options: Represent and solve equations and inequalities graphically.

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

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

Rewrite rational expressions.

Multiply and divide within 100.

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

Write expressions in equivalent forms to solve problems.

Gain familiarity with factors and multiples.

Perform arithmetic operations on polynomials.

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

Create equations that describe numbers or relationships

Add and subtract within 20.

Understand the relationship between zeros and factors of polynomials.

Work with addition and subtraction equations.

Work with radicals and integer exponents.

Generate and analyze patterns.

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

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

Use the four operations with whole numbers to solve problems.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving addition and subtraction.

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

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

Use polynomial identities to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Write and interpret numerical expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve systems of equations.

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

Analyze patterns and relationships.

Solve equations and inequalities in one variable.

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

Represent and solve problems involving multiplication and division.
problem_activity: Activity
The purpose of this activity is for students to use rational approximations of irrational numbers and to match irrational numbers to equations they are solutions to. To do this, students sort cards into sets of three consisting of:
A square or cube root value
An equation of the form
\(x^2=p\)
or
\(x^3=p\)
that the value is a solution to
A number line showing the location of the value
Identify groups using clear explanations for how they chose to arrange their sets of 3, particularly when matching the cards with a value plotted on a number line.
Launch
Arrange students in groups of 2–4. Students should not use a calculator for this activity. Tell students that they will be given cards to sort into sets of three. Distribute 27 pre-cut slips from the blackline master to each group. Group work time followed by a whole-class discussion.
Representation: Internalize Comprehension.
Chunk this task into more manageable parts to differentiate the degree of difficulty or complexity by beginning with fewer cards. For example, give students a subset of the cards (using multiples of 3) to start with and introduce the remaining cards once students have completed their initial set of matches.
Supports accessibility for: Conceptual processing; Organization
Student Facing
Your teacher will give your group a set of cards. For each card with a letter and value, find the two other cards that match. One shows the location on a number line where the value exists, and the other shows an equation that the value satisfies. Be prepared to explain your reasoning.
Student Response
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Anticipated Misconceptions
Some students may mix up cube and square roots. Encourage these students to pay close attention to the notation. They may want to fill in the “2” for the square roots similar to how the “3” is used for cube roots.
Activity Synthesis
Select 3–4 previously identified groups to share one of their sets of three cards.
Also discuss:
“What was a match that was hard to make?” (Two of the number lines have values between 4 and 5, and it took some extra reasoning to figure out that the one with the value closer to 4 was
\(\sqrt{18}\)
while the one with the point closer to 5 was
\(\sqrt[3]{100}\)
.
“If another class was going to sort these cards, what is something you would recommend they have or do that you found helpful?” (I would recommend they have a list of perfect squares and perfect cubes to help think about where the different roots are plotted on the number line.)
Speaking, Writing: MLR8 Discussion Supports.
Display sentence frames to support students as they justify their reasoning for each match. For example, “The solution to _________ (
\(x^3 = 25\)
) is _________ (
\(\sqrt[3]{25}\)
) and it is between ______ (2 and 3) on the number line, because . . .” The helps students place extra attention on language used to engage in mathematical communication, without reducing the cognitive demand of the task. It also emphasizes the importance of justification.
Design Principle: Maximize meta-awareness


correct_option_index: 15