A focused Grade 6 learning session for Comparing and Ordering Rational Numbers using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving comparing and ordering rational numbers.
Comparing and Ordering Rational Numbers means using place value, operations, and equations to reason accurately with numbers.
Question: What is the relationship between points \(P\) and \(Q\)?
Why it works: \(P\) is at \(-1\) and \(Q\) is at \(2\). Since \(-1 < 2\), point \(P\) is less than point \(Q\).
Answer: \(P < Q\) or \(-1 < 2\)
Question: Which city is coldest?
| City | A | B | C | D |
|---|---|---|---|---|
| Temperature (\degree C) | \(-5\) | \(2\) | \(-1\) | \(0\) |
Answer: City A
Question: Which is true?
Answer: Red \(<\) Blue or \(-3 < 1\)
Question: Marcus has \($5\) and Jessica has a debt of \($3\) (written as \(-3\)). Who has more money?
Why it works: \(5 > -3\), so Marcus has more money.
Answer: Marcus
Comparing and Ordering Rational Numbers becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Which list shows the numbers in order from least to greatest? \(\)-2.5,\ \ \frac{1}{4},\ \ -3,\ \ 1.75\(\)
Answer A: \(-3,\ -2.5,\ \frac{1}{4},\ 1.75\)
On a number line, more negative numbers are less. \(-3<-2.5<0<\frac{1}{4}<1.75\).
Compare \(-4\) and \(-1\) using \(<\), \(>\), or \(=\). Which symbol belongs in the box? \(\)-4 \square -1\(\)
Answer A: \(<\)
\(-4\) is further left on a number line than \(-1\), so \(-4\) is less than \(-1\).
Order these numbers from greatest to least: \(\)0.6,\ -\frac{3}{4},\ 0.1,\ -2\(\)
Answer B: \(0.6,\ 0.1,\ -\frac{3}{4},\ -2\)
Positive numbers are greater than negative numbers. Among positives: \(0.6>0.1\). Among negatives: \(-\frac{3}{4}=-0.75>-2\).
Which number is less than \(-5\)?
Answer D: \(-6\)
\(-6<-5\) because \(-6\) is further left on the number line.
What is the relationship between points \(P\) and \(Q\)?
Answer D: \(P < Q\)
\(P\) is at \(-1\) and \(Q\) is at \(2\). Since \(-1 < 2\), point \(P\) is less than point \(Q\).
Which comparison is true?
Answer D: \(-0.8 < -0.3\)
\(-0.8\) is further left on the number line than \(-0.3\), so it is less. All other comparisons are false.
A temperature of \(-8° F\) is compared to \(-3° F\). Which statement is correct?
Answer C: \(-8° F\) is colder
\(-8 < -3\), so \(-8° F\) represents a lower (colder) temperature.
If \(A = 1\) and \(B = 4\), order \(-A\), \(-B\), and \(0\).
Answer A: \(-B < -A < 0\)
\(-B = -4\) and \(-A = -1\). Since \(-4 < -1 < 0\), the order is \(-B < -A < 0\).
Which list is in order from least to greatest?
Answer B: \(-0.5,\ -0.2,\ 0.3,\ 0.8\)
All negatives come before zero, and all zeros come before positives. Among negatives, \(-0.5<-0.2\). Among positives, \(0.3<0.8\).
Compare \(-\frac{2}{3}\) and \(-\frac{1}{3}\). Which symbol makes the statement true? \(\)-\frac{2}{3} \square -\frac{1}{3}\(\)
Answer A: \(<\)
Both are negative. Since \(-\frac{2}{3} \approx -0.67\) and \(-\frac{1}{3} \approx -0.33\), we have \(-\frac{2}{3}<-\frac{1}{3}\).
Which city is coldest?
Answer A: City A
City A has the lowest temperature at \(-5° C\). Ordering: \(-5 < -1 < 0 < 2\).
