Looking for the Expressions & Equations materials for WeScheme ?
Lesson Plans
- Translating Between Words and Math
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Students learn to model verbal expressions with a visual tool known as "Circles of Evaluation".
- Simple Data Types
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Students begin to program, exploring how Numbers, Strings, Booleans and operations on those data types work in Pyret. Booleans offer an excellent opportunity for students to explore the meaning and real-world uses of inequalities.
- Contracts for Strings and Images
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Students encounter a useful representation of functions called a "Contract", which specifies the Name, Domain and Range of a function. Students learn how useful this representation is when trying to apply Functions in the programming environment, using image-producing functions to provide an engaging context for this exploration.
- Equivalence
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Students explore computation as a way to generate equivalent expressions.
- The Commutative Property
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Students discover the Commutative Property by way of Circles of Evaluation.
- The Associative Property
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Students explore Associative Property, using Circles of Evaluation as a tool to visualize groupings.
- The Additive Inverse Property
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Students develop a more nuanced interpretation of the Commutative and Associative Properties as a result of their exploration of the inverse relationship between addition and subtraction.
- The Multiplicative Inverse Property
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Students develop a more nuanced interpretation of the Commutative and Associative Properties as a result of their exploration of the inverse relationship between multiplication and division.
- Variables
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Students use properties to determine when equations with and without variables are true.
- The Identity Property
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Students discover the Identity Property by continuing their exploration of Circles of Evaluation.
- The Distributive Property
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Students develop an understanding of the Distributive Property by studying equivalent Circles of Evaluation. They then apply their understanding of the Distributive Property to make efficient mental computations.
- Absolute Value and Opposite
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Students use Circles of Evaluation to explore the effect of negation and absolute value on arithmetic and algebraic expressions.
- Absolute Value and Opposite (2)
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Students examine expressions and Circles of Evaluation that use both opposite and absolute value.
- Evaluating Exponents
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Students use Circles of Evaluation to visualize the structure of expressions that include exponents.
- Evaluating Exponent Expressions with Negative Values
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Students use Circles of Evaluation to visualize the structure of expressions with exponents and negative values.
Student Workbooks
Sometimes, the best place for students to get real thinking done is away from the keyboard! Our lesson plans are tightly integrated with a detailed Student Workbook, allowing for paper-and-pencil practice and activities that don’t require a computer. That’s why we provide a free PDF of the core workbook, as well as a link to the book with every optional exercise included.
Of course, we understand that printing them yourself can be expensive! Click here to purchase beautifully-bound copies of the student workbook from Lulu.com.
Other Resources
Of course, there’s more to a curriculum than software and lesson plans! We also provide a number of resources to educators, including standards alignment, a complete student workbook, an answer key for the programming exercises and a forum where they can ask questions and share ideas.
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Contracts Reference — Complete student-facing documentation for all the functions used in these lessons (also printed in the back of the student workbook).
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Glossary — A list of vocabulary words used in this pathway. We also provide a bilingual glossary, which defines all vocabulary words across our lessons in English and Spanish.
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Standards Alignment — Find out how our materials align with National and State Standards, as well as some of the most commonly used math textbooks.
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Teacher-Only Resources — We also offer several teachers-only materials, including an answer key to the student workbook, keys to all the exercises, and pre- and post-tests for teachers who are participating in our research study. For access to these materials, please fill out the password request form. We’ll get back to you soon with the necessary login information.
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Online Community (Discourse) — Want to be kept up-to-date about Bootstrap events, workshops, and curricular changes? Want to ask a question or pose a lesson idea for other Bootstrap teachers? These forums are the place to do it.
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.