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

Use the four operations with whole numbers to solve problems.

Rewrite rational expressions.

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Work with radicals and integer exponents.

Solve systems of equations.

Solve equations and inequalities in one variable.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

Represent and solve problems involving addition and subtraction.

Write expressions in equivalent forms to solve problems.

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

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

Represent and solve equations and inequalities graphically.

Gain familiarity with factors and multiples.

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Generate and analyze patterns.

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

Represent and solve problems involving multiplication and division.

Perform arithmetic operations on polynomials.

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

Add and subtract within 20.

Multiply and divide within 100.

Write and interpret numerical expressions.

Work with addition and subtraction equations.

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

Represent and analyze quantitative relationships between dependent and independent variables.

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

Create equations that describe numbers or relationships

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

Understand the relationship between zeros and factors of polynomials.
problem_activity: Warm-up
The purpose of this warm-up is for students to reason about square roots by estimating the value of each expression. The values given as choices are close in range to encourage students to use the square roots they know to help them estimate ones they do not. These understandings will be helpful for students in upcoming activities where they will be applying the Pythagorean Theorem.
While four problems are given, it may not be possible to share every strategy. Consider gathering only two or three different strategies per problem.
Launch
Display one problem at a time. Give students 30 seconds of quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all previous problems displayed throughout the talk. Follow with a whole-class discussion.
Student Facing
Which estimate is closest to the actual value of the expression? Explain your reasoning.
\(\sqrt{24}\)
4
4.5
5
\(\sqrt7\)
2
2.5
3
\(\sqrt{42}\)
6
6.5
7
\(\sqrt{10}\)
+
\(\sqrt{97}\)
13
13.25
13.5
Student Response
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Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. After each student shares, ask if their chosen estimate is more or less than the actual value of each expression.
Speaking: MLR8 Discussion Supports.
: Display sentence frames to support students when they explain their strategy. For example, "First, I _____ because . . ." or "I noticed _____ so I . . . ." Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Design Principle(s): Optimize output (for explanation)


correct_option_index: 6