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

Lesson 7.77.7 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

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 2

Group 2Challenge practice

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, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    −6−5−4−3−2−1123−2−112345(−5, −1)(2, −1)(2, 4)
    One vertex is missing.

    Three vertices of a rectangle are (−5, −1), (2, −1) and (2, 4). Find the fourth vertex. Then find the area.

    1. 1What is the fourth vertex?
    2. 2Find the two side lengths.
    3. 3What is the area?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −3−2−112345−2−11234(−2, 3)(4, 3)(4, −1)(−2, −1)

    A park on a map has vertices (−2, 3), (4, 3), (4, −1) and (−2, −1). Each unit is 50 feet. What is the perimeter in feet?

    1. 1Find the two side lengths in units.
    2. 2Each unit is 50 feet. What is the perimeter in feet?
    3. 3Why is the side from (4, 3) to (4, −1) 4 units, not 2?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A rectangle has vertices (−6, 2), (−1, 2) and (−1, −3). The fourth vertex is (−6, ?). What is the missing y-coordinate?

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

    The top side of a rectangle goes from (−3, 4) to (5, 4). The area is 48 square units. What is the y-coordinate of the bottom side?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    048121620240246810121416(0, 0)(24, 0)(24, 15)(0, 15)

    A store space is a rectangle with corners (0, 0), (24, 0), (24, 15) and (0, 15). Each unit is 1 foot. Rent is $2 per square foot each month. What is the monthly rent?

    Show your work
    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    Space A has corners (0, 0), (20, 0), (20, 20) and (0, 20). Space B has corners (0, 0), (30, 0), (30, 12) and (0, 12). Each unit is 1 foot. Which space has more floor area?

    1. ASpace A
    2. BSpace B
    3. CThey have the same area.
    Show your work

Explain your thinkingSpace B is longer than Space A, but Space A has more area. How can that be? Use the side lengths to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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