options: Use the four operations with whole numbers to solve problems.

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

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Create equations that describe numbers or relationships

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

Add and subtract within 20.

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

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

Gain familiarity with factors and multiples.

Solve equations and inequalities in one variable.

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

Work with addition and subtraction equations.

Write and interpret numerical expressions.

Use properties of operations to generate equivalent expressions.

Use polynomial identities to solve problems.

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

Represent and solve problems involving addition and subtraction.

Multiply and divide within 100.

Perform arithmetic operations on polynomials.

Solve systems of equations.

Understand the relationship between zeros and factors of polynomials.

Reason about and solve one-variable equations and inequalities.

Work with radicals and integer exponents.

Interpret the structure of expressions.

Analyze patterns and relationships.

Represent and solve problems involving multiplication and division.

Generate and analyze patterns.

Represent and solve equations and inequalities graphically.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Analyze and solve linear equations and pairs of simultaneous linear equations.
problem_activity: Narrative
This activity prompts students to use multiplicative comparison to determine the cost of different living expenses in Bermuda and in India. Students use these costs to interpret and solve a multi-step problem. The multi-step problem can be solved in more than one way. Students might use multiplication or division. They may also choose to estimate rather than perform each calculation. Encourage students to use the Three Reads routine as needed to solve problems.
When finding the missing prices in the table, students also have an opportunity to reason about how to find a value that is 2.5 times as much. Students are not expected to multiply whole numbers by decimals in grade 4, but may use their understanding of decimal notation and decimal fractions to estimate the cost by doubling the price in India and adding half the price or by reasoning that 2.5 is close to 3.
MLR8 Discussion Supports.
Prior to solving the problems, invite students to make sense of the situations. Monitor and clarify any questions about the context.
Advances: Reading, Representing.
Launch
Groups of 2
“We saw one example of how the same items can vary a lot in cost depending on where you live in the United States. Let’s look at the costs of some other things in two different countries—one known to be very expensive and the other known to be inexpensive.”
Activity
5 minutes: independent work time on the first question
Monitor for students who use the multiplication or division algorithm, draw diagrams, write equations, or use estimation to find the missing values.
Pause for a discussion. Select students to share their responses and reasoning for finding the costs in the table.
Highlight that to find the missing cost in Bermuda, we can multiply the cost in India by the number in the middle column, and to find the cost in India, we divide the cost in Bermuda by the number in the middle column.
4 minutes: independent work time on the second question
4 minutes: partner discussion
Student Facing
Bermuda is the most expensive country in the world and India is one of the least expensive.
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The table shows how prices of some things in the two countries compare. Estimate or calculate the missing costs and complete the table.
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In India, rent for a 1-bedroom apartment outside of a city center costs about \$76 per month. A similar apartment in Bermuda costs 23 times as much.
Utilities (electric, gas, water, and heating) for a small apartment costs about \$27 per month in India and 7 times as much in Bermuda.
If a person earns \$2,000 per month, can they afford to pay rent and utilities in Bermuda?
Student Response
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Activity Synthesis
Select students to share their responses and strategies for how they determined if they can afford to live a month in Bermuda with \$2,000.


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