Download Place The Parentheses

Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55653
Place The Parentheses
Students are given an equation and asked to place parentheses within the equation to make the equation true.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, parentheses, brackets, braces, evaluate, order of operations
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_PlaceTheParentheses_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually, in small groups, or in a whole-group setting. If the task is given in a whole-group setting, the teacher should ask each
student to explain his or her thinking and strategy.
1. The teacher provides the student with the Place the Parentheses worksheet and reads aloud the directions.
2. The teacher provides ample time for the student to complete the task.
3. After the student completes the task, the teacher should prompt the student by asking, “How did you know to place the parentheses here?”
TASK RUBRIC
Getting Started
Misconception/Error
The student does not attempt to apply the order of operations when trying to determine the correct placement of the parentheses.
Examples of Student Work at this Level
The student places the parentheses around 108 ÷ 12 and says that this is correct because 108 is the greater number.
The student places the parentheses around 12 – 6 but says that parentheses always go in the middle. The student does not complete any computation on his or her paper
in an attempt to determine how to make the equation true.
page 1 of 3 Questions Eliciting Thinking
Where can you place parentheses so that when the order of operations is applied, the result is 54?
If you apply the order of operations, is the result 54?
When you place the parentheses around this set of numbers and solve the equation, what answer do you get?
Instructional Implications
Provide the student with equations with only two operations and a given solution. Model for the student how to use the order of operations to determine where to place
the parentheses so that the equation has the given solution.
Provide the student with expressions involving two operations. Have the student explain order of operations and evaluate expressions accordingly. Eventually, the teacher
can add parentheses to the expressions. Have the student evaluate these expressions, and discuss how parentheses are always done first, regardless of the symbol(s) inside
the parentheses.
Consider using the MFAS task More Expressions (5.OA.1.1).
Moving Forward
Misconception/Error
The student makes mistakes in using the order of operations.
Examples of Student Work at this Level
The student demonstrates some understanding of the order of operations in trying to determine the correct placement of the parentheses. However, the student says
that the equation is not true because you have to multiply 6 x 3 before you divide 108 by 12.
The student places the parentheses around 6 x 3 because he or she says that according to PEMDAS, multiplication comes first. The student does not try to perform
operations in order to determine the correct placement of the parentheses.
The student makes calculation errors that he or she does not correct after prompting.
Questions Eliciting Thinking
Where can you place parentheses so that when the order of operations is applied, the result is 54?
If you apply the order of operations, is the result 54?
When you place the parentheses around this set of numbers and solve the equation, what answer do you get?
Instructional Implications
Provide the student with equations with at least three operations and a given solution. Model for the student how to use the order of operations to determine where to
place the parentheses so that the equation has the given solution.
Give the student additional practice opportunities with evaluating multi-step expressions that include the four operations and parentheses. Give the student several
highlighters to highlight each part of the expression as it is evaluated. This will help the student see which numbers and operations have been completed, step-by-step, and
help him or her follow order of operations.
Consider using the MFAS task Evaluating Expressions (5.OA.1.1)
Almost There
Misconception/Error
The student is unable to explain his or her reasoning.
Examples of Student Work at this Level
The student correctly places the parentheses around 12 – 6 and the work on his or her paper shows that the student understands the order of operations. However, the
student is unable to justify his or her reasoning in placing the parentheses around 12 – 6.
Questions Eliciting Thinking
How did you figure out that you should place the parentheses around 12 – 6? Explain all the work that you did on your paper to me.
Instructional Implications
Model for the student solving problems using the order of operations and explaining your strategy.
page 2 of 3 Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly places the parentheses around 12 – 6 and explains his or her reasoning. He or she says, “I know that 12 minus six equals 6. And 108 divided by six
equals 18, and 18 times three equals 54.” Initially, the student may try to place the parentheses around 108 ÷ 12 or the 6 x 3 but realizes that both of these options would not make a true equation. The student
perseveres and continues to work until finding that the parentheses should be placed around 12 – 6 to make the equation true.
Questions Eliciting Thinking
Another student put the parentheses around 6 x 3 because he said multiplication comes first. What did he do wrong?
What answer would you get if you put the parentheses around 6 x 3?
Instructional Implications
Encourage the student to write his or her own expressions involving the four operations as well as parentheses. The student can also make a game of this by rolling dice to
generate numbers for the expressions. The student can write these expressions on index cards and then trade cards with a partner to solve and check answers.
Provide the student with more challenging expressions to evaluate that include all four operations and parentheses. Include expressions with two or more sets of
parentheses.
Expose the student to brackets and braces using nesting within expressions.
Give the student hints about a number and have him or her work backwards to find it. From those clues, the student can create equations, using parentheses appropriately.
For example, “I am thinking of a number and if I subtract five and then divide the result by two, I’ll get 25.” This should be represented as (x – 5) ÷ 2 = 25.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Place the Parentheses worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.5.OA.1.1:
Description
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
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