much of the content comes with ready-made lesson plans and support materials (like extra readings or study guides) that can be used as-is in the classroom. and yet, there’s a ton of trusted content here with quality supporting resources that can be put to good use in the hands of enterprising teachers. 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. rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. 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. give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
use common, grade-appropriate greek or latin affixes and roots as clues to the meaning of a word (e.g., belligerent, bellicose, rebel). determine the meaning of words and phrases as they are used in a text, including vocabulary specific to domains related to history/social studies. determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area. determine an author’s point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others. determine an author’s point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints. use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot. describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events. determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text. determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. include multimedia components (e.g., graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes. use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic. introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose. introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer’s purpose. “trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims”). establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. common sense is the nation’s leading independent non-profit organization dedicated to empowering kids to thrive in a world of media and technology.
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