# Logical reasoning and problem solving

MP1 Make sense of problems and persevere in solving them. Mathematically logical reasoning and problem solving 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. Mathematically proficient students make sense of quantities and their relationships in problem situations.

MP3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. Mathematically proficient students consider the available tools when solving a mathematical problem.

These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately.

MP7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might 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. MP8 Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal.

Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice.

Please click here for the ADA Compliant version of the Math Standards. Please forward this error screen to key. Enter the characters you see below Sorry, we just need to make sure you’re not a robot. Pattern Problems: visual patterns that require students to draw what comes next. Teachers should ask students to explain how they know what comes next to develop students’ ability to explain their thinking. Animal Problems ask students to solve problems about pets and animals. Largest Sum challenges students to arrange given digits to produce the largest sum.

Smallest Sum challenges students to arrange given digits to produce the smallest sum. Pattern Block Fraction Design requires students to fill a shape with pattern blocks to create a design that meets certain requirements. Students must also write a fraction that describes the part of the total design represented by each different color pattern block. Bake Sale requires students to work backward to solve the problem. Monkey Business also requires students to work backward to figure out how many coconuts there were before each monkey ate one and took a third of what was left. Investigating Exponents challenges students to identify the different patterns found in the units digits of numbers raised to different powers. MATH TV: Problem Solving Videos are designed for middle school students.