Using Order of Operations & Parentheses

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SWBAT use parentheses in numerical expressions, & evaluate expressions with these symbols.

Big Idea

"Fish around" to find out why using numeric expressions is a good strategy to find total numbers!


5 minutes

I ask students to study a colorful picture of tropical fish (the lesson image). As simple as it sounds, the alluring colors attract students, and pulls their interest into the task. To start the conversation, I ask students:

What different types of fish they see in the tank, how would you describe these fish?

Which type of fish is a majority?

How could you figure out how many of each type of fish there are?

Students work with their table partner to consider the answers to these questions. After rotating and facilitating thinking, I announce to the class some of the teachable moments that I've noticed. This gives students the opportunity to collaborate with each other without high-stakes accountability and fear of being incorrect in front of their classmates. I use cold calling in the next section, but students have had a chance to think about this situation before hand for about 5 minutes.

I ask, "How can you write an expression that represents all the fish in the tank?" (List the numbers for each type of fish and add them.)

I ask students to suppose that three of orange type fish were removed from the tank, "How would that affect the expression?" (There would be three fewer total fish. I could subtract 3 from the number of orange fish.)

I have students look at the striped fish in the picture. The aquarium has decided to double the number of this type of fish in the tank. "What would you do now to determine the new number of this type of fish? number of fish in the aquarium? (I would multiply the "right now" number of fish by 2. Then I would change the old number with the new number in the expression.)

It's my goal here to lead students to see that using numeric expressions is a good strategy to find total numbers.

Guided Practice

35 minutes

Background Knowledge: In 4th grade, students interpreted equations as comparisons, wrote equations to represent comparisons, and multiplied or divided to solve word problems involving comparisons.

It's important for students to understand that grouping symbols affect the value of an expression by changing the order in which the operations are performed. Students have to be able to evaluate numerical expressions that have grouping symbols and write simple numerical expressions that record calculations with numbers. A numerical expression doesn't include variables and has just one possible value.

I have students imagine that they are filling aquariums of different fish. (This works for us because we recently went on a field trip to the beach, to study the Ocean ecosystem and took a small ferry boat.) Small fish are in groups of four. Medium sized fish are in groups of two. Large fish are single. All of the aquariums contain each type of fish and there may be more than one correct answer.

Aquarium A has 20 fish with more medium fish than small fish and more small fish than large fish. Aquarium B has 15 fish with more small fish than medium fish and more medium fish than large fish.

I cold call upon students to show their drawings, and explain their thinking.

Aquarium A: 5 groups of medium fish (10 fish), 2 groups of small fish (8 fish), and 2 large fish (2 fish).

Aquarium B: 2 groups of small fish (8 fish), 3 groups of medium fish (6 fish), and 1 large fish (1 fish).


To further practice, and get into the standard: we use the GP notes 1 to understand Order of Operations and Parentheses.

Independent Practice

10 minutes

Students use MP - Reason abstractly and quantitatively to use properties of operations to interpret expressions. Students work with their table partner as I facilitate and rotate. Students evaluate the following expressions without evaluating them: 

Problem 1:   19- (6 + 6)   and   19 - 6 + 6

Problem 2: A bouquet of flowers contains 4 yellow carnations, 3 red roses, and 5 pink tulips. Which expression represents how many flowers are in 10 bouquets.

a)    10 x (4 + 3 + 5)                           b)    10 x 4 + 3 + 5

c)    (10 x 4) + 3 + 5                           d)     4 + 3 + 5 x 10


I provide both a computation problem and a word problem to expose students to both types of questions in respect to the same objective. This way, I can see why students may get one or both questions wrong.


15 minutes

To close out this lesson, I have students analyze a sample student's answer for the sample problem we went through in the Guided Practice. I do this because I want my students to see a non-example. To explain it well means having to understand something that much better. By switching the way I have students do math problems it increases participation and decreases potential behavioral issues.

"Zac wrote the expression 10 - 3 + 5 to represent the problem. Explain why the expression he wrote is not correct."

In Zac's expression, the number of non-fiction books is subtracted from the total and then the number of fiction books is added. This gives the incorrect answer of 12. The correct expression, 10 - (3 + 5), uses parentheses to show that the numbers of nonfiction books and fiction books are added first, and then the sum is subtracted from the total.

This is quite an easy problem, but we are reviewing, doing test-prep, and some of my students still need me to break this down this far before adding more complicated tasks.