The Standards for Mathematical Practice (K-1): Part 2

Recently I have did professional development for teachers in our district that included a segment on the SMPs. The purpose for discussing the SMPs was for teachers to have conversations with grade-alike colleagues around the Mathematical Practice and think about the connections and application to their specific grade level  content standards. Teachers were divided into 8 groups, one group per mathematical practice, and asked to read and discuss the Mathematical Practice. Then, create a poster that describes and shows the SMP connected to content standards at the various grades levels represented (teachers were encouraged to use words, pictures, illustrations, etc). This would allow a snapshot of a possible continuum of how that mathematical practice grows and develops from grade level to grade level. After groups finished their posters, we did a gallery walk and pairs of teachers walked around to look at, discuss, and ask questions around the other SMPs,

Standards for Mathematical Practice: Kindergarten and 1st Grade

The Kindergarten and 1st grade teachers were able to discuss the SMPs and did a great job illustrating the Mathematical Practices. Here are their posters and some descriptors of what each SMP could look like at this level. 

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

Grade K & 1: SMP#1

• make predictions about what the answer and determine a possible strategy that might help them solve the problem.

• choose a method or strategy to solve to a problem. 

• explain mathematical problems in their own words. 

• explain how their picture, model, or equation represents the problem. 

• draw on classroom experience with variety of concrete objects, models, and pictures so that he or she can adjust his or her strategy, as needed, when solving a problem.

• check their answer using a different method or strategy and ask themselves, "Does this make sense?" 

• listen to classmates to understand the approaches of others. 

SMP#2 Reason abstractly and quantitatively.

Grade K & 1: SMP#2

• make sense of quantities by repetitive experiences with a variety of objects, models, and situations. 

• decontextualize a given situation by representing it symbolically, including acting out a situation, modeling it, drawing a picture, using manipulatives, or other representations. 

• contextualize by referencing the real-world mathematical situation to support, plan, and adjust the strategy and solution.  

• think quantitatively by making meaning of numbers, referencing units, and flexibly using different models and representations. 

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

Grade K & 1: SMP#3

• understand and use previous learning when discussing mathematics. 

• explain his or her thinking, and justify his or her answer. 

• communicated explanations and justifications to others. 

• respond to the arguments of others.

• construct arguments using concrete models such as objects, drawings, diagrams, and actions.

• make hypothesis and conjectures that build on a logical progression of statements from prior learning and experiences while connected it to current learning.  

• analyze situations and can recognize and use counterexamples that demonstrate when a mathematical idea is incorrect or a general statement cannot be made.  

• reason about data through making plausible arguments that take into account the context from which the data arose. 

• compare two ideas or arguments and determine when the thinking is correct or when the  reasoning is flawed. 

• explain the flaw in the mathematically thinking or procedure. 

• listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

SMP#4 Model with mathematics.

Grade K & 1: SMP#4

• apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. 

• write simple addition or subtraction equations to describe a situation.

• identify important information required to solve the mathematical real-world problem and use tools as diagrams, tables, graphs, number lines and formulas. 

• 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.

SMP#5 Use appropriate tools strategically.

Grade K & 1: SMP#5

• consider the available tools when solving a mathematical problem. These tools might include pencil and paper, base-ten blocks, linker cubes, other objects, ten-frames, counters, a hundreds charts, a number line, a ruler, etc. 

• decide when best to use a tool,  when a tool might be helpful, and recognize when a tool might not be helpful. 

SMP#6 Attend to precision.

• communicate precisely to others by using academic and mathematic vocabulary.

• explain their thinking, their mathematical expressions/sentence and their answers to classmates.

• specify units when measuring and refer to the corresponding quantities in a problem. 

• accurately and efficiently calculate addition and subtraction problems. 

SMP#7 Look for and make use of structure.

• look closely to discern patterns or structures. 

• notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. 

• look at the patterns of making ten, the basic structure of our base-ten system.  

SMP#8 Look for and express regularity in repeated reasoning.

• make connections between various counting experiences to develop a sense of numbers and their sequence, including noticing patterns within a counting sequence.

• recognize what happens to numbers when you add or subtract ten to a number, and developing an understanding of what happens when you add or subtract groups of ten to a number.

• look for and notice patterns when combining numbers.  

• evaluate the reasonableness of their results when solving problems.

Of course, these examples are not an exhaustive list of what each SMP could look like at the Kindergarten and 1st grade levels. 

Standards of Mathematical Practice Resources:

SMP Examples for Elementary Math
SMP Posters for Elementary
Standards for Mathematical Practices Progression through Grade Levels (K-12)