| Kindergarten Draft Mathematics Standards – Technical Review | |||
| Code | 2010 Standards | Refinement/Draft | Notes |
| Counting & Cardinality (CC) | |||
| Counting & Cardinality | Know number names and the count sequence. | ||
| K.CC.A.1 | Count to 100 by ones and by tens. | No refinement needed to the existing standard | No refinement needed on this standard since it meets criteria for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of counting, cardinality, and number sense. |
| K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1) | Count forward beginning from a given number instead of having to begin at 1. | Removed “within the known sequence” because of possible misinterpretation. Removed parenthesis, and added “instead of having to begin at 1” to standard. |
| K.CC.A.3 | Write numbers from 0–20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects). | No refinement needed to the existing standard | No refinement needed on this standard since it meets criteria for clarity, cognitive demand, and measurability. |
| Counting & Cardinality | Understand the relationship between numbers and quantities. | ||
| K.CC.B.4 | Connect counting to cardinality. 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. b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. c. Understand that each successive number name refers to a quantity that is one larger. |
No refinement needed to the existing standard | No refinement needed on this standard since it meets criteria for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of counting, cardinality, and number sense. |
| K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. | Count to answer questions about “how many?” when 20 or fewer objects are arranged in a line, a rectangular array, or a circle or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. | The standard was reworded to clarify the meaning and intent. |
| Counting & Cardinality | Compare numbers and quantities. | ||
| K.CC.C.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. (Include groups with up to ten objects) | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. (Include groups with up to ten objects.) | The example was deleted from the standard because it did not promote clarity. |
| K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | No refinement needed to the existing standard | No refinement needed to the existing standard as this is a neccesary standard in the progression of understanding of numeric representation of value. It meets criteria for clarity, cognitive demand, and measurability. |
| Operations and Algebraic Thinking (OA) | |||
| Operations and Algebraic Thinking | Understand addition as putting together and adding to, and understanding subtraction as taking apart and taking from. | ||
| K.0A.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (Drawings need not show details, but should show the mathematics in the problems. This applies wherever drawings are mentioned in the Standards.) | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations. | The example was deleted from the standard because it did not promote clarity. The standard now meets criteria for clarity, cognitive demand, and measurability. |
| K.0A.A.2 | Use addition and subtraction through 10 to solve word problems involving multiple problem types (See Table 1), using a variety of strategies. | Use addition and subtraction through 10 to solve word problems involving multiple problem types (See Table 1), using a variety of strategies. | The example was deleted from the standard because it did not promote clarity. “Using a variety of strategies” was added to maintain consistency. ” (See Table 1)” was added to clarify problem types appropriate to Kindergarten. |
| K.0A.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings, and record each decomposition with a drawing or equation. | ” e.g.” was removed but “by using objects or drawings” remained for clarification of the standard. The word “by” was changed to “with a drawing or equation” to clarify the language of the standard. The example was deleted from the standard because it did not promote clarity. |
| K.0A.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | 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. | ” e.g.” was removed but “by using objects or drawings” remained for clarification of the standard. |
| K.0A.A.5 | Fluently add and subtract within 5. | Fluently add and subtract through 5. | “Within”, was changed to “through”, to make sure the number 5 was understood to be included. |
| Number and Operations in Base Ten (NBT) | |||
| Number & Operations in Base Ten | Work with numbers 11-19 to gain foundations for place value. | ||
| K.NBT.A.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 or equation (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. | Compose and decompose numbers from 11 to 19 into ten ones and additional ones by using objects or drawings and record each composition or decomposition with a drawing or equation. | The phrase, “understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones” was deleted because it is already stated within the existing standard. The word “further” was changed to “additional” to clarify the language of the standard. The word “by” was changed to “with” to clarify the language of the standard. The “e.g” was removed and “by using objects or drawings” remained. The example of the equation was deleted as it does not provide limits to the standard. |
| Number & Operations in Base Ten | Use place value understanding and properties of operations to add and subtract. | ||
| K.NBT.B.2 | Demonstrate conceptual understanding of addition and subtraction through 10 using a variety of strategies. | This is a new standard that was added to adhere to the progression of whole number fluency from Kindergarten-4th grade. | |
| Measurement & Data (MD) | |||
| Measurement & Data | Describe and compare measurable attributes. | ||
| K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Describe several measurable attributes of a single object such as length and weight. | Two sentences were combined due to redundancy in the standard and provide clarity. |
| K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. | 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. | The example was deleted because it does not provide clarity or limit of the standard. |
| Measurement & Data | Classify objects and count the number of objects in categories. | Classify objects and count the number of objects in each category. | Minor wording changes for clarity. |
| K.MD.B.3 | Classify objects or people into given categoires; count the number in each cateogry and sort the cateogires by count. (Note: limit category counts to be less than or equal to 10.) | No refinement needed to the existing standard | Per public comment about sorting, it is included in this standard. Identification is inherent in classification and therefore is implied in the standard, so there was no refinement made to the standard. This is a necessary standard in the progression of measurement and data. |
| Geometry (G) | |||
| Geometry | Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). | Identify and describe shapes. | Removed the list of shapes since K.G.A.3 and K.G.B.4 state 2-D and 3-D shapes. |
| K.G.A.1 | 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. | No refinement needed to the existing standard | No refinement needed on this standard since it meets criteria for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of geometry. |
| K.G.A.2 | Correctly name shapes regardless of their orientation or overall size. | No refinement needed to the existing standard | No refinement needed on this standard since it meets criteria for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of geometry. |
| K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | No refinement needed to the existing standard | No refinement needed on this standard since it meets criteria for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of geometry. |
| Geometry | Analyze, compare, create, and compose shapes. | ||
| K.G.B.4 | 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). | 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. | The example was deleted from the standard because it did not promote clarity or limits to the standard. |
| K.G.B.5 | Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. | Model shapes in the world by building and drawing shapes. | The examples were deleted as they limited the standard. The phrase “from components” was deleted as it did not provide clarity to the standard. |
| K.G.B.6 | Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” | Model shapes in the world by building and drawing shapes. | The example was deleted from the standard because it did not promote clarity. |
| K.MP | Standards for Mathematical Practice | ||
| K.MP.1 | Make sense of problems and persevere in solving them. | Make sense of problems and persevere in solving them. Mathematically proficient students explain to themselves the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. While engaging in productive struggle to solve a problem, they continually ask themselves, “Does this make sense?” to monitor and evaluate their progress and change course if necessary. Once they have a solution, they look back at the problem to determine if the solution is reasonable and accurate. Mathematically proficient students check their solutions to problems using different methods, approaches, or representations. They also compare and understand different representations of problems and different solution pathways, both their own and those of others. | |
| K.MP.2 | Reason abstractly and quantitatively. | Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. Students can contextualize and decontextualize problems involving quantitative relationships. They contextualize quantities, operations, and expressions by describing a corresponding situation. They decontextualize a situation by representing it symbolically. As they manipulate the symbols, they can pause as needed to access the meaning of the numbers, the units, and the operations that the symbols represent. Mathematically proficient students know and flexibly use different properties of operations, numbers, and geometric objects and when appropriate they interpret their solution in terms of the context. | |
| K.MP.3 | Construct viable arguments and critique the reasoning of others. | Construct viable arguments and critique the reasoning of others. Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming, questioning, or debating the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others. | |
| K.MP.4 | Model with mathematics. | Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. | |
| K.MP.5 | Use appropriate tools strategically. | Use appropriate tools strategically. Mathematically proficient students consider available tools when solving a mathematical problem. They choose tools that are relevant and useful to the problem at hand. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful; recognizing both the insight to be gained and their limitations. Students deepen their understanding of mathematical concepts when using tools to visualize, explore, compare, communicate, make and test predictions, and understand the thinking of others. | |
| K.MP.6 | Attend to precision. | Attend to precision. Mathematically proficient students clearly communicate to others and craft careful explanations to convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely. | |
| K.MP.7 | Look for and make use of structure. | Look for and make use of structure. Mathematically proficient students use structure and patterns to provide form and stability when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed. | |
| K.MP.8 | Look for and express regularity in repeated reasoning. | Look for and express regularity in repeated reasoning. Mathematically proficient students look for and describe regularities as they solve multiple related problems. They formulate conjectures about what they notice and communicate observations with precision. While solving problems, students maintain oversight of the process and continually evaluate the reasonableness of their results. This informs and strengthens their understanding of the structure of mathematics which leads to fluency. | |
