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.
All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 1 Lesson 6 Problem Solving Investigation: Use the Four-Step Plan will give you a clear idea of the concepts.
1. Understand What facts do you know? Ben, Andy, and Kelly each live in a different city. The populations for each city are: ____; ____; and _____ What do you need to find? the population of _____ city 2. Plan I can order and round the populations. 3. Solve Order the populations from least to greatest. 225,395; 372,952; 373,926 ____ lives in the city with the least population. Round the remaining populations to the nearest thousand. 372,952 rounds to _____. 373,926 rounds to ____ Kelly lives in the city with the population that rounds to 374,000. So, Ben must live in the city that has a population of _____ 4. Check Does your answer make sense? Explain. Answer: Given that, Order the populations from least to greatest. 225,395; 372,952; 373,926. 225,395 lives in the city with the least population. 372,952 rounds to the nearest thousand is 373,000 373,926 rounded to the nearest thousand is 374,000. Kelly lives in the city with the population that rounds to 374,000. So, Ben must live in the city that has a population of 373,926.
Practice the Strategy
Apply the Strategy
Solve each problem by using the four-step plan.
Question 2. A restaurant made more than $80,000 but less than $90,000 last month. There is a 6 in the ones place, a 3 in the thousands place, a 7 in the hundreds place, and a 1 in the tens place. How much money did the restaurant make last month? Answer: Given that, The restaurant made more than $80,000 less than $90,000 last month. There is 6 in the ones place. 3 in the thousands place. 7 in the hundreds place 1 in the tens place. Therefore the restaurant make in the last month is 83,716. The 83,716 is middle of $80,000 and $90,000.
Question 3. Amy, Lisa, Angie, and Doug live in different states. The populations of those states are 885,122; 5,024,748; 4,492,076; and 2,951,996. Lisa lives in the state with the greatest population. Doug lives in the state with a 2 in the thousands place of the population. Amy lives in the state with the least population. What is the population of Angie’s state? Answer: Given that, The Amy, Lisa, Angie, and Doug live in different states. The population of 4 different states are 885,122; 5,024,748; 4,492,076; and 2,951,996. Lisa lives in the greatest population state that is 885,122. Doug lives in the state with a 2 in the thousands place of the population that is 4,492,076. Amy lives in the least population state that is 2,951,996. Therefore the Angie’s lives in the 5,024,748 population state.
Question 4. The New Meadowlands Stadium in New Jersey seats a large number of fans. There are zeros in the tens and ones places, a 2 in the thousands place, an 8 in the ten thousands place, and a 5 in the hundreds place. How many people does the stadium seat? Answer: Given that, The New Meadowlands Stadium in New Jersey seats a large number of fans. There are zeros in the tens and ones places. 2 in the thousands place 8 in the ten thousands place 5 in the hundreds place Therefore the people in the stadium seat is 82,500.
Review the Strategies
Use any strategy to solve each problem.
Question 6. The population of a city has 6 digits. There is a 3 in the tens place, a 5 in the hundred thousands place, a 6 in the ones place, and a 9 in the rest of the places. What is the population of the city? Answer: Given that, The population of a city has 6 digits. There are 3 in the tens place 5 in the hundred thousands place. 6 in the ones place 9 in the rest of the places. Therefore the population of the city is 9,500,036.
Question 7. A warehouse stores cans of paint. There is a 3 in the hundreds place, a 7 in the thousands place, a 5 in the ten thousands place, and an 8 in the rest of the places. This number has 5 digits. How many cans of paint are in the warehouse? Answer: Given that, The warehouses stores cans of paints There are 3 in the hundreds place 7 in the thousands place 5 in the ten thousands place 8 in the rest of the places. The number is a 5 digit number. Therefore the number of cans of paint are in the warehouses is 87,358.
Question 8. Mathematical PRACTICE 7 Identify Structure A car’s mileage is a five-digit number. There is a 3 in the ten thousands place, the ones place, and the tens place. There is a 9 in the hundreds place and the thousands place. What is the car’s mileage? Answer: Given that, The mileage of a car is 5 digits number. The number 3 in the ten thousands place, ones place, and tens place. There is a 9 in the hundreds place and the thousands place. Therefore the car mileage is 39,933.
Problem Solving
Question 1. A five-digit number has a 3 in the hundreds place, a 7 in the greatest place-value position, a 9 in the ones place, an 8 in the thousands place, and a 6 in the tens place. What is the number? Use the four-step plan. Answer: Given that, The five digit number has 3 in the hundreds place. 7 in the greatest place value position. 9 in the ones place. 8 in the thousands place 6 in the tens place. Therefore the five digits number is 78,369.
Question 2. Use the digits 1—7 to create a seven-digit number that can be rounded to 6,300,000. Answer: The number that can be rounded to the 6,300,000 is We need to assume that the thousands place value is less than or equal to 4 and the number in the ten thousands place is also a 4 or less than 4. Therefore the number is 6,342,517. The number 6,342,517 rounded to 6,300,000.
Question 3. A seven-digit number has a 0 in the ones place, a 6 in the ten thousands place, an 8 in the millions place, and fives in each of the remaining places. What is the number? Answer: Given that, The number is 7 digits number. The number in the ones place is 0. 6 in the ten thousands place. 8 in the millions place 5 in each remaining places. Therefore the 7 digits number is 8,565,550.
Question 5. Betsy, Carl, and Dave each live in different cities. The populations of the cities are 194,032; 23,853; and 192,034. Betsy lives in the city with the least population. Carl does not live in the city with the greatest population. What is the population of Dave’s city? Answer: Given that, Betsy, Carl, and Dave each live in different cities. The populations of the cities are 194,032; 23,853; 192,034. Betsy lives in the least population city that is 23,853. Carl does not live in the greatest population city that is 192,034. Therefore the Dave’s lives in the 194,032 population city it is the greatest population city.
Question 6. Mathematical PRACTICE 6 Explain to a Friend Explain how the value of the 7 in 327.902 will chan2e if you move it to the tens place. Answer: The 7 in the thousands place means it is 7000. If you change it to tens place its value is 70.
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Students are using artificial intelligence to create sexually explicit images of their classmates..
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Featuring Natasha Singer
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Edited by Marc Georges
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Warning: this episode contains strong language, descriptions of explicit content and sexual harassment
A disturbing new problem is sweeping American schools: Students are using artificial intelligence to create sexually explicit images of their classmates and then share them without the person depicted even knowing.
Natasha Singer, who covers technology, business and society for The Times, discusses the rise of deepfake nudes and one girl’s fight to stop them.
Natasha Singer , a reporter covering technology, business and society for The New York Times.
Using artificial intelligence, middle and high school students have fabricated explicit images of female classmates and shared the doctored pictures.
Spurred by teenage girls, states have moved to ban deepfake nudes .
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Consider the problem-solving steps applied in the following example. I know that I want to say "I don't eat eggs" to my Mexican waiter. That's the problem. I don't know how to say that, but last night I told my date "No bebo alcohol" ("I don't drink alcohol"). I also know the infinitive for "eat" in Spanish (comer).
The following list of strategies, although not exhaustive, is very useful: 1. Look for a pattern. 2. Examine related problems and determine if the same technique can be applied. 3. Examine a simpler or special case of the problem to gain insight into the solution of the original problem. 4. Make a table.
Step 4 - Implement and Monitor the Solution. When you've decided on the best solution, it's time to put it into action. The fourth and final step in effective problem solving is to put the solution into action, monitor its progress, and make any necessary adjustments. To begin, implement the solution.
2. Plan See how the facts relate to each other. Make a plan for solving the problem. Estimate the answer. 3. Solve Use your plan to solve the problem. If your plan does not work, revise it or make a new plan. 4. Examine Reread the problem. Ask, "Is my answer close to my estimate?" Ask, "Does my answer make sense for the problem?" If not ...
Key Points. The PDCA/PDSA cycle is a continuous loop of planning, doing, checking (or studying), and acting. It provides a simple and effective approach for solving problems and managing change. The model is useful for testing improvement measures on a small scale before updating procedures and working practices.
Finding a suitable solution for issues can be accomplished by following the basic four-step problem-solving process and methodology outlined below. Step. Characteristics. 1. Define the problem. Differentiate fact from opinion. Specify underlying causes. Consult each faction involved for information. State the problem specifically.
The Plan-Do-Check-Act Cycle (PDCA Cycle) is a four-step model for systematic problem solving and continuous improvement. It offers a simple and structured way for resolving business-related issues and creating positive change.This framework is widely recognized as the basis for enhancing the quality of processes, products, and services by following a logical sequence of four steps: Plan, Do ...
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 ...
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)
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 ...
How to Solve a Problem in Four Steps - The I.D.E.A. Model. 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, execute a plan and then assess your results.
The 4-step Problem Solving Method. The model we've used with clients is based on the A3 problem-solving methodology used by many "lean" production-based companies. In addition to being simpler, our 4-step method is visual, which helps remind the user what goes into each box. The steps are as follows. Develop a Problem Statement; Determine ...
Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything ...
This resource will help your students understand the Four Step Plan, get used to note-taking, and practice their problem-solving techniques. Introduce "The Four Step Plan" for problem-solving with this note-taking PowerPoint. Each slide includes a model of what students' notes should look like. The presentation includes two example math ...
There are three basic choices: troubleshooting, performance improvement, and solution engineering. The approach to select is a function of the nature of the problem to be solved. The best clues regarding which approach to use stem from the manner in which the problem came about.
6. Discovery & Action Dialogue (DAD) One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions. With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so.
How do we ensure fidelity of implementation of the 4-step problem solving process? In addition to monitoring the fidelity with which instruction and intervention are delivered, and the impact on student learning, it is critical to monitor the degree to which we engage in the problem solving process with fidelity. Multiple studies have ...
Lesson 6: Problem-Solving Investigation: Use the Four-Step Plan 1. Comparison word problems with addition and subtraction 2 Chapter 2. Addition ... Lesson 4: Problem-Solving Investigation: Draw a Diagram Unit fractions 1. Unit fractions: modeling word problems 2. Unit fractions: word problems ...
Lesson 9: Problem Solving Investigation: Use the Four Step Plan 1. Add and subtract whole numbers: word problems 2 Chapter 2. Multiply Whole Numbers ... Lesson 4: Problem Solving Investigation: Guess, Check, and Revise 1. Guess-and-check problems
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 ...
Pdf Pass Homework Practice and Problem-Solving Practice Workbook 000i_0iv_CAG5FM_111966.indd i0i_0iv_CAG5FM_111966.indd i 44/2/08 2:29:30 PM/2/08 2:29:30 PM
All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 1 Lesson 9 Problem-Solving Investigation: Use the Four-Step Plan will give you a clear idea of the concepts. ... Solve each problem using the four-step plan. Question 1. The table shows the number of ounces of buffer Marti used in different recipes. She has 6 ounces ...
All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 1 Lesson 6 Problem Solving Investigation: Use the Four-Step Plan will give you a clear idea of the concepts. ... Solve each problem by using the four-step plan. Question 1. Mathematical PRACTICE 5 Use Math Tools Mr. Kramer is buying a car. The list of prices is shown ...
Warning: this episode contains strong language, descriptions of explicit content and sexual harassment. A disturbing new problem is sweeping American schools: Students are using artificial ...