Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.GR.3

Lesson 7.7Represent Polygons on the Coordinate Plane

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems.

Why This Matters A polygon's vertices are given as coordinates: (-4.5, 3), (5, 3), (5, -3.75), and (-4.5, -3.75). What is its perimeter?

Start hereWords for this lesson

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

WordWhat it meansExample
vertexSpanish: vértice A corner point of a polygon, named by an ordered pair on the coordinate plane. named by an ordered pair
polygonSpanish: polígono A closed figure made of line segments; on the plane you draw it by plotting the vertices and connecting them in order. triangle, rectangle, square
perimeterSpanish: perímetro The total distance around a polygon — the sum of all its side lengths. add every side length
distance between verticesSpanish: distancia entre vértices When two vertices share an x- or y-coordinate, the distance between them is the absolute difference of the other coordinates. (2, 4) and (5, 4) share y, so the side is |5 − 2| = 3 units.
scaleSpanish: escala What one grid unit stands for in the real situation. 1 unit = 1 meter
Side lengthSpanish: Longitud del lado The distance between two vertices that are joined by a side. found with absolute value

How it worksWorked example

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

A rectangle has vertices (−2, 3), (5, 3), (5, −2) and (−2, −2). Each unit is 1 meter. Find its perimeter.

  1. Top side: same y, so 2 + 5 = 7 m.
  2. Right side: same x, so 3 + 2 = 5 m.
  3. Add all four sides: 7 + 5 + 7 + 5 = 24.

Answer: Perimeter = 24 m

Now you trySame steps, your turn

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

The shape is a rectangle, so the opposite sides match: two sides of 9.5 and two of 6.75.

Answer:

Say it and write itSentence starters

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

  • Vertices and share the -coordinate, so that side runs .
  • The length of that side is units because .
  • The perimeter is units because I added .
  • This polygon is a because .

Word bank vertexpolygonperimeterside lengthcoordinate planeabsolute valuehorizontalverticalrectanglesquareaddunits

Watch out!A common mistake

Subtracting coordinates without the absolute value

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.GR.3

Lesson 7.7Represent Polygons on the Coordinate Plane

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

Learning target I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems.

Why This Matters A polygon's vertices are given as coordinates: (-4.5, 3), (5, 3), (5, -3.75), and (-4.5, -3.75). What is its perimeter?

How it worksWorked example

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

A rectangle has vertices (−2, 3), (5, 3), (5, −2) and (−2, −2). Each unit is 1 meter. Find its perimeter.

  1. Top side: same y, so 2 + 5 = 7 m.
  2. Right side: same x, so 3 + 2 = 5 m.
  3. Add all four sides: 7 + 5 + 7 + 5 = 24.

Answer: Perimeter = 24 m

  1. 1Circle the letter of the best answer. Show how you know.

    Vertices (-4.5, 3) and (5, 3) share y = 3. What is the distance between them?

    1. A0.5 units
    2. B1.5 units
    3. C8 units
    4. D9.5 units
    Steps to try
    1. Which coordinate is the same? Which differs?
    2. The x-values are −4.5 and 5.
    3. Distance crosses zero: 4.5 to reach 0, then 5 more.
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  2. 2Circle the letter of the best answer. Show how you know.

    Vertices (5, 3) and (5, -3.75) share x = 5. What is the distance between them?

    1. A0.75 units
    2. B5 units
    3. C6.75 units
    4. D8.75 units
    Steps to try
    1. Which coordinate differs?
    2. The y-values are 3 and −3.75.
    3. 3 above zero plus 3.75 below zero.
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  3. 3Circle the letter of the best answer. Show how you know.

    What is the perimeter of the rectangle with side lengths 9.5 and 6.75 units?

    1. A16.25 units
    2. B26 units
    3. C32.5 units
    4. D64.125 units
    Steps to try
    1. A rectangle has four sides.
    2. Each length appears twice.
    3. 2(9.5) + 2(6.75).
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  4. 4Circle the letter of the best answer. Show how you know.

    Why are two of the terms multiplied by 2 in the perimeter calculation?

    1. ABecause perimeter always doubles the area
    2. BBecause there are two coordinates in each ordered pair
    3. CIt is a rounding rule
    4. DA rectangle's opposite sides are equal, so each length appears on two sides
    Steps to try
    1. Walk the rectangle: how many 9.5 sides?
    2. Two of each length.
    3. The 2 counts the matching sides.
    Show your work

Explain your thinkingTake a side you both put under 'Slanted.' Why does subtracting coordinates give the wrong length there, and what has to be true about two vertices for subtraction to work?

Sentence starter Subtracting works when the two vertices share ___, so for ___ I cannot ___.

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