Manipulatives and other Math Tools

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Math Practice Standard # 5 is Use appropriate tools strategically

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. 

Teachers who are developing students' capacity to "use appropriate tools strategically" make clear to students why the use of manipulatives, rulers, compasses, protractors, and other tools will aid their problem solving processes. An elementary or middle childhood teacher might have his students select different color tiles to show repetition in a patterning task. A teacher of adolescents and young adults might have established norms for accessing tools during the students' group "tinkering processes," allowing students to use paper strips, brass fasteners, and protractors to create and test quadrilateral "kite" models. Visit the video excerpts below to view multiple examples of these teachers.

Math Notebooks

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Math notebooks are places for students to keep their math work in an organized fashion. They can be as simple as folders created from construction paper, composition books, or 3-ring binders with sections to organize materials into sections. These notebooks can include notes, vocabulary, solutions to investigation problems, homework, and responses to mathematical reflections/learning logs.

Why would I use math notebooks?
You might find it helpful for students to keep their work in an organized notebook. This allows the student to learn to organize their work as well as review past content. By reviewing your students' notebooks, you can get a clearer picture of their mathematical development. Notebooks also allow family members the opportunity to see the progress of their children in math class.

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Rule of Four

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The “Rule of Four” is a way to think about math both at the entry point of a task and in the representation of math thinking. Showing our thinking through multiple representations helps us have a stronger and deeper understanding of the mathematics. It also allows us to see connections across concepts and topics in mathematics.

Why use the “Rule of Four”?
When we strive to represent our understand using the “Rule of Four,” we are asking ourselves to find deeper connections both within and across concepts. In addition, it validates multiple perspectives in mathematics.