This lesson unit is intended to help teachers assess how well students are able to: model a periodic situation, the height of a person on a Ferris wheel, using trigonometric functions; and interpret the constants a, b, c in the formula h = a + b cos ct in terms of the physical situation, where h is the height of the person above the ground and t is the elapsed time.

This lesson unit is intended to help teachers assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines and, in particular, to help identify students who find it difficult to: find, from their equations, lines that are parallel and perpendicular; and identify and use intercepts. It also aims to encourage discussion on some common misconceptions about equations of lines.

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 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.

This lesson unit is intended to help teachers assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties with: choosing an appropriate, systematic way to collect and organize data; examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile; generalizing using numerical, geometrical or algebraic structure; and describing and explaining findings clearly and effectively.

This lesson unit is intended to help you assess how well students working with square numbers are able to: choose an appropriate, systematic way to collect and organize data, examining the data for patterns; describe and explain findings clearly and effectively; generalize using numerical, geometrical, graphical and/or algebraic structure; and explain why certain results are possible/impossible, moving towards a proof.

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.

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 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 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 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 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 teachers assess how well students are able to: interpret data and evaluate statistical summaries; and critique someone elseŐs interpretations of data and evaluations of statistical summaries. The lesson also introduces students to the dangers of misapplying simple statistics in real-world contexts, and illustrates some of the common abuses of statistics and charts found in the media.

This lesson unit is intended to help you assess how well students are able to: Perform arithmetic operations, including those involving whole-number exponents, recognizing and applying the conventional order of operations; Write and evaluate numerical expressions from diagrammatic representations and be able to identify equivalent expressions; apply the distributive and commutative properties appropriately; and use the method for finding areas of compound rectangles.

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.

This lesson unit is intended to help you assess how well students are able to manipulate and calculate with polynomials. In particular, it aims to identify and help students who have difficulties in: switching between visual and algebraic representations of polynomial expressions; and performing arithmetic operations on algebraic representations of polynomials, factorizing and expanding appropriately when it helps to make the operations easier.

This lesson unit is intended to help you assess how well students are able to: Interpret a situation and represent the variables mathematically; select appropriate mathematical methods to use; explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant; interpret and evaluate the data generated and identify the optimum case; and communicate their reasoning clearly.

This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

This lesson unit is intended to help teachers assess how well students are able to: make sense of a real life situation and decide what math to apply to the problem; understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model; represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams; and interpret the results and communicate their reasoning clearly.

This lesson unit is intended to help teachers assess how well students are able to: Understand conditional probability; represent events as a subset of a sample space using tables and tree diagrams; and communicate their reasoning clearly.