Tessellations-A tessellation is created when a shape is repeated and covers a plane without any gaps or overlaps. (Taken from Bing.com)
The gifted program (SAGE) in Henry County does not have its own set of specific standards appointed for the program. In order to insure quality instruction and academic rigor in the program, the following standards have been selected to go along with the unit on Tessellations. The standards displayed below are based upon the Georgia Performance Standards.
The math concept that will be infused throughout the year with Tessellations.
Math
M1G1. Students will study and create various two and three-dimensional figures and identify basic figures (squares, circles, triangles, and rectangles) within them.
a. Build, draw, name, and describe triangles, rectangles, pentagons, and hexagons.
b. Build, represent, name, and describe cylinders, cones, and rectangular prisms.
c. Create pictures and designs using shapes, including overlapping shapes.
M1G2. Students will compare, contrast, and/or classify geometric shapes by the common attributes of position, shape, size, number of sides, and number of corners.
M1G3. Students will arrange and describe objects in space by proximity, position, and direction (near, far, below, above, up, down, behind, in front of, next to, and left or right of).
M2G1. Students will describe and classify plane figures (triangles, square, rectangle, trapezoid, quadrilateral, pentagon, hexagon, and irregular polygonal shapes) according to the number of sides and vertices and the sizes of angles (right angle, obtuse, acute).
M3M3. Students will understand and measure the perimeter of geometric figures.
a. Understand the meaning of the linear unit and measurement in perimeter.
b. Understand the concept of perimeter as being the length of the boundary of a geometric figure.
c. Determine the perimeter of a geometric figure by measuring and summing the lengths of the sides.
M3M4. Students will understand and measure the area of simple geometric figures (squares and rectangles).
a. Understand the meaning of the square unit and measurement in area.
b. Model (by tiling) the area of a simple geometric figure using square units (square inch, square foot, etc.).
c. Determine the area of squares and rectangles by counting, addition, and multiplication with models.
M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.
a. Draw and classify previously learned fundamental geometric figures and scalene, isosceles, and equilateral triangles.
b. Identify and compare the properties of fundamental geometric figures.
c. Examine and compare angles of fundamental geometric figures.
d. Identify the center, diameter, and radius of a circle.
M4M2. Students will understand the concept of angles and how to measure them.
a. Use tools, such as a protractor or angle ruler, and other methods such as paper folding, drawing a diagonal in a square, to measure angles.
b. Understand the meaning and measure of a half rotation (180¡ã) and a full rotation (360¡ã).
c. Determine that the sum of the three angles of a triangle is always 180¡ã.
M4G1. Students will define and identify the characteristics of geometric figures through examination and construction.
a. Examine and compare angles in order to classify and identify triangles by their angles.
b. Describe parallel and perpendicular lines in plane geometric figures.
c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi) by their properties.
d. Compare and contrast the relationships among quadrilaterals.
M5P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M5P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M5P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M5P4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
M5P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
M5M1. Students will extend their understanding of area of geometric plane figures.
a. Estimate the area of geometric plane figures.
b. Derive the formula for the area of a parallelogram.
c. Derive the formula for the area of a triangle.
d. Find the areas of triangles and parallelograms using formulae.
e. Estimate the area of a circle through partitioning and tiling.
f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes.
g. Derive the formula for the area of a circle.
h. Find the area of a circle using the formula and pi ¡Ö 3.14.
M5G1. Students will understand congruence of geometric figures and the correspondence of their vertices, sides, and angles.
Reading & English Language Arts:
Reading
ELA5R2 The student consistently reads at least twenty-five books or book equivalents (approximately 1,000,000 words) each year. The materials should include traditional and contemporary literature (both fiction and non-fiction) as well as magazines, newspapers, textbooks, and electronic material. Such reading should represent a diverse collection of material from at least three different literary forms and from at least five different writers.
ELA5R1 The student demonstrates comprehension and shows evidence of a warranted and responsible explanation of a variety of literary and informational texts.
a. Identifies and analyzes the elements of setting, characterization, and conflict in plot.
g. Applies knowledge of the concept that theme refers to the message about life and the world
that the author wants us to understand whether implied or stated.
i. Makes judgments and inferences about setting, characters, and events and supports them with
elaborating and convincing evidence from the text.
ELA5R3 The student understands and acquires new vocabulary and uses it
correctly in reading and writing.
Writing
ELA5W1 The student produces writing that establishes an appropriate organizational structure, sets a context and engages the reader, maintains a coherent focus throughout, and signals a satisfying closure.
ELA5W2 The student demonstrates competence in a variety of genres.
ELA5W3 The student uses research and technology to support writing.
ELA5W4 The student consistently uses a writing process to develop, revise,
and evaluate writing.
Conventions
ELA5C1 The student demonstrates understanding and control of the rules of the
English language, realizing that usage involves the appropriate application of conventions and grammar in both written and spoken formats.
Listening/Speaking/Viewing
ELA5LSV1 The student participates in student-to-teacher, student-to-student,
and group verbal interactions.
ELA5LSV2 The student listens to and views various forms of text and media in
order to gather and share information, persuade others, and express and understand ideas.
Co-Requisite - Characteristics of Science
S5CS1. Students will be aware of the importance of curiosity, honesty, openness, and skepticism in science and will exhibit these traits in their own efforts to understand how the world works.
S5CS2. Students will have the computation and estimation skills necessary for analyzing data and following scientific explanations.
S5CS3. Students will use tools and instruments for observing, measuring, and manipulating objects in scientific activities.
S5CS4. Students will use ideas of system, model, change, and scale in exploring scientific and technological matters.
S5CS5. Students will communicate scientific ideas and activities clearly.
S5CS6. Students will question scientific claims and arguments effectively.
S5CS7. Students will be familiar with the character of scientific knowledge and how it is achieved.
S5CS8. Students will understand important features of the process of scientific inquiry.
