Exploring Pascal - All Levels || Student Center || Teachers' Place

### NCTM Standards: Algebra Pre-K-2 | 3-5

"Algebraic concepts can evolve and continue to develop during prekindergarten through grade 2. They will be manifested through work with classification, patterns and relations, operations with whole numbers, explorations of function, and step-by-step processes. Although the concepts discussed in this Standard are algebraic, this does not mean that students in the early grades are going to deal with the symbolism often taught in a traditional high school algebra course.

"Even before formal schooling, children develop beginning concepts related to patterns, functions, and algebra. They learn repetitive songs, rhythmic chants, and predictive poems that are based on repeating and growing patterns. The recognition, comparison, and analysis of patterns are important components of a student's intellectual development. When students notice that operations seem to have particular properties, they are beginning to think algebraically. For example, they realize that changing the order in which two numbers are added does not change the result or that adding zero to a number leaves that number unchanged. Students' observations and discussions of how quantities relate to one another lead to initial experiences with function relationships, and their representations of mathematical situations using concrete objects, pictures, and symbols are the beginnings of mathematical modeling. Many of the step-by-step processes that students use form the basis of understanding iteration and recursion...."

"Although algebra is a word that has not commonly been heard in grades 3-5 classrooms, the mathematical investigations and conversations of students in these grades frequently include elements of algebraic reasoning. These experiences and conversations provide rich contexts for advancing mathematical understanding and are also an important precursor to the more formalized study of algebra in the middle and secondary grades. In grades 3-5, algebraic ideas should emerge and be investigated as students --

• identify or build numerical and geometric patterns;
• describe patterns verbally and represent them with tables or symbols;
• look for and apply relationships between varying quantities to make predictions;
• make and explain generalizations that seem to always work in particular situations;
• use graphs to describe patterns and make predictions;
• explore number properties;
• use invented notation, standard symbols, and variables to express a pattern, generalization, or situation."

### California Content Standards: Mathematics

Kindergarten
Students sort and classify objects.

Students use number sentences with operational symbols and expressions to solve problems.

Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction.

Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships; students represent simple functional relationships.

Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences; students know how to manipulate equations.

1. Recognize, describe, generalize, extend, and create a wide variety of patterns and relationships.
2. Analyze functional relationships to explain how a change in one quantity results in a change in another.
3. Identify patterns and relationships of geometric shapes.
4. Detect patterns and functions from statistical data.
5. Use a calculator and computer software to explore number patterns and demonstrate mathematical relationships.
6. Use patterns and functions to represent and solve problems.
7. Represent relationships using tables, verbal rules, equations, and graphs.
8. Distinguish between linear and non-linear patterns.
9. Develop the beginning concepts of variables through the use of open sentences.
10. Understand and apply the properties of the equality relationship.
11. Recognize mathematical patterns in art and architecture from a diversity of cultures.

For Student Work/Assessments, Grade-Specific Concepts/Skills, and Best Practices, visit the School District of Philadelphia Curriculum Frameworks and click on "The FRAMEWORKS GRID."

• Questions? Write to the workshop facilitators.