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🟢 Easy
1Which integer is greater: −4 or −9?
💡 Hint
Think: On the number line, which of these two sits farther to the right?
Greater always means farther right on the number line, and −4 sits to the right of −9 (closer to 0). So −4 is greater. (Think temperature: −4° is warmer than −9°.) Answer: −4
2What is the opposite of 7?
💡 Hint
Think: Same distance from 0, but on the other side — which sign does that give?
An opposite keeps the same distance from 0 but flips to the other side, which means flipping the sign. The opposite of 7 is −7.
3Evaluate the absolute value: |−6|
💡 Hint
Think: How many units is −6 from 0 — and can a distance ever be negative?
Absolute value is the distance from 0, and distance ignores direction (the sign). From −6 to 0 is 6 units, so |−6| = 6.
4Put these in order from least to greatest: 5, −2, 0, −8 Write them separated by commas.
💡 Hint
Think: Reading the number line left to right, which end holds the smallest value?
Least to greatest is just left-to-right order on the number line, and the smallest sits farthest left. Order: −8, −2, 0, 5.
5Which quadrant contains the point (3, 5)?
💡 Hint
Think: Positive x sends you which way, and positive y sends you which way? Where do they meet?
Positive x means right and positive y means up, so (+, +) lands in the top-right region: Quadrant I.
6What is the opposite of −12?
💡 Hint
Think: Flip to the other side of 0 — does a negative's opposite come out positive or negative?
Taking the opposite flips the sign across 0, so the opposite of a negative is positive. The opposite of −12 is 12.
🟡 Medium
1Fill the blank with < or >: −3 ____ −10
💡 Hint
Think: Which number is farther right on the line — that one is the greater, so it gets the open end of the symbol.
Greater means farther right, and −3 sits to the right of −10 (closer to 0). The > symbol opens toward the larger value, so −3 > −10.
2Which number has the greater absolute value: −8 or 5?
💡 Hint
Think: Strip the signs and ask which distance from 0 is bigger.
Absolute value is distance from 0, so the sign doesn't matter — only size does. |−8| = 8 and |5| = 5, and 8 > 5, so −8 has the greater absolute value. (Even though −8 itself is the smaller number!)
3Reflect the point (4, 3) across the y-axis. What are the new coordinates?
💡 Hint
Think: The y-axis is a vertical mirror — flipping side to side changes which coordinate's sign?
The y-axis is vertical, so reflecting across it flips you left-to-right — the x sign changes and y stays the same. (4, 3) → (−4, 3).
4Which quadrant contains the point (−6, 2)?
💡 Hint
Think: Negative x sends you which way, positive y sends you which way? Where do those meet?
Negative x means left and positive y means up, so (−, +) lands in the top-left region: Quadrant II.
5Put these in order from least to greatest: −1, −9, 4, −4, 2 Separate with commas.
💡 Hint
Think: Sort by position on the number line — the most-negative number comes first.
Least to greatest is left-to-right on the number line, so the most negative goes first: −9, −4, −1, 2, 4.
6Starting at the origin, you move 5 left and then 3 down. Write the point as an ordered pair.
💡 Hint
Think: Left and down each attach which sign — and which value gets written first?
Left means negative x and down means negative y, and x is always written first. The point is (−5, −3) — both negative, so Quadrant III.
🔴 Hard
1Find the distance between the points (2, 7) and (2, −4). They share the same x-coordinate.
💡 Hint
Think: Same x means a purely vertical move — how far apart are the two y-values? Try |7 − (−4)|.
When x is shared the points lie on one vertical line, so distance is just the gap between the y-values. Subtracting and taking absolute value handles the sign automatically: |7 − (−4)| = |7 + 4| = 11 units.
2Reflect the point (−3, −5) across the x-axis. What are the new coordinates?
💡 Hint
Think: The x-axis is a horizontal mirror — flipping top to bottom changes which coordinate's sign?
The x-axis is horizontal, so reflecting across it flips you top-to-bottom — the y sign changes and x stays. (−3, −5) → (−3, 5).
3True or False? −40 > −25
💡 Hint
Think: Is −40 farther left or right of −25 — and which direction means greater?
Greater means farther right, but −40 is farther left (colder, deeper) than −25, so −40 is actually smaller. The statement is False — the true one is −40 < −25.
4Which is greater: −|−8| or −5?
💡 Hint
Think: Simplify −|−8| first (work inside the bars, then apply the outer minus) — what plain number is that? Then compare on the line.
Work from the inside out: |−8| = 8, then the leading minus gives −|−8| = −8. Now compare −8 and −5 — −5 is farther right, so −5 is greater.
5Find the distance between (−6, 4) and (9, 4). They share the same y-coordinate.
💡 Hint
Think: Same y means a purely horizontal move — how far apart are the two x-values? Try |−6 − 9|.
When y is shared the points lie on one horizontal line, so distance is just the gap between the x-values. The absolute value keeps the answer positive no matter the order: |−6 − 9| = |−15| = 15 units.
6Point P = (−3, 6) is reflected across the y-axis, and that result is then reflected across the x-axis. Where does it land?
💡 Hint
Think: Each reflection flips just one coordinate's sign — apply them one at a time, in order.
Do the reflections in sequence. Across the y-axis flips x: (−3, 6) → (3, 6). Then across the x-axis flips y: (3, 6) → (3, −6). Two reflections, one for each axis, end up flipping both signs.
Grounded in CA CCSS-M, Grade 6 · 6.NS, California Department of Education. Image generated with Gemini Nano Banana Pro.
