Estimate sum or difference by rounding Order 2-digit decimals 0.1, 0.01, 0.001 Compare decimals using <, >, or = and justify Develop skills in addition and subtraction and apply them in problem solving Properties of addition and subtraction Use mental math and estimation strategies to add and subtract whole numbers Understand and model addition and subtraction of decimal fractions and common fractions with like denominators Use mental math and estimation strategies to add/subtract decimal fractions and common fractions with like denominators Solve problems requiring addition and subtraction of whole numbers, decimal fractions, and common fractions with like denominators Add and subtract 1- and 2-digit decimals Add and subtract fractions and mixed numbers with common denominators Use order of operations, including parenthesis Compute using commutative, associative, and distributive properties Use mental math and estimation Add and subtract common fractions and mixed numbers with unlike denominators Use mental math and estimation Money Model addition and subtraction by counting back change using the fewest number of coins Third Grade Fourth Grade Fifth Grade
Number and Operations Develop understanding of multiplication and division and apply them in problem solving Know multiplication facts to 10 x 10 Use arrays and area models to develop an understanding of the distributive property, to determine partial products, and to multiply a or 3-digit number by a 1-digit number. Apply and verify multiplication properties Understand effect of multiplying by multiples of 10 Understand the relationship between division and multiplication, division and subtraction Recognize the two situations of division Explain meaning of remainder Divide a 2- or 3-digit number by a 1-digit number Write mathematical expressions for division problem-solving situations Use mental math and estimation Solve problems requiring multiplication and division Multiply a 2- or 3-digit number by a 1- or number Know division facts to 100 ÷ 10 Divide by a 1- or 2-digit number Understand relationship between dividend, divisor, quotient, and remainder Understand and explain effect of multiplying or dividing the divisor and dividend by the same number Model multiplication and division of decimals by whole numbers Multiply and divide 1- and 2-digit decimals by whole numbers Use mental math and estimation Model and explain multiplication and division of decimals Multiply and divide with decimals (including less than one and greater than one) Represent division of whole numbers as fractions Model multiplication and division of common fractions Understand the relationships/rules for multiplication/division of whole numbers apply to decimals Use mental math and estimation Understand and compare fractions Understand relationship between decimal fractions and decimals (i.e. 3/10 can be written as 0.3) Understand the fraction a/b represents a equal sized parts of a whole divided into b equal sized parts Know and use decimal fractions and common fractions to represent the size of parts created by equal divisions of a whole Understand representations of equivalent common fractions and decimal fractions Use improper fractions and mixed numbers interchangeably Find equivalent fractions Simplify and compare fractions Find common denominators using concrete, pictorial, and computational models. Compare fractions and justify the comparisons Use fractions and decimals interchangeably Percents Explore and model percents using multiple representations Apply percentages to circle graphs Third Grade Fourth Grade Fifth Grade
Algebra Describe and extend numeric and geometric patterns Describe and explain quantitative relationships represented by a formula Use a symbol to represent an unknown and find the value of it Understand and apply patterns and rules to describe relationships Represent unknowns using symbols Write and evaluate mathematical expressions Use variables Substitute numbers in simple algebraic expressions Determine that a formula will be reliable regardless of type of number substituted Data Analysis and Probability Construct and interpret line plot graphs, pictographs, Venn diagrams, and bar graphs Solve problems by organizing and displaying data in charts, tables, and bar graphs Use scale increments of 1, 2, 5, and 10 Construct and interpret line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs Compare different graphical representations for a given set of data Investigate features and tendencies of graphs Identify missing information and duplications in data Determine and justify the range, mode, and median of a set of data Collect, organize, display data using the most appropriate graph (circle graphs, line graphs, bar graphs) Analyze data in a graph Compare and contrast multiple graphic representations for a single set of data and discuss advantages and disadvantages of each Determine and justify the mean, range, mode, and median of a set of data Process Skills Solve problems, Reason and evaluate mathematical arguments, Communicate mathematically, Make connections among mathematical ideas and to other disciplines, Represent mathematics in multiple ways Third Grade Fourth Grade Fifth Grade
Concepts/Skills to Maintain Comparison of numbers Addition and subtraction of multi-digit numbers Length (cm, m, in, ft, yd) Time to 5 minutes Describe and classify geometric shapes Area models (arrays) of multiplication Make change Multiplication and Division of whole numbers Area Perimeter Length Time to the minute Elapsed Time Count back change using the fewest number of coins Addition and subtraction of decimals Whole numbers computation Angle measurement Length, area, and weight Number sense Addition and subtraction of common fractions with like denominators Data usage and representation Characteristics of 2-D and 3-D shapes Order of Operations Properties of addition and multiplication Terms/Symbols quotient, whole number, decimal point, place value of 1/10 (tenth), numerator, denominator, second (unit of time), ÷, x, decimal fraction, common fraction, elapsed time, scalene triangle, isosceles triangle, equilateral triangle, bar graph, mile, kilometer, center, diameter, radius, line plot graph mixed fraction, proper fraction, improper fraction, point, ray, line, line segment, parallel, perpendicular, diagonal line, plane, weight, ounce, pound, ton, gram, kilogram, protractor, degree, rotation, parallelogram, trapezoid, rhombus, rectangular prism, pyramid, coordinate system, ordered pair, line graph, right triangle, acute triangle, obtuse triangle, net, median, mode, range, straight angle simplify, common denominator, congruence, %, percent, improper fraction, divisibility, multiple, factor, estimate, volume, tiling, irregular polygon, polygon, capacity, circumference, pi, circle graph, cup, pint, quart, gallon, milliliter, liter, mean, ≈, , π Please Note: The “Concepts/Skills to Maintain” section is not an inclusive list. Please refer to the Georgia Performance Standards for complete information.