Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.7

Lesson 7.97.4–7.9 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 7.4–7.9 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 7.4–7.9: 7.4 Compare and Order Integers and Rational Numbers, 7.5 Represent Rational Numbers on the Coordinate Plane, 7.6 Determine Distance on the Coordinate Plane, 7.7 Represent Polygons on the Coordinate Plane, 7.8 Ordered Pairs in All Four Quadrants, 7.9 Reflect Points Across Axes. Work one example from each lesson, then prove you're caught up in the mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Number lineSpanish: Recta numérica A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right. ← -3 -2 -1 0 1 2 3 →
CompareSpanish: Comparar To see if a number is bigger, smaller, or equal to another. -3 < 2 because -3 is farther left on the number line than 2
OrderSpanish: Ordenar To arrange numbers by size, from least to greatest or greatest to least. Least to greatest: -5, -2, 0, 3, 7 (left to right on the number line)
Greater thanSpanish: Mayor que The > sign, showing one number is bigger. 4 > -1 because 4 is to the right of -1 on the number line
Less thanSpanish: Menor que The < sign, showing one number is smaller. -6 < -2 because -6 is farther left — it is farther from zero
Negative integerSpanish: Entero negativo A whole number smaller than zero, like -5. -4 is 4 units to the LEFT of zero on the number line

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Compare −7 and −5. Use < or >.

  1. Find both numbers on the number line: −7 and −5
  2. Choose the number that is farther left: −7
  3. Write the comparison: −7 < −5
  4. −7 < −5
  5. Plot the point (5, 4) on the coordinate plane.
  6. Start at the origin: (0, 0)
  7. Move right 5 for x: x = 5
  8. Move up 4 for y. Draw the dot: y = 4
  9. (5, 4) is 5 units right and 4 units up from the origin.
  10. Find the distance between (−3, 2) and (4, 2).
  11. Find the coordinate that is the same: y = 2 for both
  12. Find the absolute value of each x: |−3| = 3 → |4| = 4
  13. Add, because 0 is between them: 3 + 4 = 7
  14. The distance is 7 units.
  15. Find the length of the side from (−4.5, 3) to (5, 3).
  16. Find the coordinate that is the same: y = 3 for both
  17. Add the absolute values of the x-values: |−4.5| + |5| = 4.5 + 5 = 9.5
  18. The side is 9.5 units long.
  19. Plot the point (−3, −4). Name the quadrant it is in.
  20. Move left 3, because x is negative: x = −3 → left 3
  21. Move down 4, because y is negative: y = −4 → down 4
  22. Name the quadrant from the signs: (−, −) → Quadrant III
  23. (−3, −4) is in Quadrant III.
  24. Reflect the point (3, 2) across the y-axis.
  25. Change the sign of x: 3 → −3
  26. Keep y the same: 2 → 2
  27. The reflection is (−3, 2).

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Which number is greater: −1 or −6?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • When I reflect over the x-axis, the -coordinate changes sign and the -coordinate stays the same. When I reflect over the y-axis, the -coordinate changes sign and the -coordinate stays the same.

Word bank Number lineCompareOrderGreater thanLess thanNegative integerreflectx-axisy-axisoppositesignchange

Watch out!A common mistake

A common mistake in Reflect Points Across Axes is flipping the sign of the wrong coordinate

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.7

Lesson 7.97.4–7.9 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 7.4–7.9 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 7.4–7.9: 7.4 Compare and Order Integers and Rational Numbers, 7.5 Represent Rational Numbers on the Coordinate Plane, 7.6 Determine Distance on the Coordinate Plane, 7.7 Represent Polygons on the Coordinate Plane, 7.8 Ordered Pairs in All Four Quadrants, 7.9 Reflect Points Across Axes. Work one example from each lesson, then prove you're caught up in the mixed practice.

  1. 1Complete each step, then write the final answer.

    Which is greater: −16 or −8?

    Show your work

    Hint The number farther right on a number line is greater.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Which symbol goes in −4 ___ 2? Use < or >.

    Show your work

    Hint A negative number is always left of a positive number.

    Final answer:
  3. 3Complete each step, then write the final answer.

    To plot (9, 1), how many units do you move up from the origin?

    Show your work

    Hint The second number is y. It tells how far to move up.

    Final answer:
  4. 4Complete each step, then write the final answer.

    A point is 4 units right and 6 units up from the origin. What is its y-coordinate?

    Show your work

    Hint y tells how far up the point is.

    Final answer:
  5. 5Complete each step, then write the final answer.

    Find the distance between (−1, 3) and (5, 3).

    Show your work

    Hint 0 is between −1 and 5. Add the distances from 0.

    Final answer:
  6. 6Complete each step, then write the final answer.

    Find the distance between (2, 1) and (2, 9).

    Show your work

    Hint Both y-values are positive. Subtract them.

    Final answer:
  7. 7Complete each step, then write the final answer.

    Find the length of the side from (−3, 5) to (4, 5).

    Show your work

    Hint Both points have y = 5. Add the distances from 0.

    Final answer:
  8. 8Complete each step, then write the final answer.

    A rectangle has vertices (−2, 1), (3, 1), (3, −3) and (−2, −3). Find its perimeter.

    Show your work

    Hint Find one side across and one side up and down. Then add all four sides.

    Final answer:
  9. 9Complete each step, then write the final answer.

    Which quadrant is the point (2, 7) in?

    Show your work

    Hint Both numbers are positive. Move right, then up.

    Final answer:
  10. 10Complete each step, then write the final answer.

    Which quadrant is the point (−6, −1) in?

    Show your work

    Hint Both numbers are negative. Move left, then down.

    Final answer:
  11. 11Complete each step, then write the final answer.

    Reflect (2, 5) across the y-axis. The new point is (?, 5). What is the missing x-coordinate?

    Show your work

    Hint Across the y-axis, x changes sign.

    Final answer:
  12. 12Complete each step, then write the final answer.

    Reflect (−3, −1) across the x-axis. The new point is (−3, ?). What is the missing y-coordinate?

    Show your work

    Hint Across the x-axis, y changes sign.

    Final answer:

Explain your thinkingWhat pattern do you notice about the coordinates when reflecting over the x-axis versus the y-axis?

Sentence starter When I reflect over the x-axis, the ___ -coordinate changes sign and the ___ -coordinate stays the same. When I reflect over the y-axis, the ___ -coordinate changes sign and the ___ -coordinate stays the same.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help