options: Work with equal groups of objects to gain foundations for multiplication.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use properties of operations to generate equivalent expressions.

Understand and apply properties of operations and the relationship between addition and subtraction.

Represent and solve equations and inequalities graphically.

Represent and analyze quantitative relationships between dependent and independent variables.

Reason about and solve one-variable equations and inequalities.

Create equations that describe numbers or relationships

Rewrite rational expressions.

Analyze patterns and relationships.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Write expressions in equivalent forms to solve problems.

Write and interpret numerical expressions.

Represent and solve problems involving addition and subtraction.

Understand solving equations as a process of reasoning and explain the reasoning.

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

Add and subtract within 20.

Understand properties of multiplication and the relationship between multiplication and division.

Generate and analyze patterns.

Solve systems of equations.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Understand the connections between proportional relationships, lines, and linear equations.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

Perform arithmetic operations on polynomials.
problem_activity: Activity
In this activity, students use surface area as a context to extend the order of operations to expressions with exponents. The context provides a reason to evaluate the exponent before performing the multiplication.
Launch
Give students 10 minutes of quiet work time, followed by a class discussion.
Reading: MLR6 Three Reads.
Use this routine to support students’ comprehension of the situation. In the first read, students read the text with the goal of comprehending the situation (e.g., Jada and Noah have different solutions for the surface area of the same cube). In the second read, ask students to identify important quantities that can be counted or measured (e.g., the side length of the cube; the number of faces of a cube; the area of each face of the cube). In the third read, reveal the question, “Do you agree with either of them? Explain your reasoning.” Ask students to brainstorm possible strategies to answer the question (e.g., Find the area of each face of the cube. Multiply the area by 6 to find the surface area of the cube). This will help students concentrate on making sense of the situation before rushing to a solution or method.
Design Principle(s): Support sense-making
Student Facing
A cube has side length 10 inches. Jada says the surface area of the cube is 600 in
2
, and Noah says the surface area of the cube is 3,600 in
2
. Here is how each of them reasoned:
Jada’s Method:
\(6 \boldcdot 10^2\)
\(6 \boldcdot 100\)
\(600\)
Noah’s Method:
\(6 \boldcdot 10^2\)
\(60^2\)
\(3,\!600\)
Do you agree with either of them? Explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
In finding the surface area, there is a clear reason to find
\(10^2\)
and then multiply by 6. Tell students that sometimes it is not so clear in which order to evaluate operations. There is an order that we all generally agree on, and when we want something done in a different order, brackets are used to communicate what to do first. When an exponent occurs in the same expression as multiplication or division, we evaluate the exponent first, unless brackets say otherwise. Examples:
\((3\boldcdot 4)^2 = 12^2 = 144\)
, since the brackets tell us to multiply
\(3\boldcdot 4\)
first. But
\(3\boldcdot  4^2 = 3\boldcdot  16 = 48\)
, because since there are no brackets, we evaluate the exponent before multiplying.
If students bring up PEMDAS or another mnemonic for remembering the order of operations, point out that PEMDAS can be misleading in indicating multiplication before division, and addition before subtraction. Discuss the convention that brackets or parentheses indicate that something should be evaluated first, followed by exponents, multiplication, or division (evaluated left to right), and last, addition or subtraction (evaluated left to right).


correct_option_index: 1