• Understand the meaning, representations, and uses of numbers.
• Use manipulatives, number lines, and mental arithmetic to solve problems and develop an understanding of the concepts underlying simple addition and subtraction operations.
• Collect, represent, analyze, and interpret simple data.
• Understand and use basic measurement tools relating to length, weight, angles, temperature, time, and money.
• Investigate characteristics and properties of plane and solid figures.
• Understand basic patterns and functions and simple algebraic notation.

• Understand equivalent names for numbers and common numerical relations,  including place value, fractions, pairing and ordering, and number theory.
• Gain proficiency and accuracy in computation, estimation, understanding of the meanings of operations. 
• Collect, represent, analyze, and interpret data.
• Understand and use measurement tools relating to length, weight, angles, temperature, time, and money.
• Investigate characteristics and properties of two- and three-dimensional shapes.
• Extend understanding of basic patterns and functions.
• Use algebraic notation to solve simple number sentences. 

• Count by 1s, 2s, 5s, 10s, 25s, and 100s past 1,000 with and without manipulatives, and to 10,000 with manipulatives; recognize numbers as odd or even; compare and order large numbers.   
• Develop proficiency, accuracy, and automaticity with basic addition and subtraction facts; perform two-digit addition and subtraction with whole numbers; understand the names, meanings and uses of simple fractions and simple fractional equivalencies.  
• Calculate and compare values of coin and bill combinations.  
• Use repeated addition, arrays, and skip counting to model multiplication; use equal sharing and equal grouping to model division. 
• Use graphs and charts to represent collected data and to ask and answer questions and draw conclusions.  
• Learn and apply basic probability concepts.
• Understand and use measurement tools relating to length, weight, angles, area, perimeter, volume and capacity, temperature, time, and money;  identify units and systems of measurement.
• Investigate properties and characteristics of lines, angles, and plane and solid figures.
• Use algebraic notation to represent and analyze situations and structures.

• Demonstrate automaticity and accuracy with multiplication facts and use strategies to compute or solve problems with two- and three-digit numbers multiplied by one digit.   Work with multiples of two, five, and ten. 
• Extend understanding of fractions and simple fractional equivalencies.  
• Collect and organize data, use data representation tools, and find maximum, minimum, range, mode, and median of a data set. 
• Understand and apply the basic concepts of probability, including qualitative and quantitative outcomes; make and test predictions using manipulatives and express results using accurate mathematical terms. 
• Work with whole number to 1,000,000 and decimals through the hundredths place.   Translate between whole numbers and decimals in words, base-ten notation, and with manipulatives. 
• Read, write, and model fractions and solve problems involving fractional parts. 
• Compare and contrast standard and metric measures.  
• Determine areas and perimeters. 

• Work with whole numbers to 1,000,000,000, decimals through thousandths, and negative integers.   Work with multiples and factors of whole numbers. 
• Understand the meanings and uses of fractions.  Compute with fractions, including those with like and unlike denominators.  Work with equivalencies, decimals, and percents.
• Compute accurately with whole numbers and decimals through hundredths.   Extend multiplication facts.  Multiplication and division of multi-digit whole numbers. 
• Use probability and data collection tools to ask and answer questions, draw conclusions, and make predictions.  
• Compare and contrast standard and metric measures.  Work with the perimeter, area, and volume of complex figures.   Be familiar with plotting points on a coordinate grid. 
• Work with geometric topics such as points, intersections, and rays, and with right, acute and obtuse angles, vertices, and congruency.   
• Understand patterns and functions and use algebraic notation to represent and analyze situations and structures.  
• Investigate and understand the distributive property of multiplication over addition. 

• Understand equivalent fractions; convert between fractions and mixed numbers and between fractions, decimals, and percents.  Compare and order fractions. 
• Learn to identify prime and composite numbers, factor numbers, and find prime factors.   Convert between base ten, exponential, and repeated factor notations. 
• Compute signed numbers.  Demonstrate proficiency with multiplication and division facts.   Solve problems involving the addition and subtraction of mixed numbers, division of fractions, and ratios.  
•  Use more advanced probability and data collection tools to ask and answer questions, draw conclusions, and make predictions.  
• Continue work with the systems and processes of measurement, including using formulas, defining and apply Pi appropriately, and working with standard and metric measures.  Use ordered pairs to name, locate and plot points in all four quadrants of a coordinate grid.  
• Enhance knowledge of lines and angles and apply properties of sums of angle measures in triangles and quadrangles.  Work with reflections, translations, and rotations in geometric situations.
• Represent functions using words, symbols, tables, and graphs, and use those representations to solve problems. 
• Solve open number sentences.  Use a letter variable to write an open sentence and to model a number story; solve linear equations with one unknown. 
• Evaluate and use numeric expressions containing grouping symbols and nesting grouping symbols.   Know and use appropriate orders of operations in algebraic notation.

Middle School

Clairbourn’s middle school math program is designed to allow students to complete Algebra I by the end of their 8th grade year, well-prepared to move into more advanced math in high school.

Textbook:  University of Chicago School Mathematics Project TRANSITION MATHEMATICS, Third Edition, published by McGraw Hill.

The goals of Transition Mathematics are to solidify the arithmetic already known and to prepare the student for the study of algebra and geometry.  It thoroughly integrates and makes connections to other areas of mathematics, to other disciplines, and to the real world.  Students see how each mathematical idea fits into a larger context.

Students learn to use mathematics effectively through problem solving experiences that include use of higher-order thinking skills in daily assignments, a wide variety of problem types in the questions, and open-ended problems. Activities and projects in provide engaging ways for students to work individually or in groups to explore and extend their knowledge.

Topics covered include:

              1.  Decimal notation

              2.  Number sets

              3.  Variables and their uses

              4.  Problem-solving strategies

              5.  Patterns leading to various operations

Textbooks: 
University of Chicago School Mathematics Project TRANSITION MATHEMATICS, Third Edition, published by McGraw Hill.

University of Chicago School Mathematics Project ALGEBRA, Third Edition, published by McGraw Hill.

The goals of Transition Mathematics are to solidify the arithmetic already known and to prepare the student for the study of algebra and geometry.  It thoroughly integrates and makes connections to other areas of mathematics, to other disciplines, and to the real world.  Students see how each mathematical idea fits into a larger context.

The goals of Algebra are to introduce students to the language of algebra; help prepare students for geometry and other mathematics; and help students learn about the many uses of algebra in the real world and thus be able to deal with them. 

Topics covered include:

• Patterns leading to various operations
• Real numbers, area, and volume
• Coordinate graphs and equations
• Linear sentences
• Operations in algebra

Textbook:  University of Chicago School Mathematics Project ALGEBRA, Third Edition, published by McGraw Hill.

The goals of Algebra are to introduce students to the language of algebra; help prepare students for geometry and other mathematics; and help students learn about the many uses of algebra in the real world and thus be able to deal with them. 

Students learn to use mathematics effectively through problem-solving experiences that include use of higher-order thinking skills in daily assignments, a wide variety of problem types in the questions, and open-ended problems that provide engaging ways for students to work individually or in groups to explore and extend their knowledge. 

Topics covered include:

• Slopes and lines
• Exponents and powers
• Quadratic equations
• Polynomials
• Linear systems
• Factoring