RCAS Grade 8 – Looking for Pythagoras- Instructional Roadmap
November 4 – December 20: Looking for Pythagoras
25 full days assessment, intervention, and enrichment activities are included
All Standards written in red are priority standards
Investigation
CCSS
Learning Targets:
CMP2/CMP3
(will need to create PLDs for
each target)
4/4
1
8.G.B.6 Explain a proof of the Pythagorean Theorem
 I will utilize a coordinate grid
Days
Coordinate Grids and its converse.
to explore distance
relationships. (no standards
8.G.B.8 Apply the Pythagorean Theorem to find the
connection, but implicitly
distance between two points in a coordinate grid.
needed) [1.1/1.2]
8.G.B. 7 Apply the Pythagorean Theorem to
determine unknown side lengths in right triangles in
real world and mathematical problems in two and
three dimensions.
4/6.5
Days
2
Square Roots
8.NS.A.2 Use rational approximations of rational
numbers to compute the size of irrational numbers,
locate them approximately on number line diagram,
and estimate the value of expressions.
***
Copy and
add in 2.4
Cube Roots
from CMP3
****
8.EE.A2 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 cube. Know that square root of 2 is
irrational.
6/7
Days
HS- N-QA. 3 Choose a level of accuracy appropriate
to limitation on measurement when reporting
quantities.
8.G.B.6 Explain a proof of the Pythagorean Theorem
and its converse.
3
The
Pythagorean
Theorem
8.G.B.8 Apply the Pythagorean Theorem to find the
distance between two points in a coordinate grid.

I will be able to find the area
of shapes, using properties
of rectangles and right
triangles. (no standards
connection, but implicitly
needed) [1.3]
1.) I will be able to apply my
knowledge of square roots
to find the side length of a
given square.
2.) I will be able to
approximate the value of
a square root. [LT 2.3]
3.) I will be able to find the
square root of a two
dimensional figure or the
cube root of a three
dimensional figure.
[2.3/2.4]
1.) I will be able to find the
missing side of a right triangle
using the Pythagorean Theorem.
2) I will be able to determine if a
triangle is a right triangle based
Assessments
CFA’s:
Learning targets:
1.3
Summative
Assessment:
None
CFA’s:
Learning targets: #2
Summative
Assessment:
Checkup after 2
CFA’s:
Learning targets
****
3.4 has
added good
questions in
part C.
*****
5/5
Days
****
4.2/4.3 is
moved to
Inv.5, 4.24.4 is all new
*****
5days
****
New in
CMP3
8.G.B. 7 Apply the Pythagorean Theorem to
determine unknown side lengths in right triangles in
real world and mathematical problems in two and
three dimensions.
4
Using the
Pythagorean
Theorem:
Understanding
Real Numbers
8.NS.A1 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.
8.NS.A.2 Use rational approximations of irrational
numbers to compute the size of irrational numbers,
locate them approximately on number line diagram,
and estimate the value of expressions.
5

Using the
Pythagorean
Theorem:
Analyzing
Triangles and
Circles
CCSS.Math.Content.8.G.A.4 Understand that a twodimensional figure is similar to another if the second
can be obtained from the first by a sequence of
rotations, reflections, translations, and dilations; given
two similar two-dimensional figures, describe a
sequence that exhibits the similarity between them.
8.G.B.8 Apply the Pythagorean Theorem to find the
distance between two points in a coordinate grid.
8.G.B. 7 Apply the Pythagorean Theorem to
determine unknown side lengths in right triangles in
real world and mathematical problems in two and
three dimensions.
Possible Essential Questions:
How do you find the missing side of a right triangle?
How can you estimate the value of an irrational #?
Why does the Pythagorean Theorem work?
How can we use the square root to find length or area?
on the Pythagorean Theorem.
3) I will be able to explain a proof
of the Pythagorean Theorem.[3.1]
Summative
Assessment:
Partner Quiz
1.) I will be able to
approximate and order
irrational numbers on a
number line [4.1]
2.) I will be able to convert
between rational and
irrational numbers
[4.2/4.3]
3.) I can identify numbers as
rational or irrational [4.4]
1) I will be able to use
the Pythagorean
theorem to solve
problems. [5.1]
2) I will be able to use
the Pythagorean
Theorem to analyze &
determine
relationships in special
right triangles.
[5.2/5.3]
CFA’s:
Learning targets
2/3
Summative
Assessment:
CFA’s:
Learning targets
2
Summative
Assessment:
Unit Test
Smarter
Balanced
ALDS
4
3
2
1
Use rational
numbers to
approximate
irrational
numbers.
8.NS.A
Level 4 - Students should be
able to approximate irrational
numbers & use the
approximations to solve
problems or estimate the
value of an expression.
Level 3 -Students should be able to use
rational approximations of irrational
numbers to locate them on a number line
and to make numerical comparisons;
convert between fractions and repeating
decimals; and compare rational numbers.
Level 2 -Students should be able to identify
approximate locations of familiar irrational
numbers on a number line; identify numbers as
rational or irrational; and convert between
fractions and terminating decimals.
Level 1 -Students should be able
to identify square roots of
numbers less than 100; identify
pi as not rational; and understand
that every rational number has a
decimal expansion.
Understand
and apply
the
Pythagorean
Theorem.
8.G.B
Work with
radicals and
exponents.
8.EE.A
Level 4 -Students should be
able to apply the
Pythagorean theorem to find
the distance between two
points in a coordinate system
in 3D.
Level 3 -Students should be able to apply
the Pythagorean theorem to determine the
unknown side lengths of right triangles
and to find the distance between two
points in a coordinate system in two
dimensions.
Level 2 -Students should be able to apply the
Pythagorean theorem to determine whether or not
a given triangle is a right triangle, given its side
lengths. They should be able to find the distance
between two points on a horizontal or vertical line
in a two-dimensional coordinate system.
Level 1 -Students should be able
to identify the hypotenuse and
the legs of a right triangle given
the side lengths or an image of a
right triangle.
Level 4 -Students should be
able to use scientific notation
and choose units of
appropriate size for realistic
measurements, solve
binomial quadratic and cubic
equations, and represent the
solution as a square or cube
root, respectively.
Level 3 -Students should be able to
identify that the square root of 2 is
irrational, calculate or approximate the
square or cube of a rational number, solve
quadratic and cubic monomial equations,
and represent the solution as a square or
cube root, respectively. They should be
able to work with and perform operations
with scientific notation and work with
and apply the properties of integer
exponents in order to produce or identify
equivalent numerical expressions.
Level 2 -Students should be able to identify and
calculate the cube root of familiar perfect cubes
and calculate the cube of integers. They should be
able to use appropriate tools (e.g., calculator,
pencil and paper) to translate large or small
numbers from scientific to standard notation. They
should be able to work with and apply the
properties of integer exponents of degree 2 or less
in order to produce or identify equivalent
numerical expressions.
Level 1 -Students should be able
to identify and calculate square
roots of familiar perfect squares
and calculate the square of
integers. They should be able to
translate between standard form
and scientific notation.
(slightly modified)
* Students will not be able to reach advanced in Looking for Pythagoras under clusters 8.EE.A.
Day 1
- Launch of book and 1.1
Day 2
- 1.2
Suggested Ace
Suggested Ace
Day 6
- 2.2 finish and CFA
Day 11
- 3.1
Suggested Ace
Day 3
- 1.3
- CFA 1.3
Suggested ACE: 15-25
(labsheet)
Day 4
- Reflection
-Pass back CFA
- 2.1
Day 5
- 2.2
Day 7
Day 8
- 2.3
Review Volume
- CFA 2.3
2.4
Suggested ACE: pg. 24 #7-34 ?
Day 9
- Reflection/ Review
Day 10
-Quiz
Day 12
- 3.1
Day 13
- 3.2
Day 14
3.3
Day 15
3.4
Suggested Ace
Day 16
Differentiation day
Day 17
Quiz
Day 18
4.1
Day 19
- 4.1
Suggested Ace:
Day 20
-4.2
Suggested Ace:
Day 21
- 4.3
Day 22
- 4.4
Day 23
Reflection
Review
Day 24
- Unit Test
Day 25