This lesson unit is intended to help you assess how well students …

This lesson unit is intended to help you assess how well students are able to: Model a situation; make sensible, realistic assumptions and estimates; and use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students can: Understand the concepts of length and area; use the concept of area in proving why two areas are or are not equal; and construct their own examples and counterexamples to help justify or refute conjectures.

This lesson unit addresses common misconceptions relating to probability of simple and …

This lesson unit addresses common misconceptions relating to probability of simple and compound events. The lesson will help you assess how well students understand concepts of: Equally likely events; randomness; and sample sizes.

Explore the concept of evaporative cooling through a hands-on experiment. Use a …

Explore the concept of evaporative cooling through a hands-on experiment. Use a wet cloth and fan to model an air-conditioner and use temperature and relative humidity sensors to collect data. Then digitally plot the data using graphs in the activity. In an optional extension, make your own modifications to improve the cooler's efficiency.

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help teachers identify and help students who have the following difficulties: understanding how the factored form of the function can identify a graphŐs roots; understanding how the completed square form of the function can identify a graphŐs maximum or minimum point; and understanding how the standard form of the function can identify a graphŐs intercept.

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students are able to: articulate verbally the relationships between variables arising in everyday contexts; translate between everyday situations and sketch graphs of relationships between variables; interpret algebraic functions in terms of the contexts in which they arise; and reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.

In this activity, students study gas laws at a molecular level. They …

In this activity, students study gas laws at a molecular level. They vary the volume of a container at constant temperature to see how pressure changes (Boyle's Law), change the temperature of a container at constant pressure to see how the volume changes with temperature (Charles’s Law), and experiment with heating a gas in a closed container to discover how pressure changes with temperature (Gay Lussac's Law). They also discover the relationship between the number of gas molecules and gas volume (Avogadro's Law). Finally, students use their knowledge of gas laws to model a heated soda can collapsing as it is plunged into ice water.

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties: solving problems by determining the lengths of the sides in right triangles; and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

In this 25-day Grade 2 module, students expand their skill with and …

In this 25-day Grade 2 module, students expand their skill with and understanding of units by bundling ones, tens, and hundreds up to a thousand with straws. Unlike the length of 10 centimeters in Module 2, these bundles are discrete sets. One unit can be grabbed and counted just like a banana?1 hundred, 2 hundred, 3 hundred, etc. A number in Grade 1 generally consisted of two different units, tens and ones. Now, in Grade 2, a number generally consists of three units: hundreds, tens, and ones. The bundled units are organized by separating them largest to smallest, ordered from left to right. Over the course of the module, instruction moves from physical bundles that show the proportionality of the units to non-proportional place value disks and to numerals on the place value chart.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

In Module 3, students' understanding of addition and subtraction of fractions extends …

In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Calculus is a year-long course that is comparable to calculus courses at …

Calculus is a year-long course that is comparable to calculus courses at the college or university level. In this course, the technological tools required for exploring, learning, and communicating calculus concepts include Microsoft Word with Microsoft Equation (or its equivalent) for typing math assignments, an approved graphing calculator (see a list of acceptable calculators at College Board AP Central) for the AP Calculus exam, and some type of grapher for creating graphs online such as Graphmatica (Windows) or Grapher (MAC) or an online graphing utility of your choice.

This lesson unit is intended to help you assess how students reason …

This lesson unit is intended to help you assess how students reason about geometry and, in particular, how well they are able to: use facts about the angle sum and exterior angles of triangles to calculate missing angles; apply angle theorems to parallel lines cut by a transversal; interpret geometrical diagrams using mathematical properties to identify similarity of triangles.

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties: translating between percents, decimals, and fractions; representing percent increase and decrease as multiplication; and recognizing the relationship between increases and decreases.

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, it will help you identify and help students who have difficulty: decomposing complex shapes into simpler ones in order to solve a problem; bringing together several geometric concepts to solve a problem; and finding the relationship between radii of inscribed and circumscribed circles of right triangles.

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students are able to translate between words, symbols, tables, and area representations of algebraic expressions. It will help teachers to identify and support students who have difficulty in: recognizing the order of algebraic operations; recognizing equivalent expressions; and understanding the distributive laws of multiplication and division over addition (expansion of parentheses).

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students are able to interpret distanceĐtime graphs and, in particular, to help you identify students who: interpret distanceĐtime graphs as if they are pictures of situations rather than abstract representations of them; and have difficulty relating speeds to slopes of these graphs.

This lesson unit is intended to help teahcers assess how well students …

This lesson unit is intended to help teahcers assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation.

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