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

Consecutive Integer Problems

Students will use Guess and Check Chart and Algebra to solve

Consecutive Integer word Problems

Page 2: 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

Page 3: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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

Page 4: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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

Page 5: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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)

Page 6: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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

Page 7: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

• 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

Page 8: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

• Find two consecutive integers whose sum is 95.

40+41=81? NO4140

First # + Bigger #=95Bigger #First #

Make a Guess

Keep on Guessing………..

Page 9: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

• 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

Page 10: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

SOLVING ALGEBRAICALLY

• USE GUESS & CHECK CHART TO DEFINE VARIABLES AND MAKE EQUATION!

• DEFINE VARIABLES (X IS FIRST #)

• MAKE EQUATION

• SOLVE EQUATION

• ANSWER QUESTION!

Page 11: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

• 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!

Page 12: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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

Page 13: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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

Page 14: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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

Page 15: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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

Page 16: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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

Page 17: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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.

Page 18: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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.

Page 19: Consecutive Integer Problems Students will use Guess and Check Chart and Algebra to solve Consecutive Integer word Problems

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!