# 4th Grade - Beginning Algebra

 Grade Level: 4th Skill: Algebra Topic: Beginning Algebra Goal: Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (i.e. demonstrate an understanding and the use of the concept of a variable). Skill Description: Introduction to algebra: Solve and develop mathematical problems that use variables (letters, symbols and empty boxes) to represent unknown amounts in number sentences. (i.e. v x 7 = 28 ; therefore v = 4)

## Building Blocks/Prerequisites

### Sample Problems

(1)

Which expression represents the sentence below:

24 candles came in the box, but some candles are missing.

(a) 24 + c

(b) 24 – c

(c) 24c

(b)

(2)

Find the value of the equation:

x = 12

96 ÷ x = □

(8)

(3)

Find the value of n:

5 x n = 650

(n=130)

(4)

Find a pattern and write the equation:

 Input Output p r 18 2 27 3 36 4 45 5

What is the operation pattern ____________

Write the equation _____________

(Divide by 9; r = p ÷ 9)

(5)

Use the operation and equation to fill in the input/output table:

Multiply by 7.

a x 7 = b

 Input a Output b

(a =1 b=7; a =2 b= 14; a = 3 b= 2; a= 4 b= 28)

### 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 (2 x 3 = 6).

Expression- A part of a number sentence that has numbers and operation signs, but does not have an equal sign (3 + c)

Operation- Add, subtract, multiply or divide (+, - , x, ÷)

(2)

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

• Look at the pattern from a to b

• Is the number increasing or decreasing

• If number is increasing (a + □ = b) or (a x □ = b)

• If number is decreasing (a -□ = b) or (a ÷ □ = b)

• 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.

 Input a 1 2 3 4 Output b 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 input/output tables in order to write an equation.

You can also use a multiplication table for a resource if the child is unable to find the pattern independently.

(5)

To help children understand what is being asked of them in order to solve the problem for writing expressions or equations, play a game of categorizing the two. The child will have paper strips with equations and expressions and have them figure out on a board with a T-chart where to place the strips.

### Extra Help Problems

(1)

Write an expression for:

_____________________

(b + 9)

(2)

Write an expression for:

40 blocks divided by the number of babies at the day care.

______________________

(40 ÷ b)

(3)

Write an expression for:

3 uniforms for each basketball player.

_______________________

(3b)

(4)

Write an equation for:

There are 17 muffins in the container. 8 muffins are blueberry, the rest are banana nut muffins.

____________________

(17 = 8 + m)

(5)

Write an equation for:

12 seats in a number of rows in the auditorium are 132 seats.

_________________

(132 = 12 x r)

(6)

Write an equation for:

48 pencils divided equally to 12 students in the classroom.

_________________

(48 ÷ 12 = p)

(7)

If n = 12, what is the value of :

96 ÷ n

(n = 8)

(8)

If x = 7, what is the value of:

9x

(9 x 7 = 63)

(9)

Find the value of x:

140 ÷ x = 10

(x =14)

(10)

Find the value of x:

17x = 51

(x = 3)

(11)

Find the value of y:

19 x 12 = y

(y= 228)

(12)

Find a pattern and write the equation:

 Input Output a b 21 3 28 4 35 5 42 6

What is the operation pattern ____________

Write the equation _____________

(Divide by 7; b = a ÷ 7)

(13)

Find a pattern and write the equation:

 Input Output s t 4 48 6 72 8 96 10 120

What is the operation pattern ____________

Write the equation _____________

(Multiply by 12; t = 12s)

(14)

Find a pattern and write the equation:

 Input Output p r 6 48 7 56 8 64 9 72

What is the operation pattern ____________

Write the equation _____________

(Multiply by 8; r = 8p)

(15)

Find a pattern and write the equation:

 Input a 81 72 63 54 Output b 9 8 7 6

What is the operation pattern ____________

Write the equation _____________

(Divide by 9; b = a ÷ 9)

(16)

Find a pattern and write the equation:

 Input c 9 10 11 12 Output d 99 110 121 132

What is the operation pattern ____________

Write the equation _____________

(Multiply by 11; d = c x 11)

(17)

Find a pattern and write the equation:

 Input r 18 24 30 42 Output s 3 4 5 7

What is the operation pattern ____________

Write the equation _____________

(Divide by 6; s = r ÷ 6)

(18)

Find a pattern and write the equation:

 Input m 14 16 18 20 Output n 20 22 24 26

What is the operation pattern ____________

Write the equation _____________

(Add by 6; n = m + 6)

(19)

Use the operation and equation to fill in the input/output table:

Multiply by 6.

p x 6 = r

 Input Output p r

(p = 1 r= 6; p=1 r =12; p = 3 r= 18; p =4 r =24)

(20)

Use the operation and equation to fill in the input/output table:

Multiply by 8.

s x 8 = t

 Input Output s t

( s= 2 t = 16; s= 3 t= 24;s= 4 t=32)

(21)

Use the operation and equation to fill in the input/output table:

Multiply by 11.

x x 11 = y

 Input Output x y

(x=1 y =11; x = 2 y =22; x = 3 y = 33; x =4 y =44)

(22)

Use the operation and equation to fill in the input/output table:

Divide by 3.

a ÷ 3 = b

 Input a Output b

(a = 3 b =1; a =6 b =2; a= 9 b= 3; a= 12 b =4)

(23)

Use the operation and equation to fill in the input/output table:

Divide by 5.

w ÷5 = v

 Input w Output v

(w =5 v =1; w= 10 v= 2; w= 15 v =3; w =20 v=4)

(24)

Use the operation and equation to fill in the input/output table:

Multiply by 12.

a x 12 = b

 Input a Output b

(a= 1 b=12; a=2 b=24; a =3 b=36; a=4 b=48)

(25)

Use the operation and equation to fill in the input/output table:

Divide by 2.

l ÷ 2 = n

 Input l Output n

(l= 2 n=1; l=4 n=2; l=6 n=3; l=8 n=4)