consecutive integer problems students will use guess and check chart and algebra to solve...
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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
-4,-3,-2
1,2,3
x, x+1, x+2
ConsecutiveNext Biggest
-8,-6,-4
2,4,6
x,x+2,x+4
Consecutive EvenNext Biggest Even
-3,-1,1
1,3,5
x,x+2,x+4
Consecutive OddNext Biggest Odd
Consecutive Integers(Next Biggest)
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
• Find two consecutive integers whose sum is 95.
First # + Bigger #=95Bigger #First #
Key Phrase: sum is 95
Think: Add numbers
Make a Guess & Check Chart
• Find two consecutive integers whose sum is 95.
40+41=81? NO4140
First # + Bigger #=95Bigger #First #
Make a Guess
Keep on Guessing………..
• Find two consecutive integers whose sum is 95.
47+48=95 YES4847
45+46=91? NO4645
40+41=81? NO4140
First # + Bigger #=95Bigger #First #
Make More Guesses: Need at least 3
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!
• Find two consecutive integers whose sum is 95.
X+X+1=95X+1X
47+48=95 YES4847
First # + Bigger #=95Bigger #First #
MAKING AN ALGEBRAIC EQUATIONTHE FIRST # IS X !!!
LET X = 1ST INTEGER
LET X + 1 = NEXT CONSECUTIVE INTEGER
X+X+1=95
2X+1=95
2X=94
X=47
ANSWER:
THE TWO NUMBERS ARE 47 AND 48!
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 !!!
1st even
2nd even
3rd even
Start Guessing!
Translate words to an Equation
Equation
4(1st)−2nd =2(3rd) +12
Find 3 consecutive even integers such that four times the first decreased by the second is
12 more than twice the third.
Equation
4(10)-12=2(14)+12
40-12=28+12
28=40
141210
4(2) - 4=2(6) + 12
8-4=12+12
4=24 NO!
642
4(1st)-2nd=2(3rd)+123rd even
2nd even
1st even
4(22)-24=2(26)+1288-24=52+1264=64
262422
4(20)-22=2(24)+1280-22=48+1258=60
242220
4(10)-12=2(14)+1240-12=28+1228=40
141210
4(2) - 4=2(6) + 128-4=12+124=24 NO!
642
4(1st)-2nd=2(3rd)+123rd even
2nd even
1st even
Solving Algebraically
4x-(x+2)=2(x+4)+12X+4X+2X
4(1st)-2nd=2(3rd)+123rd even
2nd even
1st even
Let x = 1st even #
Let x+2=2nd even #
Let x + 4 = 3rd even #
4x-(x+2)=2(x+4)+12
4x-x-2=2x+8+12
3x-2=2x+20
X=22
The three even numbers are 22,24,and 26
Try One Yourself
Find three consecutive even integers whose sum is -12Remember : 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 #
Even
3rd #
Even
1st+2nd+3rd=-12
-8 -6 -4 -8+-6+-4=-18
-6 -4 -2 -6+-4+-2=-12
-4 -2 0 -4+-2+0=-6
The numbers are -6,-4, and -2.
Find 3 consecutive even integers whose sum is -12.
1st#
Even
2nd #
Even
3rd #
Even
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!