Properties of Real Numbers Sorting Activity

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + 𝘹) to produce the equivalent expression 6 + 3𝘹; apply the distributive property to the expression 24𝘹 + 18𝘺 to produce the equivalent expression 6 (4𝘹 + 3𝘺); apply properties of operations to 𝘺 + 𝘺 + 𝘺 to produce the equivalent expression 3𝘺.

Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.