CCSS.Math.Content.8.NS.A

CCSS.Math.Content.8.NS.A is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.8.NS.A.1

  Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that t...

• CCSS.Math.Content.8.NS.A.2

  Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate th...

01

What Students Need to Do

Students identify rational and irrational numbers shown as fractions, roots, and decimals. They approximate irrational values with decimals, compare them, and place them on a number line.

02

What Mastery Looks Like

Students can explain that rational decimals terminate or repeat, while irrational decimals do neither. They can bound a square root between integers, estimate it, and place it accurately on a number line.

03

Common Misconceptions

Students may think every square root is irrational, including √9. They may label any long decimal irrational without checking for a repeating pattern. Some round too early and misplace values on a number line.

04

How to Assess It

Use an exit ticket: classify √49, √20, and 0.272727... as rational or irrational, then estimate √20 to the nearest tenth.

1. 01

   Give pairs cards showing fractions, roots, and decimals; have them sort the cards, justify each choice, then place values on a number line.

2. 02

   Ask, "Is every square root irrational?" Students write a claim and use examples such as √9 and √10 as evidence.

3. 03

   Play Irrational Number Line: teams draw a value card, estimate its location, and score a point when their placement is within tolerance.

4. 04

   Give a square patio with area 50 square meters; students estimate the side length and decide how accurately a builder should measure.

• CCSS.Math.Content.HSN-RN.B

  Use properties of rational and irrational numbers.

• CCSS.Math.Content.6.NS.C

  Apply and extend previous understandings of numbers to the system of rational numbers.