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# CCGPS Math Standards K-5

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### CCGPS Math Standards K-5

1. 1. Common Core Georgia Performance Standards CCGPS MathematicsStandardsKindergarten-Fifth Grade
7. 7. Georgia Department of Education7 Look for and make use of structure.Mathematically proficient students look closely to discern a pattern or structure. Young students, forexample, might notice that three and seven more is the same amount as seven and three more, or theymay sort a collection of shapes according to how many sides the shapes have. Later, students will see 7× 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributiveproperty. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. Theyrecognize the significance of an existing line in a geometric figure and can use the strategy of drawing anauxiliary line for solving problems. They also can step back for an overview and shift perspective. Theycan see complicated things, such as some algebraic expressions, as single objects or as being composedof several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a squareand use that to realize that its value cannot be more than 5 for any real numbers x and y.8 Look for and express regularity in repeated reasoning.Mathematically proficient students notice if calculations are repeated, and look both for generalmethods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that theyare repeating the same calculations over and over again, and conclude they have a repeating decimal.By paying attention to the calculation of slope as they repeatedly check whether points are on the linethrough (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3.Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x –1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As theywork to solve a problem, mathematically proficient students maintain oversight of the process, whileattending to the details. They continually evaluate the reasonableness of their intermediate results.Connecting the Standards for Mathematical Practice to the Standards for Mathematical ContentThe Standards for Mathematical Practice describe ways in which developing student practitioners of thediscipline of mathematics increasingly ought to engage with the subject matter as they grow inmathematical maturity and expertise throughout the elementary, middle and high school years.Designers of curricula, assessments, and professional development should all attend to the need toconnect the mathematical practices to mathematical content in mathematics instruction. The Standardsfor Mathematical Content are a balanced combination of procedure and understanding. Expectationsthat begin with the word “understand” are often especially good opportunities to connect the practicesto the content. Students who lack understanding of a topic may rely on procedures too heavily. Withouta flexible base from which to work, they may be less likely to consider analogous problems, representproblems coherently, justify conclusions, apply the mathematics to practical situations, use technologymindfully to work with the mathematics, explain the mathematics accurately to other students, stepback for an overview, or deviate from a known procedure to find a shortcut. In short, a lack ofunderstanding effectively prevents a student from engaging in the mathematical practices. In thisrespect, those content standards which set an expectation of understanding are potential “points ofintersection” between the Standards for Mathematical Content and the Standards for MathematicalPractice. These points of intersection are intended to be weighted toward central and generativeconcepts in the school mathematics curriculum that most merit the time, resources, innovativeenergies, and focus necessary to qualitatively improve the curriculum, instruction, assessment,professional development, and student achievement in mathematics. Georgia Department of Education Dr. John D. Barge, State School Superintendent August 19, 2011 Page 7 of 40 All Rights Reserved
11. 11. Georgia Department of EducationNumber and Operations in Base Ten K.NBTWork with numbers 11–19 to gain foundations for place value.MCCK.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones,e.g., by using objects or drawings, and record each composition or decomposition by a drawing orequation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two,three, four, five, six, seven, eight, or nine ones.Measurement and Data K.MDDescribe and compare measurable attributes.MCCK.MD.1 Describe measurable attributes of objects, such as length or weight. Describe severalmeasurable attributes of a single object.MCCK.MD.2 Directly compare two objects with a measurable attribute in common, to see whichobject has “more of”/“less of” the attribute, and describe the difference. For example, directlycompare the heights of two children and describe one child as taller/shorter.Classify objects and count the number of objects in each category.MCCK.MD.3 Classify objects into given categories; count the numbers of objects in each category andsort the categories by count.3Geometry K.GIdentify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders,and spheres).MCCK.G.1 Describe objects in the environment using names of shapes, and describe the relativepositions of these objects using terms such as above, below, beside, in front of, behind, and next to.MCCK.G.2 Correctly name shapes regardless of their orientations or overall size.MCCK.G.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).3 Limit category counts to be less than or equal to 10. Georgia Department of Education Dr. John D. Barge, State School Superintendent August 19, 2011 Page 11 of 40 All Rights Reserved
12. 12. Georgia Department of EducationAnalyze, compare, create, and compose shapes.MCCK.G. 4 Analyze and compare two- and three-dimensional shapes, in different sizes andorientations, using informal language to describe their similarities, differences, parts (e.g., number ofsides and vertices/“corners”) and other attributes (e.g., having sides of equal length).MCCK.G. 5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls)and drawing shapes.MCCK.G. 6 Compose simple shapes to form larger shapes. For example, “Can you join these twotriangles with full sides touching to make a rectangle?” Georgia Department of Education Dr. John D. Barge, State School Superintendent August 19, 2011 Page 12 of 40 All Rights Reserved
17. 17. Georgia Department of EducationTell and write time.MCC1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.Represent and interpret data.MCC1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answerquestions about the total number of data points, how many in each category, and how many more orless are in one category than in another.Geometry 1.GReason with shapes and their attributes.MCC1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versusnon-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possessdefining attributes.MCC1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles,and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones,and right circular cylinders) to create a composite shape, and compose new shapes from thecomposite shape.6MCC1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares usingthe words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.Describe the whole as two of, or four of the shares. Understand for these examples that decomposinginto more equal shares creates smaller shares.6 Students do not need to learn formal names such as “right rectangular prism.” Georgia Department of Education Dr. John D. Barge, State School Superintendent August 19, 2011 Page 17 of 40 All Rights Reserved