Teaching and Learning: Numerical Expression

It's great to start the school year with a challenging, engaging math lesson. Children love to come to school at the start of the year and learn something new. This sets the stage for a vigorous, engaging year ahead.

Teaching numerical expression lends itself to engagement and provides students with a terrific skill to use as they learn, practice, and apply mathematical operations with numbers simple and complex.

Introduction: What Do These Expressions Equal?
Evaluate one or more of the expressions below in any order by hand or with a calculator. Giving students the chance to use a calculator takes away the pressure to remember facts and to calculate correctly. This frees up all students to reach for higher level learning in this lesson. 

8 + 6 X 5 - 1/2 + (8-3)

99 - 1 + 2 X 3

Let students play with it. Some will finish quickly, others will take a bit of time, and some may not know where to begin. Give the students about 10 minutes, then ask for children to come up to the board to explain their thinking about each expression.

Teach Order of Operations

Show Flocabulary's PEMDAS movie. While some mathematicians are not in favor of PEMDAS, I still think it's a good tool for early learning with regard to Order of Operations. As students work becomes more advanced, they quickly understand where PEMDAS doesn't exactly fit, hence I still believe it's a good starting point. 

Also introduce this graphic shared by a former student:

Study and Practice
Net talk with students about what they can do to remember, study, and apply the Order of Operations. List their ideas. Then let them work with classmates to do all or some of the following activities plus any good ideas they've come up with that you want to add to the list:

• Create a mnemonic, poem, picture, or mini poster that will help you remember the Order of Operations.
• Watch the PEMDAS rap over again, then make up one of your own.
• Make up your own expressions and evaluate them. Check with the teacher.
• Write 5 different expressions and 5 different equations that equal 50 (remember expressions do not have equal signs while equations do). Use at least two different operations in each expression. Make sure you use every operation at least once. Use parentheses, brackets, and/or braces in at least two expressions.
• Use exponents in at least two expressions. 

More Practice

Study the chart below. Then determine where you might add parentheses, brackets, and/or braces to simplify the challenging expression and puzzle below. Then solve the puzzle and expression.

ASSESS

After a day or two of practice and some Khan Academy review and study related to the topic too, it's a good time to assess students' skills. This is one assessment that provides the teacher with a good understanding of what students learned and still need to know.

Related Grade Five Standards