Section	Teacher-facing learning goals
Proportional Relationships with Fractions	Lesson 1 Compare (orally and in writing) the dimensions and scale factors of multiple scaled copies of the same figure. Explain (orally) how to estimate or calculate the percentage of a rectangular area that is covered by another region. Generate the dimensions for a scaled copy of an original figure that has fractional side lengths. Lesson 2 Compare and contrast (orally and in writing) different strategies for solving a problem involving equivalent ratios with fractional quantities. Explain (orally and in writing) how to find and use a unit rate to solve a problem involving fractional quantities. Lesson 3 Calculate and interpret (orally) the constant of proportionality for a proportional relationship involving fractional quantities. Explain (orally and in writing) how to use a table with only two rows to solve a problem involving a proportional relationship. Write an equation to represent a given proportional relationship with a fractional constant of proportionality. Lesson 4 Apply the distributive property to generate algebraic expressions that represent a situation involving adding or subtracting a fraction of the initial value, and explain (orally) the reasoning. Coordinate tables, equations, tape diagrams, and verbal descriptions that represent a relationship involving adding or subtracting a fraction of the initial value. Generalize a process for finding the value that is “half as much again,” and justify (orally and in writing) why this can be abstracted as \(\frac32 x\) or equivalent. Lesson 5 Comprehend and use the term “repeating” (in spoken language) and the notation \(\overline{\phantom{“ “}}\) (in written language) to refer to a decimal expansion that keeps having the same number over and over forever. Coordinate fraction and decimal representations of situations involving adding or subtracting a fraction of the initial value. Use long division to generate a decimal representation of a fraction, and describe (in writing) the decimal that results.
Percent Increase and Decrease	Lesson 6 Coordinate statements about “percent increase” or “percent decrease” with comparisons to the original amount, e.g., a 20% increase means the new value is 120% of the original value. Draw and label a tape diagram to represent a situation that involves adding or subtracting a percentage of the initial value. Explain (orally and in writing) how to calculate the new amount given the original amount and a percentage of increase or decrease. Lesson 7 Critique (orally and in writing) double number line diagrams that represent situations involving percent increase or decrease. Generalize (orally) that the original amount corresponds to 100% and the new amount corresponds to more or less than 100%, depending on whether the situation involves an increase or decrease. Interpret a description of a situation to identify the original amount, the new amount, the change, and corresponding percentages. Label these on a double number line diagram. Lesson 8 Explain (orally and in writing) how to calculate the original amount given the new amount and a percentage of increase or decrease. Generate algebraic expressions that represent a situation involving percent increase or decrease, and justify (orally) the reasoning. Lesson 9 Comprehend that percentages do not have to be a whole number. Recognize that 0.1% of a number is 1/10 of 1% of the number. Use reasoning about place value to calculate percentages that are not whole numbers, and explain (orally) the strategy.
Applying Percentages	Lesson 10 Comprehend “sales tax” and “tip” as two contexts that involve adding a percentage of the initial amount. Explain (orally) how to calculate the total cost including a tax or tip, given the “subtotal” and the percentage. Explain (orally) how to determine the percentage of the subtotal that a tax or tip is. Lesson 11 Comprehend “interest,” “markup,” “markdown,” and “commission” as other contexts that involve adding or subtracting a percentage of the initial amount. Determine the original dollar amount before a markup, markdown, or commission. Explain (orally) how to calculate the new dollar amount after a markup, markdown, or commission. Lesson 12 Determine what information is needed to solve a problem involving sales tax and discounts. Ask questions to elicit that information. Explain (orally) how to calculate the percentage, given the dollar amounts before and after a sales tax, tip, or discount. Interpret (orally and in writing) tape diagrams that represent situations involving a sales tax, tip, or discount. Lesson 13 Compare and contrast (orally) multiple measurements of the same length that result from using rulers with different levels of precision. Describe (orally) possible sources of “measurement error” when measuring lengths. Generalize a process for calculating measurement error and expressing it as a percentage of the actual length. Lesson 14 Calculate the percent error, correct amount, or erroneous amount, given the other two of these three quantities, and explain (orally and using other representations) the solution method. Compare and contrast (orally) strategies used for solving problems about percent error with strategies used for solving problems about percent increase or decrease. Lesson 15 - Optional Comprehend that manufacturers often define a maximum acceptable percent error for characteristics of their products. Determine what information is needed to solve a problem involving percent error. Ask questions to elicit that information. Generate values that fall within the acceptable range for a measurement, given a maximum percent error.
Let's Put it to Work	Lesson 16 Generate questions (orally and in writing) about a real-world situation involving percent increase or decrease. Interpret news headlines or advertisements that include statements about percent increase and decrease. Solve a problem about a real-world situation involving percent increase or decrease and present the solution method (in writing and through other representations).

7.4 Proportional Relationships and Percentages