6.NS.1: Understanding and Solving Fraction Division Problems with Visual Models and Story Contexts

Grade: 6th Grade

Domain: NS: The Number System

Standard Description

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Domain Description

Understand and solve fraction division problems, such as (2/3) ÷ (3/4), by creating a story context and using visual fraction models. Troubleshoot real-life problems with multi-digit division, including dividing decimals. Identify the greatest common factor and least common multiple of certain whole numbers. Recognize how positive and negative numbers describe opposite values, and how 0 fits into this system.

Recognize opposite signs as indications of number positions on opposite sides of 0 on a number line. Understand the numerals in ordered pairs as number positions in quadrants on a coordinate plane. Comprehend statements of inequality as indicators of relative positions on number line diagrams (e.g. –3 > –7 indicates –3 is to the right of –7). Write, interpret, and explain real-world contexts of rational number order (e.g., –3 oC > –7 oC means –3 oC is warmer).

Understand absolute value based on distance from 0 on a number line and interpret it as size for real-world situations (e.g. write |–30| = 30 to reflect a financial debt). Differentiate between absolute value comparisons and order statements. Solve real-world and mathematical problems