Mathematics

• Counting and Cardinality: Know number names and the count sequence, count to tell the number of objects, and compare numbers.
• Operations and Algebraic Thinking: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
• Number and Operations in Base Ten: Work with numbers 11-19 to gain foundations for place value.
• Measurement and Data: Describe and and compare measurable attributes, classify objects and count the number of objects in each category.
• Geometry: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres), analyze, compare, create and compose shapes.

• Operations and Algebraic Thinking: Represent and solve problems involving addition and subtraction, understand and apply properties of operations and the relationship between addition and subtraction, add and subtract within 20, work with addition and subtraction equations.
• Number and Operations in Base Ten: Extend the counting sequence, understand place value, and use place value understanding and properties of operations to add and subtract.
• Measurements and Data: Measure lengths indirectly and by iterating length units, tell and write time, and represent and interpret data.
• Geometry: Reason with shapes and their attributes.

• Operations and Algebraic Thinking: Represent and solve problems involving addition and subtraction, add and subtract within 20, and work with equal groups of objects to gain foundations for multiplication.
• Number and Operations in Base Ten: Understand place value and use place value understanding and properties to add and subtract.
• Measurement and Data: Measure and estimate lengths in standard units, relate addition and subtraction to length, work with time and money, and represent and interpret data.
• Geometry: Reason with shapes and their attributes.

• Operations and Algebraic Thinking: Represent and solve problems involving multiplication and division, understand properties of multiplication and the relationship between multiplication and division, multiply and divide within 100, solve problems involving the four operations, and identify and explain patterns in arithmetic.
• Number and Operations in Base Ten and Fractions: Use place value understanding and properties of operations to perform multi-digit arithmetic, and develop understanding of fractions as numbers.
• Measurement and Data: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects, represent and interpret data, understand concepts of area and relate area to multiplication and addition, and recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
• Geometry: Reason with shapes and their attributes.

• Operations and Algebraic Thinking: Use the four operations with whole numbers to solve problems, gain familiarity with factors and multiples, and generate and analyze patterns.
• Number and Operations in Base Ten and Fractions: Generalize place value understanding for multi-digit whole numbers, use place value understanding and properties of operation to perform multi-digit arithmetic, extend understanding of fraction equivalence and ordering, build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers, and understand decimal notation for fractions.
• Measurement and Data: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit, represent and interpret data, and understand concepts of angles and measure angles.
• Geometry: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Students in the fifth and sixth grades possessing exceptional skills in the standards for mathematical practice are invited to participate in the Accelerated Mathematics Program. This program functions as a self-contained mathematics class, which meets during the regularly scheduled math time at each grade level.  Students in this program study the standard curriculum.  In addition, students use units of study and materials that have been specifically designed to challenge higher level thinking skills in diverse areas of mathematics.  The intent of the Accelerated Mathematics Programs is to provide students with challenging and rewarding experiences reaching well beyond the required mathematics curriculum.

• Operations and Algebraic Thinking: Write and interpret numerical expressions and analyze patterns and relationships.
• Number and Operations in Base Ten and Fractions: Use equivalent fractions as a strategy to add and subtract fractions and apply and extend previous understandings of multiplication and division to multiply and divide fractions.
• Measurement and Data: Convert like measurement units within a given measurement system, represent and interpret data, understand concepts of volume and relative volume to multiplication and to addition.
• Geometry: Graph points on the coordinate plane to solve real-world and mathematical problems and classify two-dimensional figures into categories based on their properties.

• Operations and Algebraic Thinking: Understand ratio concepts and use ratio reasoning to solve problems.
• Number and Operations in Base Ten and Fractions: Apply and extend previous understandings of multiplication and division to divide fractions by fractions, compute fluently with multi-digit numbers and find common factors and multiples, and apply and extend previous understandings of numbers to the system of rational numbers.
• Expressions and Equations: Apply and extend previous understandings of arithmetic to algebraic expressions, reason about and solve one-variable equations and inequalities, and represent and analyze quantitative relationships between dependent and independent variables.
• Geometry: Solve real-word and mathematic problems involving area, surface area, and volume.

• Statistic and Probably: Develop understanding of statistical variability and summarize and describe distributions.

Mathematics - Seventh and eigHth grade

The seventh and eighth grade mathematics curriculum are aligned to the Common Core State Standards and are taught using a spiral approach which allows the students to be exposed to probability, statistics, geometry, algebra, logic, data analysis, percents, decimals, and fractions on a regular basis. This two-year math program forms a strong foundation for the study of a modern high school math program.

In addition, articulation among grade levels and increased opportunities for formal training have provided strong support for teachers. Communication among New Trier Township teachers of mathematics has contributed significantly to our students’ mathematical success.

Individual student abilities are met through optional enrichment materials, short-term ability grouping for review of skills, and help from resource teachers outside the regular classroom. There is also available a Math Assistance class offered as one of the activity classes students can opt to take each quarter to provide additional support.

• Ratios and Proportional Relationships: Analyze proportional relationships and use them to solve real-world and mathematical problems.
• The Number System: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.
• Expressions and Equations: Use properties of operations to generate equivalent expressions and solve real-life and mathematical problems using numerical and algebraic expressions and equations.
• Geometry: Draw, construct and describe geometrical figures and describe the relationships between them, and solve real-life and mathematical problems involving angle, measures, area, surface area, and volume.
• Statistics and Probability: Use random sampling to draw inferences about a population, draw informal comparative inferences about two populations, and investigate chance processes and develop, use, and evaluate probability models.

• The Number System: Know that there are numbers that are not rational, and approximate them by rational numbers.
• Expressions and Equations: Work with radicals and integer exponents, understand the connections between proportional relationships, lines, and linear equations, and analyze and solve linear equations and pairs of simultaneous linear equations.
• Functions: Define, evaluate and compare functions and use functions to model relationships between quantities.
• Geometry: Understand congruence and similarity using physical models, transparencies, or geometry software, understand and apply the Pythagorean Theorem, and solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
• Statistics and Probability: Investigate patterns of association in bivariate data.

---

Students, who have met certain criteria, including scores obtained on standardized tests and teacher recommendations, are eligible to take the pre-algebra/algebra course sequence. In seventh grade the course of study is pre-algebra followed by algebra in eighth grade. Two levels of pre-algebra and algebra are offered: the equivalent of New Trier’s four-level and three-level courses. The material covered in the algebra course includes inequalities, graphical representations of data and formulae, translation of words into symbols and symbols into words, probability, matrices, geometry, trigonometry, and finding solutions to equations and systems of equations by using the quadratic formula, graphing, completing the square, and factoring. A graphing calculator is mandatory for this class. Placement into second-year high school math is arranged for students successfully completing algebra in eighth grade.