Using More than One Set of Grouping Symbols

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

Big Idea

Learn how important grouping symbols are!


5 minutes

My students think that they know everything about me; and it's true that they know a lot. I share a lot about my personal life (though not too much of course) in order to maintain a level of mutual respect and a sense of community. That being said, to pull my students into this lesson, I use this anchor chart to remind them about the importance of equations, and at the same time give them some "trivia". My students love when I do "trivia", so I try to incorporate it into my lessons as much as possible.

Guided Practice

20 minutes

Ms. Field's favorite bakery in town makes 634 loaves of French bread daily. They sell 350 loaves to Food Lion and 275 loaves to the nearby restaurants in Kenansville. They dontate the rest to a local homeless shelter.

Write & evaluate an expression to find the number of loaves the bakery donates over a 5-day week.

I use the GP1 Notes (Guided Practice) to guide students through understanding using more than one set of grouping symbols.

If students are having trouble, they can work with their table partner, or act out the problem. Explain to students that the expression within the innermost set of grouping symbols (the parentheses) is evaluated first. Then, the resulting expression in the outermost set of grouping symbols (the brackets) is evaluated.

Now, we work on GP2 Notes (Guided Practice) to show what we know about grouping symbols and evaluating expressions. I remind students that if an expression contains more than 1 set of grouping symbols, the expression in the innermost set is evaluated first. To assist visual learners, I use an array of colors to show the transition from one step to another. Ex: In the first step, I write the expression with parentheses, including the parentheses, (5/6 + 2/6), in orange. Then in the next step, write its value 7/6 in orange to show that it has replaced the expression in the parentheses.

As an extension, you can ask students why the fractions 7/6, 28/6, and 30/6 weren't simplified in Steps 2, 3, and 4. (It wouldn't be wrong to do this, but waiting until the last step to simplify makes things a bit easier to compute.)

Independent Practice

20 minutes

Students, in a think-pair-share, use MP7 - Look for and make use of structure. In this task, students evaluate the structures of similar expressions and use this information to determine equivalent expressions.

Normally in a T-P-S, I have students work with one table partner. In this task, since there are four answer choices, I assign four students to each group. Each person in each group is then responsible for evaluating a different expression. I let my students choose which expression they'd like to evaluate because I know them, and know this won't be an issue. You may wish to assign a certain problem to each student; this could be easily done by "numbering off". Point to a student and assign a letter, or have students pull pre-written cards with the corresponding letters. My students take turns explaining how they evaluated each expression, and discuss how the expressions are alike and different.

As I facilitate, I'm trying to get students to note that placement (or the absence) of the grouping symbols ultimately determines the value of the whole expression. Each expression has the same numbers and the same operations, the order of the operations will change for each expression. a) and d) both have a value of 27 respectively, so they are equivalent. Expression b) has a value of 15. Expression c) has a value of 0.

Sharing Out (for 5 min.) includes me asking and cold calling the following: How are these expressions alike? different? How did the grouping symbols affect the values of the expressions?

The term evaluate might be difficult for some Special Education students or ESL students, so you may wish to write "evaluate" and "value" on the board. Read each aloud and discuss with the class the meanings of the words. Explain that evaluating and expressions means finding its value. To evaluate and expression, follow the Order of Operations to perform all the operations until you find a single value.

If students have trouble, they can act out the problem. I explain to students that the expression within the innermost set of grouping symbols (the parentheses) is evaluated first. Then, the resulting expression in the outermost set of grouping symbols (the brackets) is evaluated. I encourage students to recall that addition and multiplication are commutative; and so the order of the factors or addends doesn't change the solution.

To continue working, the students solve another problem, while using MP2, reason abstractly and quantitatively to write and evaluate an expression:

Robbie is packing 180 books. He has 3 large boxes, & each box holds 25 books. He has 2 medium boxes, and each box holds 12 books. Can Robbie pack all 180 books? 

(3 x 25) + (2 x 18) + (5 x 12)

75 + 36 + 60


- I noticed a common error for this problem, and suggest that students write a separate expression for the number of books contained in each type of box. Then, the students can name the operation used to combine the 3 totals. Lastly, have students combine the 2 steps in 1 expression.


10 minutes

To close, I use cold calling to call upon students to describe what they found out during their Independent Practice.