Download 8TH GRADE PACING GUIDE unit 3 prove it

8TH GRADE PACING GUIDE
MATH INNOVATIONS UNIT 3: PROVE IT
November-Christmas Break
Standards:
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 the square root of 2 is irrational.
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.
8.NS.2: 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., π2). 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.
8.G.6: Explain a proof of the Pythagorean Theorem and it’s converse.
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.
Standard/Target
8.G.6 Knowledge Target: Explain a proof of the Pythagorean
Theorem.
Percent Proficiency:
8.EE.2 Knowledge Target: 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.
Knowledge Target: Evaluate square roots of small perfect
squares. Knowledge Target: Evaluate cube roots of small
perfect cubes. Knowledge Target: Know that the square
root of 2 is irrational.
8.G.6 Knowledge Target: Explain a proof of the converse of
the Pythagorean Theorem.
8.G.7 Knowledge Target: Recall the Pythagorean Theorem
and its converse.
8.NS.2 Knowledge Target: Approximate irrational numbers
as rational numbers. Knowledge Target: Approximately
Section/Lesson
Section 2: The Pythagorean Theorem
2.1: Surveying with Right Triangles
2.2: Patterns and Pythagoras
2.3: Proving the Discovery
# Days
Day 57
4
3
3
Study Guide
Quiz
Section 3: Using the Pythagorean
Theorem
3.1: Squares and Square Roots
*Add: 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.
*Add: Evaluate cube roots of small
perfect cubes.
1
1
Day 70
ACT:
4
A6, A12, C10, C11, C14
3.2: The Real World and Messy Numbers
*Add: Estimate the value of expressions
4
A15, C6, C16
Lewis County Middle School
Formative Assessment
ACT:
Standard/Target
locate irrational numbers on a number line. Knowledge
Target: Estimate the value of expressions involving irrational
numbers using rational approximations. 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. Reasoning
Target: Compare the size of irrational numbers using rational
approximations.
8.NS.1 Knowledge Target: Define irrational numbers.
Knowledge Target: Show that the decimal expansion of
rational numbers repeats eventually. Knowledge Target:
Convert a decimal expansion which repeats eventually into a
rational number. Knowledge Target: Show informally that
every number has a decimal expansion.
8.G.6 Knowledge Target: Define key vocabulary: square
root, Pythagorean Theorem, right triangle, legs a and b,
hypotenuse, sides, right angle, converse, base, height, proof.
Knowledge Target: Be able to identify the legs and
hypotenuse of a right triangle.
8.G.7 Reasoning Target: Solve basic mathematical
Pythagorean theorem problems and its converse to find
missing lengths of sides of triangles in two and three
dimensions. Reasoning Target: Apply Pythagorean theorem
in solving real-world problems dealing with two and three
dimensional shapes.
8.G.8 Reasoning Target: Determine how to create a right
triangle from two points on a coordinate graph. Reasoning
Target: Use the Pythagorean Theorem to solve for the
distance between two points.
Percent Proficiency:
Percent Proficiency:
Section/Lesson
involving irrational numbers using rational
approximations. 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
*Add: Show that the decimal expansion
of rational numbers repeats eventually.
*Add: Convert a decimal expansion which
repeats eventually into a rational number.
*Add: Show informally that every number
has a decimal expansion.
# Days
3.3: Going the Distance
3
Study Guide
Quiz
Study Guide
Unit Exam
1
1
Lewis County Middle School
Formative Assessment
B9, B15
Lewis County Middle School
Lewis County Middle School