6th Grade - Write Expressions Using Variables

Write Expressions Using Variables
Write and evaluate an algebraic expression for a given situation, using up to three variables.
Write algebraic expressions for sentences or word problems. Use rules for: subtraction, multiplication and division of positive, negative integers, fractions, and decimals to evaluate (solve) expressions with as many as three variables.

Sample Problems


If b = 2 evaluate:




Evaluate the expression for a = -2 and b = 6

4a + b



Evaluate the expression for a = 10, b = 5, c = -1

a/b + c – 2 + a



Rewrite the sentence as an algebraic expression, using n as some number.

8 decreased by a number n

(8 – n)


Amber bought DVDs for $18 each. Write an expression to show the total cost of d, the DVDs.


Learning Tips


Children often confuse expressions and equations. It is important they understand that they are different concepts and are solved very differently. Remind your child that an equation always has an equal sign because it is comparing two equal expressions. Expressions, however, are mathematical phrases. Algebraic expressions use a variable to represent a number. Both types of math problems are solved very differently. Equations can be solved using inverse (opposite) operations. However, expressions can only be solved by replacing the variable(s) with the given numbers and doing the calculations that result. Below are some examples of each.


4b + 2, for b = 5 or a + 2b – c, for a = 3, b = 5, c = -2


4b = 20 or 5 + c = 26


Use key words to determine the operation when converting a sentence or word problem into an algebraic expression. Here is a list of some of the words that may be used to determine which operation to use.

Addition: added to, more than, increased

Subtraction: decreased by, less than, subtracted from, taken away

Multiplication: times, multiplied by, product of, times as many

Division: quotient of, divided by


In order to be successful in writing algebraic expressions from word form, you child will need to use semantics. In other words, he/she needs to think of the words in a real-world situation to make sense of how they are related. This is especially true for subtraction and division. Though the variable and numbers can switch places to get he same result for addition and multiplication problems, this is untrue for subtraction problems. For example, 5 -3 = 2, but 3 – 5 = -2. For this reason, the placement of the variable in a subtraction or division problem is important. While working with the sentence “10 less than a number x”, many children will write 10 – x. This is incorrect. In this sentence, 10 is being taken away from x and the correct expression is x – 10. However, if the sentence say, “9 decreased by a number t” the problem would be written 9 – t because t is decreasing or taking away from the 9. For division expressions such as, “23 divided by a number z”, the expression would be written 23 r. Relitively, “the quotient m and 17”, would be p 17.


For a visual and kinesthetic approach to solving equations use sticky notes and a white board or paper. Write out an expression, such as 120 + t, for t = 5. On a small sticky note write 5. Now, have your child place the sticky note right on top of the t in the original problem. After doing this he/she will see a numerical expression: 120 – 5. Repeating this activity several times will alleviate any anxieties caused by seeing numbers mixed with letters. It allows children to see that they’re still working with numbers and simply need to substitute them into the problem.


Many expressions have more than one operation. This may overwhelm some children. If this is the case for your child, you can have him/her cover up the part of the problem they’re not working on with either a finger or sticky note. When working on paper, he/she may use different colors of ink on the different parts of the problem. Here’s a sample of this technique. Solve the expression, for a = 4 and b = 3, ab + b – 2.

a x b + b – 2 Rewrite the expression showing the multiplication sign.

4 x 3 + 3 – 2 Rewrite the expression, substituting in numerical value.

4 x 3 + 3 – 2 Write the part being solved & its answer in a different 12 + 3 – 2 color. Then rewrite the remainder of problem.

12 + 3 – 2 Rewrite the next part of the problem in another color.

15 – 2 = 13 Solve the rest of the problem.


When solving expressions with integers, fractions or decimals, always remember to be careful follow the rules to solve such problems. For example, if solving the expression t – 4.5 for t = 52.1, you’ll need to remember that you must line up the decimal point when subtracting decimals. When solving an expression like, c + ¼ for c = ½, you’ll need to recall rules for adding fractions and make the terms like. Finally, when solving problems involving integers, you’ll need to use the appropriate steps to make sure you use the correct operation and sign. For instance, if solving, y – 6, for y = -2, you’ll need to change the problem to -2 + -6 and then follow rules to solve same signs addition problems. Children may need a review of these math concepts before continuing on.


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