NCTM Standards for Grades 6-8
| Principles | Standards | Expectations | Ko's Journey |
|---|---|---|---|
| Number & Operations | Understand Numbers, ways of representing numbers, relationships amoung numbers, and number systems |
Work flexibility with fractions, decimals, and percents to solve problems. | |
| Understand and use ratios and proportions to represent quantitative relationships. | |||
| Use factors, multiples, prime factorization, and relatively prime numbers to solve problems. | |||
| Develop meaning for integers and represent and compare quantities with them. | |||
| Understand Meanings of operations and how they relate to one another |
Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers. | ||
| Compute Fluently and make reasonable estimates |
Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situtation, and apply the selected methods. | ||
| Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use. | |||
| Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios. | |||
| Algebra | Understand Patterns, relations and functions |
Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules. | |
| Represent and Analyze mathematical situations and structures using algebraic symbols |
Develop an initial conceptual understanding of different uses of variables. | ||
| Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope. | |||
| Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations. | |||
| Analyze Change in various contexts |
Use graphs to analyze the nature of changes in quantities in linear relationships. | ||
| Geometry | Specify Locations and describe spatial relationships using coordinate geometry and other representational systems |
Use coordinate geometry to represent and examine the properties of geometric shapes. | |
| Use Visualization, spatial reasoning, and geometric modeling to solve problems |
Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume. | ||
| Use visual tools such as networks to represent and solve problems. | |||
| Use geometric models to represent and explain numerical and algebraic relationships. | |||
| Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life. | |||
| Measurement | Understand measurable attributes of objects and the units, systems, and processes of measurement |
Understand relationships among units and convert from one unit to another within the same system. | |
| Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. | |||
| Apply Appropriate Techniques, tools, and formulas to determine measurements |
Solve problems involving scale factors, using ratio and proportion. | ||
| Solve simple problems involving rates and derived measurements for such attributes as velocity and density. | |||
| Problem Solving | Deepen Understanding of mathematical concepts |
Apply mathematics to everyday experiences, such as reading literature or using cellular telephones, in-line skates, kites, and paper airplanes. | |
| Connections | Look for and Make Connections to build mathematical understanding |
Comprehend how rich problem contexts involve connections to other disciplines (e.g., science, social studies, art) as well as to the real world and daily life experiences. | |
| Representations | Create, Compare, and Use various representations |
Recognize an array of representational forms for fractions, decimals, percents, and integers. |
An Example from Ko's Journey
The Medicine Poultice Problem - A Ratio Activity
Along her travels, Ko encounters a wounded wolf cub while traveling. In her guidebook, the medicine woman teaches her about the medicinal properties of plants. Ko must mix the herbs in certain ratios to save the wolf cub.
Ko encounters the hurt wolf pup.
Ko's guidebook is read to her by the medicine woman who teaches about ratios.
The interactive workbook provides the form for students to work through the problem.
And behind the scenes, a practice lesson on ratios is generated and linked to the student landing and teacher administrative pages.
