Curriculum / Math / 6th Grade / Unit 7: Geometry / Lesson 9
Math
Unit 7
6th Grade
Lesson 9 of 17
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Solve real-world problems involving distance, area, and perimeter of polygons on and off the coordinate plane.
The core standards covered in this lesson
6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
6.G.A.3 — Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
The foundational standards covered in this lesson
4.MD.A.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
6.NS.C.6 — Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson can be used as a review or flex day, or incorporated into previous lessons to include real-world applications. The concepts are continuations from previous lessons but applied to situations in context.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A new park is being built in the city. In the park, there will be a cemented walkway that will wind through the park. The walkway will be completely enclosed by a short, gated fence that will line the path on all sides of the path. The blueprint for the pathway is shown in the coordinate plane below. Each square unit in the coordinate grid represents 1 square yard.
a. The city budget includes enough funds to include 50 square yards of cement and 60 yards of fencing. Will the budget cover the necessary expenses for cement and fencing? Defend your answer.
b. Two statues will be placed at points $${(-1, 2)}$$ and $${(-1, -4).}$$ How far apart, in yards, are the two statues?
You are responsible for a small plot of land in the community garden that measures $$9$$ ft. $$\times $$ $$9$$ ft. You want to include $${48}$$ square feet of gardening space, and you want your garden to have at least one rectangle shape and at least one triangle shape.
Draw a possible plan for your garden on the grid below. Make sure you do not go outside of the $$9$$ ft. $$\times $$ $$9$$ ft. space.
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
The diagram below shows the space where a new garden will be developed. Each square unit in the grid is 1 square foot. What is the area of the new garden?
An example response to the Target Task at the level of detail expected of the students.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 8
Lesson 10
Topic A: Area of Triangles, Quadrilaterals, and Polygons
Find the area of parallelograms.
6.G.A.1
Find the area of right triangles.
Find the area of acute triangles using height and base.
Find the area of any triangle using height and base.
Find the area of polygons using composition and decomposition.
Solve real-world and mathematical problems involving area of polygons.
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Topic B: Polygons in the Coordinate Plane
Draw polygons in the coordinate plane and find area and perimeter (Part 1).
6.G.A.3
Draw polygons in the coordinate plane and find area and perimeter (Part 2).
6.G.A.1 6.G.A.3
Topic C: Volume of Rectangular Prisms
Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes.
6.G.A.2
Determine the formulas for finding volume of rectangular prisms and use the formulas to solve for volume.
Apply volume concepts to solve real-world and mathematical problems, including finding missing measurements.
Apply volume concepts to solve real-world and mathematical problems, including finding volume of figures with composite prisms.
Topic D: Nets and Surface Area
Describe features of and identify nets that match prisms and pyramids.
6.G.A.4
Create nets and use them to find surface area of three-dimensional figures.
Find the surface area of three-dimensional figures with and without nets.
Find surface area and volume in real-world problems.
6.G.A.2 6.G.A.4
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