Section	Teacher-facing learning goals
Units of Measurement	Lesson 1 Evaluate (orally) the usefulness of calculating a rate per 1 when solving problems involving unfamiliar rates. Explain (orally, in writing, and through other representations) how to solve a problem involving rates in a less familiar context, e.g., minutes per window.
Unit Conversion	Lesson 2 - Optional Compare (orally) the relative size of different units of measure for one attribute, i.e., length, volume, weight or mass. Comprehend the approximate size of 1 “inch,” “foot,” “yard,” “mile,” “millimeter,” “centimeter,” “meter,” “kilometer,” “ounce,” “pound,” “ton,” “gram,” “kilogram,” “cup,” “quart,” “gallon,” “milliliter,” and “liter.” Identify which unit is closest to the length, volume, weight, or mass of a given object, and explain (orally) the reasoning. Lesson 3 Generalize (orally and in writing) that it takes more of a smaller unit or fewer of a larger unit to measure the same quantity. Given a measurement in one unit, estimate what would be the same amount expressed in a different unit, and explain (orally) the reasoning. Lesson 4 Choose and create a double number line diagram or table to solve problems involving unit conversion. Explain (orally) how to use a “rate per 1” to solve problems involving unit conversion. Recognize that when we measure things in two different units, the pairs of measurements are equivalent ratios.
Rates	Lesson 5 Explain (orally and in writing) that if two ratios have the same rate per 1, they are equivalent ratios. Justify (orally and in writing) comparisons of speeds or prices. Recognize that calculating how much for 1 of the same unit is a useful strategy for comparing rates. Express these rates (in spoken and written language) using the word “per” and specifying the unit. Lesson 6 Calculate and interpret the two unit rates associated with a ratio, i.e., \(\frac{a}{b}\) and \(\frac{b}{a}\) for the ratio \(a:b\). Choose which unit rate to use to solve a given problem and explain the choice (orally and in writing). Comprehend the term “unit rate” (in spoken and written language) refers to a rate per 1. Lesson 7 Apply reasoning about unit rates to complete a table of equivalent ratios, and explain (orally and in writing) the solution method. Explain (orally) that if two ratios are equivalent, they have the same rate per 1. Generalize that the unit rate is the factor that takes you from one column to the other column in a table of equivalent ratios. Lesson 8 Calculate unit rates that represent speed or pace, use them to determine unknown distances or elapsed times, and explain (orally) the solution method. Interpret a verbal (written) description of a situation involving two objects moving at constant speeds, and create a diagram or table to represent the situation. Lesson 9 Apply reasoning about ratios and rates to convert and compare (in writing) distances expressed in different units. Apply reasoning about ratios and rates to justify (orally) whether a given price is a good deal. Practice grade 5 arithmetic with fractions and decimals.
Percentages	Lesson 10 Comprehend the word “percentage” (in written and spoken language) and the symbol “%” (in written language) to mean a rate per 100. Draw and label a double number line diagram to represent percentages of a dollar and to find corresponding monetary values or percentages. Lesson 11 Comprehend a phrase like “A% of B” (in written and spoken language) to refer to the value that makes a ratio with B that is equivalent to A : 100. Explain (orally) how to use a double number line diagram or table to solve problems such as A% of B is ? and A% of ? is C. State explicitly what one is finding the percentage of. Lesson 12 Choose and create diagrams to solve problems such as A% of B is ? and A% of ? is C. Draw and label a tape diagram to represent a situation involving percentages. Interpret tape diagrams that represent multiplicative comparisons and express such comparisons using fractions and percentages. Lesson 13 Explain (orally and in writing) how to solve problems involving the percentages 10%, 25%, 50%, and 75% by reasoning about the fractions \(\frac1{10}\), \(\frac1{4}\), \(\frac1{2}\), and \(\frac3{4}\). Generalize (orally) processes for calculating 10%, 25%, 50%, and 75% of a quantity. Lesson 14 Choose and create a tape diagram, double number line diagram, or table to solve problems involving percentages and explain (orally) the solution method. Determine what information is needed to solve a problem involving percentages. Ask questions to elicit that information. Lesson 15 Choose and create diagrams to calculate A% of B, and explain (orally) the solution method. Generalize a process for finding A% of B and justify (orally) why this can be abstracted as \(\frac{A}{100} \cdot B\). Identify equivalent expressions that could be used to find A% of B and justify (orally) that they are equivalent. Lesson 16 Critique or justify (orally) statements about percentages and equivalent numerical expressions. Generalize a process for finding the percentage that C is of B and justify (orally) why this can be abstracted as \(\frac{C}{B} \cdot 100\).
Let’s Put it to Work	Lesson 17 Apply rates and percentages to calculate how long it will take and how much it will cost to complete a painting project, and explain (orally) the reasoning. Make simplifying assumptions and determine what information is needed to solve a problem about painting a room.

6.3 Unit Rates and Percentages