Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (51 page)

Section 3

Standards and Activities for Grade 5

Operations and Algebraic Thinking: 5.OA.1

“Write and interpret numerical expressions.”

1. “Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.”

Background

The order of operations is a set of rules for evaluating expressions that contain multiple operations. It states that operations within grouping symbols must be completed before any other operations. There are several types of grouping symbols, the most common being parentheses. When evaluating expressions, operations within any grouping symbols must be completed first, followed by multiplication
or
division, which must be completed in order from left to right, and then addition
or
subtraction, which must be completed in order from left to right. Multiplication and division are on the same level, and addition and subtraction are on the same level; thus, for example, if a division symbol is to the left of a multiplication symbol, divide first.

Activity: Evaluating Expressions

Students will receive two expressions written on the same piece of paper. One expression has grouping symbols and the other requires grouping symbols. Working individually, students will evaluate the expression that has grouping symbols. They will then find another student who has the same answer. Now working in pairs, students will insert the required grouping symbols in their second expressions.

Materials

One copy of each of the reproducibles, “Expressions for Evaluation, I,” “Expressions for Evaluation, II,” and “Expressions for Evaluation, III”; scissors or paper cutter for the teacher.

Preparation

Make one copy of each reproducible. Cut out the 30 rows of expressions, 1, 2, 3, 4, and so on, contained on the reproducibles. Do not separate the expressions in each row.

Procedure

1.
Explain to your students that the order of operations is a set of rules used for evaluating expressions. Review the order of operations and provide a few examples, such as the following:

• answer: 16
  
• answer: 6
  
• answer: 10
  

2.
Hand out the expressions to your students and explain the activity. Each student will receive one slip of paper containing two expressions. The first expression has grouping symbols in the form of parentheses. The second expression does not. Students will work individually to simplify the first expression. Remind them to use the order of operations. (
Note:
If your class has an even number of students, but fewer than 30, you may eliminate some sets of expressions. In this case, be sure to eliminate pairs of expressions that are equal, for example, number 15 and number 17, both of which have answers of 19. If you have an odd number of students in class, you may ask a volunteer to work with two sets of cards. This student would then work in a group of three rather than a pair when inserting grouping symbols in the second expression.)

3.
Explain that after all students have an answer for their first expression, they will find another student in class who has the same answer. Students are to then work together on their second expressions. They must insert grouping symbols so that the second expression equals the value of the first expression. For example, if a first expression equaled 5, they must insert grouping symbols so that the second expression of that set equals 5.

Closure

Discuss the order of operations and strategies that students used to insert grouping symbols. Have students write a reflection to the following question: What would happen if there was no order of operations? Discuss their ideas.

Answers

Expression pairs and their answers follow. 1 and
2 and
3 and
4 and
5 and
6 and
7 and
8 and
9 and
10 and
11 and
12 and
13 and
14 and
15 and