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

Lesson 7.7Designing Polygons with a Scale

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.

Start hereWords for this lesson

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

Word	What it means	Example
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.	Plot (2, 4), (5, 4), (5, −4), (2, −4) and join them — a rectangle appears.
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 = 25 feet
Side lengthSpanish: Longitud del lado	The distance between two vertices that are joined by a side.	Found with absolute value when the points share a coordinate.

How it worksWorked example

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

A plan uses 1 unit = 10 m. A field must cover 2,400 m² and is 4 units wide. Find its real length.

Real width: 4 × 10 = 40 m.
Real length: 2,400 ÷ 40 = 60 m.
On the plan: 60 ÷ 10 = 6 units long.

Answer: 60 m long (6 units on the plan)

Say it and write itSentence starters

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

Each grid unit stands for , so units equals .
The missing vertex is because .
The area is square because I multiplied by .
I changed units into before I .

Word bank scalegrid unitvertexdimensionsareaperimeterconvertmultiplydividerectanglesquare feetside length

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 7.7Designing Polygons with a Scale

Apply Day · Version ASupported 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.

1Complete 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:
2Complete 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:
3Complete each step, then write the final answer.

A rectangle has vertices (−2, 5), (4, 5), (4, 2) and (−2, 2). Find its area.
Show your work
Hint Find the length and the width. Then multiply.
Final answer:

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

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

Lesson 7.7Designing Polygons with a Scale

Apply Day · Version BCore 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.

1Complete 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
Final answer:
2Complete 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:
3Complete each step, then write the final answer.

A rectangle has vertices (−3, 6), (3, 6), (3, 2) and (−3, 2). Find its perimeter.
Show your work
Final answer:

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

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

Lesson 7.7Designing Polygons with a Scale

Apply Day · ChallengeExtension

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.

1Circle the letter of the best answer. Show how you know.
A rectangle has vertices at (1, 1), (7, 1), (7, 5), and (1, 5). What is its perimeter?
1. A10 units
2. B12 units
3. C20 units
4. D24 units
Formula

Put the numbers in

Work it out

Answer with its unit
2Circle 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
3Complete each step, then write the final answer.

Three vertices of a rectangle are (−4, 2), (4, 2) and (4, −3). What is the area of the rectangle?
Show your work
Final answer:

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