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

2. 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

3. 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

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

5. Consecutive Integers

6. 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

7. 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

8. 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………..

9. 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= YES
ANSWER: THE TWO NUMBERS ARE 47 AND 48

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

11. 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= 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

12. 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

13. 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

14. 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

15. 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

16. 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!

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

18. 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.

19. 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!