One of the first content questions addressed in the development of PlaneMath was how to define or delimit the proposed program. In a review of candidate proposals from publishers for state math adoption in California, mathematics was presented in a range of ways, from a complete curriculum to one or two selected areas of emphasis, intended to augment existing published or adapted curricula.
In order to provide the maximum flexibility for teachers and classrooms, we decided that our program should provide materials that augment mathematics curricula.
National Council of Teachers of Mathematics (NCTM) Standards
The following are the NCTM standards for K-4th grade mathematics content, all of which are included in one or more PlaneMath lessons:
Standard 1: Mathematics as Problem Solving
- Use problem-solving approaches to investigate and understand mathematical content;
- Formulate problems from everyday and mathematical situations;
- Develop and apply strategies to solve a wide variety of problems;
- Verify and interpret results with respect to the original problem;
- Acquire confidence in using mathematics meaningfully.
Standard 2: Mathematics as Communication
- Relate physical materials, pictures, and diagrams to mathematical ideas;
- Reflect on and clarify their thinking about mathematical ideas as situations;
- Relate their everyday language to mathematical language and symbols;
- Realize that representing, discussing, reading, writing, and listening to mathematics are a vital part of learning and using mathematics.
Standard 3: Mathematics as Reasoning
- Draw logical conclusions about mathematics;
- Use models, known facts, properties, and relationships to explain their thinking;
- Justify their answers and solution process;
- Use patterns and relationships to analyze mathematical solutions;
- Believe that mathematics makes sense.
Standard 4: Mathematical Connections
- Link conceptual and procedural knowledge;
- Relate various representations of concepts or procedures to one another;
- Recognize relationships among different topics in mathematics;
- Use mathematics in other curriculum areas;
- Use mathematics in their daily lives.
Standard 5: Estimation
- Explore estimation strategies;
- Recognize when an estimate is appropriate;
- Determine the reasonableness of results;
- Apply estimation in working with quantities, measurement, computation, and problem solving.
Standard 6: Number sense and Numeration
- Construct number meanings through real-world experiences and the use of physical materials;
- Understand our numeration system by relating counting, grouping, and place-value concepts;
- Develop number sense;
- Interpret the multiple uses of numbers encountered in the real world.
Standard 7: Concepts of Whole Number Operations
- Develop meaning for the operations by modeling and discussing a variety of problem situations;
- Relate the mathematical language and symbolism of operations to problem situations and informal language;
- Recognize that a wide variety of problem structures can be represented by a single operation.
Standard 8: Whole Number Computation
- Model, explain, and develop reasonable proficiency with basic facts and algorithms;
- Use a variety of mental computation and estimation techniques;
- Use calculators in appropriate computational situations;
- Select and use computation techniques appropriate to specific problems and determine whether the results are reasonable.
Standard 9: Geometry and Spatial Sense
- Describe, model, draw, and classify shapes;
- Investigate and predict the results of combining, subdividing, and changing shapes;
- Develop spatial sense;
- Relate geometric ideas to number and measurement ideas;
- Recognize and appreciate geometry in their world.
Standard 10: Measurement
- Understand the attributes of length, capacity, weight, area, volume, time, temperature and angle;
- Develop the process of measuring and concepts related to units of measurement;
- Make and use estimates of measurement;
- Make and use measurements in problem and everyday situations.
Standard 11: Statistics and Probability
- Collect, organize and describe data;
- Construct, read and interpret displays of data;
- Formulate and solve problems that involve collecting and analyzing data;
- Explore concepts of chance.
Standard 12: Fractions and Decimals
- Develop concepts of fractions, mixed numbers, and decimals;
- Develop number sense for fractions and decimals;
- Use models to relate fractions to decimals and to find equivalent fractions;
- Use models to explore operations on fractions and decimals;
- Apply fractions and decimals to problem situations.
Standard 13: Patterns and Relationships
- Recognize, describe, extend and create a wide variety of patterns;
- Represent and describe mathematical relationships;
- Explore the use of variables and open sentences to express relationships.
The Parent/Teacher page for each lesson indicates which standards are addressed in that lesson. In addition, we have developed a matrix that shows the math standards and aeronautics topics covered in each activity. Click here to view this matrix.