## Mathematics

The math program at Tilden has six major goals:

Students will:

- become mathematical problem-solvers
- learn to communicate mathematically
- learn to reason mathematically
- become confident in their own abilities
- develop computational competence, and
- learn to value and enjoy mathematics

Students need to be engaged in experiences that help them understand and appreciate the role of mathematics in daily living, not as an abstract system of meaningless symbols, but as a useful tool for solving problems and making decisions. We encourage parents to explore the world with their children, discovering together that math is a subject we all use for life—from keeping score in a game, to choosing an outfit, to building a tree house, to buying a pet.

### Kindergarten & First Grade

Our primary mathematics program is strongly activity based, using tactile, colorful, and appealing concrete materials. The program builds an introductory understanding of patterns, sorting, classifying, counting, comparing, graphing, and simple money concepts.

Kindergarten students begin using math vocabulary, recognizing simple shapes, understanding the number sentence, working with addition and subtraction from zero to 10, exploring simple measuring and comparing problems. Math is regularly integrated into other core activities, theme study units, and science work.

First-grade math builds on and further develops understandings of these concepts. Through a variety of experiences using manipulative materials, first-grade students discover interrelated mathematical concepts, and gain insight into the patterns of our number system. They explore numbers from one through ten in depth. This work provides a foundation for the symbolic representation of number combinations and helps students develop proficiency in solving written problems. An understanding of place value, base ten, and the structure of our number system is also developed using manipulative materials. Students recognize and understand the meaning of numbers and solve addition and subtraction problems from 0-99. Beginning experiences with geometry, measurement, telling time, money, and solving simple story problems are other components of the first-grade program.

### Second and Third Grades

In the second grade, we review patterning and place value, and begin to learn carrying, starting by using blocks extensively for true understanding of what is actually going on. When this is understood, we move to borrowing, again using manipulative materials extensively. Ultimately, the goal is for second-grade students to carry and borrow to two places (or more) with solid understanding of place value as the underpinning.

Third-graders make great progress learning how to read directions and how to follow through. We review carrying and borrowing, strengthen multiplication and division understandings, and begin the decimal/fraction journey.

All second- and third-graders work with experiential, manipulative math materials to lay an excellent foundation for mathematical understanding. They also work in the Addison-Wesley math workbooks, which extend understanding by requiring very challenging oral and written explanations. Many other texts and workbooks supplement these as appropriate.

Both classes work on unlocking story problems with ever-increasing ease. Students explore and practice geometry, time, money, and measurement in groups of 4-6 once a week. The language of mathematics is used daily, and the importance of memorizing addition combinations and multiplication facts are emphasized for speed of work, depth of understanding of mathematical patterns, assessing reasonability of answers, and pure enjoyment of numbers. Patterns, puzzles, and discovery are all important parts of the curriculum. Frequent tests help check that students retain all previously-learned topics.

### Fourth Grade

Fourth grade uses the Addison-Wesley mathematics program as the foundation of our math instruction, which takes place four days a week for at least an hour a day. This text is supplemented by other material based on the National Council of Teachers of Mathematics’ Curriculum Standards. The following mathematical strands are woven throughout the fourth-grade year:

- Mathematical understanding
- Operations and computation
- Geometry
- Organizing data and using numbers
- Measurement
- Data analysis
- Thinking mathematically, inside and outside the box
- Money and time
- Mathematical symbols and language
- Commutative and associative properties
- Multiplication and division with and without decimals
- Decimals and fractions
- Perimeter and area
- Percents
- Review of carrying and borrowing
- Expanded, written, and standard form (100 + 20 + 5, one hundred twenty-five, 125)
- Sequence, ordering, and comparing
- Numeration systems
- Daily challenges and puzzles
- Identifying, choosing, and applying problem solving strategies
- Critical thinking skills
- Solving problems using mental math, estimation, calculators, and computers
- Binary number systems and digital data encoding
- Using a computer spreadsheet to manipulate and graph data

### Fifth Grade

We use the Addison Wesley Mathematics Programs as the foundation of our math instruction. Fifth-graders have math four days a week for at least an hour a day. We focus on a blend of problem solving and computational skills, demonstrating the importance of mathematics and applying math skills to realistic and everyday situations, making use of many supplemental materials. The following mathematical strands are woven throughout the fifth-grade year:

- Positive number operations and computation
- Fractions, decimals, and percents
- Rounding and estimating
- Mathematical understanding
- Expanded, written, and standard form (100 + 20 + 5, one hundred twenty-five, 125)
- Solving problems using mental math, estimation, calculators, and computers
- Critical thinking skills
- Problem solving and test-taking strategies
- Daily challenges and puzzles
- Commutative, associative, and distributive properties
- Statistics and data analysis (mean, median, mode, range, etc.)
- Measurement of time, mass, length, volume, and temperature
- Geometry
- Factoring whole numbers
- Probability
- Number theory (greatest common factor, least common multiple, divisibility, composites, and primes)
- Place value (whole numbers and decimals)
- Graphing and other visualizations of data
- Geometric and numeric patterns, functions, and algebra
- Negative numbers
- Symbols and language of math
- Point, line, and plane symmetries
- Elementary computer programming; introduction to variables in computer programming