Expressions and Equations: Tips and Tricks

Students may need help differentiating between expressions and equations and simplifying expressions.

• To help students better understand the differences between expressions and equations, write several expressions and equations on the board in word form and in standard form.

5 + 0 = 5     6 x a     Three times three is nine.

Twenty-one plus twelve   n − 6 = 18

y = x + 3     0 + 0

Have students label each as an expression or an equation. Discuss with students the differences they see between an expression and an equation. Make sure that students understand that an equation contains an equals sign, and an expression does not.

• It may be helpful to relate expressions and equations to their counterparts in language: phrases and sentences.
• An expression is like a phrase. A phrase lacks certain words that, if added to it, would make it a complete sentence; an expression also lacks something—an equals sign.
• An equation is like a sentence. Both are complete statements. In fact, equations are often called number sentences in the primary grades. Equations, like sentences, need certain components in order to be complete.
• Number cards can be wonderful tools when teaching equations. Have students help you prepare a set of 50 cards. Write a number from 0 to 9 on each card. Pass out 10 cards to each of 4 players. The first player lays down two cards and then declares addition or subtraction. The next player must lay down one or more cards that equal the expression. For example, if the first player lays down 6 and 8 and declares addition, the next player can lay down 9 and 5, because 9 and 5 equals 14, or 3, 4, and 7, because 3 + 4 + 7 equals 14. If a player cannot lay down any cards, the player must take a card from the deck, and the next player takes a turn.
• If possible, provide students with an actual double pan balance from a science lab to reinforce the concept of an equation. Unit cubes, counting tiles, or other manipulatives (coins, blocks, or similarly sized and weighted objects) can be added or subtracted to both pans to produce a balanced equation.
• Have students work in groups of two pairs. One student places a number of tiles in an envelope labeled x without disclosing the amount to the others and places it on one pan. His or her partner places some tiles in both pans until the pan balances and then records the resulting equation—for example, x + 3 = 7. The other pair is challenged to solve the equation by subtracting tiles from both pans to find x and recording the result. Students check the result by opening the envelope.
• Project the following word phrases or write them on the board and have students add number values to each to create an algebraic expression. Students can exchange their expressions with each other and simplify them. Allow students to create different versions of these phrases.

what is left
plus a bonus
coupon off
original price
how much with (or without)
decreased by
combine
worth
least change
how much more
less than
two years older
longer than
the sum (or difference)
4 pounds heavier than
price plus tax

• The sports pages of most newspapers provide an abundant supply of scores that students can use to create equations and expressions. Students can pose questions such as “How many runs did the National League and the American League score in one day?” Students can work in small groups to generate sentences such as “NL Runs + AL Runs = Total runs per day.” Have students replace one of the values in their sentence with a variable and challenge another group to solve the resulting equation.
• Some students struggle with inverse operations. Here's a simple flow chart often used in England that clearly defines undoing.