ALEX Classroom Resource

Students:

• Convert different-sized measurement units within the same system.
• Solve multi-step word problems involving conversion of metric or customary units.

Students know:

• Strategies for converting a larger unit of measure to a smaller unit in the same system.
• Relative size of customary and metric units of measure.
• Strategies for converting between units of measure in the same system.

Students are able to:

• Convert measurement units.
• Solve multi-step word problems involving measurement conversions.

Students understand that:

• the multiplicative relationship between units of measures given in the same measurement system is essential when converting units to a larger or smaller unit.

Learning Objectives:
M.5.17.1: Identify relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec.
M.5.17.2: Express measurements in a larger unit in terms of a smaller unit.
M.5.17.3: Solve two-step word problems.
M.5.17.4: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
M.5.17.5: Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
M.5.17.6: Recall basic addition, subtraction, multiplication, and division facts.

Students:
Given contextual or mathematical situations involving multiplicative comparisons,

• Use unit rate to solve missing value problems (e.g., cost per item or distance per time unit).
• Use rate language to explain the relationships between ratio of two quantities as non-complex fractions and the associated unit rate of one of the quantities in terms of the other.

Students know:

• Characteristics of multiplicative comparison situations.
• Rate and ratio language.
• Techniques for determining unit rates.
• To use reasoning to find unit rates instead of a rule or using algorithms such as cross-products.

Students are able to:

• Explain relationships between ratios and the related unit rates.
• Use unit rates to name the amount of either quantity in terms of the other quantity flexibly.
• Represent contextual relationships as ratios.

Students understand that:

• A unit rate is a ratio (a:b) of two measurements in which b is one.
• A unit rate expresses a ratio as part-to-one or one unit of another quantity.

Learning Objectives:
M.6.2.1: Define unit rate, proportion, and rate.
M.6.2.2: Create a ratio or proportion from a given word problem.
M.6.2.3: Calculate unit rate by using ratios or proportions.
M.6.2.4: Write a ratio as a fraction.

Students:
Given contextual or mathematical situations involving ratio and rate (including those involving unit pricing, constant speed, and measurement conversions),

• Represent the situations using a variety of strategies (tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes) in order to solve problems, find missing values on tables and interpret relationships and results.
• Change given rates to unit rates in order to find and justify solutions to problems.

Given contextual or mathematical situations involving percents,

• Understand the relationship between ratios, fractions, decimals and percents.
• Interpret the percent as rate per 100.
• Solve problems and justify solutions when finding the whole, given a part and the percent.
• Solve problems and justify solutions when finding the part, given the whole and the percent.
• Solve problems and justify solutions when finding percent, given the whole and the part.

Students know:

• Strategies for representing contexts involving rates and ratios including. tables of equivalent ratios, changing to unit rate, tape diagrams, double number lines, equations, and plots on coordinate planes.
• Strategies for finding equivalent ratios,
• Strategies for using ratio reasoning to convert measurement units.
• Strategies to recognize that a conversion factor is a fraction equal to 1 since the quantity described in the numerator and denominator is the same.
• Strategies for converting between fractions, decimals and percents.
• Strategies for finding the whole when given the part and percent in a mathematical and contextual situation.
• Strategies for finding the part, given the whole and the percent in mathematical and contextual situation.
• Strategies for finding the percent, given the whole and the part in mathematical and contextual situation.

Students are able to:

• Represent ratio and rate situations using a variety of strategies (e.g., tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes).
• Use ratio, rates, and multiplicative reasoning to explain connections among representations and justify solutions in various contexts, including measurement, prices and geometry.
• Understand the multiplicative relationship between ratio comparisons in a table by writing an equation.
• Plot ratios as ordered pairs.
• Solve and justify solutions for rate problems including unit pricing, constant speed, measurement conversions, and situations involving percents.
• Solve problems and justify solutions when finding the whole given a part and the percent.
• Model using an equivalent fraction and decimal to percents.
• Use ratio reasoning, multiplication, and division to transform and interpret measurements.

Students understand that:

• A unit rate is a ratio (a:b) of two measurements in which b is one.
• A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation.
• When computing with quantities the transformation and interpretation of the resulting unit is dependent on the particular operation performed.

Learning Objectives:
M.6.3.1: Define ratio, rate, proportion, percent, equivalent, input, output, ordered pairs, diagram, unit rate, and table.
M.6.3.2: Create a ratio or proportion from a given word problem, diagram, table, or equation.
M.6.3.3: Calculate unit rate or rate by using ratios or proportions with or without a calculator.
M.6.3.4: Restate real-world problems or mathematical problems.
M.6.3.5: Construct a graph from a set of ordered pairs given in the table of equivalent ratios.
M.6.3.6: Calculate missing input and/or output values in a table with or without a calculator.
M.6.3.7: Draw and label a table of equivalent ratios from given information.
M.6.3.8: Identify the parts of a table of equivalent ratios (input, output, etc.).
M.6.3.9: Compute the unit rate, unit price, and constant speed with or without a calculator.
M.6.3.10: Create a proportion or ratio from a given word problem.
M.6.3.11: Identify the two units being compared.
M.6.3.12: Define percent.
M.6.3.13: Calculate a proportion for missing information with or without a calculator.
M.6.3.14: Identify a proportion from given information.
M.6.3.15: Solve a proportion using part over whole equals percent over 100 with or without a calculator.
M.6.3.16: Form a ratio.
M.6.3.17: Convert like measurement units within a given system with or without a calculator. (Example: 120 min = 2 hrs).
M.6.3.18: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec.

Students:

• Compute a unit rate for ratios that compare quantities with different units.
• Determine the unit rate for a given ratio, including unit rates expressed as a complex fraction.

Example: if a runner runs 1/2 mile every 3/4 hour, a student should be able to write the ratio as a complex fraction.)

Students know:

• What a unit rate is and how to calculate it given a relationship between quantities.
• Quantities compared in ratios are not always whole numbers but can be represented by fractions or decimals.
• A fraction can be used to represent division.

Students are able to:
Compute unit rates associated with ratios of fractional

• lengths.
• Areas.
• quantities measured in like or different units.

Students understand that:

• Two measurements that create a unit rate are always different (miles per gallon, dollars per hour)

Learning Objectives:
M.7.1.1: Define unit rate, proportions, area, length, and ratio.
M.7.1.2: Recall how to find unit rates using ratios.
M.7.1.3: Recall the steps used to solve division of fraction problems.

Students:

• Compute a unit rate for ratios that compare quantities with different units.
• Determine the unit rate for a given ratio, including unit rates expressed as a complex fraction.
Example, if a runner runs mile every hour, a student should be able to write the ratio as a complex fraction.)

Students know:

• What and how to calculate a unit rate to represent a given relationship between quantities.
• Quantities compared in ratios are not always whole numbers but can be represented by fractions or decimals.
• A fraction can be used to represent division.

Students are able to:
Compute unit rates associated with ratios of fractional:

• Lengths.
• Areas.
• Quantities measured in like or different units.

Students understand that:

• the two measurements that create a unit rate are always different (miles per gallon, dollars per hour).