Standards for Mathematical Practice

“Thinking habits” we want kids to build in math. They focus less on getting the right answer and more on how children approach, explore, and explain problems.

Make sense of problems and persevere in solving them (SMP 1): Kids work to understand what the problem is asking, make a plan, and keep trying—even when it feels challenging.

Reason abstractly and quantitatively (SMP 2): Kids connect the math (numbers and symbols) to real meaning—what the numbers stand for in the situation.

Construct viable arguments and critique the reasoning of others (SMP 3): Kids can explain why their answer makes sense and listen carefully to decide if someone else’s thinking is correct.

Model with mathematics (SMP 4): Kids use math to describe and solve real-life situations—using pictures, tables, graphs, or equations—and check if the answer is reasonable.

Use appropriate tools strategically (SMP 5): Kids choose helpful tools (like drawings, manipulatives, rulers, or calculators) and use them in smart ways to solve problems.

Attend to precision (SMP 6): Kids calculate carefully and communicate clearly, including using correct labels, units, and math words.

Look for and make use of structure (SMP 7): Kids notice patterns and “how math is organized” (like place value or properties) to solve problems more efficiently.

Look for and express regularity in repeated reasoning (SMP 8): Kids notice when steps repeat, use those patterns to make a shortcut or rule, and check that it still works.

Early numeracy is a young child’s developing understanding of numbers and quantity, like counting with meaning, recognizing small amounts without counting, comparing more/less, and seeing how numbers can be made and broken apart (for example, 5 as 2 and 3). It matters because these skills form the foundation for later math learning and problem-solving, strongly predict future academic success, build everyday life skills (like estimating, sharing, and measuring), and can be developed naturally through play and daily routines rather than worksheets.

A robust association between young children’s early mathematical
proficiency and later academic achievement is well established.
Less is known about the mechanisms through which early mathematics skills may contribute to later mathematics and especially reading achievement