Materials as Tools for Learning
Students of all ages benefit from being able to use tools and materials to model and solve problems and explain their thinking. Encourage all students to use tools and materials and to explain how they use them. If used only when someone is having difficulty, students can get the mistaken idea that using materials is a less sophisticated and less valued way of solving a problem or modeling a solution. Therefore, they should see how different people, including the teacher, use a variety of materials to solve the same problem.
Click here to download the list of math manipulatives that are used in the SFUSD Math Core Curriculum from PreK to Algebra 2 + Precalculus. To make effective use of materials as tools for learning, teachers need to:
Adapted from TERC Taken from Implementing Investigations in Grades K2 (2008). Used with permission from Pearson Scott Foresman. Glenview, IL. 
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. Why Kids Should Use Their Fingers in Math ClassThis article by Jo Boaler and Lang Chen in the Atlantic presents evidence from brain science suggesting that far from being “babyish,” the technique is essential for mathematical achievement.
Read about How to Make the Most of Manipulatives in this article by Marilyn Burns from Instructor Magazine.
Other materials not specific to math used in
PreK12 math classrooms include:
