### Examples

Patti says the expression 12÷2×3 is equivalent to 18 because she works each operation from left to right. Gladys says the expression 12÷2×3 is equivalent to 2 because first multiplies 2×3 then divides 6 into 12. David says that Patti is correctly using order of operations and suggests that if parentheses were added, it would give more clarity.### Clarifications

*Clarification 1:*Multi-step expressions are limited to any combination of arithmetic operations, including parentheses, with whole numbers, decimals and fractions.

*Clarification 2:* Within this benchmark, the expectation is not to include exponents or nested grouping symbols.

*Clarification 3:* Decimals are limited to hundredths. Expressions cannot include division of a fraction by a fraction.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**5

**Strand:**Algebraic Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plan

## Original Student Tutorials

## Problem-Solving Tasks

## Tutorials

## Virtual Manipulative

## MFAS Formative Assessments

Students are asked to evaluate two similar expressions and explain why the answers are different.

Students are asked to insert parentheses into an expression in two different ways, evaluate each way, and explain why the answers are different.

## Original Student Tutorials Mathematics - Grades K-5

Learn to evaluate expressions that have all four operations (multiplication, division, addition, and subtraction) and parentheses as you settle debates in this interactive tutorial.

## Computer Science Original Student Tutorials

Construct efficient lines of code using condition- and if-statements to solve equations as you complete this interactive tutorial. You'll also review the order of operations in expressions.

This is part 2 of a 4-part series on coding. Click below to open the other tutorials in the series.

Learn how to perform instructions using an if statement and explore relational operators (less than, greater than, equal and not equal to) and how they are used to compare to values in this interactive tutorial.

Learn how to use repeat loops in this interactive tutorial. Repeat loops iterate though a list of instructions based on a desired number of times. Combined with variables, condition statements, if statements, and repeat loops we practice using order of operations to code.

This is part 1 of a 4-part series. Click below to check out the other tutorials in the series.

## Student Resources

## Original Student Tutorials

Learn how to use repeat loops in this interactive tutorial. Repeat loops iterate though a list of instructions based on a desired number of times. Combined with variables, condition statements, if statements, and repeat loops we practice using order of operations to code.

This is part 1 of a 4-part series. Click below to check out the other tutorials in the series.

**Bee A Coder Part 1: Declare Variables****Bee A Coder Part 2: Condition Statements****Bee A Coder Part 3: If Statements**

Type: Original Student Tutorial

Learn how to perform instructions using an if statement and explore relational operators (less than, greater than, equal and not equal to) and how they are used to compare to values in this interactive tutorial.

Type: Original Student Tutorial

Construct efficient lines of code using condition- and if-statements to solve equations as you complete this interactive tutorial. You'll also review the order of operations in expressions.

This is part 2 of a 4-part series on coding. Click below to open the other tutorials in the series.

**Bee A Coder Part 1: Declare Variables****Bee A Coder Part 3: If Statements****Bee A Coder Part 4: Repeat Loops**

Type: Original Student Tutorial

Learn to evaluate expressions that have all four operations (multiplication, division, addition, and subtraction) and parentheses as you settle debates in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Task

This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. This type of problem helps students to see structure in numerical expressions. In later grades they will be working with similar ideas in the context of seeing and using structure in algebraic expressions.

Type: Problem-Solving Task

## Tutorials

This Khan Academy tutorial video presents the impact of parentheses notation in an expression. As the tutorial does the same problem with and without parenthesis, negative numbers are part of the solution.

Type: Tutorial

In this video, you will see why it is important to have one agreed upon order of operations.

Type: Tutorial

## Virtual Manipulative

In this activity, students practice solving algebraic expressions using order of operations. The applet records their score so the student can track their progress. This activity allows students to practice applying the order of operations when solving problems. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

## Parent Resources

## Problem-Solving Tasks

The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation. Students eager to knock down all of the pins quickly develop patterns in their expressions. They may re-use parts of an expression, perhaps changing just the final operation.

Type: Problem-Solving Task

This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. This type of problem helps students to see structure in numerical expressions. In later grades they will be working with similar ideas in the context of seeing and using structure in algebraic expressions.

Type: Problem-Solving Task