5th Grade - Using Variables In Algebra

 
     
 
     
 
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5th
Algebra
Using Variables in Algebra
Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.
The ability to define a variable (a letter or symbol used to represent a number) The ability to replace a variable with a number and perform the given operation. The ability to write an expression that would lead to correctly solving the problem.
 

Sample Problems

(1)

Directions: Write an equation, solve and write what the variable represents.

Sam had 10 pennies. He gave some away and now has 4. How many did Sam give away?

( 10 – p = 4 p stands for pennies p=6)


(2)

Directions: Write an equation, solve and write what the variable represents.


Tim had 17 pencils. He bought some more at the store. Now he has 24 pencils.

( 17+p=24 p=7)

(3)

Solve for n.

23 + n= 41

( n=18)

(4)

Which of the numbers 5, 6, or 7 is the solution of the equation?

49/n=7 n= x

( n = 7)


(5)

Evaluate the expression for each value of n.

216/n n= 3, 4, 9

( n = 72, 54 , 24)


Learning Tips

(1)

Math Vocabulary:

Variable- a letter or symbol that stands for a number

Equation- an algebraic or numerical sentence that shows two quantities are equal.

Expression- combines numbers or variables with operations, but has no equal sign.


(2)

Have your child practice understanding what is meant by a variable. For example you can ask your child to give certain objects around the home a variable. “What letter can we use to represent the table if we were making up a word problem?” Your child will most likely say t because table starts with the letter t. If your child says a different letter, that is fine too. Just inform your child that a variable can be any lower case letter. Explain that the most common letters used as variables are x and n.

Give them many opportunities to fully grasp the idea of a variable. Without this knowledge your child will have a very difficult time with this standard.

(3)

Have your child review key words that determine the operation to be used for word problems. Once your child knows these key words, they will have a much easier time solving all equations and word problems.

Addition

increased by
more than
combined, together
total of
sum
added to

Subtraction

decreased by
minus, less
difference between/of
less than, fewer than

Multiplication

of
times, multiplied by
product of
increased/decreased by a
  factor of (this type can
  involve both addition or
  subtraction
and
  multiplication!)

Division

per, a
out of
ratio of, quotient of
percent (divide by 100)

Equals

is, are, was, were, will be
gives, yields
sold for

(4)

Make sure your child understands what it means to replace the variable with a given number. To help your child better understand this concept use cookies to represent the given equation. (Actually use cookies to “act out” this problem.) If you have four cookies, then you have 4 c. Some children are visual and/or kinesthetic learners so this small act will make everything connect for them.

When this concept is understood, they should be able to evaluate the following, if n = 2 17-n ( 17 – 2 =15)



(5)

When your child is having difficulties with writing expressions or equations remind them to use variables for numbers they do not know.

For example, Peter had 10 shirts. After his birthday party, he had 16 shirts. How many shirts did he receive for his birthday?

Shirts he has plus shirts received = total shirts

10 shirts + shirts received = total

10 + n = 16 n=6

10 + 6 = 16



Extra Help Problems

(1)

Directions: Write an equation and explain what the variable represents.


Erica had 24 crayons. After she put some on the table, she had 12 left in the box. How many crayons did she put on the table?

(24 – n = 12 n=crayons on table n=12)

(2)

Directions: Write an equation, solve and write what the variable represents.


Carlos had some cars. After Juan gave him 5 new pencils, he had 12. How many pencils did Carlos have to start with?

( n+5=12 n=pencils to start with n=7)

(3)

Directions: Write an equation, solve and write what the variable represents.


Joey made 7 paper airplanes. There were 22 students in the class. How many more planes does he need to make so that all his classmates can receive a plane?

( 7 + n = 22 n =planes needed n=15)

(4)

Directions: Write an equation, solve and write what the variable represents.


Stacey loves chocolate chip cookies. Her mother took a sheet of 12 cookies out of the oven. Stacey ate some. Now there are 7 left. How many did she eat?

( 12-n=7 n= the number she ate n=5 )



(5)

Directions: Write an equation, solve and write what the variable represents.


Stephanie had spent $32 for a new pair of pants. She had $14 left. How much did she have originally? ( n –$ 32 = $14 n=the original amount n= $46)


(6)

Directions: Write an equation, solve and write what the variable represents.


John had some oranges. He gave 4 to Nicole and 9 to James. Now he has 27 oranges. ( n-3-9=27 n=number of original oranges n=40


(7)

Directions: Write an equation, solve and write what the variable represents.


Some girls came to the practice. Then 12 more came to the second practice. There were 15 girls on the team.

( n+12=15 n=number of girls at the first practice n=3)



(8)

Directions: Write an equation, solve and write what the variable represents.


Don had 5 goldfish, and his friend gave him some more. Now Don has 12 goldfish. How many did his friend give him?

(5 + n = 12 n= fish given n=7)

(9)

Directions: Write an equation, solve and write what the variable represents.


A store had 93 paint brushes for sale. The store sold some on Monday and had 50 left. How many did the store sell?

( 93-n=50 n=brushes sold Monday n=43)

(10)

Directions: Write an equation, solve and write what the variable represents.


Rebecca gathered 18 pinecones. On the way home she dropped some. There are 7 pinecones in the basket.

( 18-n=7 n=the number of dropped pinecones n=11)

(11)

Solve for n.


9+n=19 (n=10)


(12)

Solve for n.


n-12=40 ( n=52)

(13)

Solve for n.


n+6=6 (n=0)


(14)

Solve for n.

81-n=60 (n=21)



(15)

Solve for n.

87-20 = n+7 ( n=60)

(16)

Which of the numbers 6, 8, or 11 is the solution of the equation?

9+n=17 (n=8)

(17)

Which of the numbers 6, 8 or11 is the solution of the equation?

n-9=2 (n=11)

(18)

Which of the numbers 6, 8, or 11 is the solution of the equation?

n+7=13 (n=6)

(19)

Which of the numbers 6, 8 or11 is the solution of the equation?

11-n=3 (n=8)

(20)

Which of the numbers 6, 8 or 11 is the solution of the equation?

27-n=16 (n=11)

(21)

Evaluate the expression for each value of n.


17*n n= 2,5,6

(n= 34,85,102)


216/n n= 3, 4, 9

( n = 72, 54 , 24)


(22)

Evaluate the expression for each value of n.

n*56 n=3,6,9

(n=168,336,504)

(23)

Evaluate the expression for each value of n.

n/3 n=27,33,36

(n=9,11,12)

(24)

Evaluate the expression for each value of n.

26-n n= 12,9,7

(n= 14,17,19)

(25)

Evaluate the expression for each value of n.

7 +(2 +n) n=13,21,32

(n=22, 30,41)


 

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