← Grade 7: Proportional Relationships
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Grade 7: Proportional Relationships
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Grade 7: Proportional Relationships — Flashcards
| Front | Back |
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| What is a proportional relationship? | A relationship between two quantities where they maintain a constant ratio (constant of proportionality) to each other, represented by equivalent ratios in a table or a straight line through the origin on a graph. |
| What is the constant of proportionality (proportional constant)? | The constant unit rate (k) in a proportional relationship; the value that relates the two quantities, often written as y = kx. |
| What is a unit rate? | A rate expressed with a denominator of 1, showing how much of one quantity corresponds to a single unit of another. |
| How do you compute a unit rate involving fractions (7.RP.1)? | By writing the ratio as a complex fraction and simplifying; e.g., walking 1/2 mile in 1/4 hour gives (1/2)/(1/4) = 2 miles per hour. |
| What are two ways to test if quantities are proportional (7.RP.2a)? | Check for equivalent ratios in a table, or graph the points on a coordinate plane and see if they form a straight line through the origin. |
| Where can you identify the constant of proportionality (7.RP.2b)? | In tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. |
| What is the standard equation form for a proportional relationship (7.RP.2c)? | y = kx (or t = pn), where k (or p) is the constant of proportionality. |
| What do the points (0,0) and (1,r) mean on a proportional relationship graph (7.RP.2d)? | (0,0) means zero of one quantity corresponds to zero of the other; (1,r) means one unit of the independent quantity corresponds to r units of the dependent quantity, where r is the unit rate. |
| What is a part-to-part ratio? | A ratio comparing one part of a whole to another part of the same whole (not the total). |
| What is a part-to-whole ratio? | A ratio comparing one part of a group to the entire whole group; fractions represent this type of relationship. |
| What is a proportion? | An equation stating that two ratios are equivalent. |
| What real-world problems can proportional relationships solve (7.RP.3)? | Simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error. |
| What is percent change? | The amount a quantity increases or decreases, expressed as a percent of the original amount. |
| What is a bar/tape model used for in this chapter? | A visual model used to represent and solve part-to-part and part-to-whole ratio and percent problems. |
| What tools are used to represent proportional relationships? | Tables, graphs, equations, and verbal descriptions. |
| What prior knowledge from 6th grade is needed for this chapter? | Writing ratios as fractions, with a colon, or in words; operating fluently with fractions and decimals; reducing fractions; converting between mixed numbers and improper fractions; and solving percent problems. |
| What does it mean for a graph of a proportional relationship to pass through the origin? | It shows that when the independent quantity is 0, the dependent quantity is also 0, confirming the relationship is proportional. |
| What is a rate? | A comparison of two quantities measured in different units. |
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