Unit Plan
Mathematics
Unit: 7
Grade: 8
Solve one‐variable linear equations, including cases with infinitely many solutions or no solutions
Solve problems involving volumes of cones, cylinders, and spheres together with previous geometry work, proportional reasoning and
multi‐step problem solving in grade 7
Pythagorean Theorem
Topic/ Theme/
6 weeks
Duration
How do we solve for missing sides and angles of triangles?
Essential
Question(s)
 Find and understand square and cube roots
Key Student
the Pythagorean Theorem to find missing sides of right triangles
Learning Objectives  Use
Use the Pythagorean Theorem to find distance on a coordinate plane
Standard
 Explore special right triangles
Skills
8.G.6( ). Explain a proof of the
Pythagorean Theorem and its converse.
Explain a proof of the
Pythagorean Theorem and its
converse.
Tell whether a triangle is a
right triangle
Resources
Supports
CMP Looking for
Pythagoras
 Above-grade level (challenging
high performers):
 On grade level:
 Below grade level:
 ELL:
 SWD:
Glencoe Chapter 5:
Lesson 5, Inquiry Lab
Common Core
Mathematics
CC 8-9, 3.2, 3,3
8.G.7( ). Apply the Pythagorean
Theorem to determine unknown side
lengths in right triangles in real-world
and mathematical problems in two and
three dimensions.
Use the Pythagorean
Theorem to find missing side
lengths
Apply the Pythagorean
Big Ideas Math: 7.3,
7.5
CMP Looking for
Pythagoras
Glencoe Chapter 5:
Lesson 6
 Above-grade level (challenging
high performers):
 On grade level:
 Below grade level:
Theorem to real-world and
word problems
8.G.8( ). Apply the Pythagorean
Theorem to find the distance between
two points in a coordinate system.
Use the Pythagorean
Theorem to find distance
between points on a
coordinate plane and in real
world problems
Common Core
Mathematics
3.3
Big Ideas Math: 7.3,
7.5
CMP Looking for
Pythagoras
Glencoe Chapter 5:
Lesson 7
Common Core
Mathematics
3.4
8.NS.2: Use rational approximations of
irrational numbers to compare the size
of irrational numbers; locate then
approximately on a number line
diagram.
Big Ideas Math: 7.3,
7.5
CMP Looking for
Pythagoras
 ELL:
 SWD:
 Above-grade level (challenging
high performers):
 On grade level:
 Below grade level:
 ELL:
 SWD:

Glencoe
Common Core
Mathematics
3.4
8.EE.2: Use square root and cube
root symbols to represent solutions
to equations of the form x 2 = p and
x3 = p, where p is a positive rational
number. Evaluate square roots of small
perfect squares and cube roots of
small perfect cubes. Know that √2 is
irrational.
Big Ideas Math: 7.4
CMP Looking for
Pythagoras
Glencoe
Common Core
Mathematics

3.4
Vocabulary
Sequence of Key Learning
Activities
Assessments
Big Ideas Math: 7.1,
7.2, 7.3, 7.4, 7.5
right triangle, leg, hypotenuse, right angle, Pythagorean Theorem, square root, squared,
formula, proof
PYTHAGOREAN THEOREM
 Understand and apply the Pythagorean Theorem
 Develop strategies for finding the distance between two points on a coordinate grid
 Explain a proof of the Pythagorean Theorem
 Use the Pythagorean Theorem and its converse to solve a variety of problems
 Use the Pythagorean Theorem to find the equation of a circle with its center located at
the origin
REAL NUMBERS
 Understand that the set of real numbers consists of rational and irrational numbers
 Interpret square roots and cube roots of numbers by making use of their related
geometric representations
 Relate the area of a square to the side length of the square
 Estimate the values of square roots
 Estimate the values of cube roots
 Relate the volume of a cube to the edge length of the cube
 Compare numbers that can be represented as fractions (rational numbers) to numbers
that cannot be represented as fractions (irrational numbers) and recognize that the set
of real numbers consists of rational and irrational numbers
 Represent rational numbers as fractions and as terminating decimals or repeating
decimals
 Recognize that irrational numbers cannot be represented as fractions and are
nonterminating, nonrepeating decimals
 Recognize that the square root of a whole number that is not a square is irrational
 Locate irrational numbers on a number line
 Use and understand properties of rational and irrational numbers
Note: Standards in bold are identified as major standards. Standards with checkmarks are standards recommended for greater
emphasis
GRADE 8 PERFORMANCE TASK: GEOMETRY
Standards
Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume.
7. G.4 Know the formulas for the area and circumference of a circle and use them to solve
problems; give an informal derivation of the relationship between the circumference and area of
a circle.
7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of
two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and
right prisms.
Understand and apply the Pythagorean Theorem.
8. G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional
figures using coordinates.
8. G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in
real-world and mathematical problems in two and three dimensions.
8. G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate
system.
Solve real-world and mathematical problems involving volume of cylinders, cones, and
spheres.
8. G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve
real-world and mathematical problems.
Skills




Plot points on a coordinate plane
Substitute into the Pythagorean Theorem and solve the equation to find the missing side of a
right triangle.
Answer word problems using the Pythagorean Theorem by drawing a diagram.
Apply formulae for perimeter, area and volume.
5
Fencing and Grassing Your Property
You want to put a fence around your large yard. There are two companies that you have found to
do the work. They have each given you a quote for how much the work will cost. Of course, you
want to find out which company will be the cheapest.
The boundary of your yard is determined by five trees. The lines connecting them form the edge
of your property. Shown below are the descriptions for the positions of the trees relative to your
house.
Tree
A
B
C
D
E
Position (relative to your house)
100 ft east
40 ft east, 80 ft south
40 ft west, 120 ft south
90 ft west, 60 ft north
20ft east, 110ft north
PART 1: On graph paper, mark the position of each of the trees on your land. Let each block of
the graph paper represent a 10-foot by 10-foot square. Using a straightedge, connect Tree A to
Tree B, Tree B to Tree C, Tree C to Tree D, and so on.
PART 2: a) Use the Pythagorean Theorem to find the length of each side of your property.
Round each answer to the nearest hundredth, if necessary.
b) Determine the perimeter of your property.
c) Company 1 says that they will complete the job for $12 per foot of fencing. Company 2 says
that they will charge you $250 for the first 100 feet of fencing and $13 for each additional foot.
Determine the cost of fencing for both companies.
d) Figure out which company will complete the job for the least amount of money
PART 3: a) A circular swimming pool with a radius of 20 ft is positioned with a center at 40 ft
west and 30 ft north. Mark the position of the pool on your graph. The depth of the swimming
pool is 5ft. Calculate the volume of water needed to fill the pool.
b) A barn is being built with corners at (30 ft north, 30 ft east); (70 ft east, 30 ft north); (30 ft
east, 20 ft south); (70 ft east, 20 ft south). Mark this barn on your graph.
c) The rest of the property is to be grassed at a cost of 20 cents per square foot. You have given
the contract for the grassing to the company who was cheapest in Step 5. They will give you a
discount of 8% on the cost of grassing. Calculate the cost of the grassing.
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Name: ________________________________
Date: ______________
Part 1: Graph of Your Property Lines
Plot the points that represent the trees that mark the edges of your property. Use the locations
given on the previous page. To make things easier, use the origin (0, 0) as the position of your
house. Remember that each grid represents 10 feet. Finally, connect the points using a
straightedge.
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Name: ________________________________
Date: ______________
Part 2: a) & b) Break your property into smaller parts and use the Pythagorean Theorem to find
the length of each side. Remember that each grid line on your graph represents 10 feet. Also
remember to round to the nearest hundredth if necessary. Show your work below.
Work for the distance from Tree A to Tree B
Work for the distance from Tree B to Tree C
Distance: ____________ ft
Distance: ____________ ft
Work for the distance from Tree C to Tree D
Work for the distance from Tree D to Tree E
Distance: ____________ ft
Distance: ____________ ft
Work for the distance from Tree E to Tree A
Work for the Perimeter of Your Property
Distance: ____________ ft
Perimeter: ____________ ft
c) Company 1 charges $12 per foot of fence. Find the cost if Company 1 completes the job.
Show work!
Cost: $ ___________
Company 2 charges $250 for the first 100 feet of fence and $13 for each additional foot. Find the
cost if Company 2 completes the job. Show work!
Cost: $ ___________
d) Both companies must charge a 6% sales tax. Determine which company will be the cheapest.
Then, find the cost including tax. Round to the nearest cent. Show work!
Company _________
Cost: $ ___________
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Part 3a) Calculate the area and volume of the swimming pool (to 1 decimal place). Don’t forget
to add the correct units.
Area: ________________
Volume: ______________
c) Calculate the area of the grassed area by first calculating the area of the entire property and
then subtracting the area of the pool and the barn. Show your working.
Calculate the cost of the grassing at $2 per square foot:
Cost: $____________
Calculate the discount given:
Discount: $___________
Calculate the final cost of the grassing:
Cost: $__________
9
Part 4: If your property was dilated by a factor of ½, what effect will this have on the perimeter?
How could you prove your answer is correct? Use the Graph below to help.
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