| 1st Grade Draft Mathematics Standards – Technical Review | |||
| Code | 2010 Standards | Refinement/Draft | Notes |
| Operations and Algebraic Thinking (OA) | |||
| 1.OA.A | Represent and solve problems involving addition and subtraction. | ||
| 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (See Table 1.) | Use addition and subtraction through 20 to solve word problems involving multiple problem types (see Table 1) using a variety of strategies. | Individual problem types were removed to help with clarity with reference to Table 1 that includes all the problem types. The examples were deleted from the standard as they illustrate instruction. The word “within” was changed to “through” to encompass the number 20. |
| 1.OA.A.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (See Table 1) | “e.g.” and “by” were deleted but the descriptors were kept to maintain the scope of the standard. it meets criteria for clarity, cognitive demand, and measurability. It now meets criteria for clarity, cognitive demand, and measurability. |
| 1.OA.B | Understand and apply properties of operations and the relationship between addition and subtraction. | ||
| 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students need not use formal terms for these properties.) | Apply properties of operations (commutative and associative properties of addition) as strategies to add and subtract through 20. (Students need not use formal terms for these properties.) | The examples were deleted from the standard as they did not clarify the limit of the standard. The standard was clarified to state “within 20” for consistency within the domain.The word “within” was changed to “through” to encompass the number 20. |
| 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. | Understand subtraction through 20 as an unknown-addend problem. (See Table 1) | The example was deleted from the standard as it did not clarify the limit of the standard. “within 20” was added to the standard to provide consistency and clarity within the domain. The word “within” was changed to “through” to encompass the number 10. |
| 1.OA.C | Add and subtract within 20. | Add and subtract through 10. | The number for the cluster was changed to 10 to reflect the fluency progression from kindergarten to second grade. The word “within” was changed to “through” to encompass the number 10. |
| 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Remove this standard | This is a strategy used when adding and subtracting and does not meet the definition for a standard. |
| 1.OA.C.5 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing 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 equivalent 6 + 6 + 1 = 12 + 1 = 13). | Fluently add and subtract through 10. | The examples were deleted from the standard as they did not clarify the limit of the standard. The examples illustrate instruction. This standard is only the fluency part of the original standard. See 1.NBT.C.7 for understanding of addition and subtraction through 20. The code changed due to removal of the previous standard. The word “within” was changed to “through” to encompass the number 10. |
| 1.OA.D | Work with addition and subtraction equations. | ||
| 1.OA.D.6 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Understand the meaning of the equal sign, regardless of its placement within an equation, and determine if equations involving addition and subtraction are true or false. | “Regardless of its placement within an equation” was added to further clarify the scope of the standard. The examples were deleted as they do not clarify the limit of the standard. The code changed due to removal of a previous standard in this domain. |
| 1.OA.D.7 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations: 8 + ? = 11, 5 = – 3, 6 + 6 = . | Determine the unknown whole number in any position in an addition or subtraction equation relating three whole numbers. | The examples were deleted from the standard as they do not clarify the limit of the standard. The examples illustrated instruction. The phrasing “in any position” was added to further clarify the scope of the standard. The code changed due to removal of a previous standard in this domain. |
| Number and Operations in Base Ten (NBT) | |||
| 1.NBT.A | Extend the counting sequence. | ||
| 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | No refinement needed to the existing standard. | No refinement needed on this standard since it meets criterion for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of Number and Operations in Base Ten. |
| 1.NBT.B | Understand place value. | ||
| 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). |
Understand that the two digits of a two-digit number represent groups of tens and some ones. Understand the following as special cases: a. 10 can be thought of as a group of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). |
“Groups of” and “some” were added to further emphasize that ten can represent a single entity (a group) and at the same time ten ones. “Group” replaced the word “bundle” for more precise mathematical language. |
| 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | No refinement needed to the existing standard. | No refinement needed on this standard since it meets criterion for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of Number and Operations in Base Ten. |
| 1.NBT.C | Use place value understanding and properties of operations to add and subtract. | ||
| 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Add through 100 using models and/or strategies based on place value, properties of operations, and the relationship between addition and subtraction. | “Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.” was deleted as it indicates instruction. “relate the strategy to a written method and and explain the reasoning used ” was deleted as it is included in the mathematical practice standards. |
| 1.NBT.C.5. | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | No refinement needed to the existing standard. | No refinement needed on this standard since it meets criterion for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of Number and Operations in Base Ten. |
| 1.NBT.C.6 | Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Add and subtract multiples of 10 through 100 using models and/or strategies based on place value, properties of operations, and the relationship between addition and subtraction. | “In the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences),” was deleted and ‘within 100’ was added to clarify the limit of the standard. “add” was added to the standard to clarify the cluster heading of adding and subtracting using place value. The word “within” was changed to “through” to encompass the number 100. |
| 1.NBT.C.7 | Demonstrate understanding of addition and subtraction through 20 using a variety of place value strategies, properties of operations, and the relationship between addition and subtraction. | Standard 1.OA.C.6 was separated into two standards to clearly show the difference between building understanding and fluency. This is the understanding portion of 1.OA.C.6 that leads to the fluency through 20 in grade 2. | |
| Measurement and Data (MD) | |||
| 1.MD.A | Measure lengths indirectly and by iterating length units. | ||
| 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Order three objects by length. Compare the lengths of two objects indirectly by using a third object. | The semicolon in this standard was replaced with a period to denote separate ideas. It meets criteria for clarity, cognitive demand, and measurability. |
| 1.MD.A.2 | Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. | Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | “Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.” was deleted as this is repetitive language already mentioned in the standard. |
| 1.MD.B | Tell and write time. | Work with time and money. | The cluster title was revised to reflect the addition of money in first grade. |
| 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Tell and write time in hours and half-hours using analog and digital clocks. | No refinement needed on this standard since it meets criterion for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of Measurement and Data. |
| 1.MD.B.4 | Identify coins by name and value (pennies, nickels, dimes and quarters). | This new standard was added per public comment to include working with coins in 1st grade. It supports the progression of money from 1st to 4th grade. | |
| Measurement & Data | Represent and interpret data. | ||
| 1.MD.C.5 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | No refinement needed. | No refinement needed on this standard since it meets criterion for clarity, cognitive demand, and measurability. This is a necessary standard in the progression of Measurement and Data. In previous standards, this was 1.MD.C.4, it is now 1.MD.C.5. Coding was changed to reflect the addition of 1.MD.C.4 |
| Geometry (G) | |||
| 1.G.A | Reason with shapes and their attributes. | ||
| 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Distinguish between defining attributes (open, closed, number of sides, vertices) versus non-defining attributes (color, orientation, size) for two-dimensional shapes; build and draw shapes to possess defining attributes. | “(e.g. triangles are closed and three-sided)” was deleted as it did not clarify the limit of the standard. “e.g.” was deleted but the descriptors were kept to maintain the scope of the standard. “two-dimensional shapes” was added to clarify the expectation of the standard. |
| 1.G.A.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 the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”) | Compose two-dimensional shapes or three-dimensional shapes to create a composite shape and compose new shapes from the composite shape. | The examples (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) and (cubes, right rectangular prisms, right circular cones, and right circular cylinders) were deleted as they were limiting to the standard. |
| 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the 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 decomposing into more equal shares creates smaller shares. | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves and fourths. , and use the phrases half of, fourth of, and quarter of. Understand that decomposing into more equal shares creates smaller shares. | It now meets criteria for clarity, cognitive demand, and measurability. |
| 1.MP | Standards for Mathematical Practice | ||
| 1.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. | |
| 1.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. | |
| 1.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. | |
| 1.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. | |
| 1.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. | |
| 1.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. | |
| 1.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. | |
| 1.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. | |
