# Mathematics Solving Problem 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.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.

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.

Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.

Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions.

The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections.

The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another.Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.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 make sense of quantities and their relationships in problem situations.They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas.They can analyze those relationships mathematically to draw conclusions.Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

• ###### Math Problem Solving Strategies solutions, examples, videos

Problem Solving Strategies - Examples and Worked Solutions of Math Problem Solving Strategies, Verbal Model or Logical Reasoning, Algebraic Model, Block Model or Singapore Math, Guess and Check Model and Find a Pattern Model, examples with step by step solutions…

• ###### High School Math Grades 10, 11 and 12 - Free Questions and.

High school math for grade 10, 11 and 12 math questions and problems to test deep understanding of math concepts and computational procedures are presented. Detailed solutions and answers to the questions are provided. Grade 12 Use Sinusoidal Functions to Solve Applications Problems with Solutions How to Solve Rational Inequalities…

• ###### Standards for Mathematical Practice Common Core State.

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.…

• ###### Photomath - Scan. Solve. Learn.

Photomath is the #1 app for math learning; it can read and solve problems ranging from arithmetic to calculus instantly by using the camera on your mobile device. With Photomath, learn how to approach math problems through animated steps and detailed instructions or check your homework for any printed or handwritten problem.…

• ###### Home—Bedtime Math

Our charitable mission is to help kids love numbers so they can handle the math in real life.…

• ###### Math Word Problems Worksheets

Math Word Problem Worksheets Read, explore, and solve over 1000 math word problems based on addition, subtraction, multiplication, division, fraction, decimal, ratio and more. These word problems help children hone their reading and analytical skills; understand the real-life application of math operations and other math topics.…

• ###### PROBLEM SOLVING, METACOGNITION AND

Problem, problem solving, and doing mathematics. It begins with "Immediate Background Curricular trends in the latter 20th Century," a brief recapitulation of the curricular trends and social imperatives that produced the 1980's focus on problem solving as the major goal of mathematics instruction. The next section, "On problems…