVES THE
PROBLEM
TO THE RESCUE
SWINGING PENDULUM
MYSTERY GRAPH
FUNCTIONING IN THE
MATH WORLD
THE GRAPHING
CALCULATOR SOLVER
A SOLVING SAMPLER
BUILDING A FOUNDATION
• LIST ALL THE FACTORS OF 144
1 , 144
2 , 72
3 , 48
4 , 36
6 , 24
8 , 18
9 , 16
12 , 12
YOU’RE THE
STORYTELLER
• CREATE A SITUATION FOR
EACH EQUATION

• SOLVE EACH EQUATION
RUNNING ON THE
OVERLAND TRAIL
• CHOOSE AND DEFINE A
VARIABLE

• WRITE AN EQUATION

• SOLVE EACH EQUATION
• ARE THESE TWO TRIANGLES
SIMILAR?

• WHAT EQUATION DID YOU
USE?
THE MYSTERY BAGS
GAME
• IF YOU TAKE THE SAME
AMOUNT OF WEIGHT FROM
BOTH PANS, IS WHAT’S LEFT
ON THE PANS ALWAYS
BALANCED?
SUBSTITUTION AND
EVALUATION
• SUBSTITUTE: IS THE STEP OF
REPLACING THE VARIABLE
WITH A NUMBER

• EVALUATION: IS THE STEP OF
FINDING A SINGLE NUMBER
FROM THE SUBST. STEP
LETTERS, NUMBERS, AND
A STORY
• ORDER OF OPERATIONS

PARAENTHESES
EXPONENTS
MULTIPLICATION OR DIVISION
CATCHING UP
• HAS THE SWAYER FAMILY
CAUGHT UP TO THE WAGON
TRAIN AFTER 6 DAYS?
CATCHING UP
• HAS THE SWAYER FAMILY
CAUGHT UP TO THE WAGON
TRAIN AFTER 15 DAYS?
CATCHING UP
• HOW MANY DAYS DO YOU
THINK IT WILL TAKE THE
SWAYER FAMILY CAUGHT UP
TO THE WAGON TRAIN?
MORE LETTERS,
NUMBERS, AND MYSTERY
BAGS
• ORDER OF OPERATIONS

PARAENTHESES
EXPONENTS
MULTIPLICATION OR DIVISION
BACK TO THE LAKE

WHAT IS YOUR RULE FROM THE
IN OUT TABLE?

D = 6/n
LINE IT UP
• WHAT KIND OF ALGEBRAIC
EXPRESSION DO YOU THINK
CAN BE USED TO REPRESENT
ANY LINEAR FUNCTION?

y = ax+b
WHOS RIGHT?

2(X + 1) OR 2X + 2
A LOT OF CHANGING
SIDES
• MAKE AND LABEL A SKETCH
OF THE LOT

• USE THE VARIABLE X
A LOT OF CHANGING
SIDES
• WRITE AN EXPRESSION OF THE
NEW LOT AS A PRODUCT OF
ITS LENGTH AND WIDTH

• WRITE AN EXPRESSION OF THE
NEW AS A SUM OF SMALLER
AREAS
WHY ARE THEY
EQUIVALENT?

• SANDY: SUBSTITUTION

• DANDY: DISTRIBUTE
DISTRIBUTING THE AREA
• WRITE AS THE PRODUCT OF
ITS LENGTH AND WIDTH

• WRITE AS THE SUM OF TWO
SMALLER AREAS
THE DISTRIBUTIVE
PROPERTY AND MYSTERY
LOTS
• MULTIPLYING THROUGH

• TAKING OUT A COMMON
FACTOR
TAKING SOME OUT, PART I

• A - ( B + C) = A - B - C
TAKING SOME OUT, PART
II
• A - ( B - C) = A - B + C
MORE SCRAMBLED
EQUATIONS AND
MYSTERY BAGS
• “UNCOMPLICATE” EACH
EQUATION BY SOLVING

• SUBSTITUTE THE VALUE OF X
BACK INTO THE EQUATION AS
A CHECK
NEW FRIENDS VISIT YOUR
HOME
• DISTRIBUTE
• COMBINE LIKE TERMS
• ISOLATE THE VARIABLE TERM
TO ONE SIDE
• DIVIDE BOTH SIDES BY THE
COEFFICIENT
FROM ONE VARIABLE TO
TWO
• SOLVING FOR Y IN TERMS OF X

•ISOLATE THE Y TERM TO ONE
SIDE
•DIVIDE Y’S COEFFICIENT ON
BOTH SIDES
GET IT STRAIGHT
• HOW DO YOU CHANGE A
LINEAR EQUATION IN ORDER
TO CHANGE THE “SLANT” OF
ITS GRAPH?

COEFFICIENT: MULTIPLY OR
DIVIDE
GET IT STRAIGHT
• HOW DO WE CHANGE THE
EQUATION IN ORDER TO SHIFT
IT UP OR DOWN?

GET IT STRAIGHT
• WHEN ARE LINEAR FUNCTIONS
MIRROR IMAGES OF ONE
ANOTHER?

CONSTANT: POSITIVE &
NEGATIVE
GET IT STRAIGHT
• WHEN DO TWO LINEAR
FUNCTIONS GIVE PARALLEL
LINES?

COEFFICIENT: SAME
GET IT STRAIGHT
• WHEN DO TWO LINEAR
FUNCTIONS GIVE
PERPENDICULAR LINES?

COEFFICIENT:NEGATIVE
RECIPROCALS
GET IT STRAIGHT
• WHAT LINEAR FUNCTIONS
GIVE HORIZONTAL LINES?

Y= #
A DISTRIBUTIVE
SUMMARY
• DEFINE THE DISTRIBUTIVE
WORDS

• INCLUDE: AREA DIAGRAMS
AND THE FOIL METHOD
ALL BY ITSELF
• SOLVING FOR Y IN TERMS OF X

•ISOLATE THE Y TERM TO ONE
SIDE
•DIVIDE Y’S COEFFICIENT ON
BOTH SIDES
MORE VARIABLE
SOLUTIONS
• SOLVING FOR Y IN TERMS OF X

–ISOLATE THE Y TERM TO
ONE SIDE
–DIVIDE Y’S COEFFICIENT
ON BOTH SIDES
A MIXED BAG
• SOLVING FOR A NUMERICAL
SOLUTION

• SOLVING FOR AN EXPRESSION
THE GRAPH SOLVES THE
PROBLEM
• UTILIZE THE TRACE BUTTON
ON THE GRAPHING
CALCULATOR
WHERE’S SPEEDY?
• UTILIZE THE TRACE BUTTON
ON THE GRAPHING
CALCULATOR
TO THE RESCUE
• N = WHERE THE HELICOPTER
FIRST DROPPED THE OBJECT
• N = 400FT
• h(T) = THE OBJECTS HEIGHT
AFTER t SECONDS SINCE ITS
BEEN DROPPED
TO THE RESCUE
• N = 400FT
• h(T) = THE OBJECTS HEIGHT
• t = SECONDS AFTER THE
OBJECT HAS BEEN DROPPED

h(t )  400  16t     2
SWINGING PENDULUM
• UTILIZE THE GRAPHING
CALCULATORS TABLES
MYSTERY GRAPH
• f(4)=y, THAT IS WHAT IS Y
WHEN x = 4

• f(x) = 7, THAT IS WHAT IS X
WHEN y = 7
FUNCTIONING IN THE
MATH WORLD
• A FUNCTION CAN BE
REPRESENTED IN FOUR WAYS:
SITUATION
EQUATION
GRAPH
IN OUT TABLE
THE GRAPHING
CALCULATOR SOLVER
• THE GRAPH IS LIKE AN
– UTILIZE THE TRACE BUTTON

• THE TABLE IS LIKE AN
– UTILIZE THE TABLES
A SOLVING SAMPLER
• MYSTERY BAGS MODEL

• UNSCRAMBLING EQUATIONS

• GRAPHING

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