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# How to make a conjecture in Calculus

3 Answers3. Active Oldest Votes. 7. Put an(x): = Dn (x1 / x) (n ≥ 0, x > 0) and bn(x) = x2nan(x)x − 1 / x . Then bn(x) is the polynomial in x and logx Eric Naslund alluded to in his comment. The bn satisfy the recursion b0(x) ≡ 1 , bn + 1(x) = (1 − logx − 2nx)bn(x) + x2b ′ n(x) (n ≥ 0) . In 2001 the average high school student. How to make a conclusion using Inductive Reasoning ### Calculus conjecture - Mathematics Stack Exchang

• A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases
• Conjecture If we look at data over the precipitation in a city for 29 out of 30 days and see that it has been raining every single day it would be a good guess that it will be raining the 30 th day as well. A conjecture is an educated guess that is based on known information
• A conjecture is a good guess or an idea about a pattern. For example, make a conjecture about the next number in the pattern 2,6,11,15 The terms increase by 4, then 5, and then 6. Conjecture: the next term will increase by 7, so it will be 17+7=24. What is a conjecture and how is it used in math
• $\begingroup$ Not only can anyone make conjectures, but if you don't have some kind of mathematical taste, you're probably not going to make interesting conjectures. Most conjectures made by most people will either be too easy or too hard, and in any case they will probably not lead to interesting research programs. $\endgroup$ - Qiaochu Yuan.

### Making a Conjecture - YouTub

Suggestions for using the Make and Test Conjecture Method Grab a student's attention by presenting them with a thought provoking research question. Engage the students by having them make a prediction (s) about possible outcomes to this question and then have them explain and share their reasoning Some Conjectures about Basic Properties of Number Operations. More than just making big ideas explicit. Want students to make conjectures because they explore important mathematical ideas. Conjecture discussions empower students to learn new mathematics, to solve problems, and to understand the mathematics they are currently learning and doin Conjectures and Math Arguments with Fourth Graders. November 2, 2017. November 2, 2017. ~ Matt Coaty. My fourth grade class just started a unit on division and fractions. Students started out the unit by observing the relationship between fractions and division. This was a realization for some students as they perceived fractions as an isolated. A conjecture is an educated guess that is based on examples in a pattern. A counterexample is an example that disproves a conjecture. Suppose you were given a mathematical pattern like h = \begin {align*}-16/t^2\end {align*}. What if you wanted to make an educated guess, or conjecture, about h Theorems, Lemmas, and Conjectures. provides a simple way to typeset the statements of Theorems, Lemmas, Conjectures and so on. For each such type of statement appearing in your text, you create an environment using the \newtheorem command. For example, \newtheorem{prop}{Proposition} sets up an environment named prop for typesetting Propositions. ### Conjectures Brilliant Math & Science Wik

1. Collatz Conjecture Calculato
2. 12.1.4 Make a conjecture about the derivative of y = cos x. Provide graphical support for your conjecture by graphing your function in Y 3 to see if it produces the same graph as the derivative. Click here for the answer. Consult a calculus book to confirm your conjecture about the derivative of y = cos x
3. ary supporting evidence, but for which no proof or disproof has yet been found
4. belief that our examples reflect a more general truth, then we state a conjecture. The Latin roots of conjecture translate to throw together—we are throwing together many observations into one idea. Conjectures are unproven claims. Once someone proves a conjecture, it is called a theorem

Conjecture Consider the function f(x) = (x - 2) n. (a) Use a graphing utility to graph f for n = 1, 2, 3, and 4. Use the graphs to make a conjecture about the relationship between n and any inflection points of the graph of f. (b) Verify your conjecture in part (a) The conclusion you draw from inductive reasoning is called the conjecture. A conjecture is not supported by truth. When making a conjecture, it is possible to make a statement that is not always true. Any statement that disproves a conjecture is a counterexample Making a conjecture is like solving a puzzle from a few of the pieces. You examine what you know and try to determine what the pattern is. The best way to get good at it is to practice working with sets of numbers to try to find the patterns and make the patterns into conjectures that describe the pattern Example 4: Use Deductive Reasoning to Validate a Conjecture Jared discovered a number trick in a book he was reading: Choose any number. Double it. Add 6. Double again. Subtract 4. Divide by 4. Subtract 2. Use inductive reasoning to make a conjecture about the relationship between the number chosen and the final result All of those reasoning math practices that are difficult to get in kind of fall together when you have them work on conjectures. Teacher: I want you to try to make a conjecture. So the end goal is to kind of analyze this whole set of functions and think about is there a conjecture you can make

Calculus. 1. answer. 0. watching. 16. views. 11 Jun 2020. Conjecture Make a conjecture about the change; in the graph of parametric equations when the sign of the parameter is changed. Explain your reasoning using examples to support your conjecture. Conjecture Make a conjecture about the change; in the graph of parametric equations when. Hey there .After making a conjecture whether in math or physics how do I check if it is on the right way?By applying special cases?About making the conjecture?Just connecting objects and forming relations?The proving part is a bit difficult but what about it?Is it also about a bit of doing it in luck, not completely purposely?When trying to prove because I am still a student, how do I do it.

Mentor. Insights Author. 12,805. 6,687. Through examples that imply the theorem. Consider the series 1+3, 1+3+5, 1+3+5+7 and revelation that they sum to squares. 4, 9, 16 Noticing the pattern one can deduce a theorem that describes the behavior seen. But it is also true that while we may see a pattern, it may not truly exist And that's. Answer to 1. Use the graph below to answer the following questions. 8 7 6 5 4 3 -3 -2 -1 2 5 6 7 8 9 X -1 -2 Calculus: Limits and Differentiability -3 a. lim Mathematicians submit proof of Erdős Coloring Conjecture Fifty years ago, several mathematicians at a dinner party were discussing graphs (points and lines, not chart graphs), and the generalization if you make the edges connecting a point (vertex) with another, able to connect multiple points

Inductive Reasoning in Geometry. Easily Explained w/ 11+ Examples! In today's geometry lesson, you're going to learn all about inductive reasoning and its many uses in the mathematical world. In addition, you're going to learn how to find patterns, make educated guesses, then prove them true or false. Let's go This lesson is designed for a math binder.Students will learn about:the definition of inductive reasoninghow to use inductive reasoning to make a conclusion and find the next term in a sequence (5 problems)the definition of a conjecturemake conjectures about 6 statementsthe definition of a countere Exercises - Patterns and Conjectures. Conjecture a formula for the sum of the first n Fibonacci numbers. Prove your guess with induction. Letting F i denote the i t h Fibonacci number (where F 0 = F 1 = 1 ), we might conjecture that. n ∑ i = 0 F i = F n + 2 − 1

12.1.3 Make a conjecture about what function the derivative of y = sin x might be. Enter the function you conjectured into Y 3 and determine if the graphs defined in Y 2 and Y 3 coincide. Click here for the answer. You should consult a calculus book for an analytic determination of the derivative of y = sin x to confirm your conjecture In this activity, a six-foot length of nylon rope is suspended at both ends to model a mathematical curve known as the hyperbolic cosine. In a write-pair-share activity, students are asked to make a conjecture concerning the nature of the curve and then embark on a guided discovery in which they attempt to determine a precise mathematical description of the curve using function notation The conjecture was based on a pattern in specifi c cases, not rules or laws about the general case; Using inductive reasoning, you can make a conjecture that you will arrive at school before your friend tomorrow. 37. Using inductive reasoning, you can make a conjecture that male tigers weigh more than female tigers because this wa The Math Behind the Fact: This conjecture has been numerically verified for all even numbers up to several million. But that doesn't make it true for all N see Large Counterexample for an example of a conjecture whose first counterexample occurs for very large N. How to Cite this Page: Su, Francis E., et al. Goldbach's Conjecture

### Conjecture (Geometry, Proof) - Mathplane

• With mathematical induction, you can prove it does! Show that the conjecture holds for a base case. Well, the sum on the left will just be 1. The formula on the right gives = 1. So the formula holds for 1. Show that whenever your conjecture holds for some number, it must hold for the next number as well
• Introduction: This site constitutes our final project for Math 5337-Computational Methods in Elementary Geometry, taken at the University of Minnesota's Geometry Center during Winter of 1996.This course could be entitled Technology in the Geometry Classroom as one of its more important objectives is to provide students (presumably math educators) with a wide variety of activities.
• conjectures and the conclusion that follows from them: 1. About half of the students who take calculus in high school take an AP course, 2. About half of those who take the AP Calculus course take the AP Calculus exam, 3. About half of those who take the AP Calculus exam receive grades of 4 or 5 (sufficient to get college credit at Rutgers), an
• Extrapolation is a way to make guesses about the future or about some hypothetical situation based on data that you already know. You're basically taking your best guess. For example, let's say your pay increases average $200 per year. You can extrapolate and say that in 10 years, your pay should be about$2,000 higher than today
• Paul Erdos said of the conjecture: Mathematics is not yet ready for such problems, but he offered $500 for a solution. Thwaites, after whom the problem is sometimes called the Thwaites' conjecture, offered up £1000 (about$1500) as well. Quantum Mechanics The fundamental principles that govern the behavior of matter

Math is filled with conjectures, creativity, and uncertainty. MP1: 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 Students may be able to come up with a conjecture if you start with some examples. You may wish to make the conjecture more plausible with some other heuristic arguments. The Math Behind the Fact: This example drives home the point that obvious facts, checked for many cases, to not constitute a proof for all integers Math 11 Foundations: Unit 8 - Logic & Geometry Sardis Secondary Foundationsmath11.weebly.com Mr. Sutcliffe Example 1: Make a conjecture about intersecting lines and the angles formed. Example 2: Use inductive reasoning to make a conjecture about the product of an odd integer and an even integer. Example 3: Make a conjecture about the sum of two odd numbers

### How to Make a Conjecture of Two Angles : Math Solutions

• Guesswork and conjectures. Formulate and write down questions and conjectures. When we make a guess in mathematics, we usually call it a conjecture. Examples. Constructing appropriate examples is extremely important. Exploration often requires looking at lots of examples
• Hypothesis is testable, and explanation is based on accepted grounds. Conjecture is proposition based on inconclusive grounds, and sometimes can not be fully tested. Another difference is that conjectures, unlike hypothesis, are used in math. If conjecture is proven, it becomes a theorem
• counterexample definition conjecture. A key term in geometry is counterexample. the way we define counterexample is an example that makes a definition or conjecture incorrect. The reason why this is important is because if you can find a counterexample for a definition, let's say a teacher asks you to write the definition of a rectangle
• Math. Make a conjecture about the next item in each sequence. 1.4,6,9,13,18. -I know that from 4 to 6 they added 2 and then from there each time the number you add is 1 more than the last one, but I don't know how to make a conjecture. Thanks
• Making and Testing Conjectures. No one found a way to predict the number of shaded squares at the meeting, but here is some of the work that each group created. My initital strategy was just to draw a whole bunch of rectangles and get a whole bunch of numbers and then see what patterns emerged
• gly interchangeably in Geometry are postulate, axiom, and conjecture. It is important, however, to know how each word is different and to know the subtle implications of using each word. These terms are especially important when working with Geometry proofs

Make and test a conjecture about the sign of the product of any three negative integers. 5. Make and test a conjecture about the sum of any fi ve consecutive integers. Find a counterexample to show that the conjecture is false. 6. The value of x2 is always greater than the value of . 7. The sum of two numbers is always greater than their. In this lesson, you Learn how inductive reasoningis used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers and shapes Inductive reasoningis the process of observing data, recognizing patterns, and making generalizations based on those patterns. You probably use inductive reasoning all the time without realizing it

Continued Lesson. This lesson is a continuation of yesterday's lesson, Making Conjectures about the Multiplies of 0-4. Goal & Introduction. To begin today's lesson, I reviewed the goal: I can determine if a number is a multiple of a given number.I explained: Yesterday, we analyzed the multiples for 0-4.Today, we are going to be focusing on the multiples of 5-9 I am making three statements here, and my question is about statement 2, asking if someone can prove or disprove it. A (possibly weaker) version of statement 2 was proved as an answer to a former question of mine on MSE (and I provide the link to that question and answer below) but I really need to know if statement 2 is truly correct or not, as it has big implications if it is correct There are many ways to be smart in mathematics, including making connections across ideas, representing problems, working with models, figuring out faulty solutions, finding patterns, making conjectures, persisting with challenging problems, working through errors, and searching for efficient solutions (Featherstone et al. 2011)

Circumference Conjecture If C is the circumference and d is the diameter of a circle, then there is a number π such that C=πd. If d=2r where r is the radius, then C=2π The most familiar example of this is the binary arithmetic of computers and digital technology. A zero and one make up their own consistent mathematical world, but similar things happen as long as you work in a number system with a prime number's worth of numbers. The mathematical Weil Conjectures make their appearance late in the book Making Best Use of DESMOS to Strengthen Your MATH Instruction (Grades 6-12) | Bureau of Education & Research (BER) is a sponsor of staff development training for professional educators in the United States and Canada offering seminars, PD Kits, self-study resources, and Online courses The process of making conjectures and breaking them with counterexamples is the fundamental way we play with and think about rich tasks, and mathematics as a whole. (Later, when we cannot find counterexamples, we turn to constructing proofs, but that's not where we begin.) An Example: 1-2 Ni This lesson is designed for a math binder.Students will learn about:the definition of inductive reasoninghow to use inductive reasoning to make a conclusion and find the next term in a sequence (5 problems)the definition of a conjecturemake conjectures about 6 statementsthe definition of a countere

Translating math to computation. but he suggested to Aaronson that transforming the Collatz conjecture into a rewrite system might make it possible to get a termination proof for Collatz. MP1: 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.

Evaluating Data & Making Conjectures. Ok, so by now we've worked our data hardcore in the exercises on the previous pages. We totaled raw numbers, calculated averages, and made pretty plots and histograms to show off the data. Now, we just need to make sure we understand what it says Calculus Calculus (MindTap Course List) Think About It The center of mass of a solid of constant density is shown in the figure. In Exercises 43-46, make a conjecture about how the center of mass ( x ¯ , y ¯ , z ¯ ) will change for the nonconstant density ρ ( x , y , z ) . Explain Step 3 Make a conjecture (a guess) about how small cases are generally related to larger cases. Notice that by moving groups of the triangles in one layer away from the center and then adding 24 extra triangles in diamond-shaped pairs, we can make the next layer of the pattern from each previous layer

Conjecture. In math, a conjecture is a math statement where we don't know if the answer is true or false. Example: If you have the pattern of 2, 6, 11, 15, then is the next number in the pattern is 20. Is this true? Might be true. But, you would have to look at it and try to figure it out Calculus Calculus of a Single Variable Conjecture Consider the function f ( x ) = ( x - 2) n . (a) Use a graphing utility to graph f for n = 1, 2, 3, and 4. Use the graphs to make a conjecture about the relationship between n and any inflection points of the graph of f . (b) Verify your conjecture in part (a) Students can make conjectures, link prior knowledge to current understanding, reason about mathematics, refine and amend their approaches, and take ownership of their mathematical knowledge. Students benefit greatly from learning to use the tools of mathematical discourse—including words, symbols, diagrams, physical models, and technology.  In this lesson you will Learn how inductive reasoningis used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers and shapes Inductive reasoningis the process of observing data, recognizing patterns, and making generalizations based on those patterns. You probably use inductive reasoning all the time without realizing it PZ Math Calculus Prep is a one-week camp that will prepare you for all the rigor of the AP Calculus curriculum. Our unique approach blends the development of a deep understanding of the big picture of Calculus with the strengthening of important foundational skills. With constant practice and individualized feedback, we'll guide students.  An Infinity of Infinities. Yes, infinity comes in many sizes. In 1873, the German mathematician Georg Cantor shook math to the core when he discovered that the real numbers that fill the number line — most with never-ending digits, like 3.14159 — outnumber natural numbers like 1, 2 and 3, even though there are infinitely many of both 4 likes • 18 shares. Share. Flip. Like. mindmatters.ai - News • 37d. Mathematicians have thought that five long-standing conjectures in graph theory might be true but they have not been able to prove them: Wagner . Read more on mindmatters.ai

### FAQ: What Is A Conjecture In Math? - Math lessons and problem

1. How do dilations map triangles? a. Make a conjecture. A dilation maps a triangle to a triangle with the same angles, and all of the sides of the image triangle are proportional to the sides of the original triangle. MP.3 Scaffolding: Some groups of students may benefit from a teacher-led model of the first exercise Make conjectures and predictions based on data. SPI 0606.1.1 Links verified on 7/3/2014. Analyzing game probabilities - multiple-choice quiz [5 problems]; Card Sharks - use your knowledge of probability to predict if the next card will be higher or lower ; Data Picking - Students collect data, enter tally marks or numbers and then select which graph is appropriate Euler and Gauss were wonderful at doing calculations, and they would do lots of calculations and then making conjectures based on the patterns they saw. Well, if Euler or Gauss had had WolframAlpha or Mathematica, they would have done a lot more. Especially when you go to WolframAlpha, it begins to start feeling like an AI A proof is a step-by-step logical argument that verifies the truth of a conjecture, or a mathematical proposition. (Once it's proved, a conjecture becomes a theorem.) It both establishes the validity of a statement and explains why it's true. A proof is strange, though. It's abstract and untethered to material experience Conjecture Answers calculus classes not only successful, but practical as well. A grant from the National Science Foundation made it possible for this experiment to go forward on a large scale. The enthusiasm of the original group of five faculty was contagious, and soon other members of the department wer

### soft question - How to propose a conjecture - Mathematics

The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on 'Conjecture and Proof'. It gives miniature introductions to various. Ever since I was little, I always labeled myself as bad at math. I was afraid of homeworks and test, afraid of math teachers and textbooks. It wasn't something completely irrational, after all I had and still have a severe case of math anxiety, which was always proven by the fact that I can't do basic things as easely as most people can

### Making and Testing Conjecture

Conjectures and Counterexamples. A conjecture is an educated guess that is based on examples in a pattern. Numerous examples may make you believe a conjecture. However, no number of examples can actually prove a conjecture. It is always possible that the next example would show that the conjecture is false Show that each conjecture is false by finding a counterexample. 17. O, then 1. 18. For any real number x, x2. 19. Every pair of supplementary angles includes one obtuse angle. Make a conjecture about each pattern. Write the next two items. 12, 111 20. 2,4, 16, . 23. Draw a square of dots. Make a conjecture about the 22

Stating the conjecture is fairly easy, and demonstrating it can be fun. We have included some nice classroom demonstrations in the Activity Sheet for this conjecture. I encourage you to try them out! The power of the Triangle Sum Conjecture cannot be understated. Many of the upcoming problem solving activities and proofs of conjectures will. Inspired by the work of the Navajo Math Circle, CAMI explores the area of rectangles and their borders, testing conjectures and making generalizations. Eric started the meeting by talking about the Navajo Math Circles , which is a joint project of the Navajo Nation and mathematicians from Math Teachers Circle Network Reasonable Conjectures. Two separate series of numbers and letters are shown below. Determine the sequential pattern of each, and predict the next several number and letters in the series. This may be the combination of two or more series. 2 7 4 9 6 11 8 13. 20 A 18 B 16 C

### Conjectures and Math Arguments with Fourth Graders

Many conjectures are the result of recognizing patterns. A mathematician notices a pattern in some small examples and conjectures that the pattern will always hold. Or a mathematician notices that two objects of study are similar in some ways and conjectures that they are similar in other ways too. level 2 Counterexamples is also a great way to practice constructing viable arguments and critiquing the reasoning of others (CCSS.Math.Practice.MP3). You can play Counterexamples as an opening game, but the language of conjectures and counterexamples has the power to animate much deeper rich tasks in the classroom established results in the construction of arguments. The student is able to make conjectures and build a logical progression of statements to explore the truth of his/her own conjecture. The student response routinely interprets his/her mathematical results in the context of the situation and reflects on whether the results make sense Conjectures now proved (theorems) For a more complete list of problems solved, not restricted to so-called conjectures, see List of unsolved problems in mathematics#Problems solved since 1995. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic names 1 Answer1. at the place where you want to restate it. As you can see, it works somewhat like the empheq environment for amsmath environments: you use a restatable environment, with two mandatory arguments: the name of the theorem-like environment, and the name of the command which will be used to restate the environment

### Conjectures and Counterexamples ( Read ) Geometry CK

Here are the answers: (for 6 and 10) I am doing the rest now 6.) Use the pattern to make a conjecture. Describe the pattern and find the next product. 4*6=24 44*6=264 444*6=2664 4444*6=26,664 The choices would be: a.) The product of a number consisting of n 4s and 6 consists of 2, n 6s, and 4 What mathematical induction says is this, let's suppose we have a conjecture. Now, how we get the conjecture is something we'll talk about in a while, but let's suppose we have the conjecture. Well, to try to show that the conjecture is true all the time, we had better be sure it's true at least sometimes. So we say, OK, let's show that the.

### Theorems, Lemmas, and Conjecture

The conjecture is actually worded a bit differently. Every even number greater than 2 can be written as the sum of two prime numbers. The initial wording of the conjecture included 2 as a number that could be written as a sum of two prime numbers but that was also assuming 1 was a prime number. 4 is the first applicable number of the conjecture Thank you. Sorry if the question came off as naive. I found my passion for mathematics late in undergrad and was unaware of the gaps I may have from only minoring in math. I recently passed my secondary math praxis and want to teach it/keep studying it. You seem knowledgeable, and you make a good point about the importance of working on problems Making Thinking Visible is a book by Ron Ritchhart, Mark Church, and Karin Morrison.  The book provides rationale for having students' thinking made visible and also shares multiple thinking routines that foster visible thinking. In addition there are Pictures of Practice to provide specific examples to show student work from classrooms Argue that your conjecture holds by either referring to a construction, or by reasoning (or both) Opposite angles of a quadrilateral in a circle. Make a circle and place four points on the circle. Make a quadrilateral using the four points. What can you say about opposite angles of the quadrilaterals? Make a conjecture and write it down

### Collatz Conjecture Calculator - Math Celebrit

The easiest math conjecture it took 74 years to prove. The Collatz conjecture is also known as the 3n + 1 problem. It's an easy problem to explain and check, and has been tested up into the. Lesson 2-1 Inductive Reasoning and Conjecture65 Determine whether each conjecture is true or false. Give a counterexample for any false conjecture. 29. Given: 1 and 2 are complementary angles. Conjecture: 1 and 2 form a right angle. 30. Given: m y 10, y 4 Conjecture: m 6 31. Given: points W, X, Y, and Z Conjecture: W, X, Y, and Z are noncollinear. 32 The directions in the title of your post say to graph the function and make a conjecture based on what you see in the graph. Note the graph of. y. shows the basic cosine curve reflected over the x-axis in other words, one could make a conjecture that. y=-\cos {x} Using Inductive Reasoning To Make Conjectures. Using Inductive Reasoning To Make Conjectures - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Solving problems by inductive reasoning, 1 inductive and deductive reasoning, Geo ch reteach with prob marked for test rev, Lesson practice a using inductive reasoning to make, Inductive and deductive.  C-74 Tessellating Quadrilaterals Conjecture - Any quadrilateral will create a monohedral tessellation. Chapter 8 C-75 Rectangle Area Conjecture - The area of a rectangle is given by the formula A=bh, where A is the area, b is the length of the base, and h is the height of the rectangle There is a paper (not accepted for publication yet) that contains several conjectures. Some of these conjectures were proven recently. The referee of the original paper requires to substitute the proven Conjectures with the Results. However, there are several papers that cite these conjectures, so I feel it would be wrong to rename them Guess the Problem Practice. How to Have Students Make and Test Conjectures - Lesson plan. Justify Answers - Justify a math statement; Lesson plan with practice follow-up. Practice Justifying Answers. Make an educated guess at the answer - Lesson plan with practice. Walrus World - learn strategies for solving real world problems