6.N.1.2 Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.
In a Nutshell
Positive rational numbers are all positive numbers that can be expressed in the form a/b. Rational numbers can be expressed as a fraction, integer, terminating decimal, or as a repeating decimal. Students have previous knowledge of comparing decimals using place value and comparing fractions and mixed numbers. Expanding on this knowledge, 6th graders will continue to compare and begin ordering rational numbers in different forms. The comparison symbols < (less than), > (greater than) and = (equal to) are used to compare the value of two rational numbers.
Student Actions

Teacher Actions


Develop deep and flexible conceptual understanding of equivalencies among fractions, decimals and percents by comparing and ordering positive rational numbers on a number line or with pictorial representations.

Use previous knowledge to continue developing mathematical reasoning when determining where rational numbers fall on the number line.
 Develop strategies to compare rational numbers and integers using comparison symbols: <, >, =. (For Example: Students could use a number line to plot rational numbers, then compare by going left to right as least to greatest.)


Implement tasks that promote reasoning and problem solving by helping students develop these strategies for comparing and ordering positive rational numbers, including converting between fractions, decimals, and percents to compare value (See 6.N.1.4)
 Use and connect mathematical representations including both concrete (Ex: fraction strips) and visual representations (Ex: grids, pictures, vertical and horizontal number lines) to guide as students visually compare positive rational numbers and integers.

Key Understandings

Misconceptions


How to compare and order positive rational numbers.

The meaning of the comparison symbols for less than (<). Greater than (>),and equal to (=).


Make mistakes with place value when comparing decimals. (Ex: Students may think 2.4 < 2.25 because 4 is less than 25.)

Incorrectly use the tick marks on a number line to count fractions. (Ex: there are only 3 tick marks between whole numbers for 1/4s which could result in students identifying sections as thirds.)

Incorrectly order fractions by failing to understand the relationship between the size of the section and the size of the denominator. (Ex: Students may think ⅓ > ½ because 3 is greater than 2.)

Not understand the correlation between fractions and decimals.

OKMath Framework Introduction
6th Grade Introduction
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