Math and the Mind's Eye
Math and the Mind's Eye (MME) units are a great way to introduce and extend visual models. This versatile collection can be taught in sequence or used individually as needed to supplement any curriculum. Hands-on explorations are easily adapted to fit changing classroom situations, diverse student backgrounds, and various grade levels. Each unit contains four to twelve activities that use models, manipulatives, sketches, and diagrams to develop and reinforce mathematical concepts and processes.
For more information about manipulatives and optional items see the Materials List. Also see the free Virtual Algebra Pieces app developed by Dr. Laurie Burton of Western Oregon University.
NEW: View overall correlations to the Common Core State Standards for Mathematical Content. Product pages for each unit include more detailed correlation information.Math and the Mind's Eye downloadable PDFs were developed from printed archival masters. As a result, some PDF functionalities, such as editing, copying, and text search, are not available.
Math and the Mind's Eye Unit I: Seeing Mathematical Relationships, pdf
Grade level: 4–6
As an introduction to visual thinking, students use manipulatives, mental images, diagrams, and sketches to solve mathematical problems. Includes masters for transparencies.
Math and the Mind's Eye Unit II: Visualizing Number Concepts, pdf
Grade level: 5–6
Students explore number concepts from basic operations to greatest common divisors and least common multiples using tile and grid paper. Transparency masters included.
Math and the Mind's Eye Unit III: Modeling Whole Numbers, pdf
Grade level: 1–4
Students use base five and base ten number pieces to model whole number concepts, including place value, grouping linear measure, addition, subtraction, multiplication, and division. Transparency masters included.
Math and the Mind's Eye Unit IV: Modeling Rationals, pdf
Grade level: 4–6
Egg cartons, fraction bars, and base ten pieces help students form understandings about fractions and decimals. Transparency masters included.
Math and the Mind's Eye Unit V: Looking at Geometry, pdf
Grade level: 5–8
Geoboards, cubes, and grids are used to explore basic concepts in geometry such as geometric figures, area, perimeter, and volume. Transparency masters included.
Math and the Mind's Eye Unit VI: Modeling Integers, pdf
Grade level: 6–7
Bicolored counting pieces are used to introduce and explore signed numbers. Transparency masters included.
Math and the Mind's Eye Unit VII: Modeling Percentages and Ratios, pdf
Grade level: 6–7
Students use counting pieces, as well as diagrams and sketches, to explore decimals, percentages, and ratios. Transparency masters included.
Math and the Mind's Eye Unit VIII: Visual Encounters with Chance, pdf
Grade level: 7
Simulations games are used to examine probability, data collection, and graphing. Transparency masters included.
Math and the Mind's Eye Unit IX: Picturing Algebra. pdf
Grade level: 6–12
Students explore formulas, algebraic notation, equivalent expressions, and equations using toothpicks and algebra pieces. Transparency masters included.
Math and the Mind's Eye Unit X: Seeing Symmetry, pdf
Grade level: 4–8
Students develop an awareness of symmetry, congruence, and angle using various visual models. Transparency masters included.
Math and the Mind's Eye Unit XI: Graphing Algebraic Relationships, pdf
Grade level: 8–12
Graphs and graphing calculators are used to describe algebraic relationships.
Math and the Mind's Eye Unit XII: Modeling Real and Complex Numbers, pdf
Grade level: 8–12
Base 6 pieces, grid paper, bicolored counting pieces, and complex number pieces are used to introduce real and complex numbers. Transparency masters included.
Math and the Mind's Eye Unit XIII: Sketching Solutions to Algebraic Equations, pdf
Grade level: 9–12
Students learn to use sketches to solve algebraic equations.
Math and the Mind's Eye Unit XIV: Looking at Linear Algebra, pdf
Grade level: 9–12
A visual geometric introduction to linear transformations, matrices, determinants, and systems of equations. Transparency masters included.