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

Lesson 7.77.7 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, 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 — one step at a time, with support.

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 examplefinding the perimeter of a rectangle from its vertices

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

A rectangle has vertices at (−8.5, 7.5), (5.5, 7.5), (5.5, −3.5), and (−8.5, −3.5). Find its perimeter.

  1. Plot the four vertices and connect them in order to draw the rectangle.
  2. Top side: the y-coordinates match, so use the x-values: −8.5 + 5.5 = 14
  3. Left side: the x-coordinates match, so use the y-values: 7.5 + −3.5 = 11
  4. Perimeter adds all four sides: 14 + 11 + 14 + 11 = 50

Answer: The rectangle measures 14 units by 11 units, so its perimeter is 50 units.

Now you trySame steps, your turn

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

A rectangle has vertices at (−6.25, 9.75), (2.75, 9.75), (2.75, −3.25), and (−6.25, −3.25). Find its perimeter.

  1. Plot the four vertices and connect them in order to draw the rectangle.
  2. Top side: the -coordinates match, so use −6.25 + 2.75 =
  3. Left side: the -coordinates match, so use + =
  4. Perimeter adds all four sides: + + + =
Answer:perimeter of the rectangle, in units

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 outA common mistake

Subtracting coordinates without the absolute value — from y = 3 down to y = −3.75 the distance is 3 + 3.75 = 6.75 units, not 3.75 − 3 = 0.75. Distances that cross zero are the whole reason the absolute value is there.

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

Lesson 7.77.7 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, 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 — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    −4−3−2−112345−4−3−2−1123(−3, 2)(4, 2)(4, −3)(−3, −3)
    Connect the vertices in order.

    A rectangle has vertices (−3, 2), (4, 2), (4, −3) and (−3, −3). Find the length of each side.

    1. 1Plot the vertices. Connect them in order.
    2. 2(−3, 2) and (4, 2) share y = 2. How long is that side?
    3. 3(4, 2) and (4, −3) share x = 4. How long is that side?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −3−2−11234−3−2−112345(−2, 4)(3, 4)(3, −2)(−2, −2)
    Area is the space inside the rectangle.

    A rectangle has vertices (−2, 4), (3, 4), (3, −2) and (−2, −2). Find its area.

    1. 1How long is the side from (−2, 4) to (3, 4)?
    2. 2How long is the side from (3, 4) to (3, −2)?
    3. 3Multiply length by width. What is the area?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A rectangle has vertices (1, 2), (7, 2), (7, 5) and (1, 5). Find its perimeter.

    Show your work

    Hint Find one side across and one side up and down. Each length appears two times.

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

    A rectangle has vertices (−1.5, 3), (4, 3), (4, −2) and (−1.5, −2). Find its perimeter.

    Show your work

    Hint Each side crosses an axis. Add the distances from 0.

    Final answer:
  5. 5Complete each step, then write the final answer.
    −5−4−3−2−11234−2−1123456(−4, 5)(3, 5)(3, −1)(−4, −1)

    A garden is a rectangle with corners (−4, 5), (3, 5), (3, −1) and (−4, −1). Each unit is 1 meter. What is the area of the garden?

    Show your work

    Hint Find the length and the width from the coordinates. Then multiply.

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

    Sam says the rectangle with vertices (−5, 1), (3, 1), (3, 4) and (−5, 4) has a perimeter of 8 + 3 = 11 units. Is he right? What is the perimeter?

    Show your work

    Hint A rectangle has four sides. How many sides did Sam add?

    Final answer:

Explain your thinkingSam added only two sides. Why must you count each length two times for the perimeter of a rectangle?

Sentence starter Sam forgot ___. · Each length counts two times because ___.

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