6.2

6.2 is a knowledge and skills statement. These are the student expectations under it.

• 6.2.A

  classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers

• 6.2.B

  identify a number, its opposite, and its absolute value

• 6.2.C

  locate, compare, and order integers and rational numbers using a number line

• 6.2.D

  order a set of rational numbers arising from mathematical and real-world contexts

• 6.2.E

  extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0

01

What Students Need to Do

Students sort numbers into whole number, integer, and rational number sets and show how those sets overlap. They find opposites and absolute values, then place, compare, and order positive and negative rational numbers. They also connect fraction notation to division and recognize that the denominator cannot be zero.

02

What Mastery Looks Like

Given mixed forms such as -3, 0.5, 7/4, and 2, students place each correctly in a nested diagram and on a number line. They justify an order using location, sign, or equivalent forms. They write a/b as a ÷ b and reject expressions with a zero denominator.

03

Common Misconceptions

Students may treat whole numbers, integers, and rational numbers as separate sets instead of nested sets. They may think absolute value makes every number negative, or that -8 is greater than -3 because 8 is greater than 3. They may compare unlike forms without converting them or allow zero as a denominator.

04

How to Assess It

Give this exit ticket: Classify, order, and plot -3, 0, 1/2, 2.5, and 4. Then name the opposite and absolute value of -3, rewrite 1/2 as division, and explain why 1/0 is invalid.

1. 01

   Tape a number line on the floor; students place rational-number cards, then stand by each card's opposite.

2. 02

   Ask, "Which is greater, -3/4 or -0.6?" Students write a claim and justify it with equivalent decimals or a number line.

3. 03

   Play number-card war with fractions, decimals, and integers; partners reveal cards, compare values, and explain before taking the pair.

4. 04

   Give temperature, debt, and elevation cards; groups order the values and explain what each opposite and absolute value means.

• 5.2

  The student applies mathematical process standards to represent, compare, and order positive rational numbers and understand relationships as related to place v...

• 7.2

  The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to extend previous know...

• 5.3

  The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problem...

• 8.2

  The student applies mathematical process standards to represent and use real numbers in a variety of forms