## Mathematics Scope and Sequence

### Vision

Mathematics is one tool by which we better understand God’s precise, orderly, and sometimes mysterious creation. As a result of a TCS mathematics education, students will value mathematics and develop proficiency in the use of mathematics. Proficiency in mathematics learning refers to conceptual understanding, procedural fluency, strategic competence, and adaptive reasoning. Students experience instruction based on Standards for Mathematical Practice. [http://www.corestandards.org/the-standards/mathematics] Students express an understanding of concepts using a variety of methods and media. Developmentally appropriate instruction challenges and supports students..

### Standards

What a TCS student will know and be able to do in Mathematics:

What a TCS student will know and be able to do in Mathematics K-4: Demonstrate understanding by applying concepts to problems in the following:

- Operations and Algebraic Thinking.
- Number and Operations in Base Ten.
- Number and Operations—Fractions.
- Measurement and Data.
- Geometry.

By the close of Pre-Algebra: Demonstrate understanding by applying concepts to problems in the following:

- Ratios and Proportional Relationship.
- The Number System.
- Expressions and Equation.
- Functions.
- Geometry.
- Statistics and Probability.

In courses Algebra I and beyond: Demonstrate understanding by applying concepts to problems in the following:

- Number and Quantity.
- Algebra.
- Functions.
- Geometry.
- Statistics and Probability.
- Modeling.

In Standards of Mathematical Practice K-12:

- Be mathematical problem solvers.
- Reason and construct mathematical arguments.
- Communicate mathematically.
- See connections both within mathematics and to other subject areas.
- Look for and make use of structure and patterns.

Theological Integration:

- See God’s orderliness and mystery reflected in mathematics.

- Kindergarten Topics
- Sorting; patterning; counting and number sense; writing numerals; composing and decomposing numbers including adding and subtracting single digit numbers; strategies for counting, adding and subtracting, and problem solving; geometry(attributes, modeling, and composing two and three dimensional shapes); measurement including time and money; graphing data; estimating; problem-solving. (Pre-Kindergarten at developmentally appropriate levels.)
- Grade 1 Topics
- Counting sequence; number sense; place value; composing and decomposing numbers; strategies for adding and subtracting single and double digit numbers; geometry (attributes and composing of two and three dimensional shapes and fractions); measuring in standard and non-standard units; telling time; counting coins; calendar; graphing data; estimating; problem solving.
- Grade 2 Topics
- Place value; properties of addition and subtraction; fluently adding and subtracting through 20; understanding and solving multi-digit addition and subtraction problems; multiplication foundations; measuring and estimating using standard units; telling time; money; graphing and interpreting data; geometry (recognizing shapes and their attributes); introduction to fractions.
- Grade 3 Topics
- Adding, subtracting, and multiplying using algorithms and strategies based on place value and the order of operations; rounding/estimating; understanding fractional parts, building and comparing equivalent fractions; properties of multiplication and division; multiplication and division facts; solving multi-step word problems; geometry, area, perimeter; representing and interpreting data; telling time, elapsed time; measuring volume and mass.
- Grade 4 Topics
- Place value for multi-digit whole numbers, rounding, comparing; properties of operations to perform multi-digit arithmetic, factors/multiples; building, finding, and comparing equivalent fractions; comparing decimal fractions; organizing, graphing, and analyzing data; solving problems involving measurement and conversions within the same system of measurement; geometry (area, perimeter, angles); multi-step problem solving.
- Grade 5 Topics
- Place value for multi-digit whole numbers and decimals through the thousandths place, rounding, comparing; properties of operations to perform multi-digit arithmetic with whole numbers and decimals; comparing, adding, subtracting, multiplying, and dividing fractions; converting measurement units within the same system of measurement, creating and interpreting line plots, organizing, graphing, and analyzing data, understanding concepts of volume and relating volume to multiplication and addition; geometry (graphing points on the coordinate plane, classifying two-dimensional figures into categories based on their properties); multi-step, real-world problem solving.