Develop a Deep and Flexible Conceptual Understanding 

Students will build upon their knowledge and generalize it towards more complex mathematical contexts. For example, students use their place value knowledge when rounding numbers and estimating. They will conceptualize through various strategies the basic multiplication principles and facts through factors of 10. They recognize the relationships between addition and subtraction, as well as the relationships between multiplication and division. They recognize connections in math that help them further their understanding of a concept and make sense of it. They understand that the mathematical principles cross into different areas of mathematics, connecting their knowledge as a whole instead of a checklist of concepts.

Students will distinguish when to use certain operations, strategies, and/or properties while modeling effective procedures efficiently. Students demonstrate fluency in basic math facts in addition, subtraction, and multiplication and then apply that knowledge when working with larger numbers and mathematical strands. They also learn to use tools that are important to everyday life, such as rulers, thermometers, and clocks.

Students will develop a toolbox of strategies for problem-solving. They apply these strategies when finding solutions and modeling. They analyze the problem, select a strategy to solve, justify and contextualize their answer. Students recognize that there can be multiple ways to justify an answer with numbers, words, pictures, symbols, charts, graphs, etc. They understand problem-solving as an iterative process; If their representation does not make sense, they re-evaluate and try another strategy.

Students will justify their thinking based on logical strategies. They ask questions such as “Does this make sense?” and “How did you get that?” when participating in mathematical discourse with peers. They use their reasoning to evaluate the validity of an answer and if there is a better way to solve the problem. They apply their mathematical reasoning in many contexts, such as analyzing function machines and tables, classifying shapes, estimating lengths and values, and determining logical combinations of bills to represent a given amount.

Students will recognize that math skills such as telling time, paying with money, and finding measurements are evident in everyday life. They begin to see the usefulness of mathematics in other contexts as well. They also understand that there may be different approaches to problem-solving, but persevere until their solutions make sense, creating resilient, effective problem-solvers.

Develop the Ability to Make Conjectures, Model, and Generalize 

Students will use tables, graphs, pictures, manipulatives, symbols, and words to determine the most efficient strategies while problem-solving. They notice patterns and relationships in their representations that help them draw conclusions when analyzing data, finding missing values, and continuing numerical and geometric sequences. They are able to create models of their strategies so their thinking becomes visible. Students begin to predict solutions based on previous problems and are able to form generalizations that are helpful in other mathematical situations. 

Students will describe their process of problem-solving using appropriate vocabulary. They justify their answers, but also listen and consider other students’ strategies. Students discuss mathematics as a way of further understanding the content and eliminating misconceptions. Communicating mathematically is a powerful way for students to contextualize their answers and determine if they need to readjust their thinking.