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Building and Solving Complex Equations

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Building and Solving Complex Equations

This lesson unit is intended to help you assess how well students are able to create and solve linear and non-linear equations. In particular, the lesson will help identify and help students who have the following difficulties:

• Solving equations where the unknown appears once or more than once.
• Solving equations in more than one way.
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#### Formative Assessment Lessons

Calculating Arcs and Areas of Sectors of Circles

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Calculating Arcs and Areas of Sectors of Circles

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.

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This lesson unit is intended to help you assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, it 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.
• Tracking and reviewing strategic decisions when problem-solving.
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#### Formative Assessment Lessons

Devising a Measure - Correlation

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Devising a Measure - Correlation

This lesson unit is intended to help you assess how well students understand the notion of positive 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.
• Evaluating alternative models of the situation.
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#### Formative Assessment Lessons

Evaluating Statements About Length and Area

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Evaluating Statements About Length and Area

This lesson unit is intended to help you 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.
• Construct their own examples and counterexamples to help justify or refute conjectures.
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#### Formative Assessment Lessons

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This lesson unit is intended to help you assess how well students are able to:

• Use the properties of exponents, including rational exponents and manipulate algebraic statements involving radicals.
• Discriminate between equations and identities.

In this lesson there is also the (optional) opportunity to consider the role of the imaginary number.

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#### Formative Assessment Lessons

Generating Polynomials from Patterns

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Generating Polynomials from Patterns

This lesson unit is intended to help you assess how well students are able to manipulate and calculate with polynomials.

• Switching between visual and algebraic representations of polynomial expressions.
• Performing arithmetic operations on algebraic representations of polynomials, factorizing and expanding appropriately when it helps to make the operations easier.
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#### Formative Assessment Lessons

How to Enact a Formative Assessment Lesson

###### Resource: Formative Assessment Lessons
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How to Enact a Formative Assessment Lesson

This resource is intended to support teachers using the Classroom Challenges (formerly called Formative Assessment Lessons) from the Mathematics Assessment Project in their class. Classroom Challenges are intended to support teachers in understanding what students understand, and provide feedback to students on their own understanding.

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#### Formative Assessment Lessons

Representing Conditional Probabilities 1

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Representing Conditional Probabilities 1

This lesson unit is intended to help you assess how well students are able to:

• Understand conditional probability.
• Represent events as a subset of a sample space using tables and tree diagrams.
• Communicate their reasoning clearly.
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#### Formative Assessment Lessons

Representing Conditional Probabilities 2

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Representing Conditional Probabilities 2

This lesson unit is intended to help you assess how well students understand conditional probability and, in particular, to help you identify and assist students who have the following difficulties:

• Representing events as a subset of a sample space using tables and tree diagrams.
• Understanding when conditional probabilities are equal for particular and general situations.
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#### Formative Assessment Lessons

Solving Problems with Circles and Triangles

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Solving Problems with Circles and Triangles

In particular, the lesson will help you identify and help students who have difficulty:

• Solving problems by determining the lengths of the sides in right triangles.
• 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.

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#### Formative Assessment Lessons

Sorting Equations of Circles 1

Resource:
Sorting Equations of Circles 1

This lesson unit is intended to help you assess how well students are able to:
Use the Pythagorean theorem to derive the equation of a circle.
Translate between the geometric features of circles and their equations.