Simple Solutions Standards Mapping
Simple SolutionsStandards MappingNorth CarolinaStandards forMathematical PracticeGradesK-8
Table of ContentsIntroduction.1Grade K.2Grade 1.4Grade 2.6Grade 3.8Grade 4.11Grade 5.14Grade 6.18Grade 7. 21Grade 8. 24
IntroductionThe purpose of this document is to demonstrate how Simple SolutionsStandards-Based Mathematics aligns with the North Carolina Standards forMathematical Practice. Each grade document aligns the standards fromthe Simple Solutions Standards-Based Mathematics series to the standardsapproved by the North Carolina Department of Public Instruction, andhighlights the standards and eligible content identified within the NorthCarolina Standards for Mathematical Practice.Simple Solutions Website:https://simplesolutions.org/North Carolina Department of Public tion-directory/departmentpublic-instructionNorth Carolina Standards for Mathematical f
Level K - MathematicsNorth Carolina Standards for Mathematical PracticeSimple Solutions StandardsCounting and Cardinality (CC)Know number names and recognize patterns in the counting sequence by:Count to 100 by ones and by tens.NC.K.CC.1 Counting to 100 by ones.K.CC.1 Counting to 100 by tens.Count forward beginning from a given number within the known sequence, instead ofCount forward beginning from a given number within the known sequence (instead ofNC.K.CC.2K.CC.2having to begin at 1.having to begin at 1).Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20,Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20NC.K.CC.3K.CC.3with 0 representing a count of no objects.(with 0 representing a count of no objects).Understand the relationship between numbers and quantities.NC.K.CC.4 When counting objects, say the number names in the standard order, pairing each object with one and only one numbername and each number name with one and only one object (one-to-one correspondence). Recognize that the last number named tells the number of objects counted regardless of their arrangement (cardinality). State the number of objects in a group, of up to 5 objects, without counting the objects (perceptual subitizing).K.CC.4Understand the relationship between numbers and quantities; connect counting tocardinality.K.CC.5Count to answer "how many?" questions about as many as 20 things arranged in a line, arectangular array, or a circle, or as many as 10 things in a scattered configuration; given anumber from 1-20, count out that many objects.Count to answer “How many?” in the following situations:NC.K.CC.5NC.K.CC.6NC.K.CC.7 Given a number from 1–20, count out that many objects. Given up to 20 objects, name the next successive number when an object is added, recognizing the quantity is onemore/greater. Given 20 objects arranged in a line, a rectangular array, and a circle, identify how many. Given 10 objects in a scattered arrangement, identify how many.Identify whether the number of objects in one group is greater than, less than, or equalto the number of objects in another group, e.g., by using matching and countingstrategies.Compare two numbers, within 10, presented as written numerals.K.CC.7 Compare two numbers between 1 and 10 presented as written numerals.Number and Operations in Base Ten (NBT)Identify whether the number of objects in one group is greater than, less than, or equal tothe number of objects in another group, e.g., by using matching and counting strategies.Compose and decompose numbers from 11 to 19 into ten ones and some further ones by:NC.K.NBT.1 Using objects or drawings. Recording each composition or decomposition by a drawing or expression. Understanding that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.K.CC.6Compose 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 aK.NBT.1drawing or equation (such as 18 10 8); understand that these numbers are composedof ten ones and one, two, three, four, five, six, seven, eight, or nine ones.Operations and Algebraic ThinNC.King (OA)Represent addition and subtraction, within 10:NC.K.OA.1 Use a variety of representations such as objects, fingers, mental images, drawings, sounds, acting out situations, verbalexplanations, or expressions. Demonstrate understanding of addition and subtraction by making connections among representations.Solve addition and subtraction word problems, within 10, using objects or drawings toNC.K.OA.2 represent the problem, when solving: Add to/Take From-Result Unknown Put Together/ Take Apart (Total Unknown and Two Addends Unknown)K.OA.1Represent addition and subtraction with objects, fingers, mental images, drawings,sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.K.OA.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., byusing objects or drawings to represent the problem.NC.K.OA.3Decompose numbers less than or equal to 10 into pairs in more than one way usingobjects or drawings, and record each decomposition by a drawing or expression.K.OA.3NC.K.OA.4For any number from 0 to 10, find the number that makes 10 when added to the givennumber using objects or drawings, and record the answer with a drawing or expression.K.OA.4NC.K.OA.5 Demonstrate fluency with addition and subtraction within 5.NC.K.OA.6 Recognize and combine groups with totals up to 5 (conceptual subitizing).Simple Solutions Learning, Inc.K.OA.502/01/20212Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., byusing objects or drawings, and record each decomposition by a drawing or equation.(e.g., 5 2 3 and 5 4 1).For any number from 1 to 9, find the number that makes 10 when added to the givennumber, e.g., by using objects or drawings, and record the answer with a drawing orequation.Fluently add and subtract within 5.Level K Mathematics Page 1 of 26
Level K - MathematicsNorth Carolina Standards for Mathematical .K.G.6Geometry (G)Describe objects in the environment using names of shapes, and describe the relativepositions of objects using positional terms.Correctly name squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders,and spheres regardless of their orientations or overall size.Identify squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, andspheres as two-dimensional or three-dimensional.Analyze and compare two- and three-dimensional shapes, in different sizes andorientations, using informal language to describe their similarities, differences, attributesand other properties.Model shapes in the world by:K.G.1Describe 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 .K.G.2Correctly name shapes regardless of their orientations or overall size.K.G.3Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").K.G.4K.G.5 Building and drawing triangles, rectangles, squares, hexagons, circles. Building cubes, cones, spheres, and cylinders.Simple Solutions StandardsAnalyze and compare two- and three-dimensional shapes, in different sizes andorientations, using informal language to describe their similarities, differences, parts(e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides ofequal length).Model shapes in the world by building shapes from components (e.g., sticks and clayballs) and drawing shapes.K.G.6 Compose simple shapes to form larger shapes.Measurement and Data (MD)Describe measurable attributes of objects; and describe several different measurableDescribe measurable attributes of objects, such as length or weight. Describe severalNC.K.MD.1K.MD.1attributes of a single objectmeasurable attributes of a single object.Directly compare two objects with a measurable attribute in common, to see whichDirectly compare two objects with a measurable attribute in common, to see whichNC.K.MD.2K.MD.2object has “more of”/“less of” the attribute, and describe the difference.object has "more of"/"less of" the attribute, and describe the difference.Classify objects into given categories; count the numbers of objects in each category andClassify objects into given categories; count the numbers of objects in each category andNC.K.MD.3K.MD.3sort the categories by count.sort the categories by count.Compose larger shapes from simple shapes.Simple Solutions Learning, Inc.02/01/20213Level K Mathematics Page 2 of 26
Level 1 - MathematicsNorth Carolina Standards for Mathematical PracticeNumber and Operations in Base Ten (NBT)NC.1.NBT.1 Count to 150, starting at any number less than 150.1.NBT.1NC.1.NBT.7 Read and write numerals, and represent a number of objects with a written numeral, to 100.Simple Solutions StandardsCount to 120, starting at any number less than 120. In this range, read and write numerals and representa number of objects with a written numeral.Understand that the two digits of a two-digit number represent amounts of tens and ones.NC.1.NBT.2NC.1.NBT.3 Unitize by making a ten from a collection of ten ones. Model the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Demonstrate that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens, with 0 ones.Compare two two-digit numbers based on the value of the tens and ones digits, recording the resultsof comparisons with the symbols , , and . A two-digit number and a one-digit number A two-digit number and a multiple of 10NC.1.NBT.6NC.1.OA.1Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count;explain the reasoning used.Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90, explaining thereasoning, using: Concrete models and drawings Number lines Strategies based on place value Properties of operations The relationship between addition and subtraction1.NBT.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results ofcomparisons with the symbols , , and .Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digitnumber and a multiple of 10, using concrete models or drawings and strategies based on place value,1.NBT.4 properties of operations, and/or the relationship between addition and subtraction; relate the strategyto a written method and explain the reasoning used. Understand that in adding two-digit numbers, oneadds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.Using concrete models or drawings, strategies based on place value, properties of operations, andNC.1.NBT.4 explaining the reasoning used, add, within 100, in the following situations:NC.1.NBT.51.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.1.NBT.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count;explain the reasoning used.Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zerodifferences), using concrete models or drawings and strategies based on place value, properties of1.NBT.6operations, and/or the relationship between addition and subtraction; relate the strategy to a writtenmethod and explain the reasoning used.Operations and Algebraic Thinking (OA)Represent and solve addition and subtraction word problems, within 20, with unknowns, by usingobjects, drawings, and equations with a symbol for the unknown number to represent the problem,when solving: Add to/Take from-Change Unknown Put together/Take Apart-Addend Unknown Compare-Difference UnknownUse addition and subtraction within 20 to solve word problems involving situations of adding to, taking1.OA.1 from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by usingobjects, drawings, and equations with a symbol for the unknown number to represent the problem.NC.1.OA.2Represent and solve word problems that call for addition of three whole numbers whose sum is lessthan or equal to 20, by using objects, drawings, and equations with a symbol for the unknown number.Solve word problems that call for addition of three whole numbers whose sum is less than or equal to1.OA.2 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to representthe problem.NC.1.OA.3Apply the commutative and associative properties as strategies for solving addition problems.1.OA.3 Apply properties of operations as strategies to add and OA.8Solve an unknown-addend problem, within 20, by using addition strategies and/or changing it to asubtraction problem.Add and subtract, within 20, using strategies such as: Counting on Making ten Decomposing a number leading to a ten Using the relationship between addition and subtraction Using a number line Creating equivalent but simpler or known sumsDemonstrate fluency with addition and subtraction within 10.Apply understanding of the equal sign to determine if equations involving addition and subtractionare true.Determine the unknown whole number in an addition or subtraction equation involving three wholenumbers.Simple Solutions Learning, Inc.1.OA.4 Understand subtraction as an unknown-addend problem.Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategiessuch as counting on; making ten (e.g., 8 6 8 2 4 10 4 14); decomposing a number leading toa ten (e.g., 13 - 4 13 - 3 - 1 10 - 1 9); using the relationship between addition and subtraction (e.g.,1.OA.6knowing that 8 4 12, one knows 12 - 8 4); and creating equivalent but easier or known sums (e.g.,adding 6 7 by creating the known equivalent6 6 1 12 1 13).Understand the meaning of the equal sign, and determine if equations involving addition andsubtraction are true or false.Determine the unknown whole number in an addition or subtraction equation relating three whole1.OA.8numbers.1.OA.702/01/20214Level 1 Mathematics Page 3 of 26
Level 1 - MathematicsNorth Carolina Standards for Mathematical PracticeNC.1.G.1Geometry (G)Distinguish between defining and non-defining attributes and create shapes with defining attributesby:1.G.1 Building and drawing triangles, rectangles, squares, trapezoids, hexagons, circles. Building cubes, right rectangular prisms, right circular cones, spheres, and right circular cylinders.Create composite shapes by:NC.1.G.2 Making a two-dimensional composite shape using rectangles, squares, trapezoids, triangles, and half-circles naming the components of thenew shape. Making a three-dimensional composite shape using cubes, rectangular prisms, cones, and cylinders, naming the components of the newshape.Partition circles and rectangles into two and four equal shares.NC.1.G.3NC.1.MD.1 Describe the shares as halves and fourths, as half of and fourth of. Describe the whole as two of, or four of the shares. Explain that decomposing into more equal shares creates smaller shares.1.G.2Simple Solutions StandardsDistinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-definingattributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quartercircles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and rightcircular cylinders) to create a composite shape, and compose new shapes from the composite shape.Partition circles and rectangles into two and four equal shares, describe the shares using the wordshalves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole astwo of, or four of the shares. Understand for these examples that decomposing into more equal sharescreates smaller shares.Measurement and Data (MD)1.G.3Order three objects by length; compare the lengths of two objects indirectly by using a third object.1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.Measure lengths with non-standard units. Express the length of an object as a whole number of non-standard length units. Measure by laying multiple copies of a shorter object (the length unit) end to end (iterating) with no gaps or overlaps.Express the length of an object as a whole number of length units, by laying multiple copies of a shorter1.MD.2 object (the length unit) end to end; understand that the length measurement of an object is the numberof same-size length units that span it with no gaps or overlaps.NC.1.MD.3Tell and write time in hours and half-hours using analog and digital clocks.1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.NC.1.MD.4Organize, represent, and interpret data with up to three categories. Ask and answer questions about the total number of data points.Organize, represent, and interpret data with up to three categories; ask and answer questions about the1.MD.4 total number of data points, how many in each category, and how many more or less are in onecategory than in another.NC.1.MD.2NC.1.MD.5 Ask and answer questions about how many in each category. Ask and answer questions about how many more or less are in one category than in another.Identify quarters, dimes, and nickels and relate their values to pennies.Simple Solutions Learning, Inc.2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using and symbolsPrep appropriately. (2.MD.8 Appears in Level 1 as "Prep")02/01/20215Level 1 Mathematics Page 4 of 26
Level 2 - MathematicsNorth Carolina Standards for Mathematical PracticeSimple Solutions StandardsNumber and Operations in Base Ten (NBT)Understand that the three digits of a three-digit number represent amounts ofhundreds, tens, and ones.Understand that the three digits of a three-digit number represent amounts ofNC.2.NBT.1 Unitize by making a hundred from a collection of ten tens.2.NBT.1hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Demonstrate that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven,eight, or nine hundreds, with 0 tens and 0 ones. Compose and decompose numbers using various groupings of hundreds, tens, and ones.NC.2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s.Read and write numbers to 1000 using base-ten numerals, number names, andNC.2.NBT.3expanded form.Compare two three-digit numbers based on meanings of the hundreds, tens, andNC.2.NBT.4ones digits, using , , and symbols to r
Mathematical Practice. Each grade document aligns the standards from the Simple Solutions Standards-Based Mathematics series to the standards approved by the North Carolina Department of Public Instruction, and highlights the standards and eligible content identified within the North Carolina Standards for Mathematical Practice.
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