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Friday, November 16, 2012

11-16-2012 How Many Peas Fill the Classroom?


Grade 6 Geometry
Solve real-world and mathematical problems involving area, surface area, and volume.
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Thursday, November 15, 2012

11-15-2012 Function, Function, What's your Function?


By the end of Grade 8

Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.
Define, evaluate, and compare functions.

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Use functions to model relationships between quantities.

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Linear Functions Part A: Basics: Slope and Intercept Part B: Finding the Equation of a Line 

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Wednesday, November 14, 2012

11-14-2012 Vigorous Vocabulary Aquisition

English Language Arts Standards
Grades 6-8
Language: Knowledge of Language

Vocabulary Acquisition and Use
L.6-8.4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 6-8 reading and content, choosing flexibly from a range of strategies.
Use context (e.g., the overall meaning of a sentence or   paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., belligerent, bellicose, rebel).
Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.
Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
L.6-8.5. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

Interpret figures of speech (Gr. 6 e.g., personification), (Gr. 7 e.g., literary, biblical, and mythological allusions), (Gr. 8 e.g. verbal irony, puns) in context.
Use the relationship between particular words (e.g., cause/effect, part/whole, item/category, synonym/antonym, analogy) to better understand each of the words.
Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., Gr. 6: stingy, scrimping, economical, un-wasteful, thrifty; Gr. 7: refined, respectful, polite, diplomatic, condescending; Gr. 8: bullheaded, willful, firm, persistent, resolute).
L.6-8.6. Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Tuesday, November 13, 2012

11-13-2012 Passively Active Language Learners

English Language Arts Standards
Grades 6-8
Language: Knowledge of Language

Knowledge of Language
L.6-8.3. Use knowledge of language and its conventions when writing, speaking, reading, or listening.
Vary sentence patterns for meaning, reader/listener interest, and style.*
Maintain consistency in style and tone.*
Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness and redundancy.*
Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact).