Primary Standards:
MAFS.5.OA.1.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
MAFS.5.OA.1.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Connecting Standards:
MAFS.5.NF.2.5: Interpret multiplication as scaling (resizing), by:
- Comparing the size of a product to the size of one factor based on the size of the other factor, without performing the indicated multiplication.
Content Knowledge:
In 5th grade, students gain a deeper understanding of expressions and equations, and discover ways to evaluate and solve computations.
In this Unit, students will work with expressions that include more than one operation and include grouping symbols. Although they have used parentheses to build expressions to solve multi-step problems in third and fourth grades, students now refine their understanding of how expressions are built and interpreted, including an understanding of order of operations to clarify and evaluate them.
In this Unit, students work with algebra vocabulary as they explore and explain problem situations and expressions. Students write expressions and equations to match the meaning of a math task or word phrase, for example “The sum of 7 and 4” can be expressed as 7 + 4. It is the goal of the standard that students interpret and write expressions with more than one operation. Understanding the order of operations allows them to do this correctly.
Students will also us their knowledge of expressions and operations to compare two expressions without the need to do the computation. For example, when comparing 5 × (27 + 3) to 5 + (27 + 3) without solving, a student may understand that adding 5 results in a total that is less than multiplying by 5.
GCG 1 – Learning Goal: As a Mathematician, I will be able to Use the Order of Operations to Evaluate Expressions
- Step 1: Use order of operations to solve 2-3 step expressions with parentheses, brackets and/or braces using whole numbers
- Step 2: Use order of operations to solve 3 or more-step expressions with parentheses, brackets and/or braces using whole numbers and fractions
- Step 3: Insert parentheses to give the expression a given value or to make a statement true and analyze errors in determined values
GCG 2 – Learning Goal: As a Mathematician, I will be able to Convert Expressions and Apply Order of Operations
- Step 1: Represent math words as a numerical expression using whole numbers
- Step 2: Represent math words as a numerical expression using whole numbers and fractions with up to 2 operations
- Step 3: Write and interpret numeric expressions with whole numbers and fractions with more than 2 operations
GCG 3 – Learning Goal: As a Mathematician, I will be able to Interpret and Compare Numerical Expressions without Evaluating