problem solving for measurement

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6: Ratio, Proportion, and Measurement

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• David Arnold
• College of the Redwoods
• 6.1: Ratio and Proportion Examples and applications of ratios are limitless: speed is a ratio that compares changes in distance with respect to time, acceleration is a ratio that compares changes in speed with respect to time, and percentages compare the part with the whole. We’ve already studied one classic ratio, the ratio of the circumference of a circle to its diameter, which gives us the definition of π.
• 6.2: Introduction to Ratios and Rates We use ratios to compare two numeric quantities or quantities with the same units.
• 6.3: Introduction to Proportion In this section, we equate ratio and rates in a construct called a proportion.
• 6.4: Unit Conversion - American System In this section we will develop a technique for converting units used in the American system. We begin with a discussion of common measurements of length in the United States.
• 6.5: Unit Conversion- Metric System The metric system of units is the standard system of units preferred by scientists. It is based on the base ten number system and its decimal format is more friendly to users of this system. There is a common set of prefixes adopted by the metric system to indicate a power of ten to apply to the base unit.
• 6.6: American Units to Metric Units and Vice-Versa We often need to convert from the American system of units to the metric system of units or vice-versa (imagine traveling to a European country using the metric system). That will be our focus in this section.
• 6.7: Use a Problem Solving Strategy (Part 1) In earlier chapters, you translated word phrases into algebraic expressions and word sentences into algebraic equations and solved some word problems that applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated. Now we'll develop a strategy you can use to solve any word problem.
• 6.8: Use a Problem Solving Strategy (Part 2) In number problems, you are given some clues about one or more numbers, and you use these clues to build an equation. Number problems don't usually arise on an everyday basis, but they provide a good introduction to practicing the Problem Solving Strategy. Some number word problems ask you to find two or more numbers. Be sure to read the problem carefully to discover how all the numbers relate to each other.
• 6.9: Solve a Formula for a Specific Variable For an object moving in at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula d = rt where d = distance, r = rate, and t = time. To solve a formula for a specific variable means to get that variable by itself with a coefficient of 1 on one side of the equation and all the other variables and constants on the other side. The result is another formula, made up only of variables.
• 6.E: Math Models and Geometry (Exercises)
• 6.S: Math Models and Geometry (Summary)

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1.8: Solving Problems in Physics

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Learning Objectives

• Describe the process for developing a problem-solving strategy.
• Explain how to find the numerical solution to a problem.
• Summarize the process for assessing the significance of the numerical solution to a problem.

Problem-solving skills are clearly essential to success in a quantitative course in physics. More important, the ability to apply broad physical principles—usually represented by equations—to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations whereas a list of facts cannot be made long enough to contain every possible circumstance. Such analytical skills are useful both for solving problems in this text and for applying physics in everyday life.

As you are probably well aware, a certain amount of creativity and insight is required to solve problems. No rigid procedure works every time. Creativity and insight grow with experience. With practice, the basics of problem solving become almost automatic. One way to get practice is to work out the text’s examples for yourself as you read. Another is to work as many end-of-section problems as possible, starting with the easiest to build confidence and then progressing to the more difficult. After you become involved in physics, you will see it all around you, and you can begin to apply it to situations you encounter outside the classroom, just as is done in many of the applications in this text.

Although there is no simple step-by-step method that works for every problem, the following three-stage process facilitates problem solving and makes it more meaningful. The three stages are strategy, solution, and significance. This process is used in examples throughout the book. Here, we look at each stage of the process in turn.

Strategy is the beginning stage of solving a problem. The idea is to figure out exactly what the problem is and then develop a strategy for solving it. Some general advice for this stage is as follows:

• Examine the situation to determine which physical principles are involved . It often helps to draw a simple sketch at the outset. You often need to decide which direction is positive and note that on your sketch. When you have identified the physical principles, it is much easier to find and apply the equations representing those principles. Although finding the correct equation is essential, keep in mind that equations represent physical principles, laws of nature, and relationships among physical quantities. Without a conceptual understanding of a problem, a numerical solution is meaningless.
• Make a list of what is given or can be inferred from the problem as stated (identify the “knowns”) . Many problems are stated very succinctly and require some inspection to determine what is known. Drawing a sketch be very useful at this point as well. Formally identifying the knowns is of particular importance in applying physics to real-world situations. For example, the word stopped means the velocity is zero at that instant. Also, we can often take initial time and position as zero by the appropriate choice of coordinate system.
• Identify exactly what needs to be determined in the problem (identify the unknowns). In complex problems, especially, it is not always obvious what needs to be found or in what sequence. Making a list can help identify the unknowns.
• Determine which physical principles can help you solve the problem . Since physical principles tend to be expressed in the form of mathematical equations, a list of knowns and unknowns can help here. It is easiest if you can find equations that contain only one unknown—that is, all the other variables are known—so you can solve for the unknown easily. If the equation contains more than one unknown, then additional equations are needed to solve the problem. In some problems, several unknowns must be determined to get at the one needed most. In such problems it is especially important to keep physical principles in mind to avoid going astray in a sea of equations. You may have to use two (or more) different equations to get the final answer.

The solution stage is when you do the math. Substitute the knowns (along with their units) into the appropriate equation and obtain numerical solutions complete with units . That is, do the algebra, calculus, geometry, or arithmetic necessary to find the unknown from the knowns, being sure to carry the units through the calculations. This step is clearly important because it produces the numerical answer, along with its units. Notice, however, that this stage is only one-third of the overall problem-solving process.

Significance

After having done the math in the solution stage of problem solving, it is tempting to think you are done. But, always remember that physics is not math. Rather, in doing physics, we use mathematics as a tool to help us understand nature. So, after you obtain a numerical answer, you should always assess its significance:

• Check your units . If the units of the answer are incorrect, then an error has been made and you should go back over your previous steps to find it. One way to find the mistake is to check all the equations you derived for dimensional consistency. However, be warned that correct units do not guarantee the numerical part of the answer is also correct.
• Check the answer to see whether it is reasonable. Does it make sense? This step is extremely important: –the goal of physics is to describe nature accurately. To determine whether the answer is reasonable, check both its magnitude and its sign, in addition to its units. The magnitude should be consistent with a rough estimate of what it should be. It should also compare reasonably with magnitudes of other quantities of the same type. The sign usually tells you about direction and should be consistent with your prior expectations. Your judgment will improve as you solve more physics problems, and it will become possible for you to make finer judgments regarding whether nature is described adequately by the answer to a problem. This step brings the problem back to its conceptual meaning. If you can judge whether the answer is reasonable, you have a deeper understanding of physics than just being able to solve a problem mechanically.
• Check to see whether the answer tells you something interesting. What does it mean? This is the flip side of the question: Does it make sense? Ultimately, physics is about understanding nature, and we solve physics problems to learn a little something about how nature operates. Therefore, assuming the answer does make sense, you should always take a moment to see if it tells you something about the world that you find interesting. Even if the answer to this particular problem is not very interesting to you, what about the method you used to solve it? Could the method be adapted to answer a question that you do find interesting? In many ways, it is in answering questions such as these science that progresses.

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Unit 14: Converting units of measure

About this unit.

Just as there's more than one way to measure something, there's more than one unit of measure! In this unit, you'll learn all about converting between different units of measure, time to metric and US customary measurements, so you can solve any word problem thrown your way.

Converting units of time

• Converting units: minutes to hours (Opens a modal)
• Converting units of time review (seconds, minutes, & hours) (Opens a modal)
• Convert units of time Get 3 of 4 questions to level up!

Converting metric units

• Converting units: metric distance (Opens a modal)
• Converting units: centimeters to meters (Opens a modal)
• Metric units of mass review (g and kg) (Opens a modal)
• Metric units of length review (mm, cm, m, & km) (Opens a modal)
• Metric units of volume review (L and mL) (Opens a modal)
• U.S. customary and metric units (Opens a modal)
• Convert units (metrics) Get 5 of 7 questions to level up!

Converting metric units word problems

• Measurement word problem: tea party (Opens a modal)
• Time word problem: Susan's break (Opens a modal)
• Convert units word problems (metrics) Get 3 of 4 questions to level up!
• Convert units multi-step word problems (metric) Get 3 of 4 questions to level up!

Converting US Customary units

• Converting units: US volume (Opens a modal)
• Same length in different units (Opens a modal)
• US Customary units of length review (in, ft, yd, & mi) (Opens a modal)
• US Customary units of weight review (oz & lb) (Opens a modal)
• US Customary units of volume review (c, pt, qt, & gal) (Opens a modal)
• Convert units (US customary) Get 5 of 7 questions to level up!

Converting US Customary units word problems

• Measurement word problem: running laps (Opens a modal)
• Measurement word problem: elevator (Opens a modal)
• Measurement word problem: blood drive (Opens a modal)
• Measurement word problem: distance home (Opens a modal)
• Converting units of measurement: FAQ (Opens a modal)
• Convert units word problems (US customary) Get 3 of 4 questions to level up!
• Convert units multi-step word problems (US customary) Get 3 of 4 questions to level up!

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How to Solve Measurement Word Problems

Measurement word problems often involve understanding and using different units of measurement. These problems might ask you to convert from one unit to another or to find a total, difference, or product of given measurements.

A Step-by-step Guide to Solving Measurement Word Problems

Here’s a simple step-by-step guide for a student to solve measurement word problems:

Step 1: Understand the Problem

First, read the problem carefully. Try to understand what the problem is asking you to do. Look for keywords or phrases that indicate what operation you should use (like ‘total’ for addition or ‘difference’ for subtraction).

The Absolute Best Book for 4th Grade Students

Mastering Grade 4 Math The Ultimate Step by Step Guide to Acing 4th Grade Math

Step 2: identify the units and numbers.

Next, write down all the measurements given in the problem, including their units (like meters, grams, hours, etc.). Also, note any numbers that might be important.

Step 3: Decide on the Operation(s)

Determine what operation or operations you need to perform to find the answer. It could be addition, subtraction, multiplication, or division. In some cases, you might need to convert one unit to another.

Step 4: Perform the Operation(s)

Do the math! If you need to convert units, do that first. Then perform the necessary operation or operations.

Step 5: Write Your Answer

Finally, write down your answer, making sure to include the correct unit. Make sure your answer makes sense in the context of the problem.

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Mastering Grade 6 Math The Ultimate Step by Step Guide to Acing 6th Grade Math

Mastering grade 5 math the ultimate step by step guide to acing 5th grade math, mastering grade 3 math the ultimate step by step guide to acing 3rd grade math, mastering grade 5 math word problems the ultimate guide to tackling 5th grade math word problems, mastering grade 2 math word problems the ultimate guide to tackling 2nd grade math word problems, mastering grade 4 math word problems the ultimate guide to tackling 4th grade math word problems.

by: Effortless Math Team about 11 months ago (category: Articles )

Effortless Math Team

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April 18, 2024

Mathematicians Explain Why Some Lengths Can’t Be Measured

Can you assign a size to every object? The surprising answer is no

By Manon Bischoff

aykut karahan/Getty Images

In the past few years, I’ve moved more than once. Time and again, I have had to measure rooms or furniture and then check whether I can arrange everything just as I had planned. When we use a tape measure, folding rule or ruler, we don’t question whether the object we are measuring is measurable. As long as something is not infinitely extended, we should be able to assign it a length, area or volume. That is exactly what mathematicians assumed—until the late 19th century, when everything changed.

For a long time, if you wanted to measure geometric objects, you proceeded as I did when moving house: take out the tape measure and off you go. Admittedly, if you wanted to determine the area underneath a complicated curve, the task became more difficult. With the development of calculus in the 17th century , mathematicians Isaac Newton and Gottfried Wilhelm Leibniz provided new measuring instruments in the form of integrals and derivatives that could be used to precisely determine the size of geometric figures. But for more than 200 years, nobody really asked themselves how objects should be measured.

At the end of the 19th century, when experts attempted to cast mathematics on a stable foundation, set theory became the cornerstone. This theory puts forward that everything—including geometric shapes and complex differential equations—can be traced back to elementary sets. But if geometric shapes are nothing other than sets, then we must find out how to measure abstract sets.

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Let’s take the interval on the number line between 0 and 1, which is written as [0, 1]. It contains an infinite number of real numbers, but, for our purposes, let’s say its length corresponds to one centimeter. Mathematicians like to calculate without units and therefore define that the interval [0, 1] has the length 1. Similarly, the interval [0, 2] has a length of 2, and so on.

Of course, experts did not simply decide this but instead derived it according to certain rules. To establish these rules, they tried to summarize all the intuitive properties that a measure such as length, area or volume should have. Namely, the measure of the empty set should be zero; the measure of an object does not change when you move the object; and the measure of nonoverlapping objects is equal to the sum of the measures of the individual objects. From these three simple conclusions, various dimensions can be defined, including the above-mentioned length dimension, which corresponds to our intuition.

To calculate the measure of nonoverlapping sets, you can add the measures of the individual sets.

Stephan Kulla/Wikimedia Commons ( CC BY-SA 3.0 )

The procedure may seem rather cumbersome: after all, you knew the result intuitively. This approach makes it possible to measure quantities more broadly, however, even those for which there is no geometric conception.

A Measure for Abstract Quantities

When mathematicians first became interested in measures, they initially studied functions (that is, the expression or rule that defines the relationship between two variables, x and y ). You may remember from secondary school that you can determine the area below a function by integrating it. For example, you might use the Riemann integral, in which you form upper and lower sums to determine the area under a curve. See, for example, the blue bars in the image below, which represent how the x axis can be divided into small intervals that can be added together to calculate the total area.

But what happens if the function is extremely complicated? If you look at the fragmented Dirichlet function, for example, you don’t get very far with the usual integral concept. The Dirichlet function χ( x ) has the value 1 if x is a rational number. Otherwise the function’s value is always zero. Graph this function and you will see that χ( x ) consists of an infinite number of points along the line y = 1 and y = 0. Because the graph of the function only consists of individual, disjointed points, it is impossible to use the Riemann integral.

The Riemann and Lebesgue integrals each define integrals by breaking them down. The Riemann integral breaks them down vertically ( blue ), and Lebesgue breaks them down horizontally ( red ).

Svebert/Wikimedia Commons ( CC0 1.0 )

Instead you need to turn to the Lebesgue integral, introduced by mathematician Henri Lebesgue in 1902 . In this case, the y axis is divided into small intervals—as in the red bars in the image above. To calculate an area, you must determine the width of the corresponding intervals on the x axis.

For all ordinary functions that are not as fragmented as the Dirichlet function, the Lebesgue integral and the Riemann integral provide exactly the same result. The advantage of the Lebesgue integral is that it can also assign an area to more complicated cases.

So to return to the Dirichlet function, in the interval [0, 1], let’s use the Lebesgue interval and divide the y axis into small sections. The points of the function only lie at y = 0 for an irrational x value or y = 1 for a rational x value, so the result is 0 times the length of all irrational numbers in the range [0, 1] plus 1 times the length of all rational numbers in [0, 1]. At this point, we need measure theory to assign a length to the abstract sets: the irrational numbers between [0, 1] and the rational numbers between [0, 1]. Because there are only countably many rational numbers (see the image and caption below for a proof of that statement), their measure is zero. The measure of the remaining irrational numbers between [0, 1] must therefore be 1 (because all real numbers in [0, 1] together have the measure 1). The area below the Dirichlet function between zero and one is therefore 1 x 0 + 0 x 1 = 0.

Consider the set M = { m 1 , m 2 , m 3 , ..., m i , ...}. Because M contains countably many elements, they can be numbered with an integer index i . To determine the dimension μ ( M ), one can make an estimate. To do this, form a small interval I i around each m i with a decreasing, arbitrarily small width ε/(2 i ): I i = [ m i − ε⁄(2 i +1 ), m i + ε⁄(2 i +1 )] and form one from it new set C = { I 1 , I 2 , I 3 ,..., I i , ...}. So C is similar to the original set except that it does not contain individual points m but rather small intervals. Overall, the measure of C would have to be at least as large as the measure of M : μ( M ) ≤ μ( C ). Now the measure of C can be calculated by assuming that ε is chosen so small that the intervals I i never overlap. The measure then corresponds to the added lengths of the intervals: μ( C ) = ∑ i ∞ ε/(2 i ) = ε. This means that the measure of M must be less than or equal to ε: μ( M ) ≤ ε. Because ε can be chosen to be arbitrarily small, the measure of M must result in zero. This proves that for every countable set, μ(M) = 0 holds.

Manon Bischoff/ Spektrum der Wissenschaft

The Measurement Problem Appears

The Lebesgue integral gave rise to the so-called measurement problem in 1902. Experts wondered whether it was possible to assign a measure to every quantity. And just three years later mathematician Giuseppe Vitali came up with a sobering answer: no, there are sets that are so jagged that they cannot be measured.

Vitali came to this realization when he constructed a concrete set for which any kind of measure fails: the Vitali set, named after him. He started simply and considered the set of all numbers between 0 and 1. He then divided this set into different areas: two numbers a and b end up in the same range if a – b results in a rational number. For example, all natural numbers and all rational numbers are in the same region. In another region, there are 0,2 + √0,2 and 0,3 + √0,2, and so on. Vitali thus divided the interval [0, 1] into (uncountably) infinitely many small parts.

To construct the Vitali set, decompose the interval [0, 1] into individual regions. Two numbers (pink and purple circles) are in the same range if their difference results in a rational number.

In the next step, he selected exactly one representative r from each of these ranges and inserted all these representatives into a new set V. The set V thus contains an uncountably large number of elements because there are an uncountably infinite number of subdivisions of the interval [0, 1]. Then Vitali turned to a trick: he investigated what happens if the set V is shifted by a rational number p , which assumes a value between [–1, 1]: V p = V + p . As a result, the rational number p is added to every element r in V. In this way, Vitali generated a countably infinite number of sets V p that contain numbers between [–1, 2]. The reason for this is that V contains numbers between [0, 1] and p adds values from the interval [–1, 1].

This is all pretty technical, but don’t worry; we’re almost there! The Vitali set V* contains all V p and, as we will see, goes beyond the concept of measure theory. We know that the measure of V* is at least as large as the measure of the interval [0, 1] (because V* is at least as large as V, which has a range from 0 to 1). On the other hand, the Vitali set is smaller than or equal to the interval [–1, 2]. This means μ ([0, 1]) = 1 ≤ μ(V*) ≤ μ([–1, 2]) = 3. Accordingly, the Vitali set must measure between 1 and 3.

The set V ranges from 0 to 1, while the values  p  range from –1 to 1. Therefore the Vitali set V* extends from –1 to 2.

Manon Bischoff /Spektrum der Wissenschaft

Now you can also calculate the measure of the Vitali set directly: μ(V*) = ∑ p μ(V p ) because there are only countably many p . The set V p contains an uncountable number of elements between [ p , 1 + p ], however, so that μ(V p ) is a finite number greater than zero. And in fact, all V p are the same size—different values of p only represent a shift, which is irrelevant for the size of a set. This means μ(V p ) = μ(V). Accordingly, the measure of the Vitali set is μ(V*) = ∑ p μ(V), i.e. a constant μ(V) that is summed infinitely often. The result of such a calculation is always infinite—regardless of how small the constant μ(V) is. This means: μ(V*) = ∞, which contradicts the above inequality 1 ≤ μ(V*) ≤ 3.

There Will Always Be Nonmeasurable Quantities

The surprising result does not mean we have done the math wrong. Rather, the Vitali set is so complex that no measure can be assigned to it. Vitali thus proved that not all quantities are measurable; there are also “nonmeasurable” quantities.

That result in itself is astonishing. After all, the Vitali set is limited and only contains real values. If you transfer this result to two-dimensional sets, you get even stranger results: for example, you can double the surface area of a sphere by decomposing it into nonmeasurable sets.

Fortunately, nonmeasurable quantities are extremely rare. In physics, for example, they do not occur—after all, decompositions of objects are limited by the size of atoms. You have to construct nonmeasurable quantities in order to come across them. And yet they are omnipresent: even in simple numerical intervals, nonmeasurable sections lurk. As it turns out, it is not so easy to get rid of such quantities. One would have to change the axioms—and thus the foundation—of mathematics to prevent the occurrence of nonmeasurable quantities .

This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission.

• Maths Questions

Measurement Questions

Measurement is the basic concept that everyone deals with in real-life situations. For instance, we generally use tonnes, kg, and g weights to purchase fruits or vegetables. When we purchase 5 kg of fruits, 5 represents the measurement and kg denotes the unit of measurement.

What is Measurement?

Measurement is the technique of finding a number that signifies the amount, quantity, and size of a thing or object. For example, the length of an object is the distance from end to end. Some basic measurements are:

• Length or distance
• Temperature

Learn more about measurement in maths here.

Measurement Questions and Answers

1. Calculate the sum of lengths: 21 m 13 cm, 33 m 55 cm and 45 m 6 cm.

21 m 13 cm + 33 m 55 cm + 45 m 6 cm

= (21 + 33 + 45) m (13 + 55 + 6) cm

= 99 m 74 cm

Therefore, the sum of given lengths = 99 m 74 cm.

2. Beena bought 3 kg 760 grams of wool to make a carpet. How much more wool does she need to make the weight 4 kg?

Given the weight of wool = 3 kg 760 grams

Let us convert this weight into grams.

3 kg 760 grams = (3 × 1000 + 760) grams

= (3000 + 760) grams

= 3760 grams

4 kg = (4 × 1000) grams = 4000 grams

Difference = (4000 – 3760) grams = 240 grams

Therefore, 240 grams of more wool is required.

3. A pile of 10 books is 10 cm high. What is the thickness of each book?

As we know,

1 cm = 10 mm

Given that the height of a pile of 10 books = 10 cm

10 books = 10 cm

= 10 x 10 mm

1 book = 100/10

Therefore, the thickness of each book = 10 mm.

4. A furlong is a unit of length used in horse racing; it equals one-eighth of a mile. To the nearest tenth, how many metres are equal to a furlong if 1.609 km equals a mile?

1.609 km = 1 mile

That means 1609 m = 1 mile

Also, one furlong = one-eighth of a mile

= (1/8) × 1.609 km

= (1/8) × 1609 m

= 201.1 m (approx)

5. The cost of 1 litre of syrup is Rs. 840.80. Find the cost of 600 ml of the syrup.

The cost of 1 litre of syrup = Rs. 840.80

1 litre = 1000 ml

The cost of 600 ml of the syrup = (600/1000) × Rs. 840.80 = Rs. 504.48

6. One inch equals 2.54 centimetres. How many centimetres tall is an 84-inch door?

1 inch = 2.54 cm

84 inch = ?

84 inch = 84 × 2.54 cm

= 213.36 cm

Thus, the door is 213.36 cm tall.

7. Vinu and Shan together weigh 72 kg 350 g. If Vinu weighs 39 kg 185 g, what is Shan’s weight?

Vinu’s weight = 39 kg 185 g

Let x be Shan’s weight.

According to the given,

39 kg 185 g + x = 72 kg 350 g

x = 72 kg 350 g – 39 kg 185 g

= (72 – 39) kg (350 – 185) g

= 33 kg 165 g

Therefore, Shan’s weight is 33 kg 165 g.

8. A tabletop measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the tabletop?

We know that,

1 m = 100 cm

1 cm = 0.01 m

Length of tabletop = 2 m 25 cm = 2.25 m

Breadth of tabletop = 1 m 50 cm = 1.50 m

Perimeter of tabletop = 2 (Length + Breadth)

= 2 (2.25 + 1.50)

Therefore, the perimeter of the tabletop is 7.5 m.

9. Two sides of a triangle are 11 cm and 15 cm. If the perimeter of the triangle is 36 cm, find its third side.

Let x cm be the third side of the triangle.

Two sides: 11 cm and 15 cm

Perimeter of triangle = 36 cm

11 + 15 + x = 36

26 + x = 36

x = 36 – 26

Hence, the third side of the triangle is 10 cm.

10. The weight of a rice packet is 40 kg 360 g. What is the total weight of 6 rice packets of the same weight?

Weight of a rice packet = 40 kg 360 g

Number of rice packets = 6

Total weight = 6 × weight of one rice packet

= 6 × (40 kg 360 g)

= (6 × 40) kg (6 × 360) g

= 240 kg 2160 g

= 240 kg (2000 + 160) g

= (240 + 2) kg 160 g

= 242 kg 160 g

Thus, the total weight of 6 rice packets = 242 kg 160 g.

Practice Questions on Measurement

• If a watermelon’s weight is 1 kg 300 g, find the weight of 12 watermelons.
• Which is the best estimation for the length of a pen?
• Convert 2550 mm to metres and cm.
• A water tank can hold 1500 l of water in it. If it has 960 l 550 ml of water; how much water can be poured into it?
• The length of a goods train is 266 m. The length of a passenger train is 113 m. Which train is longer in length? And by how much?

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Indirect Measurement – Explanation and Examples

JUMP TO TOPIC

What Is Indirect Measurement?

Pythagorean theorem, similar triangles and proportionality, practice questions:, answer key:.

Indirect measurements are different from direct measurements and are mostly applied or used when direct measurement is not possible. It can be done by using the Pythagorean theorem, similar triangles, and proportions.

This topic will help you understand the concept of indirect measurement and how to use it, as well as cover multiple numerical examples so that you can grasp the concept quickly.

Indirect measurement is a method that is used in scenarios where direct measurement is not possible . These methods can be used to measure the width of the river and the height of an object using its shadow or other available measurements.

Indirect measurement in surveying is another example. Basically, we will model the given scenario in the form of triangles and then calculate the desired value using proportions, similar triangles, and the Pythagorean theorem .

For example , you want to measure the height of a tree but you do not have the tools to measure the height of the tree directly. In such a scenario, you will have to measure the height of the tree indirectly.

We can measure the height of the tree by standing next to it while using indirect measurement methods such as a mirror or the shadow of the tree. Both methods need the presence of sunlight, otherwise, both of these methods won’t work. Let us discuss both of these methods in detail .

Suppose a person is standing in front of the tree while a mirror is placed on the ground in between them.

The person is standing in such a way that he or she can easily see the tip of the tree. If the person is looking at the mirror, then by using the reflection property of the light and a mirror we can create a concurrent angle at each side of the mirror.

If we assume the person is standing straight and the tree is also straight like an arrow, then we can assume that both are standing at $90^{o}$ angle. We can create similar triangles for this case and then solve for the height of the tree .

Let’s continue with the same example, but this time we will use the shadow of the person and the tree to generate similar triangles.

Suppose a person is standing in front of the tree while the sun is out and if we assume the angle of the sun remains constant, then the shadow cast by the person and the tree can be used to draw similar triangles .

If we assume the person and tree are standing straight at an angle of $90^{o}$ and if we draw a line from the top of the tree and the person to the end of their shadows, then it gives us two similar triangles .

Indirect Measurement Techniques

There are several techniques that can be used to solve problems where direct measurement is not possible.

The Pythagorean or Pythagoras theorem is a theorem that is used to formulate a relation between three sides of a right-angle triangle . According to the Pythagorean theorem, if a right angle triangle is given, then the relation for the three sides of the triangle can be given as:

$c^{2}= a^{2}+ b^{2}$

The Pythagorean theorem can be used as an indirect measurement technique.

For example , we want to estimate the length of the bridge that needs to be built across a river. If we know the distance across the river and the height of the land on the higher side of the river, then the bridge will be like a hypotenuse in a right-angle triangle. If the distance across the river is $20$ meters and the height of the bank (on the higher side of the river ) is $5$ meters, then the length of the bridge can be calculated as:

$c^{2} = b^{2} + c^{2}$

$c^{2} = 20^{2} + 5^{2}$

$c^2 = 400 + 25 = 425$

$c = \sqrt {425} \cong 20.62$ meters.

Similar triangles’ properties are extensively used in solving problems via indirect measurement. Two triangles are said to be similar if their corresponding angles are similar or concurrent .

The shapes of both triangles are similar while the size of the triangles may vary. If we can draw two similar triangles for a given problem, then we can find the missing data of the triangles by using the proportions method .

Similar triangles and proportionality can simply be named as triangle proportionality theorem. Let us study a simple example of triangle proportionality.

$\dfrac{AD}{DB} = \dfrac{AE}{EC}$

$\dfrac{10}{15} = \dfrac{x}{20}$

$x = \dfrac{2\times 20}{3}$

$x = \dfrac{40}{3}$cm

Let us now study various direct and indirect measurement examples.

Allan has a tree outside his house, but he cannot measure its height directly as the tree is quite high, so you are required to help Allan to determine the height of the tree. During this time of the day, the shadow of the tree is $150$ ft while the shadow of Allan (if he stands in front of the tree) is $5$ ft. If Allan is $4$ ft tall, what is the height of the tree?

We are taking the length of both shadows at the same time, so the angle of the sun will remain constant and if the tree and Allan are making an angle of $90^{o}$ i.e they are standing dead straight vertically, then we can assume that Allan is standing parallel to the tree and we will have two similar triangles.

Let “$x$” be the height of the tree, then by using the triangle proportionality theorem we can write:

$\dfrac{4 ft}{x} = \dfrac{5}{150}$

$\dfrac{4 ft}{x} = \dfrac{1}{30}$

$x = 4 \times 30 = 120$ ft

Sana has a pole outside her house that she wants to measure the length of, but she cannot measure it directly. You are required to help Sana out in the calculation of the height of the pole using the mirror method.

Sana is $1.8$ meters tall and she can see the top of the pole if she places the mirror on the ground while standing $5$ meters away from the mirror. The mirror is $35$ meters away from the pole. What is the height of the pole?

If we assume that both the pole and Sana are standing at $90^{o}$ angle, then the reflection of the mirror will create triangles having congruent angles. Hence, two similar triangles are created and we can use the triangle proportionality theorem to determine the height of the pole.

Let “$x$” be the height of the pole, then by using the triangle proportionality theorem we can write:

$\dfrac{35 m}{5 m} = \dfrac{x}{1.8 m}$

$7 = \dfrac{x}{1.8 m}$

$x = 1.8 \times 7 = 12.6$ meter

A building casts a shadow that is $35$ meters long while at the same time a man standing parallel to the building casts a shadow that is $4.5$ meters long. If the man is $4$ meters tall, what is the height of the building?

$\dfrac{35 m}{4.5 m} = \dfrac{x}{4 m}$

$7.7 = \dfrac{x}{4 m}$

$x = 4 \times 7.7 = 31$ meter approx.

Nancy is playing basketball on the basketball court outside her house. Nancy knows she is $5$ ft tall and she is casting a shadow that is $5.5$ ft tall while the hoop of the basketball is $10$ ft tall. What is the length of the shadow of the basketball hoop?

Let “x” be the length of the shadow of the hoop, then by using the triangle proportionality theorem we can write:

$\dfrac{5 ft}{5.5 ft} = \dfrac{10 ft}{x}$

$0.909 = \dfrac{10}{x}$

$x = \dfrac{10}{0.909} = 11$ ft approx.

1. For the picture given below, is the $\triangle ABC \cong \triangle EDC$? How is $AB$ parallel to $DE$? If both the triangles are similar, then calculate the width of the river if $AB = 25$ ft, $BC = 30$ ft, and $DE = 60$ ft.

2. A tree casts a shadow that is $40$ ft long, while at the same time a man standing parallel to the tree casts a shadow that is $5$ ft long. If the man is $4.5$ ft tall, what is the height of the tree?

$\triangle ABC$ is concurrent to $\triangle EDC$. As angle B and angle D, both are right angles while $\angle ABC \cong \angle ECD$ as both are vertical angles and hence, by A. A similarity postulates both these triangles are called similar triangles .

As both the triangles are similar and by A.  A postulate $\angle ABC \cong \angle ECD$, if the alternate interior angles are congruent to each other then the corresponding line segments are parallel to each other . Hence, $AB || DE$.

The width of the river is can be determined by calculating the length of the CD. We can do that by using the triangle proportionality theorem .

$\dfrac{30 ft}{CD} = \dfrac{25}{60}$

$CD = 72$ ft.

$\dfrac{40 ft}{5 ft} = \dfrac{x}{4.5 ft}$

$8 = \dfrac{x}{4.5 ft}$

$x = 4.5 \times 8 = 36$ ft.

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5 Fun Measurement Activities for Your Elementary Classroom

• Math , Math Games , Project Based Learning

Teaching students how to measure length naturally lends itself to a hands-on learning experience. But you may be ready to take things up a notch from your go-to classroom measurement scavenger hunt. These measurement activities create a more meaningful, engaging experience that connects this real-world skill to your classroom.

All five of the ideas I’m sharing today will allow your students to experience your measurement unit in unique, hands-on ways, and truly help them build a strong foundational understanding of how to measure length. 

Get Rulers That Set Your Students Up for Success

When your elementary students are getting the hang of measuring length, provide rulers that start at zero without that extra gap at the beginning . This will help them get more accurate measurements out of the gate and boost their confidence as they work to master this new skill. 

These flexible rulers by ETA Hand-To-Mind are the only rulers you’ll ever need. Here’s why you’ll love them:

• The alternating colored bands make it easy for students to see where one inch (or centimeter) ends and the next begins. This bold visual is so helpful in reinforcing the concept of how long each unit of measure is, which boosts measuring accuracy and efficiency. 
• The flexible plastic makes these rulers last longer than those other hard plastic rulers you can grab at the dollar spot during back-to-school season. 
• Each inch is divided into 4ths, making it easy to teach ¼, ½, and ¾ inch without all the other lines found on most rulers. 
• The end of the ruler is 0. There isn’t that pesky little gap before the 0 that makes it tricky for young learners to make accurate measures when first learning this new concept. 

Use A Project As Your Summative Measurement Assessment 

Bring a hands-on focus to your length measurement unit by celebrating students’ learning with a unique math project that sparks friendly competition . Measure-Thon has everything you need (including a completed sample project and editable rubric) which makes adding this measurement activity to your schedule a no-brainer. 

During the Measure-Thon simulation, your students will compete in four measuring events. They will test their physical strength as they blow, kick, flick, and toss a cotton ball through the air. They’ll also flex their mental power as they measure the distance their cotton ball travels using centimeters, inches, and feet. 

Here are the steps your students will take as they work towards becoming champion Mathlete :

• Warm Up (students learn everything they need to know to compete)
• Locker Room (students meet their team & gather equipment before competing)
• Competition (students compete in all four events, measure, and record their results)
• Team Meeting (students add their results to the class graphs and analyze their data)
• Award Ceremony (event champions and participants receive awards)

A detailed teacher’s guide outlines every step of the Measure-Thon experience with clear visuals and step-by-step instructions. A ready-to-use slide deck helps you guide students through each phase of this measurement activity. Rubrics and reflection prompts will encourage your students to reach their learning goals throughout the project. 

The format of this math project makes it an ideal resource for:

• A focal point for a measurement room transformation 
• An alternative assessment that allows you to measure student understanding on a deeper level as a culmination to your 2nd grade measurement unit. 
• At your seat & hands-on enrichment during math workshop or guided math
• Math center work
• Parent volunteer or teacher’s aide enrichment station

Teachers love using this measurement project in their classrooms:

♥ “I used this as a cumulative review at the end of our measurement chapter. My kids had so much fun! Everyone was engaged, and everyone was able to fully participate. Perfect activity. Thank you!” – Elizabeth P.

♥ “Oh my goodness… talk about engagement!! My kids LOVED this activity! I was also observed during one of the days, so I appreciated the standards and station posters to give clear direction! Thank you!” – Kacie B.

♥ “I love this project and how it involves all the students! We did this for a week following our measurement unit as a review for our upcoming test. I will continue to use this every year!” – Elise V.

♥ “This is a fantastic resource to use with students to emphasize skills in measurement. I found this when I was looking for additional resources to use after our measurement unit and love how this is laid out.” – Caitlin A.

♥ “My kids went crazy for this!” – Ashley L.

If you click the button above, you will be directed to the original Measure-Thon. I also have a fall-themed version and a winter-themed version in my shop.

Using Unique Games To Help Students Articulate Their Measurement Knowledge 

Math games are a friendly way to invite students to show their understanding of length measurement through conversation and problem-solving. 

When you carefully select games that give your students an opportunity to practice foundational measurement skills while having fun & communicating with their classmates , learning becomes more effortless. 

If you are looking for games that get your students up, moving, talking, and laughing, Core Inspiration’s Hands-On Measurement Games are a perfect measurement activity for your classroom. 

One of the best things about these math games is you can easily walk around the room while students play and get a better idea of each student’s understanding of the measurement skills you’ve introduced so that you can plan and adjust instruction accordingly. 

No printable worksheets to add to your grading pile… just straightforward, meaningful observation data. Your students will have so much fun playing , they won’t even notice how much “work they’re getting done” and how much data you’re able to collect!   

When you use these math games in your classroom, you will effortlessly:

• Build student independence through hands-on measurement learning each day 
• Foster collaboration between students 
• Help students develop math communication skills
• Develop stronger measurement problem-solving skills in your learners

No matter how you organize your math block, these games make it a breeze to incorporate hands-on measurement practice in your elementary classroom. Teachers have successfully used these games for:

• Hands-on rotation during math workshop
• Partner work /math with someone 
• Low-prep station for aides and parent volunteers 
• Guided math centers
• Alternative assessment tools

Here’s why teachers like you love using these hands-on math games in their classrooms:

♥ “These hands-on games were a wonderful way to add play into our math centers. They were highly engaging and helped solidify skills students were working on in a fun and active way. “ – Bethany T.

♥ “My students loved this resource and gave some great in-class collaboration working together with a partner to learn about measurements and how to choose and use the appropriate tools.” – Rachel S. 

♥ “My students loved getting up and moving while working on their measurement skills. These were some of our favorite stations in the unit!” – Kimberly C. 

Bring Some Creative Thinking To Your Measurement Unit 

When you hear creativity and measurement in the same sentence, art projects are probably one of the first things that come to mind. If you’re not up for a math-themed art project this time around but still want to harness your students’ creativity and push them to think outside the box, give these no-prep measurement activities a try . 

Each printable measurement activity in this resource leads to: 

• hands-on exploration
• creative thinking
• math reasoning
• modeling to find solutions

The open-ended questions included in each measurement activity make this resource the perfect self-differentiation tool and give you insight into how deeply your students understand measurement math concepts.

Bring Choice To Your Measurement Word Problem Practice

Boost engagement and problem-solving skills during your measurement unit by providing your students with a variety of multi-step word problems written at different mastery level s. Differentiated instruction just got a whole lot easier for you and more motivating for your students! 

With three types of task cards to choose from, your students will participate in rigorous problem-solving opportunities that meet them at their current level of understanding.

Differentiated Measurement Activities At 3 Problem-Solving Levels:

• Making Meaning Tasks are designed for students who are working to apply and master second-grade measuring length concepts.
• Challenge Tasks are designed for students who are ready to take their learning to the next level and tackle more advanced, complex word problems. 
• Transfer Tasks are designed for students who are ready to demonstrate their mastery of a standard through carefully-crafted summative assessment problems.  Each of these higher-order tasks requires students to evaluate, design, analyze, make connections, or find patterns while problem-solving. 

These measurement activities build problem-solving skills as students:

• Carefully analyze what math skills are required to find a solution.
• Create detailed math models that show their math reasoning.
• Record their solution in a complete sentence.

THE EASY BUTTONS FOR YOUR MEASURING LENGTH UNIT

With these five must-haves, you can provide effective differentiation to ensure all students have adequate hands-on practice during your measurement unit. To make your teacher life even easier, I’ve linked all five of the resources I’ve shared in this post in the list below. I hope your measurement unit is more fun, easier, and more effective than ever before!

• Measure-Thon Math Project
• 2nd Grade Length Measurement Hands-On Games
• 2nd Grade Length Measurement  Differentiated Task Cards
• 2nd Grade Ready, Set, Think No Prep Measurement Printables
• Favorite Rulers by ETA Hand-To-Mind
• Read more about: Math , Math Games , Project Based Learning

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2: Measurement and Problem Solving

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Chemistry, like all sciences, is quantitative. It deals with quantities , things that have amounts and units. Dealing with quantities is very important in chemistry, as is relating quantities to each other. In this chapter, we will discuss how we deal with numbers and units, including how they are combined and manipulated.

• 2.1: Taking Measurements Chemists measure the properties of matter and express these measurements as quantities. A quantity is an amount of something and consists of a number and a unit. The number tells us how many (or how much), and the unit tells us what the scale of measurement is. For example, when a distance is reported as “5 kilometers,” we know that the quantity has been expressed in units of kilometers and that the number of kilometers is 5.
• 2.2: Scientific Notation - Writing Large and Small Numbers Chemists often work with numbers that are exceedingly large or small. For example, entering the mass in grams of a hydrogen atom into a calculator requires a display with at least 24 decimal places. A system called scientific notation avoids much of the tedium and awkwardness of manipulating numbers with large or small magnitudes.
• 2.3: Significant Figures - Writing Numbers to Reflect Precision Uncertainty exists in all measurements. The degree of uncertainty is affected in part by the quality of the measuring tool. Significant figures give an indication of the certainty of a measurement. Rules allow decisions to be made about how many digits to use in any given situation.
• 2.4: Significant Figures in Calculations To round a number, first decide how many significant figures the number should have. Once you know that, round to that many digits, starting from the left. If the number immediately to the right of the last significant digit is less than 5, it is dropped and the value of the last significant digit remains the same. If the number immediately to the right of the last significant digit is greater than or equal to 5, the last significant digit is increased by 1.
• 2.5: The Basic Units of Measurement Metric prefixes derive from Latin or Greek terms. The prefixes are used to make the units manageable. The SI system is based on multiples of ten. There are seven basic units in the SI system. Five of these units are commonly used in chemistry.
• 2.6: Problem Solving and Unit Conversions During your studies of chemistry (and physics also), you will note that mathematical equations are used in a number of different applications. Many of these equations have a number of different variables with which you will need to work. You should also note that these equations will often require you to use measurements with their units. Algebra skills become very important here!
• 2.7: Solving Multistep Conversion Problems Sometimes you will have to perform more than one conversion to obtain the desired unit.
• 2.8: Units Raised to a Power Conversion factors for area and volume can also be produced by the dimensional analysis method. Just remember that if a quantity is raised to a power of 10 both the number and the unit must be raised to the same power of 10.
• 2.9: Density Density is a physical property found by dividing the mass of an object by its volume. Regardless of the sample size, density is always constant.
• 2.E: Homework Chapter 2
• 2.E: Homework Chapter 2 Answers

• Open access
• Published: 22 April 2024

The power of laughter: a study on humor and creativity in undergraduate nursing education in Egypt

• Mona Metwally El-Sayed 1 ,
• Eman Sameh AbdElhay 2 ,
• Manal Mohammed Hawash 3 &
• Samah Mohamed Taha 2  

BMC Nursing volume  23 , Article number:  259 ( 2024 ) Cite this article

Metrics details

Creativity in nursing education is crucial for developing practical problem-solving skills, and humor is a valuable tool for stress management and fostering a positive learning environment. This study explored the relationship between creativity and humor among nursing students.

A cross-sectional survey was conducted with 265 convenient undergraduate nursing students aged 20 to 25. The Short Scale of Creative Self (SSCS) and the Multidimensional Sense of Humor Scale (MSHS) were used to measure creativity and various aspects of humor.

Showed a significant positive correlation between humor and creativity ( r  = 0.238, p  < 0.001). Positive correlations were found between Humor Production, Coping or Adaptive Humor, and Appreciation of Humor with creativity ( r  = 0.254, 0.230, and 0.461, p  < 0.001, respectively). In contrast, Attitudes Toward Humor and Humorous People were negatively correlated with creativity ( r =-0.343, p  < 0.05). Humor accounted for 16.2% of the variance in creativity.

The study concluded a strong link between humor and creativity, with positive correlations observed between creative self-efficacy and creative personal identity with different aspects of humor. The study recommends the incorporation of humor into nursing education and healthcare settings to encourage creative problem-solving and reduce burnout among students and staff.

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Introduction

Nursing education gives individuals the necessary knowledge and skills to become competent healthcare providers. The American Association of Colleges of Nursing (AACN) reports that improving the educational level of nurses leads to better patient outcomes, lower mortality rates, reduced readmission rates, and shorter hospital stays [ 1 ]. Learning in nursing is usually facilitated through course materials, quizzes, assignments, and discussions. Students are encouraged to actively engage in learning and find ways to improve their understanding. However, some challenges may negatively impact their academic achievement, such as boredom [ 2 ], disinterest in the course, withdrawal, and reluctance to take responsibility [ 3 ]. Humor can create a less intimidating learning environment, increasing students’ motivation to complete their assigned activities [ 4 , 5 , 6 ].

Humor is a playful and light-hearted approach that can ease tension, handle uncomfortable situations, and enhance communication and comprehension in educational settings [ 7 ]. It is a complex phenomenon that involves cognitive, emotional, behavioral, psychological, and social aspects [ 8 , 9 ]. It is a fundamental part of daily life and can act as a coping mechanism [ 8 ]. Humor is a positive experience that transcends cultural and social boundaries. It is the ability to recognize and appreciate the comical aspects of a situation [ 9 ]. Humor can play a vital role in engaging students in learning by directing their attention to the necessary information and creating a pleasant, emotional, and social atmosphere [ 10 ]. Humor can boost motivation in the learning process and improve students’ creative thinking abilities throughout learning activities [ 10 ].

Using humor in nursing education can be effective if it follows specific standards that ensure its positive impact. These standards include appropriateness, timing, and sensitivity to the needs of students. It is important to use humor respectfully, upholding the students’ dignity and not detracting from the seriousness of the educational environment [ 11 ]. To balance lightheartedness and professionalism, it is crucial to use humor in moderation and prevent it from becoming a distraction. Humor can be a valuable tool to break the ice, foster rapport, and reduce stress for students and educators. By applying humor thoughtfully and in line with these criteria, nursing students can have an enhanced educational experience while maintaining professionalism and respect [ 11 , 12 ].

Nursing education in Egypt considers creativity a fundamental skill. Creativity is crucial in helping nurses provide top-notch patient care as nursing tasks become more complicated [ 13 ]. Creativity lies in systematically generating innovative and meaningful ideas, and it is a vital component of nursing education, encompassing the arts and sciences [ 14 ]. It is a complex and multifaceted concept with various definitions [ 15 , 16 ]. Studies have demonstrated that promoting creative problem-solving skills and fostering creativity through teaching innovative teaching methods among nursing students can improve their academic performance [ 13 , 17 , 18 , 19 ]. Therefore, it is crucial to identify the factors influencing their creativity to promote creative thinking among nursing students.

Although the research agenda stresses the significance of exploring various areas, such as personalities and impediments, in education, there has been limited empirical research on creativity in nursing education [ 20 , 21 ]. However, the National Curriculum Standards in Undergraduate Nursing Program (NCSN) emphasizes that creativity, aesthetics, ethics, politics, and technical expertise are essential tools that enable students to make meaningful contributions to the care network, emphasizing patient care and a commitment to the healthcare system [ 22 ].

Chen and colleagues (2019) discovered that an excellent sense of humor is often associated with higher creative abilities. The confluence model explains the mechanism behind humor and its positive effects on creativity. From a cognitive perspective, understanding humor requires utilizing critical, creative skills. Positive emotions can lead to higher cognitive flexibility and more free associations, which benefit creativity. The emotional perspective highlights how humor fosters a positive attitude toward creativity. Appreciating humor can create positive emotions that may result in better creative output. Lastly, the motivational perspective clarifies how the happiness derived from humor leads to a strong motivation to engage in creative activities [ 23 ]. While some research indicates that positive emotions may promote unconventional ideas, other studies suggest that positive emotions may not necessarily confer any advantage in creative performance [ 24 ].

Research in nursing and education highlights the importance, relevance, and beneficial effects of incorporating humor in enhancing the educational experience [ 25 , 26 ]. Humor aids in mitigating stress and fostering a sense of unity among students and faculty, creating a more supportive and cooperative atmosphere [ 11 ]. This can stimulate creativity by inspiring students to think innovatively and tackle challenges with a fresh mindset. Incorporating humor and creativity in undergraduate nursing education is indispensable for developing well-rounded and capable nurses who can adeptly handle the complexities of patient care [ 12 ]. By creating a fun and engaging learning environment, students can be more motivated and inspired to excel in their studies. This benefits the students and enhances the quality of care they can provide for their patients [ 25 ].

The significance of humor and creativity in nursing education is paramount. Integrating these concepts in nursing education is essential for nurturing a new generation of skilled, knowledgeable, compassionate, and resilient nurses. Nevertheless, there appears to be a research gap in this field, particularly in Egypt and the MENA region. This study aimed to bridge this gap by investigating the relationship between humor and creativity among nursing students to understand how humor can foster creativity and enhance nursing practices.

Research hypothesis

Nursing students with higher humor would have higher creativity.

Research design

An observational cross-sectional survey, adhering to STROBE guidelines, was used, and data collection occurred from April 1st to June 30th, 2023.

The study was conducted at the College of Nursing at Mansoura University, which is affiliated with the Ministry of Higher Education in Egypt. The college offers nine undergraduate nursing programs through a credit-hour system.

Participants

The target population for this study was the 2nd-semester students enrolled during the 2022–2023 academic year.

Sample size calculation

The sample size for this study was determined using specific procedures. The population data was based on the total number of registered students in the 2nd semester of 2022–2023 at the College of Nursing, Alexandria University, which was 805. The Office of Undergraduate Nursing Students provided this data. The desired precision and confidence level was set at an absolute error (d) of 5%, a type 1 error (α) of 5%, a z-score of 1.96, and a 95% confidence level, based on previous studies by Goriup et al. (2017) and Barutcu (2017) [ 27 , 28 ]. The formula \( \frac{\left(Z1- a/2\right)*p(1-p)}{d2}\) was used to calculate the required sample size, resulting in a minimum sample size of 238. After considering an unresponsive rate of 10%, the final sample size was adjusted to 265.

Inclusion and exclusion criteria

The study was conducted with 2nd -semester undergraduate students from the College of Nursing at El-Mansoura University during the 2022–2023 academic year. Inclusion in the research was voluntary, and those who chose not to participate were excluded. Furthermore, students with self-reported pre-existing psychiatric conditions who received pharmacological or psychotherapies for such conditions were also excluded.

Sampling and recruitment

A convenient sample of undergraduate students was recruited. The total number of invited students was 291. Sixteen refused to participate, 4 initially accepted, withdrew, and did not complete the questionnaires, and 6 were deemed ineligible. These final 265 participants formed the basis for the subsequent analysis ( Fig.  1 ) .

Flow chart of participants’ recruitment process

Study measures

Demographic characteristics data sheet.

The researchers developed it to elicit demographic characteristics of the participants, such as age, gender, marital status, region of residence, living arrangement, recreational activities, family monthly income, and work while studying.

Short scale of creative self (SSCS)

The SSCS evaluates two aspects of creativity: Creative Self-Efficacy (CSE) and Creative Personal Identity (CPI) [ 29 ]. The scale consists of 11 items, with six dedicated to the CSE subscale and five to the CPI subscale. Each item is scored on a 5-point Likert scale, where 1 signifies “definitely not,” and 5 represents “definitely yes.” The total score can range from 11 to 55, with higher scores indicating greater creativity. The CSE subscale scores can range from 6 to 30, and the CPI subscale scores can range from 5 to 25. The internal consistency of the two subscales was further supported by high Cronbach’s alpha values: 0.83 for CSE and 0.89 for CPI.

Multidimensional sense of humor scale (MSHS)

The MSHS is a comprehensive tool for assessing various aspects of humor [ 30 ]. It consists of 24 items that capture four independent dimensions of humor: (i) humor production and creativity, e.g., “Other people tell me that I say funny things.” (ii) coping or adaptive humor, e.g., “Uses of humor help to put me at ease.” (iii) appreciation of humor, e.g., “Humor helps me cope.” and (iv) attitudes toward humor and humorous people. “Calling somebody a “comedian” is a real insult”. The scale is presented as a 5-point Likert scale, ranging from 0 (strongly disagree) to 4 (strongly agree), with a possible total score between 0 and 96, calculated by summing the scores of each factor. The scale demonstrated high internal consistency, as indicated by a high Cronbach’s alpha of 0.91.

Ethical approval

Official permissions for the study were secured from the responsible authorities at the College of Nursing, Mansoura University. Before inclusion in the study, participants had to provide informed consent, which involved signing a document. The study’s purpose was communicated to the participants, emphasizing the anonymity of their responses and the assurance of confidentiality. Detailed instructions were provided on how to respond to the study tools. Utmost care was taken to respect the privacy and confidentiality of the data, which was maintained throughout the study. Students were informed of their right to participate and their freedom to withdraw from the study.

Pilot study and reliability

Prior to the commencement of the main study, a preliminary pilot study was conducted involving 20 nursing students. These students did not participate in the main study. The pilot study confirmed that all the tools used were accurate, Comprehensible, and suitable for the study. The internal consistency of the study measures was evaluated using Cronbach’s Alpha test.

Data collection

After the pilot study participants were excluded, a convenient sample was selected. Trained researchers conducted structured interviews with each participant, collecting necessary data using data collection tools. Each interview, lasting approximately 10–15 min, was conducted in a private setting, such as an empty classroom or clinical lab, to ensure privacy. Informed consent was obtained from each participant, ensuring their anonymity and confidentiality. The interviewers held no authority over the students, and there were no incentives for participation. The students were reassured that their participation was voluntary and that they had the right to withdraw without repercussions. All responses were kept confidential. To ensure the accuracy and completeness of the information, researchers meticulously reviewed the responses to the data collection tool provided by each participant.

Data analysis

Data analysis was performed using IBM SPSS software (version 26.0). A meticulous review and verification were conducted following data entry to ensure accuracy. The distribution normality of quantitative variables was evaluated using Kolmogorov-Smirnov and Shapiro’s tests. Cronbach’s alpha was used to assess the internal consistency of the research instruments, thereby indicating their reliability. The humor and creativity subscales were summarized using means (M), standard deviations (SD), and frequencies or percentages for categorical variables. Pearson’s correlation coefficient measured the strength and direction of the relationship between two normally distributed quantitative variables. A multiple linear regression analysis was carried out to determine the impact of various humor domains on creativity. All results were deemed significant at the 5% ( p  < 0.05).

Table  1 shows that the majority were female (61.51%). The age distribution was even, with 32.83% being 20 or older, 28.68% between 21 and 24 years, and 38.49% being 25 years or more. Most participants were single (93.58%) and lived with their families (74.71%). The participants were almost evenly split between urban (53.20%) and rural (46.80%) residences. Regarding income, 25.66% reported their family income as insufficient, while 51.32% found it somewhat sufficient, and 23.02% considered it sufficient. A significant majority of the students (90.94%) worked while studying. Regarding recreational activities, 70.19% engaged in sports, 33.21% in art and music, 93.96% enjoyed going on trips, 26.04% participated in campus activities, and 50.57% participated in cultural activities.

Table  2 presents the participants’ average scores on the Self-Concept of Creativity Scale (SSCS) and the Multidimensional Sense of Humor Scale (MSHS). The SSCS mean score for the Creative Self-Efficacy subscale was 22.29 (SD = 4.76); for the Creative Personal Identity subscale, it was 19.31 (SD = 2.52). The total mean score for the SSCS was 41.60 (SD = 7.28). Regarding the MSHS, the mean scores were as follows: 21.48 (SD = 2.56) for the Humor Production and Creativity subscale, 14.27 (SD = 2.68) for the Coping or Adaptive Humor subscale, 7.56 (SD = 1.96) for the Appreciation of Humor subscale, and 8.58 (SD = 2.48) for the Attitudes Toward Humor and Humorous People subscale. The total mean score for the MSHS was 51.89 (SD = 9.68).

Table  3 presents the Pearson correlation coefficients (r) between various aspects of humor and creativity among the participants. The Creative Self-Efficacy subscale demonstrated a significant positive correlation with the Humor Production and Creativity subscale ( r  = 0.224, p  < 0.001) and the Appreciation of Humor subscale ( r  = 0.529, p  < 0.05). However, it negatively correlated with the Attitudes Toward Humor and Humorous People subscale ( r =-0.224, p  < 0.05). Similarly, the Creative Personal Identity subscale exhibited significant positive correlations with the Humor Production and Creativity subscale ( r  = 0.265, p  < 0.001) and the Appreciation of Humor subscale ( r  = 0.417, p  < 0.05). It also negatively correlated with the Attitudes Toward Humor and Humorous People subscale ( r =-0.251, p  < 0.05). The total scores of the SSCS displayed significant positive correlations with the Humor Production and Creativity subscale ( r  = 0.254, p  < 0.001), the Coping or Adaptive Humor subscale ( r  = 0.230, p  < 0.05), the Appreciation of Humor subscale ( r  = 0.461, p  < 0.05), and the total of the MSHS ( r  = 0.238, p  < 0.001). However, they had a negative correlation with the Attitudes Toward Humor and Humorous People subscale ( r =-0.343, p  < 0.05).

Table  4 presents a multiple linear regression analysis examining the effect of various aspects of humor on creativity among participants. The model was statistically significant (F = 169.782, p  < 0.001) and explained 16.2% of the variance in creativity (Adjusted R^2 = 0.162). All four humor variables showed significant effects on creativity. Specifically, the Humor Production and Creativity subscale (B = 0.226, Beta = 0.102, p  < 0.001) and the Coping or Adaptive Humor subscale (B = 0.071, Beta = 0.121, p  < 0.001) had positive effects on creativity. However, the Appreciation of Humor subscale (B=-0.100, Beta = 0.075, p  = 0.005) and Attitudes Toward Humor and Humorous People subscale (B=-0.209, Beta = 0.377, p  < 0.001) had negative effects on creativity.

Creativity is vital for nursing education, economic development, and individual well-being. The nursing profession requires creative individuals with researcher roles who have access to knowledge and can produce and use information [ 26 ]. Expanding creativity enables modern nursing applications and greater problem-solving. The current study investigated the creativity of nursing students and the elements that influence it, such as humor.

The present study revealed that nursing students possess moderate creativity, as evaluated through the SSCS, with mean scores of 22.29 and 19.31 for CSE and CPI, respectively, and a total mean of 41.60. These findings were consistent with a cross-sectional study involving 720 medical students, which found that the majority demonstrated moderate creativity. The study identified several factors that can enhance creativity, including problem-based learning, critical thinking, concept mapping, teamwork, and innovative teaching methods [ 31 ]. Another study by Qian et al. (2023) suggested that creative self-efficacy (CSE) impacts an individual’s readiness to experiment with new ideas, effort levels, and resilience when faced with challenges. Those with high CSE will likely possess sufficient psychological capital to withstand uncertainties and difficulties, leading to increased motivation, cognitive resources, and activities to meet contextual demands [ 32 ].

Along the same line, Karwowski (2016) employed a crossover longitudinal and sequential approach to examine the development of CSE and creative personal identity (CPI) beliefs over time. The study involved 976 Polish participants aged between 15 and 60 who responded to the Short Scale of Creative Self. The results indicated that these beliefs remain stable in the short term (six months), but significant changes can be observed after 20 months. The study found evidence of growth in both constructs as individuals transition from adolescence to early adulthood. However, a decrease in CPI was observed in all age groups, except those aged 15 to 24, which showed a significant increase [ 33 ]. Moreover, a focus group study explored the perspectives of medical students, postgraduate medical trainees, and medical specialists on creativity within the medical context. The study concluded that participants perceived creativity as a form of art encompassing thought and action. Creative problem-solving strategies, considered the “creative part” of critical thinking, can enhance students’ critical thinking skills. These strategies encourage students to be open-minded, curious, and reflective and think and conceptualize outside the box. This process fosters the development of their intuition, associative ability, and metaphor usage [ 34 ].

These findings could be related to the fact that in the healthcare industry, nursing students must have the requisite skills and knowledge to tackle real-life scenarios. While indispensable, clinical training can be overwhelming due to its unique challenges. From witnessing the natural progression of death to dealing with highly contagious illnesses in real time and technological advancements, these experiences can be daunting [ 35 ]. The challenges they confront necessitate the application of new concepts and abilities, prompting personal introspection and self-examination. Working with limited resources and alongside individuals with poor clinical skills forces them to learn and grow, thus becoming better prepared to handle real-life situations. Modern teaching methods of “blending learning” require self-learning, and search places a premium on creative thinking, enabling students to become innovative problem solvers.

Our research has uncovered an exciting insight - most participants scored moderate on the humor scale, with a mean score of 51.89. This finding indicates how humor is deeply ingrained in Egyptian society, where using humor to alleviate difficult situations is widely accepted [ 36 ]. Such a cultural disposition aligns with a study conducted by Jiang et al. (2019), which examined the impact of culture on the perception and usage of humor and its mental health benefits. The study found that Easterners view humor less positively than their Western counterparts. They also use humor less often as a coping mechanism, primarily due to this perception. However, despite the cultural differences, Westerners and Easterners show similar patterns in the relationship between their humor and psychological well-being scores [ 37 ]. Numerous studies have shown that incorporating humor into the therapeutic relationship can positively impact the nurse’s mental health and understanding of the patient’s care needs [ 36 , 37 , 38 , 39 , 40 ]. According to Chelly et al. (2022), humor helps nurses alleviate stress and anxiety while humanizing the issue. Though the context in which humor can be used is highly influenced by personal factors, such as age, gender, and personality, its use is strongly recommended. However, it is necessary to use humor cautiously and in appropriate circumstances, as there may be barriers to its use [ 41 ].

Our findings indicated that the total scores of SSCS showed a significant positive correlation with Humor Production and Creativity ( r  = 0.254), Coping or Adaptive Humor ( r  = 0.230), and Appreciation of Humor ( r  = 0.461). However, there was a negative correlation between Attitudes toward Humor and Humorous People ( r =-0.343). Furthermore, the authors performed multiple linear regression analyses to determine the impact of various humor components on nursing students’ creativity. The model was statistically significant, accounting for 16.2% of the variance in creativity (Adjusted R^2 = 0.162). These findings could be linked to humor in educational environments, appreciated for its capacity to create a relaxed atmosphere and improve interpersonal dynamics, demonstrating humor’s diverse roles in various aspects of life. Nursing students employ humor as a coping mechanism to deal with challenges, such as imagining humorous scenarios, sharing jokes, or indulging in amusing conduct. This coping humor fosters creative problem-solving, positive emotions, resilience, and mental well-being [ 11 , 12 , 36 ].

These findings were congruent with another study on 228 psychological counselors aged between 23 and 52 years—of which 130 were female and 98 were male—which found a positively significant correlation between psychological resilience, psychological well-being, and coping humor. Research indicates that a sense of humor can improve physical and psychological health and overall well-being [ 42 ].

Ghayas and Malik (2013) also found that humor predicts creativity and sociability levels in university undergraduates. Moreover, humor’s creation and performance dimensions were strong predictors of creativity. In contrast, the elaboration subscale of creativity significantly predicted humor. The attitude towards humor and humorous people, along with the humor subscale, were the only significant predictors of sociability [ 43 ]. Similarly, Biemans and Huizingh (2023) employed a mixed-methods study design and found that being in a humorous mood improves creativity in specific creative situations. They highlight how research into the impact of humor on creativity and innovation can take new directions [ 44 ]. Moreover, Kocak (2018) studied the influence of various humor types on creativity and the role of university innovation environments in this relationship. The study involved 362 academics from Turkish universities. The findings revealed that aggressive humor negatively correlates with academic creativity while self-enhancing and affiliative humor positively correlate. Self-defeating humor, however, showed no significant link with creativity. The study also found that the innovation climate moderately affects the relationship between humor styles and creativity. These findings highlight the potential of different humor styles to enhance organizational productivity and creativity [ 45 ].

Nursing implications

This study’s findings present several implications for nursing education and practice. The positive correlation between humor and creativity suggests that integrating humor-based activities and creative problem-solving training into the curriculum could enhance students’ creativity. As a valuable tool for stress management, humor could help reduce burnout among students, potentially improving their inventive problem-solving skills. Nursing educators can incorporate relevant humor into their lessons using various forms such as cartoons, spontaneous humor, role-playing, jokes, and funny stories to engage students effectively. Moreover, it could help develop more effective communication strategies, improve patient-nurse relationships, and apply innovative nursing interventions to manage health problems and enhance the overall quality of patient care. Humor can make patients feel more comfortable and open during interactions, leading to better communication and, ultimately, better health outcomes.

Study limitations

This study offers important insights into the connection between humor and creativity in nursing education. However, it has several limitations. The findings are based on a non-probability convenient sampling technique, which may limit their applicability to a broader population. The study’s cross-sectional design prevents the establishment of a causal relationship between humor and creativity. The reliance on self-report measures could introduce social desirability bias. Future research could address these limitations using objective measurement tools, such as observational or peer-rated instruments and probability sampling methods. Longitudinal studies could provide a more nuanced understanding of how the relationship between humor and creativity evolves. Furthermore, exploring personality traits, learned helplessness, academic burnout, self-evaluation, motivation, and cultural influences as covariates with humor and creativity. Further experimental studies on humor-based activities and creative problem-solving training in nursing education to improve student creativity, stress levels, and academic performance. These studies can provide concrete evidence for the benefits of humor and creativity in healthcare settings.

Conclusion and recommendations

Our findings underscored a significant correlation between various facets of humor and creativity. Positive correlations were observed between creative self-efficacy and creative personal identity with different aspects of humor, such as humor production, coping or adaptive humor, and appreciation of humor. Conversely, negative correlations were found with unfavorable attitudes towards humor and humorous individuals. Considering these findings, it is crucial to maintain a comfortable and humorous atmosphere in nursing education settings. Such an environment encourages creative problem-solving skills and can help reduce burnout among nursing students and staff. Therefore, it is recommended that humor be integrated into the educational system and healthcare settings to enhance creativity and overall well-being.

Data availability

The datasets used or analyzed in this study are available from the corresponding author upon reasonable request.

Abbreviations

Kolmogorov-Smirnov

Statistical Package for Social Sciences

Research Ethical Committee

Short Scale of Creative Self

Creative Self-Efficacy

Creative Personal Identity

Multidimensional Sense of Humor Scale

American Association of Colleges of Nursing

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Acknowledgements

The authors would like to thank the students who participated in this work.

The Science, Technology, & Innovation Funding Authority (STDF), in cooperation with the Egyptian Knowledge Bank (EKB), provides open-access funding.

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ME and MH planned and designed the research. ST and EE contributed to the methodology and data analysis. The manuscript was reviewed and approved by the research team.

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The entire procedure followed the pertinent rules and recommendations of the Declaration of Helsinki ( DoH , 2008). The Research Ethics Committee of El-Mansoura University’s Faculty of Nursing granted the required formal consent and authority to conduct the study ( IRB 00013620/121/3/2023). Participants in the research provided written informed consent.

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El-Sayed, M.M., AbdElhay, E.S., Hawash, M.M. et al. The power of laughter: a study on humor and creativity in undergraduate nursing education in Egypt. BMC Nurs 23 , 259 (2024). https://doi.org/10.1186/s12912-024-01913-0

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