SOLVE IT!

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SOLVE IT!

• SOLVING LINEAR EQUATIONS
• WRITING EQUATIONS
• DISTRIBUTING
• TRACING POINTS ON GRAPHS

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MEMORIES OF YESTERYEAR
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BUILDING A FOUNDATION
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YOURE THE STORYTELLER
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RUNNING ON THE OVERLAND TRAIL
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LAMPPOST SHADOWS
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THE MYSTERY BAGS GAME
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YOURE THE JESTER
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SUBSTITUTION AND EVALUATION
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LETTERS, NUMBERS, AND A STORY
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CATCHING UP
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MORE LETTERS, NUMBERS, AND MYSTERY BAGS
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BACK TO THE LAKE
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WHAT WILL IT ANSWER?
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LINE IT UP
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WHOS RIGHT?
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A LOT OF CHANGING SIDES
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WHY ARE THEY EQUIVALENT?
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ONE EACH WAY
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DISTRIBUTING THE AREA
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THE DISTRIBUTIVE PROPERTY AND MYSTERY LOTS
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VIEWS OF THE DISTRIBUTIVE PROPERTY
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TAKING SOME OUT, PART I
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SUBTRACTING SOME SUMS
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TAKING SOME OUT, PART II
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RANDY, SANDY, AND DANDY RETURN
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EQUATION TIME
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MORE SCRAMBLED EQUATIONS AND MYSTERY BAGS
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OLD FRIENDS AND NEW FRIENDS
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NEW FRIENDS VISIT YOUR HOME
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FROM ONE VARIABLE TO TWO
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GET IT STRAIGHT
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A DISTRIBUTIVE SUMMARY
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ALL BY ITSELF
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MORE VARIABLE SOLUTIONS
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WHERES SPEEDY?
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A MIXED BAG
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THE GRAPH SOLVES THE PROBLEM
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TO THE RESCUE
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SWINGING PENDULUM
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MYSTERY GRAPH
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FUNCTIONING IN THE MATH WORLD
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THE GRAPHING CALCULATOR SOLVER
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A SOLVING SAMPLER
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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

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YOURE THE STORYTELLER

• CREATE A SITUATION FOR EACH EQUATION
• SOLVE EACH EQUATION

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RUNNING ON THE OVERLAND TRAIL

• CHOOSE AND DEFINE A VARIABLE
• WRITE AN EQUATION
• SOLVE EACH EQUATION

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LAMPPOST SHADOWS

• ARE THESE TWO TRIANGLES SIMILAR?
• WHAT EQUATION DID YOU USE?

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THE MYSTERY BAGS GAME

• IF YOU TAKE THE SAME AMOUNT OF WEIGHT FROM BOTH
  PANS, IS WHATS LEFT ON THE PANS ALWAYS BALANCED?

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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

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LETTERS, NUMBERS, AND A STORY

• ORDER OF OPERATIONS
• PARAENTHESES
• EXPONENTS
• MULTIPLICATION OR DIVISION
• ADDITION OR SUBTRACTION

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CATCHING UP

• HAS THE SWAYER FAMILY CAUGHT UP TO THE WAGON
  TRAIN AFTER 6 DAYS?

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CATCHING UP

• HAS THE SWAYER FAMILY CAUGHT UP TO THE WAGON
  TRAIN AFTER 15 DAYS?

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CATCHING UP

• HOW MANY DAYS DO YOU THINK IT WILL TAKE THE
  SWAYER FAMILY CAUGHT UP TO THE WAGON TRAIN?

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MORE LETTERS, NUMBERS, AND MYSTERY BAGS

• ORDER OF OPERATIONS
• PARAENTHESES
• EXPONENTS
• MULTIPLICATION OR DIVISION
• ADDITION OR SUBTRACTION

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BACK TO THE LAKE
WHAT IS YOUR RULE FROM THE IN OUT TABLE?

• D 6/n

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LINE IT UP

• WHAT KIND OF ALGEBRAIC EXPRESSION DO YOU THINK
  CAN BE USED TO REPRESENT ANY LINEAR FUNCTION?

y axb
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WHOS RIGHT?

• 2(X 1) OR 2X 2

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A LOT OF CHANGING SIDES

• MAKE AND LABEL A SKETCH OF THE LOT
• USE THE VARIABLE X

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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

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WHY ARE THEY EQUIVALENT?

• RANDY REPEATED ADDITION
• SANDY SUBSTITUTION
• DANDY DISTRIBUTE

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DISTRIBUTING THE AREA

• WRITE AS THE PRODUCT OF ITS LENGTH AND WIDTH
• WRITE AS THE SUM OF TWO SMALLER AREAS

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THE DISTRIBUTIVE PROPERTY AND MYSTERY LOTS

• MULTIPLYING THROUGH
• TAKING OUT A COMMON FACTOR

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TAKING SOME OUT, PART I

• A - ( B C) A - B - C

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TAKING SOME OUT, PART II

• A - ( B - C) A - B C

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MORE SCRAMBLED EQUATIONS AND MYSTERY BAGS

• UNCOMPLICATE EACH EQUATION BY SOLVING
• SUBSTITUTE THE VALUE OF X BACK INTO THE EQUATION
  AS A CHECK

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NEW FRIENDS VISIT YOUR HOME

• DISTRIBUTE
• COMBINE LIKE TERMS
• ISOLATE THE VARIABLE TERM TO ONE SIDE
• DIVIDE BOTH SIDES BY THE COEFFICIENT

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FROM ONE VARIABLE TO TWO

• SOLVING FOR Y IN TERMS OF X

• ISOLATE THE Y TERM TO ONE SIDE
• DIVIDE YS COEFFICIENT ON BOTH SIDES

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GET IT STRAIGHT

• HOW DO YOU CHANGE A LINEAR EQUATION IN ORDER TO
  CHANGE THE SLANT OF ITS GRAPH?

COEFFICIENT MULTIPLY OR DIVIDE
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GET IT STRAIGHT

• HOW DO WE CHANGE THE EQUATION IN ORDER TO SHIFT
  IT UP OR DOWN?

CONSTANT ADD OR SUBTRACT
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GET IT STRAIGHT

• WHEN ARE LINEAR FUNCTIONS MIRROR IMAGES OF ONE
  ANOTHER?

CONSTANT POSITIVE NEGATIVE
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GET IT STRAIGHT

• WHEN DO TWO LINEAR FUNCTIONS GIVE PARALLEL LINES?

COEFFICIENT SAME
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GET IT STRAIGHT

• WHEN DO TWO LINEAR FUNCTIONS GIVE PERPENDICULAR
  LINES?

COEFFICIENTNEGATIVE RECIPROCALS
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GET IT STRAIGHT

• WHAT LINEAR FUNCTIONS GIVE HORIZONTAL LINES?

Y
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A DISTRIBUTIVE SUMMARY

• DEFINE THE DISTRIBUTIVE PROPERTY IN YOUR OWN
  WORDS
• INCLUDE AREA DIAGRAMS AND THE FOIL METHOD

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ALL BY ITSELF

• SOLVING FOR Y IN TERMS OF X

• ISOLATE THE Y TERM TO ONE SIDE
• DIVIDE YS COEFFICIENT ON BOTH SIDES

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MORE VARIABLE SOLUTIONS

• SOLVING FOR Y IN TERMS OF X

• ISOLATE THE Y TERM TO ONE SIDE
• DIVIDE YS COEFFICIENT ON BOTH SIDES

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A MIXED BAG

• SOLVING FOR A NUMERICAL SOLUTION
• SOLVING FOR AN EXPRESSION

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THE GRAPH SOLVES THE PROBLEM

• UTILIZE THE TRACE BUTTON ON THE GRAPHING
  CALCULATOR

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WHERES SPEEDY?

• UTILIZE THE TRACE BUTTON ON THE GRAPHING
  CALCULATOR

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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

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TO THE RESCUE

• N 400FT
• h(T) THE OBJECTS HEIGHT
• t SECONDS AFTER THE OBJECT HAS BEEN DROPPED

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SWINGING PENDULUM

• UTILIZE THE GRAPHING CALCULATORS TABLES

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MYSTERY GRAPH

• f(4)y, THAT IS WHAT IS Y WHEN x 4
• f(x) 7, THAT IS WHAT IS X WHEN y 7

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FUNCTIONING IN THE MATH WORLD

• A FUNCTION CAN BE REPRESENTED IN FOUR WAYS
• SITUATION
• EQUATION
• GRAPH
• IN OUT TABLE

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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

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A SOLVING SAMPLER

• MYSTERY BAGS MODEL
• UNSCRAMBLING EQUATIONS
• GRAPHING