Consecutive Integer Problems

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Presentation transcript:

Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

What are Consecutive Integers? Consecutive means: NEXT BIGGEST 2,3,4 5,6,7 -2,-1,0 -12,-11,-10, ALGEBRA: X, X+1,X+2

What are Consecutive Integers? Consecutive EVEN means: NEXT BIGGEST EVEN INTEGER 2,4,6 12,14,16 -2,0,2 -12,-10,-8 ALGEBRA: X, X+2,X+4

What are Consecutive Integers? Consecutive ODD means: NEXT BIGGEST ODD INTEGER 1,3,5 11,13,15 -3,-1,1 -15,-13,-11 ALGEBRA: X, X+2,X+4

Consecutive Integers

Setting Up A Guess & Check Chart Set up a column for each NUMBER in problem The last column should be for AN EQUATION OR RELATIONSHIP

Make a Guess & Check Chart Find two consecutive integers whose sum is 95. Make a Guess & Check Chart First # Bigger # First # + Bigger #=95 Key Phrase: sum is 95 Think: Add numbers

Find two consecutive integers whose sum is 95. Make a Guess First # Bigger # First # + Bigger #=95 40 41 40+41=81? NO Keep on Guessing………..

Make More Guesses: Need at least 3 Find two consecutive integers whose sum is 95. Make More Guesses: Need at least 3 First # Bigger # First # + Bigger #=95 40 41 40+41=81? NO 45 46 45+46=91? NO 47 48 47+48=95 YES ANSWER: THE TWO NUMBERS ARE 47 AND 48

SOLVING ALGEBRAICALLY USE GUESS & CHECK CHART TO DEFINE VARIABLES AND MAKE EQUATION! DEFINE VARIABLES (X IS FIRST #) MAKE EQUATION SOLVE EQUATION ANSWER QUESTION!

MAKING AN ALGEBRAIC EQUATION Find two consecutive integers whose sum is 95. MAKING AN ALGEBRAIC EQUATION THE FIRST # IS X !!! First # Bigger # First # + Bigger #=95 47 48 47+48=95 YES X X+1 X+X+1=95 X+X+1=95 2X+1=95 2X=94 X=47 ANSWER: THE TWO NUMBERS ARE 47 AND 48! LET X = 1ST INTEGER LET X + 1 = NEXT CONSECUTIVE INTEGER

Find 3 consecutive even integers such that four times the first decreased by the second is 12 more than twice the third. Set up chart !!! Translate words to an Equation Start Guessing! Equation 1st even 2nd even 3rd even

Find 3 consecutive even integers such that four times the first decreased by the second is 12 more than twice the third. Equation 1st even 2nd even 3rd even 4(1st)-2nd=2(3rd)+12 2 4 6 4(2) - 4=2(6) + 12 8-4=12+12 4=24 NO! 10 12 14 4(10)-12=2(14)+12 40-12=28+12 28=40

1st even 2nd even 3rd even 4(1st)-2nd=2(3rd)+12 2 4 6 4(2) - 4=2(6) + 12 8-4=12+12 4=24 NO! 10 12 14 4(10)-12=2(14)+12 40-12=28+12 28=40 20 22 24 4(20)-22=2(24)+12 80-22=48+12 58=60 22 24 26 4(22)-24=2(26)+12 88-24=52+12 64=64

Solving Algebraically 1st even 2nd even 3rd even 4(1st)-2nd=2(3rd)+12 X X+2 X+4 4x-(x+2)=2(x+4)+12 4x-(x+2)=2(x+4)+12 4x-x-2=2x+8+12 3x-2=2x+20 X=22 Let x = 1st even # Let x+2=2nd even # Let x + 4 = 3rd even # The three even numbers are 22,24,and 26

Try One Yourself Find three consecutive even integers whose sum is -12 Remember : When working with negative numbers, the next biggest one is to the right on the number line! -6 -5 -4 -3 -2 -1 0

Find 3 consecutive even integers whose sum is -12. 1st# Even 2nd # 3rd # 1st+2nd+3rd=-12 -8 -6 -4 -8+-6+-4=-18 -2 -6+-4+-2=-12 -4+-2+0=-6 The numbers are -6,-4, and -2.

Find 3 consecutive even integers whose sum is -12. 1st# Even 2nd # 3rd # 1st+2nd+3rd=-12 x x+2 x+4 x+x+2+x+4=-12 Let x = 1st even X + 2=2nd even X+4 = 3rd even x+x+2+x+4=-12 3x+6=-12 3x=-18 x=-6 The numbers are -6,-4, and -2.

Wrapping It Up-Consecutive Integers How do you label your Guess & Check chart? How do you decide which column is x? What is the most important thing to remember when working with negative integers? All numbers and Equation The 1st number The next consecutive number is to the RIGHT on number line!