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 visualize two-dimensional cross-sections of representations of three-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing two-dimensional cross-sections at different points along a plane of a representation of a three-dimensional object.

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: work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles; Identify and understand the significance of a counter-example; Prove, and evaluate proofs in a geometric context.

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 use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.

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 create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.

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 solve problems involving area and arc length of a sector of a circle using radians. It assumes familiarity with radians and should not be treated as an introduction to the topic. This lesson is intended to help you identify and assist students who have difficulties in: Computing perimeters, areas, and arc lengths of sectors using formulas.Finding the relationships between arc lengths, and areas of sectors after scaling.

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

This lesson unit is intended to help teahcers assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties; computing measurements using formulas; decomposing compound shapes into simpler ones; using right triangles and their properties to solve real-world problems.

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 exponential and linear functions and in particular to identify and help students who have the following difficulties: translating between descriptive, algebraic and tabular data, and graphical representation of the functions; recognizing how, and why, a quantity changes per unit intervale; and to achieve these goals students work on simple and compound interest problems.

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: Select appropriate mathematical methods to use for an unstructured problem; interpret a problem situation, identifying constraints and variables, and specify assumptions; work with 2- and 3-dimensional shapes to solve a problem involving capacity and surface area; and communicate their reasoning clearly.

This lesson unit is intended to help you assess whether students recognize ...

This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who: use inappropriate additive strategies in scaling problems, which have a multiplicative structure; rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems; and see multiplication as making numbers bigger, and division as making numbers smaller.

This lesson unit is intended to help assess how well students are ...

This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.

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 the Pythagorean theorem to derive the equation of a circle; and translate between the geometric features of circles and their equations.

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 the equations of circles and their geometric features; and sketch a circle from its equation.

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: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.

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 are able to solve problems involving area and volume, and in particular, to help you identify and assist students who have difficulties with the following: computing perimeters, areas and volumes using formulas; and finding the relationships between perimeters, areas, and volumes of shapes after scaling.

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.

This lesson unit is intended to help you to assess how well ...

This lesson unit is intended to help you to assess how well students are able to understand the meanings of the terms â€˜Greatest Common Factorâ€™ (GCF) and â€˜Least Common Multipleâ€™ (LCM). In particular, the lesson will help you to identify and help students who: *Confuse GCFs and LCMs *Lack a sense of what values of GCF or LCM might be reasonable for a given pair of numbers.

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: 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 ...

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 students to: * Compare, convert ...

This lesson unit is intended to help students to: * Compare, convert between and order fractions, decimals and percents. * Use area and linear models of fractions, decimals and percents to understand equivalence. Students are asked to apply and extend previous understandings of numbers to the system of rational numbers.

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.

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 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 ...

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 ...

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 ...

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).

The lesson is 22 pages and about interpreting equations. It starts off ...

The lesson is 22 pages and about interpreting equations. It starts off with the mathematical goals and standards for the lesson. The resource is laid out with easy to follow instructions. There are various bolded titles starting with an introduction, materials needed, it gives a suggested lesson outline, along with practice examples. The resource uses black and red text to show the difference between what the teacher needs to do/say and wha the student needs to do.

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 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 ...

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 ...

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 ...

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 is designed to help students develop strategies for solving optimization ...

This lesson is designed to help students develop strategies for solving optimization problems. Such problems typically involve using limited resources to greatest effect, as in, for example, the allocation of time and materials to maximize profit. Before the lesson, students attempt the problem individually. You then review their work and formulate questions for students to answer in order to improve their solutions.At the start of the lesson, students work alone answering your questions.Students are then grouped and engage in a collaborative discussion of the same task. In the same small groups, students are given sample solutions to comment on and evaluate.In a whole-class discussion, students explain and compare solution strategies seen and used.Finally, students revise their individual solutions and comment on what they have learned. Materials required Each individual student will need a copy of the task, some plain paper, a calculator, and a copy of the How Did You Work? questionnaire.Each small group of students will need copies of the Sample Responses to Discuss.Graph paper should be kept in reserve and used only when necessary or requested. Time needed Approximately 15 minutes before the lesson, a 1-hour lesson, and 10 minutes in a follow-up lesson.

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: 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 ...

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.

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

This lesson unit is intended to help teachers assess how well students understand conditional probability, and, in particular, to help teachers identify and assist students who have the following difficulties: representing events as a subset of a sample space using tables and tree diagrams; and understanding when conditional probabilities are equal for particular and general situations.

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

This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students: explore relationships between variables in everyday situations; find unknown values from known values; find relationships between pairs of unknowns, and express these as tables and graphs; and find general relationships between several variables, and express these in different ways by rearranging formulae.

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 a situation and represent the constraints and variables mathematically; select appropriate mathematical methods to use; explore the effects of systematically varying the constraints; interpret and evaluate the data generated and identify the optimum case, checking it for confirmation; and communicate their reasoning clearly.

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