Understand ordering and absolute value of rational numbers.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
On a number line that runs left to right, numbers get larger as you move right. That simple fact is the basis for ordering rational numbers in sixth grade. The statement -3 > -7 is true because -3 sits to the right of -7, and in context it means something like -3 °C is warmer than -7 °C. Students write, read and explain inequality statements like this for integers, fractions and decimals.
Absolute value is the second idea. The absolute value of a number is its distance from 0, so |-30| = 30 and |30| = 30. In context, absolute value gives size without direction: an account balance of -30 dollars represents a debt of 30 dollars. The standard ends with a subtle point that trips up many learners. A balance less than -30 dollars, such as -45, is a smaller number but a bigger debt. Students must tell apart a comparison of values (-45 < -30) from a comparison of magnitudes (|-45| > |-30|).
Students often think -8 is greater than -3 because 8 is greater than 3. Placing both on a number line shows -8 is further left, so it is less.
The rule works, but students who cannot explain absolute value as distance struggle with context questions. Always connect |-5| to 5 steps from 0.
A balance of -50 dollars is less than -20 dollars, yet the debt is larger. Ask 'which is the smaller number?' and 'which is the bigger debt?' as separate questions.
Sam's account balance is -45 dollars and Lee's is -30 dollars. Write an inequality comparing the balances, then decide who owes more.
Answer: -45 < -30, and Sam owes more because |-45| = 45 is greater than |-30| = 30.
Use contexts where both comparisons matter: temperatures (which is colder versus which is further from 0), elevations below sea level, and money owed. A vertical number line drawn as a thermometer helps students see that 'below' means 'less'.
Assessments often present four statements and ask which are true, mixing order and absolute value. Practice explaining each statement in words, for example '-6 °F is colder than -2 °F, so -6 < -2'.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: B) -3 > -7
On a number line, -3 is to the right of -7, so -3 is greater: -3 > -7.
Answer: 18
Absolute value is distance from 0. -18 is 18 units from 0, so |-18| = 18.
Answer: D) -2, -1.5, 0, 3/4
-2 is furthest left, then -1.5, then 0, then 3/4.
Answer: A) Town B is warmer because -5 > -12
-5 is to the right of -12 on the number line, so -5 > -12 and Town B is warmer.
Answer: 9
|-9| = 9 and |4| = 4. 9 is larger.
Answer: C) The diver at -40 feet is deeper, and -40 < -25
-40 is further below sea level, so it is deeper. As numbers, -40 < -25.
A full lesson with slides, activities and an exit ticket on ordering rational numbers and absolute value, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.NS.C.7 with an answer key, ready in about a minute.
Make a worksheet →Turn ordering rational numbers and absolute value into a quiz students answer online that marks itself, with a class summary for you.
Build a test →The absolute value of a number is its distance from 0 on the number line, so it is never negative. For example |-7| = 7 and |7| = 7.
Because they answer different questions. -50 is less than -10, but a 50-dollar debt is larger than a 10-dollar debt. Students must know which comparison a situation needs.