In Kindergarten students develop their interest and confidence in using mathematics. They develop one-to-one correspondence, conservation of number, counting (by ones to 30), using numerals to represent quantity, comparing numbers and quantities, the ability recognize, reproduce and invent patterns, sorting and classifying objects, and the ability to model simple addition and subtraction problems to ten with drawings and concrete objects. They also begin to explore shapes, measurement, and data.
In First Grade students continue to develop the skills and concepts they began in kindergarten: counting to 100, reading writing and sequencing numbers to 100, expanding understandings of shape, measurement and data while beginning to explore probability, etc. They develop strategies for solving and recording combining and separating story problems. They learn that numbers can be broken into groups in multiple ways and find combinations of numbers up to about 20. They begin to learn that ten ones can be seen simultaneously as ten things or as a single thing (i.e. one group of ten) through extensive exploration of tens and ones.
In Second Grade students continue to develop the skills and concepts they began in the previous grades. They develop more extensive and sophisticated strategies for solving and recording combining and separating story problems. They learn to use multiples of five and ten as landmark numbers. They learn that our number system is based on tens and has repeating patterns that recur throughout the counting numbers, that the value of a digit depends on its place in the number and that zero is a place holder. They learn that ten ones can be seen simultaneously as ten things or as a single thing (i.e. one group of ten) and that the same principle applies to ten tens and one hundred. They expand their understandings of shape, measurement, data, probability, and explore fractions of both areas and sets.
In Third Grade students continue to develop the skills and concepts they began in the previous grades. They develop more extensive and sophisticated strategies for solving and recording story problems involving the four basic operations. They deepen their understanding that ten ones can be seen simultaneously as ten things or as a single thing (i.e. one group of ten) and that the same principle applies to ten tens and one hundred. They explore multiplication and division concepts through arrays and develop an initial understanding of factors, multiples, and fractional parts. They use landmark numbers and the distributive property to solve multiplication problems with factors greater than 10. They complete mastery of single digit addition and subtraction facts and begin learning simple multiplication facts. They become competent in solving addition and subtraction problems using multiple strategies that are supported by an understanding of numbers and operations. They expand their understandings of shape, measurement, data, probability, and explore fractions of both areas and sets. (See note on the place of the U.S. standard algorithms in our curriculum on page __.)
In Fourth Grade students continue to develop the skills and concepts they began in the previous grades. They develop more extensive and sophisticated strategies for solving and recording story problems involving the four basic operations. They expand their understanding of our base ten system and the relationships of each place to adjacent places to ten thousand and to tenths. They solidify their understanding of multiplication and division and extend their understanding of factors, multiples – learning to break numbers apart and recombine them (ex. 23 x 7 = (20 x 7) + (3 x 7)); and learning to unitize groups (in “six groups of 7” the groups of seven can each be thought of simultaneously as seven individual items and as a single group of seven). They develop the ability to compare and order fractions and focus on understanding equivalence. Addition and subtraction of fractions are explored but algorithms are not taught. They learn basic multiplication facts to 12 x 12. They expand their understandings of 2-D and 3-D shapes, coordinate grids, measurement, data, and probability. (See note on the place of the U.S. standard algorithms in our curriculum.)
In Fifth Grade students continue to develop the skills and concepts they began in the previous grades. They develop more extensive and sophisticated strategies for solving and recording story problems involving the four basic operations. They study fractions, decimals and percents, learning that fractions, decimals, and percents are different ways to represent the same number and that one can move back and forth among these notations and choose the one most appropriate for a specific situation. They come to understand that a fraction can represent a fraction of an area or a group; that every fraction has an infinite number of equivalents; that equivalent parts may or may not be congruent. They learn to compare fractions. They learn to compute with fractions, decimals and percents (excluding division). They expand their understanding of our base ten system and the relationships of each place to adjacent places to ten thousand and to ten thousandths. They solidify their understanding of multiplication and division and extend their understanding of factors and multiples. They review (or finish learning) all basic computation facts. They explore volume and units of volume and measure and classify angles. They expand their understandings of data and probability. (See note on the place of the U.S. standard algorithms in our curriculum .)
In Sixth Grade students continue to develop the skills and concepts they began in the previous grades. They develop more extensive and sophisticated strategies for solving and recording story problems involving the four basic operations. They deepen their understanding of fractions, decimals and percents, learning to computer fluently with them (except division of fractions) and apply them to real world problems. They explore factors, multiples, squares, and primes and use them to solve problems. They learn that in some situations it is possible to answer the question, “How likely is it?” and express the probability of an event of outcome in mathematical terms: that experimental and theoretical probabilities are often different and usually approach each other as the number of trials increases, and that probabilities can be used to make good decisions. They examine mathematical relationships between sides and angles and between area and perimeter. They use concrete materials to represent algebraic equations, learning that by adding, subtracting, multiplying or dividing each side of an equation by the same number, we can find the values of an unknown quantity (variable) in the equation. They review all basic computation facts. They explore volume and units of volume and measure and classify angles. They learn to use mean, median, and mode to describe and analyze data.
We welcome your feedback to the Mathematics Curriculum Guide. Please send comments to Mathematics@arps.org.