By the end of this unit, students are expected to:
Understand fractions and decimals as numbers that can be located on the number line, compared, counted, partitioned, and decomposed.
Expand interpretations of a fraction to include expressing a fraction as a part–whole relationship, as a number, and as an indicated division
Reason about the roles of the numerator and denominator in each of the interpretations of a fraction
Use multiple interpretations of proper fractions, improper fractions, and mixed numbers
Use decimals to represent fractional quantities with attention to place value
Recognize that fractions are called rational numbers and that rational numbers are points on the number line
Use the number line to reason about rational number relationships
Use benchmarks to estimate the values of fractions and decimals and to compare and order fractions and decimals
Recognize that fractions can represent both locations and distances on the number line
Recognize that a number and its opposite are at equal distances from zero on the number line; the opposite of a is –a and the opposite of –a is a
Recognize that the absolute value of a number is its distance from 0 on the number line and use that value to describe real-world quantities
Introduce percent as a part–whole relationship in which the whole is not necessarily out of 100, but is scaled or partitioned to be “out of 100” or “per 100”
Apply a variety of partitioning strategies to solve problems
Understand ratios as comparisons of two numbers.
Use ratios and associated rates to compare quantities
Distinguish between a difference, which is an additive comparison, and a ratio, which is a multiplicative comparison
Distinguish between fractions as numbers and ratios as comparisons
Apply a variety of scaling strategies to solve problems involving ratios and unit rates
Recognize that a unit rate is a ratio in which one of the quantities being compared has a value of 1; use rate language in the context of a ratio relationship
Scale percents to predict new outcomes
Understand equivalence of fractions and ratios, and use equivalence to solve problems.
Recognize that equivalent fractions represent the same amount, distance, or location; develop strategies for finding and using equivalent fractions
Recognize that comparing situations with different-sized wholes is difficult without some common basis of comparison
Use partitioning and scaling strategies to generate equivalent fractions and ratios and to solve problems
Develop meaningful strategies for representing fraction amounts greater than 1 or less than –1 as both mixed numbers and improper fractions
Recognize that equivalent ratios represent the same relationship between two quantities; develop strategies for finding and using equivalent ratios
Build and use rate tables of equivalent ratios to solve problems
What is a Ratio? - AAA Math description and practice
Ratios Coloring Game - Practice in representing ratios
Ratio Jeopardy - Multi-player review on ratios
What is a Unit Rate? - AAA Math description and practice
Braining Camp Lesson on Rate - Lesson on rates and unit rates with interactive practice
What is a Unit Price? - AAA Math description and practice
Unit Rate and Unit Price Jeopardy - Individual or multi-player practice
What is Absolute Value? - AAA Math description and practice