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
Measurement Time Determine elapsed time to full, half, and quarter hours Capacity and Volume Measurement Use milliliters, liters, fluid ounces, cups, pints, quarts, and gallons Compare units within one system Linear Measurement Use kilometers and miles Measure to nearest ¼ inch, ½ inch, and millimeter Estimate length Compare one unit to another within a single system of measurement Weight Measurement Measure weight in customary and metric units Compare one unit to another within a single system of measurement Geometric Figures Estimate area and volume Derive formula for area of parallelogram, triangle, and circle Find areas of triangles, parallelograms, and circles using formulae (pi ≈ 3.14) Estimate area of circle (partitioning, tiling) Find area of regular and irregular polygons by dividing into squares, rectangles, or triangles Derive formula for circumference of circle Determine circumference of circle using the formula and pi ≈ 3.14 Understand and identify units used in computing volume Derive formula for volume of cube and rectangular prism Compute volume of cube and rectangular prism using formulae Understand similarities/differences between volume and capacity Geometric Figures Understand perimeter (linear unit, length of the boundary of a figure) Determine perimeter by measuring and summing lengths of sides Understand and measure area using square units Model area by tiling Determine area of squares and rectangles Geometric Figures Use tools to measure angles Understand half and full rotations Determine that 3 angles in a triangle always total 180° Geometry Two-Dimensional Figures Describe/classify triangles by sides as scalene, isosceles, and equilateral Identify/compare properties of geometric figures Examine/compare angles of geometric figures Identify center, diameter, and radius of circle Two-Dimensional Figures Define/classify triangles by angles Describe parallel and perpendicular lines in plane geometric figures Examine and classify quadrilaterals (parallelograms, squares, rectangles, trapezoids, rhombi) by their properties Compare and contrast relationships among quadrilaterals Locate and name a point in the first quadrant Graph ordered pairs in first quadrant Two-Dimensional Figures Understand congruence of geometric figures and correspondence of vertices, sides, and angles Understand the relationship of the circumference of a circle to its diameter is pi (π ≈ 3.14) Three-Dimensional Figures Compare and contrast cube and rectangular prism by faces, edges, and vertices Describe parallel and perpendicular lines in a rectangular prism Build models for 3-D figures using nets and other representations 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.