# Mathematics Support

### Ratios and Proportional Relationships

Understanding Proportional Relationships

Application of Proportional Relationships

## Understanding Proportional Relationships

### Students will be able to...

• Reason about and compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
• Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing if the graph is a straight line through the origin.
• Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• Represent proportional relationships by equations.
• Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

*Instructional videos in the hyperlinks above are meant to support C2.0 content, but may use vocabulary or strategies not emphasized by MCPS.

The Common Core State Standards require a balance of three fundamental components that result in rigorous mathematics acquisition: deep conceptual understanding, procedural skill, and mathematical applications and modeling.

### In school, your child will…

• Reason about and compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.
• Decide whether two quantities are in a proportional relationship.
•  How can you determine if the number of gallons needed is proportional to the number of days?

• Represent proportional relationships by equations.
• Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation.
•  Explain how the graph shows or does not show the two quantities being proportional to each other.
• What does the ordered pair (0, 0) represent in the context of the problem? (300, 300)?

### At home, your child can…

• Determine the amount of ingredients needed when modifying recipes.
•  If our recipe calls for 2 1/2 cup of flour for every 3/4 cup of brown sugar, how much flour is needed if we used 1 cup of brown sugar?
•  Determine the unit price of an item at the grocery store.
•  If a 32 oz. bottle of Gatorade costs \$0.88, what is the price per ounce?
•  Decide whether two quantities are in a proportional relationship.
• the price of a movie ticket compared to the age of the person
• the number of hours worked and the amount of money earned

*Additional Practice links support C2.0 content, but may use vocabulary or strategies not emphasized by MCPS.

## Application of Proportional Relationships

### Students will be able to...

• Solve problems involving scale drawings of geometric figures.
• Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• Represent proportional relationships by equations.
• Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
• Understand that rewriting an expression in different forms in a context can shed light on the problem and how the quantities in it are related.

*Instructional videos in the hyperlinks above are meant to support C2.0 content, but may use vocabulary or strategies not emphasized by MCPS.

The Common Core State Standards require a balance of three fundamental components that result in rigorous mathematics acquisition: deep conceptual understanding, procedural skill, and mathematical applications and modeling.

### In school, your child will…

• Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
• Represent proportional relationships by equations.
• (0.12)s = 6 and 12/100 = 6/s, where s represents the total number of students.

• Use proportional relationships to solve multistep ratio and percent problems.
• Understand that rewriting an expression in different forms in context can shed light on the scenario and how the quantities in it are related.
• 15% gratuity on a \$30 meal.
• 0.15 x 30 = g, where g is the amount of the gratuity
• 30 (1 + 0.15) = t, where t is the total amount (meal and gratuity)

### At home, your child can...

• Interpret the scale on a map when planning an upcoming trip. Use the given scale to estimate the distance of your trip.
• If the trail we want to hike is 2 inches on the map, how can we use the scale to determine the length of the trail in miles?

• Determine the amount of tax that will be due when grocery shopping.
• If the subtotal of the grocery bill for the week is \$150.62, and MD State sales tax is 6%, what is the total bill?

• Determine the amount of a posted discount and calculate the new price.
• Determine the final price of an item after applying a given discount and sales tax.
• Determine the gratuity amount when eating out.
The text passage provides an overview of proportional relationships and their applications, including several examples and questions that can be used to assess understanding. It includes both questions and answers within the context of the examples.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Mathematics Support

### Ratios and Proportional Relationships

Understanding Proportional Relationships

Application of Proportional Relationships

## Understanding Proportional Relationships

### Students will be able to...

• Reason about and compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
• Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing if the graph is a straight line through the origin.
• Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• Represent proportional relationships by equations.
• Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

*Instructional videos in the hyperlinks above are meant to support C2.0 content, but may use vocabulary or strategies not emphasized by MCPS.

The Common Core State Standards require a balance of three fundamental components that result in rigorous mathematics acquisition: deep conceptual understanding, procedural skill, and mathematical applications and modeling.

### In school, your child will…

• Reason about and compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.
• Decide whether two quantities are in a proportional relationship.
•  How can you determine if the number of gallons needed is proportional to the number of days?

• Represent proportional relationships by equations.
• Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation.
•  Explain how the graph shows or does not show the two quantities being proportional to each other.
• What does the ordered pair (0, 0) represent in the context of the problem? (300, 300)?

### At home, your child can…

• Determine the amount of ingredients needed when modifying recipes.
•  If our recipe calls for 2 1/2 cup of flour for every 3/4 cup of brown sugar, how much flour is needed if we used 1 cup of brown sugar?
•  Determine the unit price of an item at the grocery store.
•  If a 32 oz. bottle of Gatorade costs \$0.88, what is the price per ounce?
•  Decide whether two quantities are in a proportional relationship.
• the price of a movie ticket compared to the age of the person
• the number of hours worked and the amount of money earned

*Additional Practice links support C2.0 content, but may use vocabulary or strategies not emphasized by MCPS.

## Application of Proportional Relationships

### Students will be able to...

• Solve problems involving scale drawings of geometric figures.
• Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• Represent proportional relationships by equations.
• Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
• Understand that rewriting an expression in different forms in a context can shed light on the problem and how the quantities in it are related.

*Instructional videos in the hyperlinks above are meant to support C2.0 content, but may use vocabulary or strategies not emphasized by MCPS.

The Common Core State Standards require a balance of three fundamental components that result in rigorous mathematics acquisition: deep conceptual understanding, procedural skill, and mathematical applications and modeling.

### In school, your child will…

• Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
• Represent proportional relationships by equations.
• (0.12)s = 6 and 12/100 = 6/s, where s represents the total number of students.

• Use proportional relationships to solve multistep ratio and percent problems.
• Understand that rewriting an expression in different forms in context can shed light on the scenario and how the quantities in it are related.
• 15% gratuity on a \$30 meal.
• 0.15 x 30 = g, where g is the amount of the gratuity
• 30 (1 + 0.15) = t, where t is the total amount (meal and gratuity)

### At home, your child can...

• Interpret the scale on a map when planning an upcoming trip. Use the given scale to estimate the distance of your trip.
• If the trail we want to hike is 2 inches on the map, how can we use the scale to determine the length of the trail in miles?

• Determine the amount of tax that will be due when grocery shopping.
• If the subtotal of the grocery bill for the week is \$150.62, and MD State sales tax is 6%, what is the total bill?

• Determine the amount of a posted discount and calculate the new price.
• Determine the final price of an item after applying a given discount and sales tax.
• Determine the gratuity amount when eating out.
user
The text passage provides an overview of proportional relationships and their applications, including several examples and questions that can be used to assess understanding. It includes both questions and answers within the context of the examples.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS