# Mathematics

#### The language of math and thinking logically should become as natural as thinking in language.

The program is structured so that each student will be challenged at his or her current level of performance with fun, relevant, practical, and appealing activities that tap into the remarkable cognitive potential of each child. Teachers strive to instill a positive attitude about math and to ensure that each child will experience success in his or her math level.

Countryside offers math levels A through G, Pre-Algebra, Algebra, and Advanced Math. The math levels are not identified by grade as they are more challenging than traditional grade levels in math. The University of Chicago *Everyday Math Program* has been incorporated for math levels B through H giving the curriculum a backbone and sense of continuity from year to year. This backbone is listed on the grade reports which outline a base set of objectives at each level, describing a view of how mathematical skills are developed through the years. In addition to supplementing the *Everyday Math Program* with additional skills practice, teachers are also able to adjust the difficulty of the course using challenge problems and/or more in depth material, should the level of the class be higher than that of the material.

Instruction occurs in small groups of 6-20 students. Children are grouped by instructional level for mathematics and may participate in a group at another grade level.

At the middle school level, Countryside currently offers the following courses: Level G, Pre-Algebra, Algebra, and Advanced Math. Pre-Algebra and Algebra utilize textbooks from the University of Chicago School Mathematics Project, which is a continuation of the Everyday Math Program. As with the lower grade levels, course objectives are outlined on grade reports to allow for a clear view of goals for the various classes. In the advanced math class, students' algebra skills are reviewed in a more rigorous fashion using more complex problems, and geometry topics are also explored.

#### Level A

- Strong knowledge of place value of whole numbers up to 100.

- Strategies for solving single and double digit addition and subtraction problems

- Recognition of appropriate units of measurement in everyday life (time, length, temperature)

- Understanding fractions as equal parts of a whole (1/2, 1/3, and 1/4)

- Building and operating a store based on our unit of study. Using the skills of addition, subtraction, money, and figuring change.

#### Level B

- Strong knowledge of place value of whole numbers up to 1,000

- Strategies for solving single and double digit addition and subtraction problems

- Recognition of appropriate units of measurement in everyday life (time, length, weight, volume, capacity)

- Understanding fractions as equal parts of a whole (1/2, 1/3, 1/4, 1/6, 1/8, 1/10, 1/12)

- Recognition and classification of 2 and 3 dimensional shapes (sides, corners & faces)

- Building and Operating a super computer and snack/vending machine applying the skills of addition, subtraction, money, and figuring change

Level C

- Place Value and Number Sense (sees patterns, writes and counts up to 100,000)

- Addition with Regroupings (adding two-digit and three-digit numbers together)

- Subtraction with Regroupings (including subtraction across three zeros)

- Area and Perimeter (of regular polygons and 3-dimensional shapes)

- Geometry (points, lines, and angles to identify shapes)

- Measurement (standard and non-standard measurement)

- Graphs (Bar Graph, Pictograph, Line Graph, and Pie Graph)

- Money (adding and subtracting with decimal point)

- Basic Multiplication, Basic Division, and Estimation (through a variety of formats)

- Fractions (as they relate to division of wholes and groups as well as equivalency)

Level D

- Whole numbers through billions (adding, subtracting, expanded form, comparing)

- Use of rounding and estimation

- Multiplying a 2 digit number by a 2 or 3 digit number

- Dividing a 3 digit number by a 1 digit number

- Fractions (adding, subtracting, comparing, equivalent)

- Decimals through hundredths (reading and writing, comparing, adding, subtracting, relationship to fractions

- Use of data to predict and graph future outcomes (mode, median, range)

- Geometric vocabulary, concepts and relationships

- Accuracy in recording measurements and appropriate use of units (customary and metric, linear, weight, capacity, temperature); elapsed time

- Students also journal about math

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Level E

- Whole numbers through billions (reading and writing)

- Multi-step computations involving decimals, fractions, and integers

- Patterns and functions in solving problems with variables (word problems, graphs, charts, tables)

- Construction and measurement of angles and two and three-dimensional geometric shapes

- Measuring in U.S. customary and metric units (length, volume, weight, area)

- Collection, recording, and organization of data (surveys, maps, tables, graphs, charts, and diagrams)

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Level F

- Estimates order of magnitude for addition, subtraction, multiplication, and division problems, including rounding whole numbers and decimals

- Uses exponents and scientific notation

- Learns and uses "order of operations" rules to solve problems

- Adds, subtracts, multiplies and divides whole numbers, decimals, and fractions

- Converts between fraction, decimal, and percent representation of a number

- Determines appropriate treatment of remainders in division problems

- Derives and solves number sentences based on word involving multiple operations

- Uses variables to represent unknown quantities in equations

- Accurately measures and constructs angles and shapes using a compass, straight edge, and protractor

- Identifies polygons and solves problems related to their angle measure

- Solves problems related to area, volume, and capacity using U.S. customary and metric units

####

Level G

- Collects, records, organizes and analyzes data in various types of graphs and mean, median, and mode

- Applies operations with fractions, mixed numbers, decimals, percents, integers, and exponents

- Uses and converts U.S. customary and metric units

- Uses ratios and proportions as problem-solving techniques

- Analyzes angles and triangles

- Uses variables to solve equations and formulas for perimeter, area, volume, and surface area.

- Applies mathematical skills to solving real-life problems

####

Pre-Algebra

- Solves one-step problems involving fractions, decimals, integers, and percents using early algebra skills

- Classifies sets of real numbers and understands properties of real numbers

- Uses statistics and probability to compare the outcome of real-world events

- Solves simple rate problems and uses rates to convert measurement units, including English and metric

- Discovers geometric relationships of angles, polygons, triangles, quadrilaterals, and polyhedra

- Investigates computation logic using number theory (factors, multiples, multiplication, fractions, divisibility rules)

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Algebra

- Methods for simplifying and solving equations (multi-step equations, systems of equations and inequalities, quadratic equations)

- Graphing equations as a method of solving problems and analyzing trends (equations, inequalities, systems of equations, parabolas)

- Algebraic representation of solving word problems

- Connections with geometric, algebraic, and arithmetic concepts

- Investigates real-world patterns for solving problems and visualizing trends

####

Advanced Math

- Applies Algebra I techniques to solve multi-step problems

- Understands function notation and translations of linear, quadratic, and polynomial functions

- Matrix notation as representation of systems, including operations, determinants, and reduced row echelon form

- Writes math proofs and definitions; understands logical writing is an important tool in all fields of mathematics

- Discovers properties of Euclidean geometry, including similarity, congruency, linearity, perpendicularity