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Modeling Conditional Probabilities 1: Lucky Dip

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Modeling Conditional Probabilities 1: Lucky Dip

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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.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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تنمية الحس بالمقياس

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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.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Drawing to Scale: Designing a Garden

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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.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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تفسير الرسوم البيانية المتعلقة بالوقت والسرعة

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تفسير الرسوم البيانية المتعلقة بالوقت والسرعة

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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تقييم العبارات حول الاحتمال (الأرجحية)

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Modeling: Making Matchsticks

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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; interpret and evaluate the data generated; and communicate their reasoning clearly.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Repeating Decimals

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This lesson unit is intended to help teachers assess how well students are able to: translate between decimal and fraction notation, particularly when the decimals are repeating; create and solve simple linear equations to find the fractional equivalent of a repeating decimal; and understand the effect of multiplying a decimal by a power of 10.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Increasing and Decreasing Quantities by a Percent

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Increasing and Decreasing Quantities by a Percent

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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.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Steps to Solving Equations

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This lesson unit is intended to help teachers assess how well students are able to: form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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هندسة التعليم الفني المهني: هيكلة المنزل

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هندسة التعليم الفني المهني: هيكلة المنزل

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This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Material Type:: Activity/Lab; Assessment; Homework/Assignment; Lesson Plan
Provider:: National Association of State Directors of Career Technical Education Consortium
Provider Set:: Career Technical Education
Date Added:: 03/05/2012

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Mean, Median, Mode, and Range

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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.

Material Type:: Activity/Lab; Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Author:: Shell Center Team
Date Added:: 01/17/2013

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Lines and Linear Equations

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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.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Using Positive and Negative Numbers in Context

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Using Positive and Negative Numbers in Context

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This lesson unit is intended to help teachers assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the structures: starting temperature + change in temperature = final temperature final temperature Đ change in temperature = starting temperature final temperature Đ starting temperature = change in temperature.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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تحديد المثلثات المتشابهة

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Evaluating Statements About Length and Area

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Evaluating Statements About Length and Area

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Modeling Situations With Linear Equations

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Modeling Situations With Linear Equations

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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.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Solving Geometry Problems: Floodlights

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This lesson unit is intended to help teachers assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, this unit aims to identify and help students who have difficulty in: making a mathematical model of a geometrical situation; drawing diagrams to help with solving a problem; identifying similar triangles and using their properties to solve problems; and tracking and reviewing strategic decisions when problem-solving.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Solving Linear Equations in Two Variables

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Solving Linear Equations in Two Variables

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This lesson unit is intended to help teachers assess how well students are able to formulate and solve problems using algebra and, in particular, to identify and help students who have the following difficulties: solving a problem using two linear equations with two variables; and interpreting the meaning of algebraic expressions.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Estimations and Approximations: The Money Munchers

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Estimations and Approximations: The Money Munchers

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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.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Optimizing: Security Cameras

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This lesson unit is intended to help sixth grade teachers assess how well students are able to: Analyze a realistic situation mathematically; construct sight lines to decide which areas of a room are visible or hidden from a camera; find and compare areas of triangles and quadrilaterals; and calculate and compare percentages and/or fractions of areas.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Solving Quadratic Equations: Cutting Corners

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Solving Quadratic Equations: Cutting Corners

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This lesson unit is intended to help teachers assess how well students are able to solve quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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تقدير الطول باستخدام التدوين العلمي

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This lesson unit is intended to help teachers assess how well students are able to: estimate lengths of everyday objects; convert between decimal and scientific notation; and make comparisons of the size of numbers expressed in both decimal and scientific notation.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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تفسير العبارات الجبرية

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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).

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Representing Polynomials

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This lesson unit is intended to help teachers assess how well students are able to translate between graphs and algebraic representations of polynomials. In particular, this unit aims to help you identify and assist students who have difficulties in: recognizing the connection between the zeros of polynomials when suitable factorizations are available, and graphs of the functions defined by polynomials; and recognizing the connection between transformations of the graphs and transformations of the functions obtained by replacing f(x) by f(x + k), f(x) + k, -f(x), f(-x).

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Modeling: Having Kittens

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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; make sensible estimates and assumptions; investigate an exponentially increasing sequence; and communicate their reasoning clearly.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Representing Data 1: Using Frequency Graphs

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Representing Data 1: Using Frequency Graphs

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This lesson unit is intended to help teachers assess how well students: are able to use frequency graphs to identify a range of measures and make sense of this data in a real-world context; and understand that a large number of data points allow a frequency graph to be approximated by a continuous distribution.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Representing Data 2: Using Box Plots

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This lesson unit is intended to help teachers assess how well students are able to interpret data using frequency graphs and box plots. In particular this unit aims to identify and help students who have difficulty figuring out the data points and spread of data from frequency graphs and box plots. It is advisable to use the lesson: Representing Data 1: Frequency Graphs, before this one.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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معالجة متعددات الحدود

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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.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Inscribing and Circumscribing Right Triangles

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Inscribing and Circumscribing Right Triangles

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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ابتكار مقياس للارتباط

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This lesson unit is intended to help teachers assess how well students understand the notion of correlation. In particular this unit aims to identify and help students who have difficulty in: understanding correlation as the degree of fit between two variables; making a mathematical model of a situation; testing and improving the model; communicating their reasoning clearly; and evaluating alternative models of the situation.

Material Type:: Assessment; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Modeling: Rolling Cups

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This lesson unit is intended to help teachers assess how well students are able to: choose appropriate mathematics to solve a non-routine problem; generate useful data by systematically controlling variables; and develop experimental and analytical models of a physical situation.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Comparing Investments

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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تشكيل المعادلات التربيعية

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Modeling Conditional Probabilities 2

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Optimization Problems: Boomerangs

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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الوظائف ومواقف الحياة اليومية

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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مسائل هندسية: الدوار والمثلثات

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Sharing Costs: Travelling to School

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This lesson unit is intended to help teachers assess how well students are able to solve a real-world modeling problem. There are several correct approaches to the problem, including some that involve proportional relationships.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP); Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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Medical Testing

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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.

نوع المادة:: التقييم; Lesson Plan
Provider:: Shell Center for Mathematical Education; U.C. Berkeley
Provider Set:: Mathematics Assessment Project (MAP)
Date Added:: 04/26/2013

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