West Virginia

Counting and Cardinality

• Know number names and the count sequence.

  • M.K.1 Count to 100 by ones and by tens.

    • Learn to count to 3 (K-B.1)
    • Count pictures - up to 3 (K-B.2)
    • Count on frames - up to 3 (K-B.5)
    • Learn to count to 5 (K-D.1)
    • Count pictures - up to 5 (K-D.2)
    • Count dots - 0 to 5 (K-D.5)
    • Count on frames - up to 5 (K-D.6)
    • What number comes next? - up to 5 (K-D.17)
    • Learn to count to 10 (K-J.1)
    • Count pictures - up to 10 (K-J.2)
    • Count dots - up to 10 (K-J.4)
    • Count on ten frames - up to 10 (K-J.6)
    • Count blocks - up to 10 (K-J.7)
    • What number comes next? - up to 10 (K-L.1)
    • Count pictures - up to 20 (K-EE.4)
    • Count dots - 0 to 20 (K-EE.5)
    • Count on ten frames - up to 20 (K-EE.6)
    • Count blocks - up to 20 (K-EE.7)
    • Count on a chart - up to 20 (K-GG.1)
    • Count on ten frames - up to 30 (K-JJ.1)
    • Count on a chart - up to 30 (K-JJ.2)
    • Count blocks - up to 30 (K-JJ.5)
    • Learn to skip-count by tens (K-KK.1)
    • Skip-count by tens (K-KK.2)
    • Count groups of ten (K-KK.3)
    • Count pictures - up to 100 (K-LL.3)
    • Count blocks - up to 100 (K-LL.4)
    • Count on the hundred chart (K-LL.5)
    • Sequences - count by ones or tens (K-LL.9)

  • M.K.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

    • Count up to find the next number - up to 5 (K-D.15)
    • Count up to find the next number - up to 10 (K-L.2)
    • Count forward - up to 10 (K-L.8)
    • Complete a sequence - up to 10 (K-L.10)
    • Count up to find the next number - up to 20 (K-GG.2)
    • Count forward - up to 20 (K-GG.6)
    • Complete an increasing sequence - up to 20 (K-GG.9)
    • Count forward - up to 30 (K-JJ.4)
    • Count forward on the hundred chart (K-LL.6)
    • Count up to find the next number - up to 100 (K-LL.7)
    • Count forward - up to 100 (K-LL.8)

  • M.K.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

    • Identify numbers - up to 3 (K-A.1)
    • Choose the number that you hear - up to 3 (K-A.2)
    • Count pictures - up to 3 (K-B.2)
    • Count on frames - up to 3 (K-B.5)
    • Identify numbers - 0 to 5 (K-C.3)
    • Choose the number that you hear - 0 to 5 (K-C.4)
    • Count pictures - up to 5 (K-D.2)
    • Count dots - 0 to 5 (K-D.5)
    • Count on frames - up to 5 (K-D.6)
    • Identify numbers - up to 10 (K-I.1)
    • Choose the number that you hear - up to 10 (K-I.2)
    • Names of numbers - up to 10 (K-I.3)
    • Count pictures - up to 10 (K-J.2)
    • Count dots - up to 10 (K-J.4)
    • Count on ten frames - up to 10 (K-J.6)
    • Count blocks - up to 10 (K-J.7)
    • Identify numbers - up to 20 (K-DD.1)
    • Write the number you hear - up to 20 (K-DD.2)
    • Names of numbers - up to 20 (K-DD.3)
    • Count pictures - up to 20 (K-EE.4)
    • Count dots - 0 to 20 (K-EE.5)
    • Count on ten frames - up to 20 (K-EE.6)
    • Count blocks - up to 20 (K-EE.7)

• Count to tell the number of objects.

  • M.K.4 Understand the relationship between numbers and quantities; connect counting to cardinality.

    • M.K.4.a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

      • Learn to count to 3 (K-B.1)
      • Count pictures - up to 3 (K-B.2)
      • Count on frames - up to 3 (K-B.5)
      • Count out stickers - up to 3 (K-B.6)
      • Show numbers on frames - up to 3 (K-B.8)
      • Learn to count to 5 (K-D.1)
      • Count pictures - up to 5 (K-D.2)
      • Count dots - 0 to 5 (K-D.5)
      • Count on frames - up to 5 (K-D.6)
      • Count out stickers - up to 5 (K-D.9)
      • Show numbers on frames - up to 5 (K-D.11)
      • Learn to count to 10 (K-J.1)
      • Count pictures - up to 10 (K-J.2)
      • Count dots - up to 10 (K-J.4)
      • Count on ten frames - up to 10 (K-J.6)
      • Count out stickers - up to 10 (K-J.11)
      • Show numbers on ten frames - up to 10 (K-J.13)
      • Count pictures - up to 20 (K-EE.4)
      • Count dots - 0 to 20 (K-EE.5)
      • Count on ten frames - up to 20 (K-EE.6)
      • Count pictures in arrays and circles - up to 20 (K-EE.8)
      • Show numbers on ten frames - up to 20 (K-EE.9)

    • M.K.4.b Understand that the last number name said tells the number of objects counted and the number of objects is the same regardless of their arrangement or the order in which they were counted.

      • Learn to count to 3 (K-B.1)
      • Represent numbers with pictures - up to 3 (K-B.9)
      • Represent numbers with shapes - up to 3 (K-B.10)
      • Learn to count to 5 (K-D.1)
      • Represent numbers with pictures - up to 5 (K-D.12)
      • Represent numbers with shapes - up to 5 (K-D.14)
      • Learn to count to 10 (K-J.1)
      • Represent numbers - up to 10 (K-J.14)
      • Represent numbers - up to 20 (K-EE.10)

    • M.K.4.c Understand that each successive number name refers to a quantity that is one larger.

      • One more with pictures - up to 5 (K-E.1)
      • One more on frames - up to 5 (K-E.2)
      • One more - up to 5 (K-E.3)
      • One more with pictures - up to 10 (K-K.1)
      • One more on frames - up to 10 (K-K.2)
      • One more - up to 10 (K-K.3)
      • One more - up to 20 (K-FF.1)

  • M.K.5 Count to answer questions (e.g., "How many?" ) about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

    • Count pictures - up to 3 (K-B.2)
    • Count shapes - up to 3 (K-B.3)
    • Count cubes - up to 3 (K-B.4)
    • Count on frames - up to 3 (K-B.5)
    • Count out stickers - up to 3 (K-B.6)
    • Show numbers with cubes - up to 3 (K-B.7)
    • Show numbers on frames - up to 3 (K-B.8)
    • Represent numbers with pictures - up to 3 (K-B.9)
    • Represent numbers with shapes - up to 3 (K-B.10)
    • Count pictures - up to 5 (K-D.2)
    • Count shapes in rows - up to 5 (K-D.3)
    • Count cubes - up to 5 (K-D.4)
    • Count dots - 0 to 5 (K-D.5)
    • Count on frames - up to 5 (K-D.6)
    • Count scattered pictures - up to 5 (K-D.7)
    • Count scattered shapes - up to 5 (K-D.8)
    • Count out stickers - up to 5 (K-D.9)
    • Show numbers with cubes - up to 5 (K-D.10)
    • Show numbers on frames - up to 5 (K-D.11)
    • Represent numbers with pictures - up to 5 (K-D.12)
    • Represent numbers with pictures - 0 to 5 (K-D.13)
    • Represent numbers with shapes - up to 5 (K-D.14)
    • Count pictures - up to 10 (K-J.2)
    • Count cubes - up to 10 (K-J.3)
    • Count dots - up to 10 (K-J.4)
    • Count shapes in rows - up to 10 (K-J.5)
    • Count on ten frames - up to 10 (K-J.6)
    • Count scattered pictures - up to 10 (K-J.8)
    • Count scattered shapes - up to 10 (K-J.9)
    • Count shapes in rings - up to 10 (K-J.10)
    • Count out stickers - up to 10 (K-J.11)
    • Show numbers with cubes - up to 10 (K-J.12)
    • Show numbers on ten frames - up to 10 (K-J.13)
    • Represent numbers - up to 10 (K-J.14)
    • Count pictures - up to 20 (K-EE.4)
    • Count dots - 0 to 20 (K-EE.5)
    • Count on ten frames - up to 20 (K-EE.6)
    • Count pictures in arrays and circles - up to 20 (K-EE.8)
    • Show numbers on ten frames - up to 20 (K-EE.9)
    • Represent numbers - up to 20 (K-EE.10)

• Compare numbers.

  • M.K.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group (e.g., by using matching and counting strategies).

    • Are there the same number? - up to 5 (K-F.1)
    • More - compare by matching up to 5 (K-F.3)
    • Fewer - compare by matching up to 5 (K-F.4)
    • Fewer and more - compare by matching up to 5 (K-F.5)
    • Fewer, more, and same - up to 5 (K-F.6)
    • Greater - compare by matching up to 5 (K-F.7)
    • Less - compare by matching up to 5 (K-F.8)
    • Are there enough? - up to 5 (K-F.9)
    • Fewer and more - compare by counting up to 5 (K-F.10)
    • Fewer and more - compare in a mixed group up to 5 (K-F.11)
    • Greater than, less than, or equal to - compare by counting up to 5 (K-F.12)
    • Count pictures and show a number that is greater, less, or equal - up to 5 (K-F.13)
    • Show a number greater than, less than, or equal to a given number up to 5 (K-F.14)
    • Fewer and more - compare by matching (K-M.1)
    • Fewer, more, and same (K-M.2)
    • Greater and less - compare by matching up to 10 (K-M.3)
    • Are there enough? (K-M.4)
    • Fewer and more - compare by counting (K-M.6)
    • Fewer and more - compare in a mixed group (K-M.7)
    • Greater than, less than, or equal to - compare by counting up to 10 (K-M.8)
    • Count pictures and show a number that is greater, less, or equal - up to 10 (K-M.9)
    • Show a number greater than, less than, or equal to a given number up to 10 (K-M.10)

  • M.K.7 Compare and order two numbers between 0-20 presented as written numerals.

    • Compare numbers up to 20 (K-HH.3)
    • Put numbers up to 20 in order (K-HH.4)

Operations and Algebraic Thinking

• Understand addition as putting together and adding to and understand subtraction as taking apart and taking from.

  • M.K.8 Represent addition and subtraction with strategies using objects, fingers, mental images, drawings, sounds (e.g., claps), and acting out situations, verbal explanations, expressions, and equations.

    • Put together numbers using cubes - sums up to 5 (K-N.1)
    • Build cube trains to add up to 5 - words (K-N.2)
    • Addition sentences up to 5 - which model matches? (K-N.3)
    • Addition sentences up to 5 - what does the model show? (K-N.4)
    • Write addition sentences for pictures - sums up to 5 (K-N.5)
    • Put together numbers using cubes - sums up to 10 (K-R.1)
    • Build cube trains to add up to 10 - words (K-R.2)
    • Addition sentences up to 10 - which model matches? (K-R.3)
    • Addition sentences up to 10 - what does the model show? (K-R.4)
    • Write addition sentences for pictures - sums up to 10 (K-R.5)
    • Turn words into an addition sentence - sums up to 10 (K-R.6)
    • Take away cubes - numbers up to 5 (K-V.1)
    • Subtraction sentences up to 5 - which model matches? (K-V.2)
    • Subtraction sentences up to 5 - what does the model show? (K-V.3)
    • Subtraction sentences up to 5 - what does the cube train show? (K-V.4)
    • Write subtraction sentences for pictures - up to 5 (K-V.5)
    • Take away cubes - numbers up to 10 (K-Y.1)
    • Subtraction sentences up to 10 - which model matches? (K-Y.2)
    • Subtraction sentences up to 10 - what does the model show? (K-Y.3)
    • Subtraction sentences up to 10 - what does the cube train show? (K-Y.4)
    • Write subtraction sentences for pictures - up to 10 (K-Y.5)
    • Turn words into a subtraction sentence - numbers up to 10 (K-Y.6)

  • M.K.9 Solve addition and subtraction word problems and add and subtract within 10 by using objects or drawings to represent the problem.

    • Add with cubes - sums up to 5 (K-O.1)
    • Build cube trains to add up to 5 - addition sentences (K-O.2)
    • Add with pictures - sums up to 5 (K-O.3)
    • Add two numbers - sums up to 5 (K-O.4)
    • Make a number using addition - sums up to 5 (K-P.5)
    • Build cube trains to solve addition word problems - sums up to 5 (K-Q.1)
    • Addition word problems with pictures - sums up to 5 (K-Q.2)
    • Write addition sentences for word problems with pictures - sums up to 5 (K-Q.3)
    • Addition word problems - sums up to 5 (K-Q.4)
    • Model and write addition sentences for word problems - sums up to 5 (K-Q.5)
    • Add with cubes - sums up to 10 (K-S.1)
    • Build cube trains to add up to 10 - addition sentences (K-S.2)
    • Add with pictures - sums up to 10 (K-S.3)
    • Add two numbers - sums up to 10 (K-S.5)
    • Complete the addition sentence to make 10 - with models (K-S.6)
    • Make a number using addition - sums up to 10 (K-T.8)
    • Build cube trains to solve addition word problems - sums up to 10 (K-U.1)
    • Addition word problems with pictures - sums up to 10 (K-U.2)
    • Write addition sentences for word problems with pictures - sums up to 10 (K-U.3)
    • Addition word problems - sums up to 10 (K-U.4)
    • Model and write addition sentences for word problems - sums up to 10 (K-U.5)
    • Subtract with cubes - numbers up to 5 (K-W.1)
    • Subtract with pictures - numbers up to 5 (K-W.2)
    • Subtract - numbers up to 5 (K-W.3)
    • Make a number using subtraction - numbers up to 5 (K-W.4)
    • Complete the subtraction sentence - numbers up to 5 (K-W.5)
    • Subtraction word problems with pictures - numbers up to 5 (K-X.1)
    • Write subtraction sentences for word problems with pictures - up to 5 (K-X.2)
    • Use cube trains to solve subtraction word problems - up to 5 (K-X.3)
    • Subtraction word problems - numbers up to 5 (K-X.4)
    • Model and write subtraction sentences for word problems - up to 5 (K-X.5)
    • Subtract with cubes - numbers up to 10 (K-Z.1)
    • Subtract with pictures - numbers up to 10 (K-Z.2)
    • Subtract - numbers up to 10 (K-Z.4)
    • Make a number using subtraction - numbers up to 10 (K-Z.5)
    • Subtraction word problems with pictures - numbers up to 10 (K-AA.1)
    • Write subtraction sentences for word problems with pictures - up to 10 (K-AA.2)
    • Use cube trains to solve subtraction word problems - up to 10 (K-AA.3)
    • Subtraction word problems - numbers up to 10 (K-AA.4)
    • Model and write subtraction sentences for word problems - up to 10 (K-AA.5)
    • Add or subtract - numbers up to 5 (K-BB.1)
    • Add or subtract - numbers up to 10 (K-BB.2)
    • Addition and subtraction - ways to make a number (K-BB.3)
    • Add and subtract with 0 (K-BB.6)
    • Addition and subtraction word problems with pictures (K-CC.1)
    • Use cube trains to solve addition and subtraction word problems - up to 10 (K-CC.2)
    • Addition and subtraction word problems (K-CC.3)
    • Model and write addition and subtraction sentences for word problems (K-CC.4)

  • M.K.10 Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

    • Complete the addition sentence - sums up to 5 (K-O.5)
    • Take apart numbers using cubes - sums up to 5 (K-P.1)
    • Make a number different ways using cubes - sums up to 5 (K-P.2)
    • Take apart numbers up to 5 - addition sentences (K-P.3)
    • Take apart numbers in different ways - sums up to 5 (K-P.4)
    • Make a number using addition - sums up to 5 (K-P.5)
    • Complete the addition sentence - sums up to 10 (K-S.8)
    • Take apart numbers using cubes - sums up to 10 (K-T.1)
    • Make a number different ways using cubes - sums up to 10 (K-T.2)
    • Decompose a number up to 10 (K-T.4)
    • Take apart numbers up to 10 - addition sentences (K-T.5)
    • Take apart numbers in different ways - sums up to 10 (K-T.7)
    • Make a number using addition - sums up to 10 (K-T.8)

  • M.K.11 For any number from 1 to 9, find the number that makes 10 when added to the given number by using objects or drawings, and record the answer with a drawing or equation.

    • Count to fill a ten frame (K-L.4)
    • Complete the addition sentence to make 10 - with models (K-S.6)
    • Complete the addition sentence to make 10 (K-S.7)
    • Take apart 10 using cubes (K-T.3)
    • Take apart 10 - addition sentences (K-T.6)

  • M.K.12 Fluently (efficiently, flexibly, and accurately) add and subtract within 5 using various strategies.

    • Add two numbers - sums up to 5 (K-O.4)
    • Complete the addition sentence - sums up to 5 (K-O.5)
    • Make a number using addition - sums up to 5 (K-P.5)
    • Subtract - numbers up to 5 (K-W.3)
    • Make a number using subtraction - numbers up to 5 (K-W.4)
    • Complete the subtraction sentence - numbers up to 5 (K-W.5)
    • Add or subtract - numbers up to 5 (K-BB.1)
    • Related facts with models - numbers up to 5 (K-BB.4)

• Recognize patterns.

  • M.K.13 Recognize and create recognizable patterns using colors, shapes, sizes, and sounds with support and guidance.

    • Color patterns (K-MM.1)
    • Size patterns (K-MM.2)
    • Shape patterns (K-MM.3)

Number and Operations in Base Ten

• Work with numbers 11–19 to gain foundations for place value.

  • M.K.14 Compose and decompose numbers from 11 to 19 into ten ones and larger two-digit numbers by using objects or drawings and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones (one ten) and one, two, three, four, five, six, seven, eight, or nine ones.

    • Make teen numbers: words (K-II.2)
    • Take apart teen numbers: words (K-II.4)
    • Understand tens and ones - up to 20 (K-II.5)
    • Make and take apart teen numbers: tens and ones (K-II.6)
    • Make teen numbers: addition sentences (K-II.8)
    • Take apart teen numbers: addition sentences (K-II.10)
    • Make and take apart teen numbers: addition sentences (K-II.12)

Measurement and Data

• Describe and compare measurable attributes.

  • M.K.15 Describe measurable attributes of objects, such as length or weight and describe several measurable attributes of a single object.

    • Long and short (K-WW.1)
    • Tall and short (K-WW.2)
    • Wide and narrow (K-WW.3)
    • Light and heavy (K-WW.4)
    • Holds more or less (K-WW.5)
    • Covers more or less (K-WW.6)
    • Compare size, weight, and capacity (K-WW.7)
    • Should you measure size, weight, or capacity? (K-WW.8)

  • M.K.16 Directly compare two objects with a measurable attribute in common, to see which object has "more of" or "less of" the attribute and describe the difference.

    • Long and short (K-WW.1)
    • Tall and short (K-WW.2)
    • Wide and narrow (K-WW.3)
    • Light and heavy (K-WW.4)
    • Holds more or less (K-WW.5)
    • Covers more or less (K-WW.6)
    • Compare size, weight, and capacity (K-WW.7)

• Classify objects and count the number of objects in each category.

  • M.K.17 Classify objects into given categories, count the numbers of objects in each category, and sort the categories by count. Category counts should be limited to less than or equal to 10. (e.g., Identify coins and sort them into groups of 5s or 10s.)

    • Fewer and more - compare by counting (K-M.6)
    • Fewer and more - compare in a mixed group (K-M.7)
    • Different (K-OO.1)
    • Same (K-OO.2)
    • Same and different (K-OO.3)
    • Sort circles (K-PP.8)
    • Sort two-dimensional shapes (K-PP.9)
    • Classify shapes by color (K-UU.1)
    • Classify and sort by color (K-UU.2)
    • Classify and sort by shape (K-UU.3)
    • Classify and sort (K-UU.4)
    • Classify, sort, and count (K-UU.5)
    • Sort, count, and compare (K-UU.6)
    • Count shapes in a Venn diagram (K-UU.7)
    • Sort shapes into a Venn diagram (K-UU.8)
    • Make picture graphs (K-VV.2)

• Work with money.

  • M.K.18 Identify coins: penny, nickel, dime, quarter.

    • Coin names - penny through quarter (K-YY.1)

  • M.K.19 Count pennies to 20.

    • Count money - pennies only (K-YY.3)

Geometry

• Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

  • M.K.20 Describe objects in the environment using names of shapes and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind and next to.

    • In front of and behind (K-NN.1)
    • Inside and outside (K-NN.2)
    • Above and below (K-NN.3)
    • Beside and next to (K-NN.4)
    • Left, middle, and right (K-NN.5)
    • Top, middle, and bottom (K-NN.6)
    • Location in a grid (K-NN.7)
    • Two-dimensional shapes in the real world (K-SS.1)
    • Three-dimensional shapes in the real world I (K-SS.2)
    • Three-dimensional shapes in the real world II (K-SS.3)
    • Three-dimensional shapes - above and below (K-SS.4)
    • Three-dimensional shapes - beside and next to (K-SS.5)

  • M.K.21 Correctly name shapes regardless of their orientations or overall size.

    • Circles (K-PP.1)
    • Triangles (K-PP.2)
    • Rectangles (K-PP.3)
    • Squares (K-PP.4)
    • Hexagons (K-PP.5)
    • Select two-dimensional shapes (K-PP.6)
    • Name the two-dimensional shape (K-PP.7)
    • Sort circles (K-PP.8)
    • Sort two-dimensional shapes (K-PP.9)
    • Spheres (K-RR.3)
    • Cubes (K-RR.4)
    • Cones (K-RR.5)
    • Cylinders (K-RR.6)
    • Select three-dimensional shapes (K-RR.7)
    • Name the three-dimensional shape (K-RR.8)

  • M.K.22 Using real-life objects, identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").

    • Flat and solid shapes (K-RR.1)

• Analyze, compare, create, and compose shapes.

  • M.K.23 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners"), and other attributes (e.g., having sides of equal length).

    • Curved parts (K-QQ.1)
    • Count corners (K-QQ.2)
    • Square corners (K-QQ.3)
    • Count sides (K-QQ.4)
    • Equal sides (K-QQ.5)
    • Count sides and corners (K-QQ.6)
    • Compare sides and corners (K-QQ.7)
    • Compare shapes using attributes (K-QQ.8)
    • Describe solid shapes (K-RR.2)
    • Identify shapes traced from solids (K-RR.9)

  • M.K.24 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

  • M.K.25 Compose simple shapes to form larger shapes (e.g., "Can these two triangles, with full sides touching, join to make a rectangle?").

    • Compose simple two-dimensional shapes (K-PP.10)
    • Build and take apart three-dimensional shapes (K-RR.10)