Using Manipulatives for High School Mathematics Introductions Think about an experience traveling to a place for the first time? Did you feel confused about your bearings even though you had a map or GPS? After a few days, did you become more familiar with the area and recognize familiar landmarks? As you continued to explore, did you become more confident each time you ventured out? We can think about our firsthand experiences with mathematics in a similar way. Many areas of mathematics are unfamiliar, abstract and confusing to students. We have to help our students develop the confidence they need and show them how the areas of mathematics are related to one another and what they should do if they forget facts or procedures. There has been a long tradition for using manipulatives in teaching mathematics which is supported by solid research. Manipulatives allow students to use concrete models to help them understand abstract mathematical concepts and they help students to communicate mathematically with the teacher and other classmates. Research also indicates that using manipulatives can improve the environment of a math class. Using manipulatives engage students and increase their interest and enjoyment of mathematics. In 2013, the National Council of Supervisors of Mathematics issued a position statement on the use of manipulatives in the classroom for mathematics instruction to improve student achievement. “in order to develop every student’s mathematical proficiency, leaders and teachers must systematically integrate the use of concrete and virtual manipulatives into classroom instruction at all grade levels.”

Admit Slip Exploring Solids & Cross Sections Investigation #1 Creating a Solids from 2D Objects Supply the participants with pencils and post-its. Tell them to follow the directions on the Admit Slip – Investigation #1. This is a simple activity that uses everyday objects as manipulatives to explore 3D objects generated by rotating 2D objects (G-GMD.B.4). This concept can be very difficult for students who cannot visualize 3D objects that are drawn in 2D, so working with 3D models can be helpful for them to visualize the correct solid. This experience will also help the student recall this concept at another time or they can simulate it on their own to help remember. ANSWERS: The square or rectangular post-it rotated will generate a cylinder. The triangular post-it rotated will generate a cone. The circular post-it rotated will generate a sphere.

Admit Slip Exploring Solids & Cross Sections Investigation #2 Cross Sections of Geometric Solids For Investigation #2, supply the participants with a clear cylindrical container and a clear cube for best results or just use any cylindrical container and a cube (a half-pint milk container is suggested). Fill the containers about 1/3 full with colored liquid. Participants should describe the 2D geometric shape of the surface of the water. Specific directions are given for the cylinder, but more freedom to explore is given for the cube. This is another concept that is difficult for students to visualize, so using models brings the problem to life and creates an experience that will have lasting results. ANSWERS: Click on each 3D object to observe videos of the answers. Cylinder – cross section can be a circle, oval or ellipse, and a rectangle or parallelogram. Cube – cross section can be a square, rectangle, parallelogram, pentagon, and hexagon (the pentagon and hexagon may be difficult for students to identify).

Agenda Admit Slip What are manipulatives? Benefits of using manipulatives CCSS & 8 Mathematical Practices Activities – Using Manipulatives HS Math Classes Creating lessons with manipulatives Next Steps What are manipulatives? - Define and give examples of concrete and virtual manipulatives. Benefits of using manipulatives – Research that proves that using manipulatives aids directly in the cognitive process, how manipulatives engage students and increase their enjoyment of mathematics, and how the long-term use of manipulatives has a positive effect on student achievement. CCSS & 8 Mathematical Practices – Using manipulatives to help students understand the content of the CCSS in each course and how the 8 Mathematical Practices support the use of manipulatives. Activities – Using Manipulatives in HS Math Classes – Sample activities for Algebra I, Geometry, & Algebra II that use manipulatives to enhance the content for specific topics in each course. Creating lessons with manipulatives – Incorporating manipulatives in existing lessons. Next Steps – Where to get manipulatives, making manipulatives, using virtual manipulatives, games with manipulatives, professional development on incorporating manipulatives in the classroom

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