Kindergarten Standards for Mathematical Practice

The K-12 Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. This page gives examples of what the practice standards look like in Kindergarten.

Information taken from the

North Carolina Department of Public Instruction


Explanations and Examples

1. Make sense of problems and persevere in solving them.

Mathematically proficient students in Kindergarten examine problems (tasks), can make sense of the meaning of the task and find an entry point or a way to start the task. Kindergarten students also begin to develop a foundation for problem solving strategies and become independently proficient on using those strategies to solve new tasks. In Kindergarten, students‟ work focuses on concrete manipulatives before moving to pictorial representations. Kindergarten students also are expected to persevere while solving tasks; that is, if students reach a point in which they are stuck, they can reexamine the task in a different way and continue to solve the task. Lastly, at the end of a task mathematically proficient students in Kindergarten ask themselves the question, “Does my answer make sense?”

2. Reason abstractly and quantitatively.

Mathematically proficient students in Kindergarten make sense of quantities and the relationships while solving tasks. This involves two processes- decontexualizing and contextualizing. In Kindergarten, students represent situations by decontextualizing tasks into numbers and symbols. For example, in the task, “There are 7 children on the playground and some children go line up. If there are 4 children still playing, how many children lined up?” Kindergarten students are expected to translate that situation into the equation: 7-4 = ___, and then solve the task. Students also contextualize situations during the problem solving process. For example, while solving the task above, students refer to the context of the task to determine that they need to subtract 4 since the number of children on the playground is the total number of students except for the 4 that are still playing. Abstract reasoning also occurs when students measure and compare the lengths of objects.

3. Construct viable arguments and critique the reasoning of others.

Mathematically proficient students in Kindergarten accurately use mathematical terms to construct arguments and engage in discussions about problem solving strategies. For example, while solving the task, “There are 8 books on the shelf. If you take some books off the shelf and there are now 3 left, how many books did you take off the shelf?” students will solve the task, and then be able to construct an accurate argument about why they subtracted 3 form 8 rather than adding 8 and 3. Further, Kindergarten students are expected to examine a variety of problem solving strategies and begin to recognize the reasonableness of them, as well as similarities and differences among them.

4. Model with mathematics.

Mathematically proficient students in Kindergarten model real-life mathematical situations with a number sentence or an equation, and check to make sure that their equation accurately matches the problem context. Kindergarten students rely on concrete manipulatives and pictorial representations while solving tasks, but the expectation is that they will also write an equation to model problem situations. For example, while solving the task “there are 7 bananas on the counter. If you eat 3 bananas, how many are left?” Kindergarten students are expected to write the equation 7-3 = 4. Likewise, Kindergarten students are expected to create an appropriate problem situation from an equation. For example, students are expected to orally tell a story problem for the equation 4+5 = 9.

5. Use appropriate tools strategically.

Mathematically proficient students in Kindergarten have access to and use tools appropriately. These tools may include counters, place value (base ten) blocks, hundreds number boards, number lines, and concrete geometric shapes (e.g., pattern blocks, 3-d solids). Students should also have experiences with educational technologies, such as calculators, virtual manipulatives, and mathematical games that support conceptual understanding. During classroom instruction, students should have access to various mathematical tools as well as paper, and determine which tools are the most appropriate to use. For example, while solving the task “There are 4 dogs in the park. If 3 more dogs show up, how many dogs are they?” Kindergarten students are expected to explain why they used specific mathematical tools.”

6. Attend to precision.

Mathematically proficient students in Kindergarten are precise in their communication, calculations, and measurements. In all mathematical tasks, students in Kindergarten describe their actions and strategies clearly, using grade-level appropriate vocabulary accurately as well as giving precise explanations and reasoning regarding their process of finding solutions. For example, while measuring objects iteratively (repetitively), students check to make sure that there are no gaps or overlaps. During tasks involving number sense, students check their work to ensure the accuracy and reasonableness of solutions.

7. Look for and make use of structure.

Mathematically proficient students in Kindergarten carefully look for patterns and structures in the number system and other areas of mathematics. While solving addition problems, students begin to recognize the commutative property, in that 1+4 = 5, and 4+1 = 5. While decomposing teen numbers, students realize that every number between 11 and 19, can be decomposed into 10 and some leftovers, such as 12 = 10+2, 13 = 10+3, etc. Further, Kindergarten students make use of structures of mathematical tasks when they begin to work with subtraction as missing addend problems, such as 5- 1 = __ can be written as 1+ __ = 5 and can be thought of as how much more do I need to add to 1 to get to 5?

8. Look for and express regularity in repeated reasoning.

Mathematically proficient students in Kindergarten begin to look for regularity in problem structures when solving mathematical tasks. Likewise, students begin composing and decomposing numbers in different ways. For example, in the task “There are 8 crayons in the box. Some are red and some are blue. How many of each could there be?” Kindergarten students are expected to realize that the 8 crayons could include 4 of each color (4+4 = 8), 5 of one color and 3 of another (5+3 = 8), etc. For each solution, students repeated engage in the process of finding two numbers that can be joined to equal 8.

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