Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
Enduring understanding (Big Idea): Students will understand that the Pythagorean Theorem connects square roots,
coordinates, slope, distance, area, and distances in a plane.
Essential Questions:






Is it appropriate and useful to use the Pythagorean Theorem in this situation? How do I know this?
How are square roots and areas of squares related? How are cube roots and volume of cubes related?
How can I estimate the square root of a number?
How can I find the length between two points?
Compare and contrast the Pythagorean Theorem and Distance Formula?
Explain how to use the Distance Formula to compute the perimeter and area of triangles and polygons.
BY THE END OF THIS UNIT:
Students will know…
1. The difference between rational and irrational numbers and
every number has a decimal expansion
2. Perfect square and cube roots are rational and non-perfect
roots are irrational
3. Pythagorean Theorem: a2 + b2 = c2
4. Midpoint Formula: M=  x1  x 2 , y1  y 2 
2
2


5.
Distance Formula: d =
( x 2  x1 ) 2  ( y 2  y1 ) 2
Vocabulary:
rational, irrational, square root, cube root, area, volume, hypotenuse,
legs, right angle, right triangle, coordinate plane, x-coordinate, ycoordinate, ordered pair
Unit Resources
Connecting Algebra & Geometry through coordinates
Mathematical Practices in Focus:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of
others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
CCSS-M Included:
8.EE.2, 8.G.6-8, G.GPE.4-7, 8.NS.1-2
Suggested Pacing:
15 -20 DAYS
Released Test Questions:
Algebra I: 27, 28, 43, 44, 46
8th Grade: 7, 8, 9, 27, 30, 43, 44
Grade 8 Stations Book
The Number System pg. 1
Geometry Set 5 pg. 154, Set 6 pg. 161
Algebra I Project Binder:
Pages 315 – 319, 327 – 329, 330 – 338, 355 - 375
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Students will be able to…
8.NS.1: I can distinguish between rational and irrational numbers and
recognize any number that be expressed as a fraction is a rational
number. I can convert repeating decimals into their fraction equivalent
using patterns or algebraic reasoning.
8.NS.2 : I can locate rational and irrational numbers on a number line.
I can approximate irrational numbers using rational numbers.
8.EE.2: I can recognize perfect square and cube roots as rational
and non-perfect square and cube roots as irrational. I can evaluate
perfect square and cube roots. I can solve equations in the form x2 =
p and x3 = p, where p is positive rational number.
8.G.6: I can explain the proof of the Pythagorean Theorem and its
converse.
8.G.7: I can apply the Pythagorean Theorem to determine unknown
side lengths in right triangles in real- world and math problems in two
and three dimensions.
8.G.8: I can apply the Pythagorean Theorem to find the distance
between two points in a coordinate system.
G.GPE.4: I can use coordinates to prove simple geometric theorems
algebraically.
G.GPE.5: I can prove the slope criteria for parallel lines. I can prove
the slope criteria for perpendicular lines. Apply the slope criteria for
parallel lines to solve geometric problems. Apply the slope criteria for
perpendicular lines to solve geometric problems.
G.GPE.6: I can find the point on a directed line segment between two
given points that divides the segment in a given ratio.
G.GPE.7: I can use coordinates to calculate perimeters of polygons. I
can use coordinates to calculate areas of triangles. I can use
coordinates to calculate areas of rectangles.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
CORE CONTENT
Cluster Title: Expressions and Equations: Work with radicals and integer exponents.
Standard 8.EE.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = 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.
Concepts and Skills to Master:



Evaluate the square roots of small perfect squares and cube roots of small perfect cubes.
Represent the solutions to equations using square root and cube root symbols.
Understand that all non-perfect square roots and cube roots are irrational.
SUPPORTS FOR TEACHERS
Critical Background Knowledge

Understand and use inverse operations to solve equations.
Academic Vocabulary
square, square root,
, cube, cube root,
, radical, irrational, rational, real number system,
Suggested Instructional Strategies:


Resources:
Use the geometric representations of square area and
cube volumes and their relation to the side length.
Use the idea of inverse operations to introduce the
concept of roots.
NCDPI Unpacking:
8.EE.2: Students recognize perfect squares and cubes,
understanding that non-perfect squares and non-perfect cubes
are irrational. Students recognize that squaring a number and
taking the square root √ of a number are inverse operations;
3
likewise, cubing a number and taking the cube root
are
inverse operations. Note: there is no negative cube root since
multiplying 3 negatives would give a negative. This
understanding is used to solve equations containing square or
cube numbers. Rational numbers wouldhave perfect squares or
perfect cubes for the numerator and denominator. In the
standard, the value of p for square root and cube root equations
must be positive.

Textbook Correlation: LFP - Investigations 2, 3, & 4

Squares, Square Roots and Exponential Expressions

MARS Concept DevelopmentLesson (MS):
The Pythagorean Theorem: Square Areas
Texas Instrument Lessons: PH.2.2. - Unit 2 Investigation 2:
Squaring Off (pp. 19 - 30); PH.2.3. - Unit 2 Investigation 3: The
Pythagorean Theorem (pp. 31 - 45);PH.2.4. - Unit 2 Investigation
4: Using the Pythagorean Theorem (pp. 46 - 64)– See Link on
Math Secondary Wiki
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
Sample Assessment Tasks
Skill-based task
1. If a square has an area of 9/16 square inches, what is
the length of a side?
2. If a cube has a volume of 0.125 cubic meters, what are
the dimensions of the cube?
Problem Task
1. Is the square root of a number always smaller than the number
itself? Explain
2. 42 = 16 and 16 = ±4
NOTE: (-4)2 = 16 while -42 = -16 since the negative is not being
squared. This difference is often problematic for students,
especially with calculator use.

3.
and
4. Solve: x2 = 25
2
Solution: x = ± 25
x = ±5
are two solutions because 5 • 5 and -5 • -5 will both
NOTE: There
equal 25.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
CORE CONTENT
Cluster Title: Understand and Apply the Pythagorean Theorem
Standard 8.G.6: Explain a proof of the Pythagorean Theorem and its converse
Concepts and Skills to Master:
 Know that in a right triangle a² + b² = c² (the Pythagorean Theorem).
 Understand and explain a proof of the Pythagorean Theorem.
 Understand and explain a proof of the converse of the Pythagorean Theorem.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Understand the relationship between a and a2, b and b2, c and c2.
 Understand the relationship between squares and square roots.
Academic Vocabulary
right triangle, leg, hypotenuse, square, Pythagorean Theorem, square root
Suggested Instructional Strategies:
Resources:
 Consider introducing this with an application
 Textbook Correlation: LFP - Investigation 3
regarding distance.
 MARS Tasks (HS):
E04: Proofs Of The Pythagorean Theorem
 Explore various proofs of the Pythagorean
Theorem and discuss the logic within each.
E08: Pythagorean Triples
 MARS Problem Solving Lesson (HS): Proofs of
NCDPI Unpacking:
the Pythagorean Theorem
8.G.6: Using models, students explain the Pythagorean
 Texas Instrument Lessons: PH.2.3. - Unit 2
Theorem, understanding that the sum of the squares of the
Investigation 3: The Pythagorean Theorem (pp.
legs is equal to the square of the hypotenuse in a right
31 - 45)– See Link on Math Secondary Wiki
triangle. Students also understand that given three side
 Prentice Hall Algebra I pg. 600 10-1
lengths with this relationship forms a right triangle.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
Sample Assessment Tasks
Skill-based task
1. A triangle has side lengths 23, 24, and 25, is this a right
triangle? Justify your answer.
2. Explain the logical reasoning behind a proof of the
Pythagorean Theorem.
Problem Task
1. Investigate the historical context of one of the proofs of
the Pythagorean Theorem and present the proof in context
to the class.
2. The distance from Jonestown to Maryville is 180 miles,
the distance from Maryville to Elm City is 300 miles, and the
distance from Elm City to Jonestown is 240 miles. Do the
three towns form a right triangle? Why or why not?
Solution: If these three towns form a right triangle, then 300
would be the hypotenuse since it is the greatest distance.
1802 + 2402 = 3002
32400 + 57600 = 90000
90000 = 90000 
These three towns form a right triangle.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
CORE CONTENT
Cluster Title: Understand and Apply the Pythagorean Theorem
Standard 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.
Concepts and Skills to Master:
 Use the Pythagorean Theorem to solve for a missing side of a right triangle given the other two sides.
 Use the Pythagorean Theorem to solve problems in real-world contexts, including three-dimensional contexts.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Solve an equation using squares and square roots.
 Use rational approximations of irrational numbers to express answers.
Academic Vocabulary
right triangle, leg, hypotenuse, Pythagorean Theorem, square, square root,
Suggested Instructional Strategies:
Resources:
1. Find and solve right triangles in career situations such
 Textbook Correlation: LFP - Investigations 3 & 4
as construction.
 Texas Instrument Lessons: PH.2.3. - Unit 2
Investigation 3: The Pythagorean Theorem (pp.
31 - 45); PH.2.4. - Unit 2 Investigation 4: Using the
Pythagorean Theorem (pp. 46 - 64)– See Link on
Math Secondary Wiki
 MARS Task:
Jane's TV
Pythagorean Triples
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
Sample Assessment Tasks
Skill-based task
1. If the height of a cone is 10 meters and the radius is 6
meters, what is the slant height?
Problem Task
1. TV’s are measured along their diagonal to find their dimension.
How does a 52-inch HD (wide-screen) TV compare to a traditional
52-inch (full screen) TV?
2. The Irrational Club wants to build a tree house. They have a 9foot ladder that must be propped diagonally against the tree. If the
base of the ladder is 5 feet from the bottom of the tree, how high
will the tree house be off the ground?
Solution:
a 2 + 5 2 = 92
a2 + 25 = 81
a2 = 56
a 2 = 56
a=

56 or ~7.5
 3. Find the length of d in the figure to the right if a = 8 in., b = 3 in.
and c = 4in.

Solution:
First find the distance of the hypotenuse of the triangle formed with
legs
a and b.
82 + 3 2 = c 2
642 + 92= c2
73 = c2
73 = c 2
73 in. = c
 The 73 is the length of the base of a triangle with c as the other
leg and d is the hypotenuse.
To find the length of d:
73 2 + 42 = d2

73 + 16 = d2
89 = d2
89 = d 2

89 in. = d




 From the above problem, students can discover the formula,
𝑑 2 = 𝑙 2 + 𝑤 2 + ℎ2
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
CORE CONTENT
Cluster Title: Understand and apply the Pythagorean Theorem.
Standard 8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Concepts and Skills to Master:
 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
•Use the Pythagorean Theorem to solve for the hypotenuse of a right triangle.
Academic Vocabulary
right triangle, distance formula, leg, hypotenuse, Pythagorean Theorem, square, square root,
Suggested Instructional Strategies:
Resources:
 Overlap a map with a coordinate grid and use the
 Textbook Correlation: LFP - Investigation 3
Pythagorean Theorem to find the distance between
two locations.
 Texas Instrument Lessons: PH.2.3. - Unit 2
 Investigate the relationship between the
Investigation 3: The Pythagorean Theorem (pp.
Pythagorean Theorem and the distance formula.
31 - 45);– See Link on Math Secondary Wiki
 Use the Pythagorean Theorem to explore and
categorize triangles and quadrilaterals on a
coordinate system.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
Sample Assessment Tasks
Skill-based task
Problem Task
Using the Pythagorean Theorem, find the distance between 1. List 3 coordinate pairs that are 5 units away from the origin in
the first quadrant. Describe how to find the points and justify your
(4,2) and (7,10).
reasoning. (Note: Points on the axes are not in the quadrant.)
2. Find the length of AB .

Solution:
Form a right triangle so that the given line segment is the
hypotenuse. Use Pythagorean Theorem to find the distance
(length) between the two points.
3. Find the distance between (-2, 4) and (-5, -6).
Solution:
The distance between -2 and -5 is the horizontal length; the
distance between 4 and -6 is the vertical distance.
Horizontal length: 3
Vertical length: 10
102 + 32 = c2
100 + 9 = c2
109 = c2
109 = c 2
109 = c


 Students find area and perimeter of two-dimensional figures on
the coordinate plane, finding the distance between each segment
of the figure. (Limit one diagonal line, such as a right trapezoid or
parallelogram)
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
CORE CONTENT
Cluster Title: Know that there are numbers that are not rational, and approximate them by rational numbers.
Standard 8.NS.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a
decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which
repeats eventually into a rational number.
Concepts and Skills to Master:




Know that real numbers that are not rational are irrational.
Understand that finite decimal expansions of irrational numbers are approximations.
Show that rational numbers have decimal expansions that repeat eventually.
Convert a decimal expansion, which repeats eventually, into a rational number.
SUPPORTS FOR TEACHERS
Critical Background Knowledge



Understand the subsets of the real number system (natural numbers, whole numbers, integers, rational numbers).
Convert rational numbers to decimals using long division (terminating and repeating) (7.NS.2d).
Solving one-step equations.
Multiplication property of equality

Academic Vocabulary
Decimal expansion, repeating decimal, termination decimal, rational, irrational, square root,
Suggested Instructional Strategies:
Resources:


Use double bubble maps to compare and contrast rational
and irrational numbers and have students write about the
similarities and differences between real numbers
Have students discover the pattern for denominators of 9,
and 11 by having them do long division and write about what
they notice in the quotient. Have them make a conjecture
about fractions that have dominators of 9, and 11.
NCDPI Unpacking:
8.NS.1: Students understand that Real numbers are either rational or
irrational. They distinguish between rational and irrational numbers,
recognizing that any number that can be expressed as a fraction is a
rational number. The diagram below illustrates the relationship between
the subgroups of the real number system.
Students recognize that the decimal equivalent of a fraction will either
terminate or repeat. Fractions that terminate will have denominators
containing only prime factors of 2 and/or 5. This understanding builds
on work in 7th grade when students used long division to distinguish
between repeating and terminating decimals. Students convert
repeating decimals into their fraction equivalent using patterns or
algebraic reasoning.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
,п

Textbook Correlation: LFP - Investigation 4.1

MARS Concept DevelopmentLesson(MS) :
Repeating Decimals

Texas Instrument Lessons: PH.2.4. - Unit 2
Investigation 4: Using the Pythagorean Theorem
(pp. 46 - 64));– See Link on Math Secondary Wiki
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
Sample Assessment Tasks
Skill-based task
1. Convert 0.352̅ to a fraction.
Problem Task
1. Suppose you have a fraction with a denominator of 7. What is
the longest string of non-repeating digits that will occur in the
decimal expansions of the number? (Hint: Use the long division
algorithm to show that for a denominator of n, there are only n
possible remainders, 0 to n-1.)
2. Change 0. 4 to a fraction.

Let x = 0.444444…..
 Multiply both sides so that the repeating digits will be in front
of the decimal. In this example, one digit repeats so both
sides are multiplied by 10, giving 10x = 4.4444444….

Subtract the original equation from the new equation.
10x = 4.4444444….
– x = 0.444444…..
9x = 4

Solve the equation to determine the equivalent fraction.
9x = 4
9 9
4
x= 9
Additionally, students can investigate repeating patterns that
occur when fractions have denominators of 9, 99, or 11.

4
5
3. 9 is equivalent to 0. 4 , 9 is equivalent to 0. 5 , etc.

Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
 

Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
CORE CONTENT
Cluster Title: Know that there are numbers that are not rational, and approximate them by rational numbers.
Standard 8.NS.1: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate
them approximately on a number line diagram, and estimate the value of expressions (e.g., п 2). For example, by truncating
the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on
to get better approximations.
Concepts and Skills to Master:
 Compare and order irrational numbers.
 Place irrational numbers on a number line.
 Use approximations of irrational numbers to estimate the value of expressions.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
• Compare and place rational numbers on a number line.
• Approximate irrational numbers as fractions or decimals.
Academic Vocabulary
rational, irrational, decimal expansion, square root, √, п, truncating, rounding
Suggested Instructional Strategies:
Resources:
 Construct the Wheel of Theodorus to create
 Textbook Correlation: LFP - Investigation 4, 10.2,
physical lengths of the square roots of the counting
10.3
numbers. Transfer those lengths onto a number
line.
 Wheel of Theodorus Project:
http://www.ldlewis.com/Teaching-Mathematics-with Find increasingly accurate estimations for square
Art/Wheels.html
roots of numbers by guess- and-check with a
calculator.
• Texas Instrument Lessons: PH.2.4. - Unit 2
NCDPI Unpacking:
Investigation 4: Using the Pythagorean Theorem
8.NS.2: Students locate rational and irrational numbers on
(pp. 46 - 64));– See Link
the number line. Students compare and order rational and
irrational numbers. Students also recognize that square
roots may be negative and written as - 28 . Additionally,
students understand that the value of a square root can be
approximated between integers and that non-perfect
square roots are irrational. 
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
Sample Assessment Tasks
Skill-based task
1. Place the following numbers on a number line: 5.3,
1.7…,√10, 2, п/2
2. Find between which two integers lies? 42
Problem Task
1. Explain when each approximation of п (3.14, 3, 22/7) is
useful in calculating the circumference of a circle. Compare
the answers you would get with each approximation.
(Extension: Research how different cultures have
approximated pi.)
2. Compare 2 and 3




Solution: Statements for the comparison could include:
2 and 3 are between the whole numbers 1 and 2
3 is between 1.7 and 1.8
2 is less than 3

3. Find an approximation of

28
Determine the perfect squares 28 is between, which
would be 25 and 36.

The square roots
 of 25 and 36 are 5 and 6 respectively,
so we know that 28
 is between 5 and 6.

Since 28 is closer to 25, an estimate of the square root
would be closer to 5. One method to get an estimate is
to divide
 3 (the distance between 25 and 28) by 11 (the
distance between the perfect squares of 25 and 36) to
get 0.27.
The estimate of 28 would be 5.27 (the actual is 5.29).


Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
CORE CONTENT
Cluster Title: Use coordinates to prove simple geometric theorems algebraically
Standard G.GPE.4: Use coordinates to prove simple geometric theorems algebraically. For examples, prove or disprove
that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies
on the circle centered at the origin and containing the point (0, 2)
Concepts and Skills to Master:
 Use coordinates to prove simple geometric theorems algebraically, focusing on lines, segments, and angles.
 Prove that points in a plane determine defined geometric figures.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Calculate slopes, including slopes of parallel and perpendicular lines
 Understand the relationship between parallel and perpendicular lines
 Calculate distances using the distance formula
 Understand basic properties of geometric figures (i.e. segment length, Pythagorean Theorem, coordinates)
 Understand the basic properties of polygons.
Academic Vocabulary
Altitude, diagonal, perpendicular, bisector, perpendicular bisector, median, parallel Pythagorean theorem
Suggested Instructional Strategies:
Resources:
 Explore properties of geometric figures plotted on a
 Textbook Correlation: Concept Byte- Distance
coordinate axes system using graphing technology
and Midpoint p. 605
and dynamic software
 MARS Apprentice Task: Square (G.GPE 4 through
 Generalize coordinates of geometric figures using
G.GPE 7)
variables for one or more of the vertices
NCDPI Unpacking:
G.GPE.4: Use the concepts of slope and distance to prove
that a figure in the coordinate system is a special geometric
shape.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Sample Assessment Tasks
Skill-based task
Prove or disprove that triangle ABC with coordinates
A(-1,2), B(1, 5), C(-2, 7) is an isosceles right triangle.
Unit Title: Connecting Algebra & Geometry Part
Problem Task
1. Take a picture or find a picture which includes a polygon.
Overlay the picture on a coordinate plane (manually or
electronically). Determine the coordinates of the vertices.
Classify the polygon. Use the coordinates to justify the
classification.
2. The coordinates are for a quadrilateral, (3, 0), (1, 3),
(-2, 1), and (0,-2). Determine the type of quadrilateral made
by connecting these four points? Identify the properties used
to determine your classification. You must give confirming
information about the polygon.
3. If Quadrilateral ABCD is a rectangle, where A(1, 2),
B(6,0), C(10,10) and D(?, ?) is unknown.
a. Find the coordinates of the fourth vertex.
b. Verify that ABCD is a rectangle, providing evidence
related to the sides and angles.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
CORE CONTENT
Cluster Title: Use coordinates to prove simple geometric theorems algebraically
Standard G.GPE.6: Find the point on a directed line segment between two given points that partitions the segment in a
given ratio. At this level, focus on finding the midpoint of a segment
Concepts and Skills to Master:
 Given two points on a line, find the point that divides the segment into an equal number of parts.
 Given a midpoint and an endpoint, find the other endpoint
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Solving equations
 Coordinate plane
Academic Vocabulary
Segment, midpoint, endpoint, coordinates
Suggested Instructional Strategies:
Include real-world examples. (e.g. superimpose a
coordinate grid onto a map of North Carolina, choose an
endpoint and a midpoint, have students determine the
other endpoint and identify the city)
NCDPI Unpacking:
G.GPE.6: Given two points on a line, find the point that
divides the segment into an equal number of parts. If
finding the mid-point, it is always halfway between the two
endpoints. The x-coordinate of the mid-point will be the
mean of the x-coordinates of the endpoints and the ycoordinate will be the mean of the y-coordinates of the
endpoints. At this level, focus on finding the midpoint of a
segment.
Resources:
 Textbook Correlation: Concept Byte- Distance
and Midpoint pg. 605
 Open-ended Journal Prompts:
-Describe how to find the midpoint of a line segment.
Include an example.
-Describe how to find an endpoint of a line segment if you
know the coordinates of the midpoint and one endpoint.
Include an example.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Sample Assessment Tasks
Skill-based task
Find the midpoint between (-3, 6) and (7, -9).
Unit Title: Connecting Algebra & Geometry Part
Problem Task
1. If you are given the midpoint of a segment and one
endpoint. Find the other endpoint.
a. midpoint: (6, 2) endpoint: (1, 3)
b. midpoint: (-1, -2) endpoint: (3.5, -7)
2. If Jennifer and Jane are best friends. They placed a map
of their town on a coordinate grid and found the point at
which each of their houses lies. If Jennifer’s house lies at (9,
7) and Jane’s house is at (15, 9) and they wanted to meet in
the middle, what are the coordinates of the place they
should meet?
3. If general points N at (a,b) and P at (c,d) are given. Why
are the coordinates of point Q (a,d)? Can you find the
coordinates of point M?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
CORE CONTENT
Cluster Title: Use coordinates to prove simple geometric theorems algebraically
Standard G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g. using
the distance formula.
Concepts and Skills to Master:
 Use the distance formula to compute perimeters of polygons and areas of triangles and rectangles
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Find perimeter and area of a variety of shapes, including irregular shapes. Use the distance formula
Academic Vocabulary
Perimeter, polygon, area, distance formula
Suggested Instructional Strategies:
Resources:
 Graph polygons using coordinates. Determine side
 TeacherTube G.GPE.7
lengths and perimeters of polygons. Calculate
 Coordinate Stations Coordinate Stations
areas of triangles and rectangles.
 Given a triangle, use slopes to verify that the
length and height are perpendicular. Find the area
 Explore perimeter and area of a variety of
polygons, including convex, concave, and
irregularly shaped polygons
NCDPI Unpacking:
G.GPE.7: Students should find the perimeter of polygons
and the area of triangles and rectangles using coordinates
on the coordinate plane.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Middle School Math I Unit #8
Unit Title: Connecting Algebra & Geometry Part
Sample Assessment Tasks
Skill-based task
Calculate the area of triangle ABC with altitude CD, given
A(-4, -2), B(8, 7), C(1, 8) and D(4, 4).
Problem Task
1. Find the area and perimeter of a real-world shape using a
coordinate grid and Google Earth.
Select a shape (your yard, a parking lot, the school, etc).
Use the tool menu to overlay a grid. Use coordinates to find
the perimeter and area of the shape you selected.
Determine the scale factor of the picture as related to the
actual real-life view. Find the actual perimeter and area.
2. John was visiting three cities that lie on a coordinate grid
at (-4, 5), (4, 5), and (-3, -4). If he visited all the cities and
ended up where he started, what is the distance in miles he
traveled?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.