Relationship to
Summarizing and Note-taking
34 points
Main Idea, Details, How
Arguing (in the sense of defending or justifying one's thinking)
29 points
How
Articulating generalizations and principles
29 points
How
Providing feedback to students (“corrective,” timely, specific)
29 points
Grading
Using nonlinguistic representations
27 points
Strategy
Using advance (graphic) organizers
22 points
All Steps
The National Council of Teachers of Mathematics endorses the use of such strategies as those appearing in “Four-Step Problem Solving”—particularly the step requiring students to explain their answers—as effective for producing students’ math competency, as described in NCTM publications such as Principles and Standards for School Mathematics. Excerpts from NCTM documents validate the district's problem-solving strategy. Some of the key ideas and teaching standards identified include the following.
Relationship of “Four-Step Problem Solving” and the TEKS
Although the TEKS for elementary math do not mention a graphic organizer for problem-solving, they do require that students in grades 1-5 learn and do the following things in the area of “Underlying Processes and Mathematical Tools.”
Instructional Methods Behind “Four-Step Problem Solving”
Teachers will use a variety of techniques as they instruct students regarding “Four-Step Problem Solving.” They will
For success with “Four-Step Problem Solving,” talking must occur prior to writing. Students will be shown how to bridge the span between math and language to express their reasoning in a way that uses logical sequences and proper math vocabulary terms. Once students have mastered the ability to communicate out loud with the teacher and with peers, they can transition to developing the skill of conducting an “internal dialogue” for solving problems independently.
Students Using “Four-Step Problem Solving”
Use of a common graphic organizer at all schools would greatly benefit our ever-shifting population of students—not only those whose families move often, but also those affected by boundary changes we continue to experience as we grow. District-wide staff development has focused on acquainting all elementary math teaching staff with “Four-Step Problem Solving,” and outlining expectations for students’ problem-solving knowledge and skills outlined in the TEKS at each grade-level.
Because it is the steps in the problem that are important, not the graphic representation itself, vertical math teams on each campus, working with the building principal, have the option of selecting or designing a graphic organizer, as long as it fulfills the four-step approach. Alternatives to “The Q” include a four-pane “window pane” or a simple list of the four steps. Another scheme adopted by some schools is being called SQ-RQ-CQ-HQ, which uses the old three steps plus a new fourth step—the “HQ” is the "how" step. Schools using SQ-RQ-CQ-HQ should consider how the advent of online testing will impact its use.
Putting “The Four-Step Problem Solving Plan” into Action
In class, students will use “Four-Step Problem Solving” in a variety of circumstances.
Students can expect to see “Four-Step Problem Solving” used in all phases of math instruction, including assessments. Students will be given problems and asked to identify the main idea, details, and process used, as well as solve for a calculation.
The district’s expectation is that students will ultimately use “Four-Step Problem Solving” for all story problems, unless directed otherwise. When students clearly understand the process and concepts they are studying, teachers may choose to limit the writing of the “how.” Improved student achievement comes in classrooms that routinely and consistently use all four steps of the process.
Using this approach should reduce the number of problems students are assigned. Completing the “Four-Step Problem Solving” should take only a few minutes. As students become familiar with the graphic organizer, they will be able to increase the pace of their work. Students can save time by writing only the main idea (instead of copying the entire question) and by using words or phrases in describing the “how” (instead of complete sentences).
For years, researchers of results on the National Assessment of Educational Progress ( NAEP ) and the Trends in International Mathematics and Science Study ( TIMSS ) have cited curricular and instructional differences between U.S. schools and schools in countries that outperform us in mathematics. For example, Japanese students study fewer concepts and work fewer problems than American students do. In Japan , students spend their time in exploring multiple approaches to solving a problem, thereby deepening their understanding of mathematics. Depth of understanding is our goal for students, too, and we believe that the four-step problem-solving plan will help us achieve this goal.
The ultimate goal is that students learn to do the four steps without the use of a pre-printed form. This ability becomes necessary on assessments such as TAKS, since security rules prohibit the teacher from distributing any materials. In 2007, when students may first be expected to take TAKS online, students will need a plan for problem-solving on blank paper to ensure that they don’t just, randomly select an answer—they can’t underline and circle on the computer monitor’s glass.
Assessment and Grading with “The Four-Step Problem Solving Plan”
Assignments using “The Four-Step Problem Solving Plan” may include daily work, homework, quizzes, and tests (including district-developed benchmarks). CFISD’s grade-averaging software includes options for all these categories. As with other assignments, grades may be taken for individuals or for partners/groups. Experienced teachers are already familiar with all these grading scenarios.
Teachers may use a rubric for evaluating student work. The rubric describes expectations for students’ responses and guides teachers in giving feedback. Rubrics may be used in many subjects in school, especially for reviewing students’ written compositions in language arts.
A range of “partial credit” options is possible, depending on the teacher’s judgment regarding the student’s reasoning and thoroughness. Students may be asked to redo incomplete portions to earn back points. Each campus makes a decision about whether the process will be included in one grade or if process will be a separate grade.
Knowledge of students’ thinking will help the teacher to provide the feedback and/or the re-teaching that will get a struggling student back on track, or it will allow the teacher to identify students who have advanced understanding in mathematics so that their curriculum can be adjusted. Looking at students' work and giving feedback may require additional time because the teacher is examining each student's thought processes, not just checking for a correct numeric answer.
Because students’ success in communicating their understanding of a math concept does not require that they use formal language mechanics (complete sentences, perfect spelling, etc.) when completing “The Four-Step Problem Solving Plan,” the rubric does not address these skills, leading math teachers to focus and assign grades that represent the students’ mastery of math concepts.
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Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.
Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?
Simplified Equation: 17 - x = 8
Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?
Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)
Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}
Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?
Simplified: 40 - 10 - 5
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This is the 4 step problem-solving process that I taught to my students for math problems, but it works for academic and social problems as well. Ed Latimore. Writer, retired boxer, self-improvement enthusiast. ... Finding the solution to a math problem is already stressful. Forcing the student to also figure out what problem needs solving is ...
A highly sought after skill, learn a simple yet effective four step problem solving process using the concept IDEA to identify the problem, develop solutions...
Step 1: Understanding the problem. We are given in the problem that there are 25 chickens and cows. All together there are 76 feet. Chickens have 2 feet and cows have 4 feet. We are trying to determine how many cows and how many chickens Mr. Jones has on his farm. Step 2: Devise a plan.
Can one (or more) of the following strategies be used? (A strategy is defined as an artful means to an end.) 1. Guess and test. 11. Solve an equivalent problem. 2. Use a variable. 12.
Choose a strategy, or combination of strategies. Make a record of false starts, and your corrections. Carry out the plan. Clearly and precisely describe verbally each step of the plan. Verify that each step has been done correctly. Provide mathematical justification for the step (a convincing argument)
Polya's four step method for problem solving is. 1) Understand the Problem-Make sure you understand what the question is asking and what information will be used to solve the problem. 2) Devise a ...
4-Step Plan Problem Solving Strategies EXPLORE 1. What do you know? 2. What do the terms mean? 3. What do you need to fi nd? PLAN 1. Choose a strategy. 2. How do the facts relate to each other? 3. Estimate the answer. SOLVE 1. Use your strategy to solve the problem. 2. Pay close attention to the details of the problem. 3. If the plan does not ...
Here are five strategies to help students check their solutions. 1. Use the Inverse Operation. For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7.
QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and ...
In 1945, Pólya published the short book How to Solve It, which gave a four-step method for solving mathematical problems: Understand the problem. Devise a plan. Carry out the plan. ... Problem Solving Strategy 9 (Find the Math, Remove the Context). Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant ...
Think math is boring? You won't anymore! Let me guess - you don't believe me, right? Well I can assure you this interactive and engaging video helps put prob...
Solving a math problem involves first gaining a clear understanding of the problem, then choosing from among problem solving techniques or strategies, followed by actually carrying out the solution, and finally checking the solution. See this article for more information about this four-step math problem solving procedure, with several problem solving techniques presented and discussed for ...
This problem-solving plan consists of four steps: details, main idea, strategy, and how. As students work through each step, they may use "graphic representations" to organize their ideas, to provide evidence of their mathematical thinking, and to show their strategy for arriving at a solution. Main Idea. In this step, the student is a ...
16. Do a simulation. 7. Draw a diagram. 17. Use a model. 8. Use direct reasoning. 2.3.1: George Polya's Four Step Problem Solving Process is shared under a license and was authored, remixed, and/or curated by LibreTexts.
Learn the steps you can follow to solve any math word problem.We hope you are enjoying this video! For more in-depth learning, check out Miacademy.co (https:...
The Totally 10 summer math assignment is all about solving real-world, everyday math problems. It is helpful to approach each problem using the four-step method described here and used in math class. Using this four-step method each time you solve an open-ended question will help you to be more organized, confident and successful when solving ...
The following formula will come in handy for solving example 6: Perimeter of a Rectangle = 2 (length) + 2 (width) Example 6 : In a blueprint of a rectangular room, the length is 1 inch more than 3 times the width. Find the dimensions if the perimeter is to be 26 inches. Step 1: Understand the problem.
To begin this task, we now discuss a framework for thinking about problem solving: Polya's four-step approach to problem solving. Polya's four-step approach to problem solving 1. Preparation: Understand the problem Learn the necessary underlying mathematical concepts Consider the terminology and notation used in the problem: 1.
This online course is intended to provide users with an understanding of the broad concepts of the 4-step problem solving process. The course includes the critical elements and guiding questions within each step, features sample data sources, and provides checks for understanding throughout. If you have a Thinkific account, access An Overview ...
How to solve Math problems using the 4 step plan
4-Step Plan Problem Solving Strategies EXPLORE 1. What do you know? 2. What do the terms mean? 3. What do you need to fi nd? PLAN 1. Choose a strategy. 2. How do the facts relate to each other? 3. Estimate the answer. SOLVE 1. Use your strategy to solve the problem. 2. Pay close attention to the details of the problem. 3. If the plan does not ...
The 4-Step Problem-Solving Process. This document is the third in a series intended to help school and district leaders maximize the effectiveness and fluidity of their multi-tiered system of supports (MTSS) across different learning environments. Specifically, the document is designed to support the use of problem solving to improve outcomes ...
Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects. Basic Math; ... Solving Equations; Multi-Step Equations and Inequalities; Factors, Fractions, and Exponents; Operations with Fractions ...
Find full-length practice tests on Bluebook™ as well as downloadable paper (nonadaptive) practice tests to help you prepare for the SAT, PSAT/NMSQT, PSAT 10, and PSAT 8/9.
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