## MSTAR Interventions

### Key Ideas

• A proportion is an equation made up of 2 equivalent ratios. (See Lesson 1.)
• A proportional relationship exists when 2 ratios are equivalent. (See Lesson 1.)
• 2 ratios are proportional if they simplify to the same ratio. (See Lesson 2.)
• Additive thinking is present when a constant number is added to a value to get the resulting value. (See Lesson 3.)
• Multiplicative thinking is present when a value is multiplied by a constant rate to get the resulting value. (See Lessons 3 and 4.)
• A proportional relationship exists when multiplicative thinking is present. (See Lesson 3.)
• Given a scenario and table of values, a rule can be determined. This rule can be used to find any missing value in the table. (See Lesson 4.)
• If given the y value in the table, the x value can be determined by performing the inverse operation. (See Lesson 4.)
• To find the missing value in a proportion, determine and use the scale factor. (See Lesson 5.)
• A unit rate describes how many units of 1 quantity for 1 unit of another quantity. (See Lesson 6.)
• A missing value of a proportion can be found by finding the unit rate of the complete ratio and then multiplying the fraction representing the unit rate by a scale factor. (See Lesson 6.)
• 2 ratios are proportional if the equivalent ratios resulting from finding a common denominator have the same numerator. (See Lesson 7.)
• To find the missing value in a proportion, find a common denominator of the 2 fractions representing the ratios and set the new numerators equal to each other. (See Lesson 8.)
• To find missing values by using common denominators, multiply the denominator of 1 fraction representing a ratio by the numerator of the fraction representing the other ratio and vice versa. Then set these products equal to each other and solve the equation to find the missing value. (See Lesson 9.)
• Patterns found when using common denominators to prove proportionality lead to the idea of cross products. (See Lesson 10.)
• Cross products can be used to prove proportionality. If the 2 numerators are equal, the ratios are proportional. If the 2 numerators are not equal, the ratios are not proportional. (See Lesson 10.)
• Cross products can be used to find a missing value in a proportion by setting the numerators equal to each other and solving the equation. (See Lesson 11.)
• 1 method may be more efficient than the others when finding the missing value in a proportion. (See Lesson 12.)
• A proportion from a word problem can be written in multiple formats and still accurately describe the scenario. (See Lesson 13.)
• A proportion can be written to find a missing value from a situation that models a proportional relationship. (See Lesson 14.)
• When writing a proportion, using units or labels for the quantities being compared is essential to ensure that like ratios are compared. (See Lesson 14.)
• A percent is an amount out of 100. (See Lesson 15.)
• A ratio comparing 2 amounts can be set equivalent to a ratio with a denominator of 100 to determine a percentage. (See Lesson 15.)
• For 2 figures to be similar, all corresponding angles must be congruent and all pairs of corresponding lengths must be proportional or form the same ratio. (See Lesson 16.)
• To find the missing length in similar figures, set up a proportion comparing corresponding side lengths. (See Lesson 16.)
• Graphs of proportional relationships pass through the origin. Graphs of nonproportional relationships do not pass through the origin. (See Lesson 17.)