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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
LAMPPOST SHADOWS
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
WHAT WILL IT ANSWER?
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
  LAMPPOST SHADOWS
• 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
 ADDITION OR SUBTRACTION
      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
 ADDITION OR SUBTRACTION
  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?
• RANDY: REPEATED ADDITION

• 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?


CONSTANT: ADD OR SUBTRACT
    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
  PROPERTY IN YOUR OWN
  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
  ANSWER KEY
 – UTILIZE THE TRACE BUTTON


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

• UNSCRAMBLING EQUATIONS

• GRAPHING

				
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