A focused Grade 6 learning session for Finding Area on the Coordinate Plane using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving finding area on the coordinate plane.
Finding Area on the Coordinate Plane means measuring how much flat space a figure covers by using equal-sized square units.
Question: What is the area of the rectangle shown?
Why it works: Width: \(7-1=6\) units. Height: \(3-1=2\) units. Area \(=6\times2=12\) square units.
Answer: \(12\) square units
Question: A garden plot is rectangular with vertices at \((1,1)\), \((9,1)\), \((9,4)\), and \((1,4)\). What is the area of the garden?
Answer: \(24\) square units
Question: What is the area of the rectangle with vertices at \((2,1)\), \((8,1)\), \((8,6)\), and \((2,6)\)?
Answer: \(30\) square units
Question: A student is calculating the area of a triangle with base 8 units and height 6 units. The student writes: Area \(= 8 \times 6 = 48\) square units. What is the student's error?
Why it works: The formula for a triangle is Area \(= \frac{1}{2} \times \text{base} \times \text{height}\). The student multiplied base and height but forgot the \(\frac{1}{2}\) factor. The correct area \(= \frac{1}{2} \times 8 \times 6 = 24\) square units.
Answer: The correct area is \(24\) square units.
Finding Area on the Coordinate Plane becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Area means every square unit inside the figure.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A rectangle has vertices at \((2,1)\), \((8,1)\), \((8,5)\), and \((2,5)\). What is its area?
Answer C: \(24\) square units
Length \(=8-2=6\); width \(=5-1=4\). Area \(=6\times4=24\) square units.
What is the area of the rectangle shown?
Answer B: \(12\) square units
Width: \(7-1=6\) units. Height: \(3-1=2\) units. Area \(=6\times2=12\) square units.
A square is drawn on the coordinate plane with vertices at \((2,2)\), \((8,2)\), \((8,8)\), and \((2,8)\). What is its area?
Answer D: \(36\) square units
Side length: \(8-2=6\) units. Area of square \(=6^2=36\) square units.
A garden plot is rectangular with vertices at \((1,1)\), \((9,1)\), \((9,4)\), and \((1,4)\). What is the area of the garden?
Answer C: \(24\) square units
Width: \(9-1=8\) units. Height: \(4-1=3\) units. Area \(=8\times3=24\) square units.
What is the area of the rectangle with vertices at \((2,1)\), \((8,1)\), \((8,6)\), and \((2,6)\)?
Answer B: \(30\) square units
Width: \(8-2=6\) units. Height: \(6-1=5\) units. Area \(=6\times5=30\) square units.
A rectangle on the coordinate plane has vertices at \((1,1)\), \((7,1)\), \((7,7)\), and \((1,7)\). What is its area?
Answer C: \(36\) square units
Width: \(7-1=6\) units. Height: \(7-1=6\) units. Area \(=6\times6=36\) square units.
What is the area of the shaded rectangle?
Answer D: \(32\) square units
Width: \(10-2=8\) units. Height: \(6-2=4\) units. Area \(=8\times4=32\) square units.
A floor plan section is rectangular with corners at \((3,2)\), \((9,2)\), \((9,5)\), and \((3,5)\). What is its area?
Answer D: \(18\) square units
Width: \(9-3=6\) units. Height: \(5-2=3\) units. Area \(=6\times3=18\) square units.
Find the area of the rectangle with vertices at \((3,3)\), \((8,3)\), \((8,8)\), and \((3,8)\).
Answer B: \(25\) square units
Width: \(8-3=5\) units. Height: \(8-3=5\) units. Area \(=5\times5=25\) square units.
What is the area of this rectangle?
Answer B: \(30\) square units
Width: \(7-1=6\) units. Height: \(7-2=5\) units. Area \(=6\times5=30\) square units.
A rectangle has vertices at \((2,3)\), \((9,3)\), \((9,8)\), and \((2,8)\). What is its area in square units?
Answer C: \(35\) square units
Width: \(9-2=7\) units. Height: \(8-3=5\) units. Area \(=7\times5=35\) square units.
