The foundation for success in high school mathematics and beyond is laid in the early years of elementary school. Students learn both essential skills and concepts in numerical fluency, place values, whole number operations, fractions and decimals, and problem solving. New concepts are carefully modeled and developed with ample practice for numerical fluency. Students learn to communicate about mathematics and explain their reasoning. Grades K-5 establishes this foundation, while middle school begins the transition into Pre-Algebra and Algebra.
Students develop an understanding of addition and subtraction strategies for basic addition facts and related subtraction facts through 20. They understand whole number relationships, including grouping in tens and ones. Students learn about data, graphs and probability, counting money, telling time, calendar use , measurement, geometry, patterns, and spatial sense.
Students learn addition and subtraction facts and strategies, place value to four digits, number concepts and patterns, adding and subtracting 2 and 3 digit numbers with regrouping, data and graphs, probability, counting and using money, time, solid figures, plane figures and spatial sense, patterns, length, perimeter, area, weight, mass, capacity, temperature, fractions, comparing and ordering numbers, and multiplication and division concepts from 0-6.
Students learn place value to six digits; addition and subtraction of four digit numbers; working with money and telling time, bar and line graphs, basic probability concepts; and multiplication and division of one digit numbers. Students are introduced to fractions and decimals. They learn to select appropriate problem solving methods, including calculation, formulas, estimation, and using equations to solve word problems.
Students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare simple fractions and decimals. They add and subtract fractions with like denominators and add and subtract decimals. They understand the properties of, and the relationships between, plane geometric figures. They collect, represent, and analyze data to answer questions.
Students increase their facility with the four basic arithmetic operations applied to fractions, decimals and positive and negative numbers. They know and use common measuring units to determine length and area and know and use formulas to determine the volume of simple geometric figures. Students know the concept of angle measurement and use a protractor and compass to solve problems. They use grids, tables, graphs and charts to record and analyze data.
Students master the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative integers; they accurately compute and solve problems. They apply their knowledge to statistics and probability. Students understand the concepts of mean, median, and mode of data sets and how to calculate the range. They analyze data and sampling processes for possible bias and misleading conclusions; they use addition and multiplication of fractions routinely to calculate the probabilities for compound events. Students conceptually understand and work with ratios and proportions; they compute percentages (such as tax, tips, interest). Students use letters for numbers in formulas involving geometric shapes and in ratios to represent an unknown part of an expression. They solve one-step linear equations.