4th Grade - Equations With Variables

 
     
 
     
 
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4th
Algebra
Equations with Variables
Understand than an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given.
Solve for the value of the variable y when the value of the variable x is given (i.e. x = 4; solve y = 3x + 5. Input the value of x: y = (3 x 4) + 5. Therefore, y = 17.
 

Sample Problems

(1)

Find the value of y, when x = 9

y = 4x + 23


(y =59)

(2)

Use the equation to complete the function table:

y = 8x – 5


Input

x

1

2

3

4

Output

y






(y = 3; 11; 19; 27)

(3)

Complete the function table and make the (x, y) into ordered pairs:

y = 3x – 2

Input

x

1

2

3

4

Output

y






______ ______ ______ ______


[(1,1) (2,4) (3,7) (4,10)]

(4)

Which ordered pair is not related to the equation below:

y = 6x + 8


  1. (3, 26)

  2. (4, 31)

  3. (5, 38)

  4. (7,50)


(b)

(5)

Which equation relates to the function table below:


Input

x

1

2

3

4

Output

y

1

3

5

7


  1. y = x + 3

  2. y = 2x + 1

  3. y = 2x -1


(c)

Learning Tips

(1)

Math Vocabulary


Variable- a letter or symbol that stands for any number


Equation- a number sentence which states that two amounts are equal

Ordered Pairs- A pair of numbers used to locate a point on a coordinate grid. The first number tells how far to move horizontally (x) and the second number tells how far to move vertically (y). (x, y)


Function table- a table that matches each input value with an output value. The output values are determined by the function (which is the equation).



(2)

How to find a rule for the input/output table or function table:

  • Look at the pattern from x to y

  • Is the number increasing or decreasing

  • If number is increasing (x + □ = y) or (x times □ = y)

  • If number is decreasing (x -□ = y) or (x ÷ □ = y)

  • Test the rule: by plugging in the number you think is making the pattern, to see if it works for all numbers in the table.

  • Write the rule in words (i.e. Multiply by 2)


Input

x

1

2

3

4

Output

y

2

4

6

8

(3)

Explain variable by practicing with missing numbers, the missing number (box) is replaced with a letter.


Prior to fourth grade, children would have encountered the skill of finding the missing number in a math problem (i.e. 4 + □ = 7). Explain that the blank is being replaced by a letter. They are still trying to find the missing number for the letter.

(4)

Practice skip counting, so child can find the patterns in the function tables in order to determine the equation.


Practice math facts in order to for the child to complete the function tables with ease.

(5)

How to find ordered pairs:

Ordered Pairs (x, y)—later graphed on the coordinate grid with an x-axis and y-axis.

The child will have an equation that states the value of x.

The child will use the value of x in order to find the value of y.

For example: x = 2. Solve the equation to find y.


y = 3x-1; So, y = (3 x 2) -1


y = 5


The ordered pairs are (2, 5), which is (x, y).


Extra Help Problems

(1)

Find the value of y, when x = 4

y = 2x + 8


(y = 16)

(2)

Find the value of y, when x = 6

y = (18 ÷ x) + 12


(y = 15)

(3)

Find the value of y, when x = 15

y = 3x – 11


(y = 34)

(4)

Find the value of y, when x = 3

y = (x + 12) ÷ 5


(y = 3)

(5)

Find the value of y, when x = 10

y = (x – 4) x 9


(y = 54)

(6)

Use the equation to complete the function table:

y = 2x + 7


Input

x

1

2

3

4

Output

y






(y = 9; 11; 13; 15)

(7)

Use the equation to complete the function table:

y = (x + 5) x 2


Input

x

0

2

4

6

Output

y






(y = 10; 14;18; 22)

(8)

Use the equation to complete the function table:

y = (x ÷ 3) + 3


Input

x

3

9

12

15

Output

y






(y = 4; 6; 7; 8)

(9)

Use the equation to complete the function table:

y = (24 ÷8) + x


Input

x

7

8

9

10

Output

y






(y= 10; 11; 12; 13)

(10)

Use the equation to complete the function table:

y = 7x – 1


Input

x

1

2

3

4

Output

y






(y = 6; 13; 20; 27)

(11)

Use the equation to complete the function table:

y = (x +4) x 5


Input

x

0

2

6

8

Output

y






(y = 20; 30; 50; 60)

(12)

Complete the function table and make the (x, y) into ordered pairs:

y = 8x – 8

Input

x

1

2

3

4

Output

y






______ ______ ______ ______


[(1, 0) (2,8) (3,16) (4,24)]

(13)

Complete the function table and make the (x, y) into ordered pairs:

y = x - 12

Input

x

16

17

18

19

Output

y






______ ______ ______ ______


[(16,4) (17,5) (18,6) (19,7)]

(14)

Complete the function table and make the (x, y) into ordered pairs:

y = (12 ÷ x) + 2

Input

x

2

3

4

6

Output

y






______ ______ ______ ______


[(2,8) (3,6) (4,5) (6,4)]

(15)

Complete the function table and make the (x, y) into ordered pairs:

y = 3x + 5

Input

x

1

2

3

4

Output

y






______ ______ ______ ______


[(1,8) (2,11) (3,14) (4,17)]

(16)

Which ordered pair is not related to the equation below:

y = 4x + 3


  1. (2, 11)

  2. (3, 15)

  3. (4, 19)

  4. (5, 22)


(d)

(17)

Which ordered pair is not related to the equation below:

y = 5x – 2


  1. (1, 3)

  2. (2, 9)

  3. (3,13)

  4. (4,18)


(b)

(18)

Which ordered pair is not related to the equation below:

y = x – 1 + 4


(a) (6, 9)

(b) (8, 11)

(c) (10, 12)

(d) (12, 15)


(c)

(19)

Which ordered pair is not related to the equation below:

y = 7x + 2

(a) (1, 9)

(b) (3, 23)

(c) (5, 37)

(d) (7, 53)


(d)

(20)

Which ordered pair is not related to the equation below:

y = (x ÷ 4) + 3


  1. (4, 3)

  2. (8, 5)

  3. (12, 6)

  4. (16, 7)


(a)

(21)

Which equation relates to the function table below:


Input

x

2

4

6

8

Output

y

11

15

19

23


  1. y = 3x + 7

  2. y = 2x + 7

  3. y = (7 + x) – 1


(b)

(22)

Which equation relates to the function table below:


Input

x

1

2

3

4

Output

y

1

7

13

19


  1. y = 5x –1

  2. y = 3x + 2

  3. y = 6x - 5


(c)

(23)

Which equation relates to the function table below:


Input

x

5

6

7

8

Output

y

10

11

12

13


(a) y = (x + 2) + 3

(b) y = (x – 2) + 3

(c) y = ( x + 3) – 2


(a)

(24)

Which equation relates to the function table below:


Input

x

2

3

4

6

Output

y

20

14

11

8


  1. (36 ÷ x) + 2

  2. (24 ÷ x) + 2

(c) (18 ÷ x) + 2


(a)

(25)

Which equation relates to the function table below:


Input

x

3

5

7

9

Output

y

5

7

9

11


  1. y = x + 3

  2. y = 2x + 3

(c) y = (x -1) + 3


(c)

 

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