​Materials as Tools for Learning

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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:
  • Get to Know the Materials
Teachers need to be familiar with the materials students will use. Depending on the grade level, these might include cubes, pattern blocks, Geoblocks, Geoboards, geometric solids, rulers, compasses, protractors, and Algebra Tiles. The SFUSD units describe particular materials in detail and their classroom use.
  • Organize the Materials
Most teachers organize their materials in small sets, often labeled with the name and a picture of the material. It is important to store manipulatives where they are easily accessible to students. In addition to manipulatives, items such as calculators, coins, 100 charts, and paper (blank and grid) are important mathematical tools that should be available to students. Some SFUSD units describe the preparation of specific materials in detail.
  • Introduce New Materials Thoughtfully
Students need time to explore a new material before using it in structured activities. By freely exploring a material, students will discover many of its important characteristics and will have some understanding of when it might make sense to use it. Although some free exploration should be built into regular math time, many teachers make materials available to students during free time or before or after school.
  • Make Materials Accessible
​The more available materials are, the more likely students are to use them. Having materials available means that they are readily accessible and that students are allowed to make decisions about which tools to use, and when and how to use them. Because particular tools work best for certain projects or tasks, students should be encouraged to think about which material best meets their needs. While students may need materials close by initially, they should gradually be expected to decide what they need and get materials on their own.
  • Establish Clear Expectations
​In order to use materials as tools for learning, students need to be clear about how such materials should (and should not) be used and cared for.
  • Sharing Materials. Conversations about sharing are critical.
  • Using Materials Appropriately. Rules and policies for the appropriate use of manipulatives should be established at the beginning of the year. This might include things such as not throwing the materials, not drawing on them, and so on. Consider asking the students to suggest rules for how materials should and should not be used. Students are often more attentive to rules and policies that they have helped create.
  • Cleaning Up Materials. Making an announcement a few minutes before the end of a work time helps prepare students for the transition that is about to occur. Then, give students several minutes to return materials to their containers and shelves and to double check the floor for any stray materials.
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Adapted from TERC
​Taken from Implementing Investigations in Grades K-2 (2008). Used with permission from
Pearson Scott Foresman. Glenview, IL.

Distance Learning

We have compiled a list of SFUSD Recommended Virtual Manipulatives for Grades K-5 to use during distance learning. If you wish to purchase physical manipulatives for your students, the Math Learning Center offers grade level kits that correspond very closely to the materials we use. 

Manipulatives and SMPs

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 Class

This 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 
PreK-12 math classrooms include:
  • Plain white paper in many sizes
  • Graph paper
  • Chart paper
  • Cardstock
  • Sentence strips
  • Index cards
  • Sticky notes
  • Composition notebooks – lines and/or graph
  • Markers
  • Tape 
  • Scissors 
  • Glue
  • Mini whiteboards