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.

Start hereWords for this lesson

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

WordWhat it meansExample
Compare and Order IntegersSpanish: Comparar y ordenar enteros Use a number line to decide which integers are greater or less and place them in order. −5 < −2 < 0 < 3
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

How it worksWorked example

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

Lesson 7.4 — Compare and Order Integers and Rational Numbers: The number farther to the left is always less; the number farther to the right is always greater.

  1. Lesson 7.5 — Represent Rational Numbers on the Coordinate Plane: Always start at the origin (0, 0), move right/left first, then up/down.
  2. Lesson 7.6 — Determine Distance on the Coordinate Plane: If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values.
  3. Lesson 7.7 — Represent Polygons on the Coordinate Plane: When two vertices share a coordinate, the side between them is the absolute difference of the coordinates that differ.
  4. Lesson 7.8 — Ordered Pairs in All Four Quadrants: The signs of (x, y) tell you the quadrant: (+,+) is I, (-,+) is II, (-,-) is III, (+,-) is IV.
  5. Lesson 7.9 — Reflect Points Across Axes: Reflect over the x-axis: the y-coordinate changes sign. Reflect over the y-axis: the x-coordinate changes sign.

Now you trySame steps, your turn

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

From 7.4: Now let's compare -2 and 3. Which one is to the left on the number line? The -2 is left of zero.

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 Compare and Order IntegersNumber lineCompareOrderGreater thanLess thanreflectx-axisy-axisoppositesignchange

Watch outA common mistake

A common mistake in Reflect Points Across Axes is flipping the sign of the wrong coordinate — changing the x-coordinate when reflecting over the x-axis, instead of the y-coordinate (or vice versa for the y-axis). For example, to reflect (3, -5) over the x-axis, a student might flip the x-coordinate and write (-3, -5), but reflecting over the x-axis only changes the sign of the y-coordinate: (3, -5) becomes (3, 5). Before you submit, ask: 'Did I flip the sign of the coordinate that matches the axis I'm reflecting over — y for the x-axis, x for the y-axis?'

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.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 7.4) Which statement is TRUE?

    1. A-5 < -2
    2. B-4 > 0
    3. C-3 > -1
    4. D-1 < -6

    Hint Sketch a quick number line. For negatives, 'greater' means closer to zero, not a bigger digit.

    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    (Lesson 7.4) Which integer is the LEAST: -3, 5, -8, 2, 0?

    1. A-8
    2. B-3
    3. C0
    4. D5

    Hint 'Least' means farthest LEFT on the number line — for negatives, that's the one farthest below zero.

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    (Lesson 7.5) Which ordered pair names a point 3 units right and 7 units up from the origin?

    1. A(0, 7)
    2. B(3, 7)
    3. C(3, 3)
    4. D(7, 3)

    Hint Re-read the moves: 3 units right, then 7 units up. Which move comes first in an ordered pair?

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    (Lesson 7.5) What are the coordinates of the origin?

    1. A(0, 0)
    2. B(0, 1)
    3. C(1, 1)
    4. D(1, 0)

    Hint The origin is the exact spot where the x-axis and y-axis cross. Picture that crossing point.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    (Lesson 7.6) What is the distance between (-4, 3) and (2, 3)?

    1. A2 units
    2. B4 units
    3. C6 units
    4. D8 units

    Hint Both points have y = 3, so they sit on the same horizontal line — only the x-values differ.

    Show your work

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.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help