options: Add and subtract within 20.

Interpret the structure of expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Represent and solve equations and inequalities graphically.

Rewrite rational expressions.

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

Multiply and divide within 100.

Represent and solve problems involving addition and subtraction.

Generate and analyze patterns.

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

Use the four operations with whole numbers to solve problems.

Use polynomial identities to solve problems.

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

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

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

Use properties of operations to generate equivalent expressions.

Solve equations and inequalities in one variable.

Work with radicals and integer exponents.

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

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

Gain familiarity with factors and multiples.

Create equations that describe numbers or relationships

Analyze patterns and relationships.

Perform arithmetic operations on polynomials.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

Work with addition and subtraction equations.

Represent and solve problems involving multiplication and division.

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

Understand and apply properties of operations and the relationship between addition and subtraction.
problem_activity: Narrative
The purpose of this warm-up is to elicit observations about differences in costs of living in different parts of the United States. It prepares students to look for and make sense of multiplicative comparisons later in the lesson. It also helps elicit what students know about how the different costs may be different depending on where you live.
Students may notice and wonder many things about the data in the table and both additive and multiplicative comparisons are likely to come up. Some students may note that an item costs “some dollars more” in San Francisco than in Fort Wayne, while others may say it costs “some number of times as much” based on the quantities or their estimation of the quantities. In the synthesis, focus student discussion on additive and multiplicative comparison.
Launch
Groups of 2
Display the table.
Activity
“What do you notice? What do you wonder?”
1 minute: quiet think time
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice? What do you wonder?
|                                                             | San Francisco, CA | Fort Wayne, IN |
|-------------------------------------------------------------|-------------------|----------------|
|                         population                          |      805,235      |    253,691     |
|                       milk (1 gallon)                       |      \$4.45       |     \$2.14     |
|                       bread (1 loaf)                        |      \$3.54       |     \$1.82     |
|                     gasoline (1 gallon)                     |      \$3.70       |     \$2.42     |
|                        movie ticket                         |       \$15        |      \$12      |
|                internet connection (1 month)                |       \$70        |      \$50      |
| rent for a 3 bedroom apartment in the city center (1 month) |      \$6,000      |    \$1,500     |
|                       cost of a house                       |    \$1,400,000    |   \$160,000    |
Student Response
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Activity Synthesis
“How could you compare the cost for renting an apartment in San Francisco to the cost in Fort Wayne? How could you use multiplication to compare the costs?”
As needed, “About how many more times as much is the cost of a house in San Francisco compare to the cost of a house in Fort Wayne?”
“The prices of the things you need to live, like food, clothing, and shelter, are called the cost of living. The cost of living can be very different depending on where in the world you live. Today we are going to compare the cost of living in different places around the world.”


correct_option_index: 14