Grade 1 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 at Grade 1.

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 Grade 1 examine problems (tasks), can make sense of the meaning of the task and find an entry point or a way to start the task. Grade 1 students also develop a foundation for problem solving strategies and become independently proficient on using those strategies to solve new tasks. In Grade 1, students’ work builds from Kindergarten and still heavily relies on concrete manipulatives and pictorial representations. The exception is when the CCSS uses to the word fluently, which denotes mental mathematics. Grade 1 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 Grade ask themselves the question, ―Does my answer make sense?

2. Reason abstractly and quantitatively.

Mathematically proficient students in Grade 1 make sense of quantities and the relationships while solving tasks. This involves two processes- decontexualizing and contextualizing. In Grade 1, students represent situations by decontextualizing tasks into numbers and symbols. For example, in the task, ―There are 60 children on the playground and some children go line up. If there are 20 children still playing, how many children lined up? Grade 1 students are expected to translate that situation into the equation: 60 – 20 = ___ 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 20 since the number of children on the playground is the total number except for the 20 that are still playing. The processes of reasoning also applies to Grade 1, as they look at ways to partition 2-dimensional geometric figures into halves, and fourths.

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

Mathematically proficient students in Grade 1 accurately use definitions and previously established answers to construct viable arguments about mathematics. For example, while solving the task, ―There are 15 books on the shelf. If you take some books off the shelf and there are now 7 left, how many books did you take off the shelf?‖ students will use a variety of strategies to solve the task. After solving the class, Grade 1 students are expected to share problem solving strategies and discuss the reasonableness of their classmates’ strategies.

4. Model with mathematics.

Mathematically proficient students in Grade 1 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. Grade 1 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 11 bananas on the counter. If you eat 4 bananas, how many are left?‖ Grade 1 students are expected to write the equation 11-4 = 7. Likewise, Grade 1 students are expected to create an appropriate problem situation from an equation. For example, students are expected to create a story problem for the equation 13-7 = 6.

5. Use appropriate tools strategically.

Mathematically proficient students in Grade 1 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 and virtual manipulatives that support conceptual understanding and higher-order thinking skills. 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 12 + 8 = __, students explain why place value blocks are more appropriate than counters.

6. Attend to precision.

Mathematically proficient students in Grade 1 are precise in their communication, calculations, and measurements. In all mathematical tasks, students in Grade 1 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 Grade 1 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 7+4 = 11, and 4+7 = 11. While decomposing two-digit numbers, students realize that any two-digit number can be broken up into tens and ones, e.g. 35 = 30 + 5, 76 = 70+6. Further, Grade 1 students make use of structure when they work with subtraction as missing addend problems, such as 13- 7 = __ can be written as 7+ __ = 13 and can be thought of as how much more do I need to add to 7 to get to 13?

8. Look for and express regularity in repeated reasoning.

Mathematically proficient students in Grade 1 begin to look for regularity in problem structures when solving mathematical tasks. For example, when adding up three one-digit numbers and using the make 10 strategy or doubles strategy, students engage in future tasks looking for opportunities to employ those same strategies. For example, when solving 8+7+2, a student may say, ―I know that 8 and 2 equal 10 and then I add 7 to get to 17. It helps to see if I can make a 10 out of 2 numbers when I start.‖ Further, students use repeated reasoning while solving a task with multiple correct answers. For example, in the task ―There are 12 crayons in the box. Some are red and some are blue. How many of each could there be?‖ Grade 1 students are expected to realize that the 12 crayons could include 6 of each color (6+6 = 12), 7 of one color and 5 of another (7+5 = 12), etc. In essence, students are repeatedly finding numbers that will add up to 12.

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