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Algebra by Example

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Algebra by Example

Here are a set of classroom tested re-engagement tasks to support students in rethinking key ideas across Algebra.

Algebra II Regents Questions Aligned to Big Ideas
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Algebra II Regents Questions Aligned to Big Ideas

These Regents questions have been aligned to the Big Ideas in our Algebra II course. They could be useful to understanding the goals of a particular Big Idea or to use to create a quiz for students for a particular Big Idea. Each Big Idea corresponds to one week of instruction.

These documents were created using the free New Visions’ Quiz Banker Add-on by filtering the Algebra II Regents exams by Unit and Big Idea.

Algebra I Regents Questions Aligned to Big Ideas
Resource:
Algebra I Regents Questions Aligned to Big Ideas

These Regents questions have been aligned to the Big Ideas in our Algebra I course. They could be useful to understanding the goals of a particular Big Idea or to use to create a quiz for students for a particular Big Idea. Each Big Idea corresponds to one week of instruction.

These documents were created using the free New Visions’ Quiz Banker Add-on by filtering the Algebra I Regents exams by Unit and Big Idea.

Comparing Investments

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Comparing Investments

This lesson is intended to help you 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 interval.
• To achieve these goals students work on simple and compound interest problems.

The domains directly supported in this challenge (A-SSE, F-LE) are directly tested and build students practice in constructing and understanding algebraic modeling.

Concrete Examples

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Concrete Examples

Concrete examples can support student learning.

Note that this resource is written assuming a student is studying on their own but the principle can be still applied to designing lessons for students.

Data Visualizations

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Data Visualizations

These interactive data visualizations display historical data from students across the New Visions network and alignment of questions from the New York State Regents exams to Common Core mathematics.

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#### Data Visualizations

Dual Coding

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Dual Coding

Visuals matched to text support student learning.

Note that this resource is written assuming a student is studying on their own but the principle can be still applied to designing lessons for students.

Elaboration

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Elaboration

Moving beyond recalling answers and trying to determine why those answers are true supports student learning.

Note that this resource is written assuming a student is studying on their own but the principle can be still applied to designing lessons for students.

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This lesson is intended to help you 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 you identify and help students who have the following difficulties:

• Understanding how the factored form of the function can identify a graph’s roots.
• Understanding how the completed square form of the function can identify a graph’s maximum or minimum point.
• Understanding how the standard form of the function can identify a graph’s intercept.

The domains directly supported in this challenge (A-SSE, F-IF) are directly tested and are crucial for students using algebraic structures in both equation-based and function-based test situations.

Functions and Everyday Situations

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Functions and Everyday Situations

This lesson is intended to support students in making connections between situations and graphs representing those situations. This lesson is intended to help you 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.
• Reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.

The domains directly supported in this challenge (F-IF, F-LE) are directly tested and are crucial for students using function relationships in both equation-based and function-based test situations.

Generalizing Patterns: Table Tiles

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Generalizing Patterns: Table Tiles

This lesson is intended to help you 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 lesson 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.
• Describing and explaining findings clearly and effectively.

The domain directly supported in this challenge (F-BF) is directly tested and supports students ability to draw the connections between function representations (pattern, table, graph, rule) and interpretations.

Geometry Regents Questions Aligned to Big Ideas
Resource:
Geometry Regents Questions Aligned to Big Ideas

These Regents questions have been aligned to the Big Ideas in our Geometry course. They could be useful to understanding the goals of a particular Big Idea or to use to create a quiz for students for a particular Big Idea. Each Big Idea corresponds to one week of instruction.

These documents were created using the free New Visions’ Quiz Banker Add-on by filtering the Geometry Regents exams by Unit and Big Idea.