Download GEOMETRY NR MZHS 2016 PEARSON FINAL

MOUNT VERNON CITY SCHOOL DISTRICT
Geometry NR
MZHS
Curriculum Guide
THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE
GEOMETRY NR CURRICULUM AT MANDELA / ZOLLICOFFER HIGH
SCHOOL (MZHS).
2016-2017
Mount Vernon City School District
Board of Education
Lesly Zamor
President
Adriane Saunders
Vice President
Board Trustees
Charmaine Fearon
Dr. Serigne Gningue
Rosemarie Jarosz
Micah J.B. McOwen
Omar McDowell
Darcy Miller
Wanda White
Superintendent of Schools
Dr. Kenneth R. Hamilton
Deputy Superintendent
Dr. Jeff Gorman
Assistant Superintendent of Business
Ken Silver
Assistant Superintendent of Human Resources
Denise Gagne-Kurpiewski
Assistant Superintendent of School Improvement
Dr. Waveline Bennett-Conroy
Associate Superintendent for Curriculum and Instruction
Dr. Claytisha Walden
Administrator of Mathematics and Science (K-12)
Dr. Satish Jagnandan
2
TABLE OF CONTENTS
I.
COVER ...............................................................................................................................1
II.
MVCSD BOARD OF EDUCATION ...............................................................................2
III.
TABLE OF CONTENTS ..................................................................................................3
IV.
IMPORTANT DATES ......................................................................................................4
V.
VISION STATEMENT .....................................................................................................5
VI.
PHILOSOPHY OF MATHEMATICS CURRICULUM
……………. 6
VII.
NYS P-12 COMMON CORE LEARNING STANDARDS
……………..7
VII.
MVCSD CCLS GEOMTRY NR MZHS PACING GUIDE
…………... 11
VIII. WORD WALL
…………... 16
IX.
SETUP OF A MATHEMATICS CLASSROOM
…………... 17
X.
SECONDARY GRADING POLICY
…………... 18
XI.
SAMPLE NOTEBOOK RUBRIC
…………... 19
XII.
CLASSROOM AESTHETICS
…………... 20
XIII. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON
3
…………... 21
IMPORTANT DATES 2016-17
REPORT CARD
MARKING
PERIOD
MARKING PERIOD
BEGINS
MARKING
PERIOD ENDS
DURATION OF
INSTRUCTION
September 6, 2016
INTERIM
PROGRESS
REPORTS
October 7, 2016
MP 1
November 10, 2016
MP 2
November 14, 2016
December 16, 2016
January 27, 2017
MP 3
January 30, 2017
March 10, 2017
April 21, 2017
MP 4
April 24, 2017
May 19, 2017
June 23, 2017
10 weeks – 44
Days
10 weeks – 46
Days
10 weeks – 49
Days
9 weeks – 43
Days
The Parent Notification Policy states “Parent(s) / guardian(s) or adult students are
to be notified, in writing, at any time during a grading period when it is apparent that the student may fail or is performing unsatisfactorily in any course or grade
level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during
the grading period when it becomes evident that the student's conduct or effort
grades are unsatisfactory.”
4
VISION STATEMENT
True success comes from co-accountability and co-responsibility. In a coherent
instructional system, everyone is responsible for student learning and student
achievement. The question we need to constantly ask ourselves is, "How are our
students doing?"
The starting point for an accountability system is a set of standards and
benchmarks for student achievement. Standards work best when they are well
defined and clearly communicated to students, teachers, administrators, and
parents. The focus of a standards-based education system is to provide common
goals and a shared vision of what it means to be educated. The purposes of a
periodic assessment system are to diagnose student learning needs, guide
instruction and align professional development at all levels of the system.
The primary purpose of this Instructional Guide is to provide teachers and
administrators with a tool for determining what to teach and assess. More
specifically, the Instructional Guide provides a "road map" and timeline for
teaching and assessing the Common Core Learning Standards.
I ask for your support in ensuring that this tool is utilized so students are able to
benefit from a standards-based system where curriculum, instruction, and
assessment are aligned. In this system, curriculum, instruction, and assessment are
tightly interwoven to support student learning and ensure ALL students have equal
access to a rigorous curriculum.
We must all accept responsibility for closing the achievement gap and improving
student achievement for all of our students.
Dr. Satish Jagnandan
Administrator for Mathematics and Science (K-12)
5
PHILOSOPHY OF MATHEMATICS CURRICULUM
The Mount Vernon City School District recognizes that the understanding of mathematics is
necessary for students to compete in today’s technological society. A developmentally
appropriate mathematics curriculum will incorporate a strong conceptual knowledge of
mathematics through the use of concrete experiences. To assist students in the understanding and
application of mathematical concepts, the mathematics curriculum will provide learning
experiences which promote communication, reasoning, and problem solving skills. Students will
be better able to develop an understanding for the power of mathematics in our world today.
Students will only become successful in mathematics if they see mathematics as a whole, not as
isolated skills and facts. As we develop mathematics curriculum based upon the standards,
attention must be given to both content and process strands. Likewise, as teachers develop their
instructional plans and their assessment techniques, they also must give attention to the
integration of process and content. To do otherwise would produce students who have temporary
knowledge and who are unable to apply mathematics in realistic settings. Curriculum,
instruction, and assessment are intricately related and must be designed with this in mind. All
three domains must address conceptual understanding, procedural fluency, and problem solving.
If this is accomplished, school districts will produce students who will
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.
6
New York State P-12 Common Core Learning Standards for
Mathematics
Mathematics - High School Geometry: Introduction
An understanding of the attributes and relationships of geometric objects can be applied in
diverse contexts—interpreting a schematic drawing, estimating the amount of wood needed to
frame a sloping roof, rendering computer graphics, or designing a sewing pattern for the most
efficient use of material.
Although there are many types of geometry, school mathematics is devoted primarily to plane
Euclidean geometry, studied both synthetically (without coordinates) and analytically (with
coordinates). Euclidean geometry is characterized most importantly by the Parallel Postulate,
that through a point not on a given line there is exactly one parallel line. (Spherical geometry, in
contrast, has no parallel lines.)
During high school, students begin to formalize their geometry experiences from elementary and
middle school, using more precise definitions and developing careful proofs. Later in college
some students develop Euclidean and other geometries carefully from a small set of axioms.
The concepts of congruence, similarity, and symmetry can be understood from the perspective of
geometric transformation. Fundamental are the rigid motions: translations, rotations, reflections,
and combinations of these, all of which are here assumed to preserve distance and angles (and
therefore shapes generally). Reflections and rotations each explain a particular type of symmetry,
and the symmetries of an object offer insight into its attributes—as when the reflective symmetry
of an isosceles triangle assures that its base angles are congruent.
In the approach taken here, two geometric figures are defined to be congruent if there is a
sequence of rigid motions that carries one onto the other. This is the principle of superposition.
For triangles, congruence means the equality of all corresponding pairs of sides and all
corresponding pairs of angles. During the middle grades, through experiences drawing triangles
from given conditions, students notice ways to specify enough measures in a triangle to ensure
that all triangles drawn with those measures are congruent. Once these triangle congruence
criteria (ASA, SAS, and SSS) are established using rigid motions, they can be used to prove
theorems about triangles, quadrilaterals, and other geometric figures.
Similarity transformations (rigid motions followed by dilations) define similarity in the same
way that rigid motions define congruence, thereby formalizing the similarity ideas of "same
shape" and "scale factor" developed in the middle grades. These transformations lead to the
criterion for triangle similarity that two pairs of corresponding angles are congruent.
The definitions of sine, cosine, and tangent for acute angles are founded on right triangles and
similarity, and, with the Pythagorean Theorem, are fundamental in many real-world and
theoretical situations. The Pythagorean Theorem is generalized to non-right triangles by the Law
of Cosines. Together, the Laws of Sines and Cosines embody the triangle congruence criteria for
7
the cases where three pieces of information suffice to completely solve a triangle. Furthermore,
these laws yield two possible solutions in the ambiguous case, illustrating that Side-Side-Angle
is not a congruence criterion.
Analytic geometry connects algebra and geometry, resulting in powerful methods of analysis and
problem solving. Just as the number line associates numbers with locations in one dimension, a
pair of perpendicular axes associates pairs of numbers with locations in two dimensions. This
correspondence between numerical coordinates and geometric points allows methods from
algebra to be applied to geometry and vice versa. The solution set of an equation becomes a
geometric curve, making visualization a tool for doing and understanding algebra. Geometric
shapes can be described by equations, making algebraic manipulation into a tool for geometric
understanding, modeling, and proof. Geometric transformations of the graphs of equations
correspond to algebraic changes in their equations.
Dynamic geometry environments provide students with experimental and modeling tools that
allow them to investigate geometric phenomena in much the same way as computer algebra
systems allow them to experiment with algebraic phenomena.
Connections to Equations.
The correspondence between numerical coordinates and geometric points allows methods from
algebra to be applied to geometry and vice versa. The solution set of an equation becomes a
geometric curve, making visualization a tool for doing and understanding algebra. Geometric
shapes can be described by equations, making algebraic manipulation into a tool for geometric
understanding, modeling, and proof.
Mathematical Practices
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.
Geometry Overview
Congruence
• Experiment with transformations in the plane
• Understand congruence in terms of rigid
motions
• Prove geometric theorems
• Make geometric constructions
Expressing Geometric Properties with Equations
• Translate between the geometric description
and the equation for a conic section
• Use coordinates to prove simple geometric
theorems algebraically
Geometric Measurement and Dimension
• Explain volume formulas and use them to solve
problems
• Visualize relationships between twodimensional
and three-dimensional objects
Similarity, Right Triangles, and Trigonometry
• Understand similarity in terms of similarity
transformations
• Prove theorems involving similarity
• Define trigonometric ratios and solve problems
involving right triangles
• Apply trigonometry to general triangles
Modeling with Geometry
• Apply geometric concepts in modeling
situations
Circles
• Understand and apply theorems about circles
• Find arc lengths and areas of sectors of circles
8
Congruence
G-CO
Experiment with transformations in the plane
1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the
undefined notions of point, line, distance along a line, and distance around a circular arc.
2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other points as outputs. Compare
transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry
it onto itself.
4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph
paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure
onto another.
Understand congruence in terms of rigid motions
6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion
on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they
are congruent.
7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only
if corresponding pairs of sides and corresponding pairs of angles are congruent.
8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence
in terms of rigid motions.
Prove geometric theorems
9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal
crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points
on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base
angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel
to the third side and half the length; the medians of a triangle meet at a point.
11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are
congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms
with congruent diagonals.
Make geometric constructions
12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string,
reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle;
bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector
of a line segment; and constructing a line parallel to a given line through a point not on the line.
13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Similarity, Right Triangles, & Trigonometry
G-SRT
Understand similarity in terms of similarity transformations
1. Verify experimentally the properties of dilations given by a center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. 2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are
similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all
corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems involving similarity
9
4.
5.
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two
proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric
figures.
Define trigonometric ratios and solve problems involving right triangles
6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to
definitions of trigonometric ratios for acute angles.
7. Explain and use the relationship between the sine and cosine of complementary angles.
8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Apply trigonometry to general triangles
9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and
non-right triangles (e.g., surveying problems, resultant forces).
Circles
G-C
Understand and apply theorems about circles
1. Prove that all circles are similar.
2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between
central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a
circle is perpendicular to the tangent where the radius intersects the circle.
3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral
inscribed in a circle.
4. (+) Construct a tangent line from a point outside a given circle to the circle.
Find arc lengths and areas of sectors of circles
5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius,
and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a
sector.
Expressing Geometric Properties with Equations
G-GPE
Translate between the geometric description and the equation for a conic section
1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square
to find the center and radius of a circle given by an equation.
2. Derive the equation of a parabola given a focus and directrix.
3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of
distances from the foci is constant.
Use coordinates to prove simple geometric theorems algebraically
4. Use coordinates to prove simple geometric theorems algebraically. For example, 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).
5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find
the equation of a line parallel or perpendicular to a given line that passes through a given point).
6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
formula.
Geometric Measurement & Dimension
G-GMD
Explain volume formulas and use them to solve problems
10
1.
2.
3.
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a
cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other
solid figures.
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Visualize relationships between two-dimensional and three-dimensional objects
4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify threedimensional objects generated by rotations of two-dimensional objects.
Modeling with Geometry
G-MG
Apply geometric concepts in modeling situations
1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a
human torso as a cylinder).
2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile,
BTUs per cubic foot).
3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical
constraints or minimize cost; working with typographic grid systems based on ratios).
11
GEOMETRY NR - MZHS PACING GUIDE
This guide using Geometry © 2015 was created to provide teachers with a time frame to complete the New York State Mathematics
Geometry Curriculum.
CHAPTER / LESSONS
PACING
FALL
SPRING
CHAPTER 1 TOOLS OF GEOMETRY
1-1 Nets and Drawings for Visualizing Geometry Prepares for G-CO.A.1
1-2 Points, Lines, and Planes G-CO.A.1
1-3 Measuring Segments G-CO.A.1, G-GPE.B.6
1-4 Measuring Angles G-CO.A.1
1-5 Exploring Angle Pairs Prepares for G-CO.A.1
• Concept Byte: Compass Designs Prepares for G-CO.D.12
1-6 Basic Constructions G-CO.A.1, G-CO.D.12
• Concept Byte: Exploring Constructions Prepares for G-CO.D.12
1-7 Midpoint and Distance in the Coordinate Plane Prepares for G-GPE.B.4 and GGPE.B.7; also G-GPE.B.6
• Review: Classifying Polygons Prepares for G-MG.A.1
1-8 Perimeter, Circumference, and Area N-Q.A.1
• Concept Byte: Comparing Perimeters and Areas Prepares for G-MG.A.2
15
Sept. 6 –
Sept. 26
Feb. 2- Mar.
1
CHAPTER 2 REASONING AND PROOF
2-1 Patterns and Inductive Reasoning Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11
2-2 Conditional Statements Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11
• Concept Byte: Logic and Truth Tables Prepares for G-CO.C.9, G-CO.C.10, and
G-CO.C.11
2-3 Biconditionals and Definitions Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11
2-4 Deductive Reasoning Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11
2-5 Reasoning in Algebra and Geometry Prepares for G-CO.C.9, G-CO.C.10, and GCO.C.11
2-6 Proving Angles Congruent G-CO.C.9
11
Sept. 27 –
Oct. 18
Mar. 2 – Mar.
17
12
CHAPTER / LESSONS
PACING
FALL
SPRING
CHAPTER 3 PARALLEL AND PERPENDICULAR LINES
3-1 Lines and Angles G-CO.A.1, Prepares for G-CO.D.12
• Concept Byte: Parallel Lines and Related Angles G-CO.D.12, Prepares for GCO.C.9
3-2 Properties of Parallel Lines G-CO.C.9
3-3 Proving Lines Parallel Extends G-CO.C.9
3-4 Parallel and Perpendicular Lines G-MG.A.3
• Concept Byte: Perpendicular Lines and Planes Extends G-CO.A.1
3-5 Parallel Lines and Triangles G-CO.D.10
• Concept Byte: Exploring Spherical Geometry Extends G-CO.A.1
3-6 Constructing Parallel and Perpendicular Lines G-CO.D.12, G-CO.D.13
3-7 Equations of Lines in the Coordinate Plane Prepares for G-GPE.B.5
3-8 Slopes of Parallel and Perpendicular Lines G-GPE.B.5
13
Oct. 19 –
Nov. 4
Mar. 20 –
Apr. 5
CHAPTER 4 CONGRUENT TRIANGLES
4-1 Congruent Figures Prepares for G-SRT.B.5
• Concept Byte: Building Congruent Triangles Prepares for G-SRT.B.5
4-2 Triangle Congruence by SSS and SAS G-SRT.B.5
4-3 Triangle Congruence by ASA and AAS G-SRT.B.5
• Concept Byte: Exploring AAA and SSA Extends G-SRT.B.5
4-4 Using Corresponding Parts of Congruent Triangles G-CO.D.12, G-SRT.B.5
• Concept Byte: Paper-Folding Conjectures G-CO.D.12
4-5 Isosceles and Equilateral Triangles G-CO.C.10, G-CO.D.13, G-SRT.B.5
Algebra Review: Systems of Linear Equations Reviews A-REI.C.6
4-6 Congruence in Right Triangles G-SRT.B.5
4-7 Congruence in Overlapping Triangles G-SRT.B.5
13
13
Nov. 7 – Nov. Apr. 6 – May
29
2
CHAPTER / LESSONS
CHAPTER 5 RELATIONSHIPS WITHIN TRIANGLES
• Concept Byte: Investigating Midsegments Prepares for G-CO.C.10
5-1 Midsegments of Triangles G-CO.C.10, G-SRT.B.5
5-2 Perpendicular and Angle Bisectors G-CO.C.9, G-CO.D.12, G-SRT.B.5
• Concept Byte: Paper Folding Bisectors Prepares for G-C.A.3
5-3 Bisectors in Triangles G-C.A.3
• Concept Byte: Special Segments in Triangles Prepares for G-CO.C.10
5-4 Medians and Altitudes G-CO.C.10, G-SRT.B.5
5-5 Indirect Proof Extends G-CO.C.10
• Algebra Review: Solving Inequalities Reviews A.CED.A.1
5-6 Inequalities in One Triangle Extends G-CO.C.10
5-7 Inequalities in Two Triangles Extends G-CO.C.10
CHAPTER 6 POLYGONS AND QUADRILATERALS
• Concept Byte: Exterior Angles of Polygons Prepares for G-SRT.B.5
6-1 The Polygon-Angle Sum Theorems G-SRT.B.5
6-2 Properties of Parallelograms G-CO.C.11, G-SRT.B.5
6-3 Proving That a Quadrilateral Is a Parallelogram G-CO.C.11, G-SRT.B.5
6-4 Properties of Rhombuses, Rectangles, and Squares G-CO.C.11, G-SRT.B.5
6-5 Conditions for Rhombuses, Rectangles, and Squares G-CO.C.11, G-SRT.B.5
6-6 Trapezoids and Kites G-SRT.B.5
6-7 Polygons in the Coordinate Plane G-GPE.B.7
6-8 Applying Coordinate Geometry Prepares for G-GPE.B.4
• Concept Byte: Quadrilaterals in Quadrilaterals G-CO.D12
6-9 Proofs Using Coordinate Geometry G-GPE.B.4
MVCSD GEOMETRY NR - MZHS TEST
14
PACING
FALL
SPRING
13
Nov. 30 –
Dec. 16
May 3 – May
22
15 / 11
Dec. 19 – Jan.
18
May 23 –
June 8
JAN. 19
JUNE 9
Although pacing will vary somewhat in response to variations in school calendars, needs of students, your school's years of experience
with the curriculum, and other local factors, following the suggested pacing and sequence will ensure that students benefit from the
way mathematical ideas are introduced, developed, and revisited across the year.
15
WORD WALLS ARE DESIGNED …
•
•
•
•
•
•
•
•
to promote group learning
support the teaching of important general
principles about words and how they work
Foster reading and writing in content area
Provide reference support for children during their reading and writing
Promote independence on the part of young students as they work with words
Provide a visual map to help children remember connections between words and the
characteristics that will help them form categories
Develop a growing core of words that become part of their vocabulary
Important Notice
• A Mathematics Word Wall must be present in every mathematics classroom.
Math Word Wall
l
l
Create a math word
wall
Place math words on
your current word
wall but highlight
them in some way.
SETUP OF THE MATHEMATICS CLASSROOM
I.
Prerequisites for a Mathematics Classroom
• Teacher Schedule
• Class List
• Seating Chart
• Code of Conduct / Discipline
• Grade Level Common Core Learning Standards (CCLS)
• Updated Mathematics Student Work
• Mathematics Grading Policy
• Mathematics Diagrams, Charts, Posters, etc.
• Grade Level Number Line
• Grade Level Mathematics Word Wall
• Mathematics Portfolios
• Mathematics Center with Manipulatives (Grades K - 12)
II.
Updated Student Work
A section of the classroom must display recent student work. This can be of any
type of assessment, graphic organizer, and writing activity. Teacher feedback must
be included on student’s work.
III.
Board Set-Up
Every day, teachers must display the Lesson # and Title, Objective(s), Common
Core Learning Standard(s), Opening Exercise and Homework. At the start of
the class, students are to copy this information and immediately begin on the
Fluency Activity or Opening Exercise.
Student’s Name:
Teacher’s Name:
School:
Date:
Lesson # and Title:
Objective(s)
CCLS:
Opening Exercise:
IV.
Spiraling Homework
Homework is used to reinforce daily learning objectives. The secondary purpose
of homework is to reinforce objectives learned earlier in the year. The
assessments are cumulative, spiraling homework requires students to review
coursework throughout the year.
17
SECONDARY MATHEMATICS GRADING POLICY
This course of study includes different components, each of which are assigned the
following percentages to comprise a final grade. I want you--the student--to understand
that your grades are not something that I give you, but rather, a reflection of the work
that you give to me.
COMPONENTS
1.
Common Assessments
→
35%
2.
Quizzes
→
20%
3.
Homework
→
20%
4.
Notebook and/or Journal
→
10%
5.
Classwork / Class Participation
→
15%
o Class participation will play a significant part in the determination of your
grade. Class participation will include the following: attendance, punctuality
to class, contributions to the instructional process, effort, contributions during
small group activities and attentiveness in class.
Important Notice
As per MVCSD Board Resolution 06-71, the Parent Notification Policy states
“Parent(s) / guardian(s) or adult students are to be notified, in writing, at any time during
a grading period when it is apparent - that the student may fail or is performing
unsatisfactorily in any course or grade level. Parent(s) / guardian(s) are also to be
notified, in writing, at any time during the grading period when it becomes evident that
the student's conduct or effort grades are unsatisfactory.”
18
SAMPLE NOTEBOOK SCORING RUBRIC
Student Name:
Teacher Name:
Criteria
4
3
2
1
Completion of
Required Sections
All required
sections are
complete.
One required
section is
missing.
Two or three
required sections
are missing.
More than three
required sections
are missing.
Missing Sections
No sections of
the notebook are
missing.
One sections of
the notebook is
missing.
Two sections of the
notebook are
missing.
Three or more
sections of the
notebook are
missing.
Headers / Footers
No required
header(s) and/or
footer(s) are
missing within
notebook.
One or two
required
header(s) and/or
footer(s) are
missing within
notebook.
Three or four
required header(s)
and/or footer(s) are
missing within
notebook.
More than four
required header(s)
and/or footer(s) are
missing within
notebook.
Organization
All assignment
and/or notes are
kept in a logical
or numerical
sequence.
One or two
assignments
and/or notes are
not in a logical or
numerical
sequence.
Three or Four
assignments and/or
notes are not in a
logical or
numerical
sequence.
More than four
assignments and/or
notes are not in a
logical or
numerical
sequence.
Neatness
Overall notebook
is kept very neat.
Overall notebook
is kept in a
satisfactory
condition.
Overall notebook is
kept in a below
satisfactory
condition.
Overall notebook is
unkept and very
disorganized.
Total
Teacher’s Comments:
19
Points
CLASSROOM AESTHETICS
“PRINT–RICH” ENVIRONMENT CONDUCIVE TO LEARNING
TEACHER NAME:
COURSE / PERIOD:
ROOM:
CHECKLIST
YES
•
Teacher Schedule
•
Class List
•
Seating Chart
•
Code of Conduct / Discipline
•
Grade Level Mathematics CCLS
•
Mathematics Grading Policy
•
Mathematics Diagrams, Posters, Displays, etc.
•
Grade Level Number Line
•
Updated Student Work (Projects, Assessments, Writing, etc.)
•
Updated Student Portfolios
•
Updated Grade Level Mathematics Word-Wall
•
Mathematics Centers with Manipulatives
•
Organization of Materials
•
Cleanliness
Principal Signature:
Date:
Asst. Pri. Signature:
Date:
20
NO
SYSTEMATIC DESIGN OF A MATHEMATICS LESSON
What are the components of a Mathematics Block?
Component
Fluency Practice
• Information processing theory supports the view that automaticity in math facts is
fundamental to success in many areas of higher mathematics. Without the ability to retrieve
facts directly or automatically, students are likely to experience a high cognitive load as they
perform a range of complex tasks. The added processing demands resulting from inefficient
methods such as counting (vs. direct retrieval) often lead to declarative and procedural errors.
Accurate and efficient retrieval of basic math facts is critical to a student’s success in
mathematics.
Opening Exercise - Whole Group
• This can be considered the motivation or Do Now of the lesson
• It should set the stage for the day's lesson
• Introduction of a new concept, built on prior knowledge
• Open-ended problems
Conceptual Development - Whole Group (Teacher Directed, Student Centered)
• Inform students of what they are going to do. Refer to Objectives. Refer to the Key Words
(Word Wall)
• Define the expectations for the work to be done
• Provide various demonstrations using modeling and multiple representations (i.e. model a
strategy and your thinking for problem solving, model how to use a ruler to measure items,
model how to use inch graph paper to find the perimeter of a polygon,)
• Relate to previous work
• Provide logical sequence and clear explanations
• Provide medial summary
Application Problems - Cooperative Groups, Pairs, Individuals, (Student Interaction &
Engagement, Teacher Facilitated)
• Students try out the skill or concept learned in the conceptual development
• Teachers circulate the room, conferences with the students and assesses student work (i.e.
teacher asks questions to raise the level of student thinking)
• Students construct knowledge around the key idea or content standard through the use of
problem solving strategies, manipulatives, accountable/quality talk, writing, modeling,
technology applied learning
Student Debrief - Whole Group (Teacher Directed, Student Centered)
• Students discuss their work and explain their thinking
• Teacher asks questions to help students draw conclusions and make references
• Determine if objective(s) were achieved
• Students summarize what was learned
• Allow students to reflect, share (i.e. read from journal)
Homework/Enrichment - Whole Group (Teacher Directed, Student Centered)
• Homework is a follow-up to the lesson which may involve skill practice, problem solving
and writing
21
•
•
Homework, projects or enrichment activities should be assigned on a daily basis.
SPIRALLING OF HOMEWORK - Teacher will also assign problems / questions pertaining
to lessons taught in the past
Remember: Assessments are on-going based on students’ responses.
Assessment: Independent Practice (It is on-going! Provide formal assessment when
necessary / appropriate)
• Always write, use and allow students to generate Effective Questions for optimal learning
• Based on assessment(s), Re-teach the skill, concept or content using alternative strategies
and approaches
Important Notice
•
All lessons must be numbered with corresponding homework. For example, lesson #1 will
corresponded to homework #1 and so on.
•
Writing assignments at the end of the lesson (closure) bring great benefits. Not only do they
enhance students' general writing ability, but they also increase both the understanding of
content while learning the specific vocabulary of the disciplines.
•
Spiraling Homework
o Homework is used to reinforce daily learning objectives. The secondary purpose of
homework is to reinforce objectives learned earlier in the year. The assessments are
cumulative, spiraling homework requires students to review coursework throughout the
year.
•
Manipulative must be incorporated in all lessons. With students actively involved in
manipulating materials, interest in mathematics will be aroused. Using manipulative
materials in teaching mathematics will help students learn:
a. to relate real world situations to mathematics symbolism.
b. to work together cooperatively in solving problems.
c. to discuss mathematical ideas and concepts.
d. to verbalize their mathematics thinking.
e. to make presentations in front of a large group.
f. that there are many different ways to solve problems.
g. that mathematics problems can be symbolized in many different ways.
h. that they can solve mathematics problems without just following teachers' directions.
22