Learning Domain: Functions

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

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Learning Domain: Common Themes

Standard: A system can include processes as well as things.

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Learning Domain: Common Themes

Standard: If a system in equilibrium is disturbed, it may return to a very similar state of equilibrium, or it may undergo a radical change until the system achieves a new state of equilibrium with very different conditions, or it may fail to achieve any type of equilibrium.

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Learning Domain: Common Themes

Standard: Graphs and equations are useful (and often equivalent) ways for depicting and analyzing patterns of change.

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Learning Domain: Common Themes

Standard: Symbolic equations can be used to summarize how the quantity of something changes over time or in response to other changes.

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Learning Domain: The Physical Setting

Standard: Some atoms and molecules are highly effective in encouraging the interaction of others.

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Learning Domain: The Physical Setting

Standard: Substances react chemically in characteristic ways with other substances to form new substances with different characteristic properties.

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Learning Domain: The Physical Setting

Standard: The idea of atoms explains chemical reactions: When substances interact to form new substances, the atoms that make up the molecules of the original substances combine in new ways.

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Learning Domain: The Physical Setting

Standard: Atoms and molecules are perpetually in motion. Increased temperature means greater average energy of motion, so most substances expand when heated.

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Learning Domain: The Mathematical World

Standard: Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.

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Science Domain: Physical Sciences

Topic: Chemical Reactions

Standard: Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred. [Clarification Statement: Examples of reactions could include burning sugar or steel wool, fat reacting with sodium hydroxide, and mixing zinc with hydrogen chloride.] [Assessment boundary: Assessment is limited to analysis of the following properties: density, melting point, boiling point, solubility, flammability, and odor.]

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Cluster: Use functions to model relationships between quantities

Standard: 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.

Degree of Alignment: 2 Strong (1 user)

Cluster: Mathematical practices

Standard: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Degree of Alignment: Not Rated (0 users)