Consecutive Integer Problems

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Consecutive Integer Problems

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

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What are Consecutive Integers?

• Consecutive means NEXT BIGGEST

2,3,4 5,6,7 -2,-1,0
-12,-11,-10,
ALGEBRA X, X1,X2
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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, X2,X4
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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, X2,X4
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Consecutive Integers
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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

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• Find two consecutive integers whose sum is 95.

Make a Guess Check Chart
First Bigger 95
Bigger
First
Key Phrase sum is 95 Think Add numbers
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• Find two consecutive integers whose sum is 95.

Make a Guess
First Bigger 95
Bigger
First
404181? NO
41
40
Keep on Guessing..
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• Find two consecutive integers whose sum is 95.

Make More Guesses Need at least 3
First Bigger 95
Bigger
First
404181? NO
41
40
454691? NO
46
45
474895 YES
48
47
ANSWER THE TWO NUMBERS ARE 47 AND 48
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SOLVING ALGEBRAICALLY

• USE GUESS CHECK CHART TO DEFINE VARIABLES AND
  MAKE EQUATION!
• DEFINE VARIABLES (X IS FIRST )
• MAKE EQUATION
• SOLVE EQUATION
• ANSWER QUESTION!

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• Find two consecutive integers whose sum is 95.

MAKING AN ALGEBRAIC EQUATION
THE FIRST IS X !!!
First Bigger 95
Bigger
First
474895 YES
48
47
XX195
X1
X
XX195 2X195 2X94 X47
ANSWER THE TWO NUMBERS ARE 47 AND 48!
LET X 1ST INTEGER LET X 1 NEXT CONSECUTIVE
INTEGER
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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



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Find 3 consecutive even integers such that four
times the first decreased by the second is 12
more than twice the third.
Equation
4(1st)-2nd2(3rd)12
3rd even
2nd even
1st even
4(2) - 42(6) 12 8-41212 424 NO!
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4
2
4(10)-122(14)12 40-122812 2840
14
12
10
14
4(1st)-2nd2(3rd)12
3rd even
2nd even
1st even
4(2) - 42(6) 12 8-41212 424 NO!
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4
2
4(10)-122(14)12 40-122812 2840
14
12
10
4(20)-222(24)12 80-224812 5860
24
22
20
4(22)-242(26)12 88-245212 6464
26
24
22
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Solving Algebraically
4(1st)-2nd2(3rd)12
3rd even
2nd even
1st even
4x-(x2)2(x4)12
X4
X2
X
4x-(x2)2(x4)12 4x-x-22x812 3x-22x20 X22
Let x 1st even Let x22nd even Let x 4
3rd even
The three even numbers are 22,24,and 26
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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
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Find 3 consecutive even integers whose sum is -12.
1st Even 2nd Even 3rd Even 1st2nd3rd-12
-8 -6 -4 -8-6-4-18
-6 -4 -2 -6-4-2-12
-4 -2 0 -4-20-6
The numbers are -6,-4, and -2.
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Find 3 consecutive even integers whose sum is -12.
1st Even 2nd Even 3rd Even 1st2nd3rd-12
x x2 x4 xx2x4-12
Let x 1st even X 22nd even X4 3rd even
xx2x4-12 3x6-12 3x-18 x-6
The numbers are -6,-4, and -2.
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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!