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1.6 More Numbers
Quiz by Grace Hirsch
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Select all the numbers that can be used as a common denominator to rewrite the fractions __ 2 6 and __ 1 2 . A 3 D 12 B 6 E 16 C 8 2 Aaron ran __ 5 8 mile to his friendâs house. Then he ran another __ 1 4 mile to the park. 1 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 4 Which equation shows how many miles Aaron ran? A __ 5 8 â __ 1 4 = __ 2 8 C __ 5 8 + __ 1 4 = __ 7 8 B __ 5 8 â __ 1 4 = __ 3 8 D __ 5 8 + __ 1 4 = __ 8 8 3 Select all the expressions that can be used to find the sum of __ 6 8 and ___9 12. A ___ 36 48 + ___ 36 48 D ___ 18 20 + ___ 17 20 B ___ 24 36 + ___ 27 36 E ___ 18 24 + ___ 18 24 C ___ 14 16 + ___ 13 16 4 Write a pair of equivalent fractions for __ 3 4 and __ 2 5 using a common denominator of 20. __ 3 4 = __ 2 5 = 5 Katie spent __ 4 5 hour painting and __ 1 2 hour drawing. ? 1 1 2 1 5 1 5 1 5 1 5 How much more time in hours did she spend painting than drawing? 6 Dave is planting a garden. He plants cucumbers in ___2 12 of his garden and tomatoes in __ 2 3 of his garden. What fraction of his garden does Dave plant with cucumbers and tomatoes? 7 Of the students in Mariaâs class, __ 2 5 have dogs and __ 1 3 have cats. No students have both a dog and a cat. What fraction represents how many more students in Mariaâs class have dogs? 52 Š Houghton Mifflin Harcourt Publishing Company Module 6 ⢠Form A Name Module Test DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-C 9 Mr. Gonzales used __ 3 4 quart of broth and __ 1 2 quart of milk to make soup. How many quarts of liquid did he use? Part A Complete the fraction model to represent the problem. 1 1 2 1 4 1 4 1 4 Part B Write an equation to show how many quarts of liquid Mr. Gonzales used to make soup. 10 A bowl of cereal contains __ 2 3 cup of oats and __ 2 8 cup of raisins. Write a numerical expression using equivalent fractions with a common denominator of 24 to model how many more cups of oats than raisins there are in the bowl. 11 Jessica read __ 1 6 of her book on Thursday, __ 2 9 of her book on Friday, and __ 1 2 of her book on Saturday. Part A Write a numerical expression using equivalent fractions to model how much of her book she has read so far. Part B What fraction of her book has Jessica read?
Generate all of these 25 questions Part A: Each correct answer is worth 5. 1. The regular pentagon shown has a side length of 2 cm. The perimeter of the pentagon is (A) 2 cm (B) 4 cm (C) 6 cm (D) 8 cm (E) 10 cm 2 cm 2. The faces of a cube are labelled with 1, 2, 3, 4, 5, and 6 dots. Three of the faces are shown. What is the total number of dots on the other three faces? (A) 6 (B) 8 (C) 10 (D) 12 (E) 15 3. The equation that best represents \a number increased by _ve equals 15" is (A) n ô 5 = 15 (B) n _ 5 = 15 (C) n + 5 = 15 (D) n + 15 = 5 (E) n _ 5 = 15 4. The line graph shows the number of bobbleheads sold at a store each year. The sale of bobbleheads increased the most between (A) 2016 and 2017 (B) 2017 and 2018 (C) 2018 and 2019 (D) 2019 and 2020 (E) 2020 and 2021 Number of 2016 2017 2018 2019 2020 Year Sale of Bobbleheads 2021 Bobbleheads 20 40 60 80 5. Starting at 72, Aryana counts down by 11s: 72; 61; 50; : : : . What is the last number greater than 0 that Aryana will count? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 6. In the diagram, \ABC = 90_. The value of x is (A) 68 (B) 23 (C) 56 (D) 28 (E) 26 Day of the Week 44° x° A B C x° 7. Which of the following values is closest to zero? (A) ô1 (B) 5 4 (C) 12 (D) ô4 5 (E) 0:9 Grade 8 8. A jar contains 267 quarters. One quarter is worth $0.25. How many quarters must be added to the jar so that the total value of the quarters is $100.00? (A) 33 (B) 53 (C) 103 (D) 133 (E) 153 9. A package of 8 greeting cards comes with 10 envelopes. Kirra has 7 cards but no envelopes. What is the smallest number of packages that Kirra needs to buy to have more envelopes than cards? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 10. For the points in the diagram, which statement is true? (A) e > c (B) b < d (C) f > b (D) a < e (E) a > c y x (e, f ) (a, b) (c, d ) Part B: Each correct answer is worth 6. 11. The 26 letters of the English alphabet are listed in an in_nite, repeating loop: ABCDEFGHIJKLMNOPQRSTUVWXY ZABC : : : What is the 258th letter in this sequence? (A) V (B) W (C) X (D) Y (E) Z 12. A public holiday is always celebrated on the third Wednesday of a certain month. In that month, the holiday cannot occur on which of the following days? (A) 16th (B) 22nd (C) 18th (D) 19th (E) 21st 13. A circular spinner is divided into three sections. An arrow is attached to the centre of the spinner. The arrow is spun once. The probability that the arrow stops on the largest section is 50%. The probability it stops on the next largest section is 1 in 3. The probability it stops on the smallest section is (A) 1 4 (B) 2 5 (C) 1 6 (D) 2 7 (E) 3 10 14. A positive number is divisible by both 3 and 4. The tens digit is greater than the ones digit. How many positive two-digit numbers have this property? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 15. A rectangular pool measures 20 m by 8 m. There is a 1 m wide walkway around the outside of the pool, as shown by the shaded region. The area of the walkway is (A) 56 m2 (B) 60 m2 (C) 29 m2 (D) 52 m2 (E) 50 m2 20 m 8 m 1 m Grade 8 16. The results of asking 50 students if they participate in music or sports are shown in the Venn diagram. What percentage of the 50 students do not participate in music and do not participate in sports? (A) 0% (B) 80% (C) 20% (D) 70% (E) 40% Music Sports 15 5 20 17. There are 2 3 as many golf balls in Bin F as in Bin G. If there are a total of 150 golf balls, how many fewer golf balls are in Bin F than in Bin G? (A) 15 (B) 30 (C) 50 (D) 60 (E) 90 18. In the sequence shown, Figure 1 is formed using 7 squares. Each _gure after Figure 1 has 5 more squares than the previous _gure. What _gure has 2022 squares? (A) Figure 400 (B) Figure 402 (C) Figure 404 (D) Figure 406 (E) Figure 408 Figure 1 Figure 2 Figure 3 19. Mateo's 300 km trip from Edmonton to Calgary passed through Red Deer. Mateo started in Edmonton at 7 a.m. and drove until stopping for a 40 minute break in Red Deer. Mateo arrived in Calgary at 11 a.m. Not including the break, what was his average speed for the trip? (A) 83 km/h (B) 94 km/h (C) 90 km/h (D) 95 km/h (E) 64 km/h 20. Equilateral triangle ABC has sides of length 4. The midpoint of BC is D, and the midpoint of AD is E. The value of EC2 is (A) 7 (B) 6 (C) 6:25 (D) 8 (E) 10 Part C: Each correct answer is worth 8. 21. The positive factors of 6 are 1, 2, 3, and 6. There are two perfect squares less than 100 that have exactly _ve positive factors. What is the sum of these two perfect squares? (A) 177 (B) 80 (C) 145 (D) 52 (E) 97 22. In the list p; q; r; s; t; u; v, each letter represents a positive integer. The sum of the values of each group of three consecutive letters in the list is 35. If q + u = 15, then p + q + r + s + t + u + v is (A) 85 (B) 70 (C) 80 (D) 90 (E) 75 Grade 8 23. The net shown is folded to form a cube. An ant walks from face to face on the cube, visiting each face exactly once. For example, ABCFED and ABCEFD are two possible orders of faces the ant visits. If the ant starts at A, how many possible orders are there? (A) 24 (B) 48 (C) 32 (D) 30 (E) 40 A D B C E F 24. The number 385 is an example of a three-digit number for which one of the digits is the sum of the other two digits. How many numbers between 100 and 999 have this property? (A) 144 (B) 126 (C) 108 (D) 234 (E) 64 25. Student A, Student B, and Student C have been hired to help scientists develop a new avour of juice. There are 4200 samples to test. Each sample either contains blueberry or does not. Each student is asked to taste each sample and report whether or not they think it contains blueberry. Student A reports correctly on exactly 90% of the samples containing blueberry and reports correctly on exactly 88% of the samples that do not contain blueberry. The results for all three students are shown below. Student A Student B Student C Percentage correct on samples 90% 98% (2m)% containing blueberry Percentage correct on samples 88% 86% (4m)% not containing blueberry Student B reports 315 more samples as containing blueberry than Student A. For some positive integers m, the total number of samples that the three students report as containing blueberry is equal to a multiple of 5 between 8000 and 9000. The sum of all such values of m is (A) 45 (B) 36 (C) 24 (D) 27 (E) 29
Make a test, with answers best on the following: Conduct an investigation to provide evidence that living things are made of cells; either one cell or many different numbers and types of cells. Supporting Content LS1.A: Structure and Function ⢠All living things are made up of cells, which is the smallest unit that can be said to be alive. An organism may consist of one single cell (unicellular) or many different numbers and types of cells (multicellular). (MS-LS-1.1) Further Explanation: Emphasis is on developing evidence that living things are made of cells, distinguishing between living and non-living things, and understanding that living things may be made of one cell or many and varied cells. In multicellular organisms, the body is a system of multiple interacting subsystems. These subsystems are groups of cells that work together to form tissues and organs that are specialized for particular body functions. (MS-LS-1.3) Further Explanation: Emphasis is on the conceptual understanding that cells form tissues and tissues form organs specialized for particular body functions. Examples could include the interaction of subsystems within a system and the normal functioning of those systems. Organisms reproduce, either sexually or asexually, and transfer their genetic information to their offspring. (MS-LS-1.4) ⢠Living things share certain characteristics. (These include response to environment, reproduction, energy use, growth and development, life cycles, made of cells, etc.) (MS-LS1.4) Further Explanation: Examples should include both biotic and abiotic items, and should be defended using accepted characteristics of life. Plants, algae (including phytoplankton), and many microorganisms use the energy from light to make sugars (food) from carbon dioxide from the atmosphere and water through the process of photosynthesis, which also releases oxygen. These sugars can be used immediately or stored for growth or later use. (MS-LS-1.5) Further Explanation: Emphasis is on tracing movement of matter and flow of energy. Supporting Content LS1.C: Organization for Matter and Energy Flow in Organisms ⢠Within individual organisms, food moves through a series of chemical reactions (cellular respiration) in which it is broken down and rearranged to form new molecules, to support growth, or to release energy. (MS-LS-1.6) Further Explanation: Emphasis is on describing that molecules are broken apart and put back together and that in this process, energy is released and on understanding that the elements in the products are the same as the elements in the reactants. Organisms, and populations of organisms, are dependent on their environmental interactions both with other living things and with nonliving factors. (MS-LS-2.1) ⢠In any ecosystem, organisms and populations with similar requirements for food, water, oxygen, or other resources may compete with each other for limited resources, access to which consequently constrains their growth and reproduction. (MS-LS-2.1) ⢠Growth of organisms and population increases are limited by access to resources. (MS-LS-2.1) Further Explanation: Emphasis is on cause and effect relationships between resources and growth of individual organisms and the numbers of organisms in ecosystems during periods of abundant and scarce resources. Similarly, predatory interactions may reduce the number of organisms or eliminate whole populations of organisms. Mutually beneficial interactions, in contrast, may become so interdependent that each organism requires the other for survival. Although the species involved in these competitive, predatory, and mutually beneficial interactions vary across ecosystems, the patterns of interactions of organisms with their environments, both living and nonliving, are shared. (MS-LS-2.2) Further Explanation: Emphasis is on predicting consistent patterns of interactions in different ecosystems in terms of the relationships among and between organisms and abiotic components of ecosystems. Examples of types of interactions could include competitive, predatory, and mutually beneficial. Food webs are models that demonstrate how matter and energy is transferred between producers, consumers, and decomposers as the three groups interact within an ecosystem. Transfers of matter into and out of the physical environment occur at every level. Decomposers recycle nutrients from dead plant or animal matter back to the soil in terrestrial environments or to the water in aquatic environments. The atoms that make up the organisms in an ecosystem are cycled repeatedly between the living and nonliving parts of the ecosystem. (MS-LS-2.3) Further Explanation: Emphasis is on describing the conservation of matter and flow of energy into and out of various ecosystems, and on defining the boundaries of the system. Ecosystems are dynamic in nature; their characteristics can vary over time. Disruptions to any physical or biological component of an ecosystem can lead to shifts in all its populations. (MSLS-2.5) Further Explanation: Emphasis is on recognizing patterns in data and making warranted inferences about changes in populations, and on evaluating empirical evidence supporting arguments about changes to ecosystems. Biodiversity describes the variety of species found in Earthâs terrestrial and oceanic ecosystems. The completeness or integrity of an ecosystemâs biodiversity is often used as a measure of its health. (MS-LS-2.6) Supporting Content LS4.D: Biodiversity ⢠Changes in biodiversity can influence humansâ resources, such as food, energy, and medicines, as well as ecosystem services that humans rely onâfor example, water purification and recycling. (MS-LS-2.6) Supporting Content ETS1.B: Developing Possible Solutions ⢠There are systematic processes for evaluating solutions with respect to how well they meet the criteria and constraints of a problem. (MS-LS-2.6) Further Explanation: Examples of ecosystem services could include water purification, nutrient recycling, and prevention of soil erosion. Examples of design solution constraints could include scientific, economic, and social considerations. Genes are located in the chromosomes of cells, with each chromosome pair containing two variants of each of many distinct genes. Each distinct gene chiefly controls the production of specific proteins, which in turn affects the traits of the individual. Structural changes to genes (mutations) can result in changes to proteins, which can affect the structures and functions of the organism and thereby change traits. (MS-LS-3.1) Supporting Content LS3.B: Variation of Traits ⢠In addition to variations that arise from sexual reproduction, genetic information can be altered because of mutations. Though rare, mutations may result in significant changes to the structure and function of proteins. Changes can be beneficial, harmful, or neutral to the organism. (MS-LS-3.1) Further Explanation: Emphasis is on conceptual understanding that changes in genetic material may result in making different proteins. Organisms reproduce, either sexually or asexually, and transfer their genetic information to their offspring. (MS-LS-3.2) Supporting Content LS3.A: Inheritance of Traits ⢠Variations of inherited traits between parent and offspring arise from genetic differences that result from the subset of chromosomes (and therefore genes) inherited. (MS-LS-3.2) Supporting Content LS3.B: Variation of Traits ⢠In sexually reproducing organisms, each parent contributes half of the genes acquired (at random) by the offspring. Individuals have two of each chromosome and hence two alleles of each gene, one acquired from each parent. These versions may be identical or may differ from each other. (MS-LS-3.2) Further Explanation: Emphasis is on using models such as simple Punnett squares and pedigrees, diagrams, and simulations to describe the cause and effect relationship of gene transmission from parent(s) to offspring and resulting genetic variation. The collection of fossils and their placement in chronological order is known as the fossil record and documents the change of many life forms throughout the history of the Earth. Anatomical similarities and differences between various organisms living today and between living and once living organisms in the fossil record enable the classification of living things. (MS-LS-4.1, MS-LS-4.2) Further Explanation: Emphasis is on finding patterns of changes in the level of complexity of anatomical structures in organisms and the chronological order of fossil appearance in the rock layers. The collection of fossils and their placement in chronological order is known as the fossil record and documents the change of many life forms throughout the history of the Earth. Anatomical similarities and differences between various organisms living today and between living and once living organisms in the fossil record enable the classification of living things. (MS-LS-4.1, MS-LS-4.2) Further Explanation: Emphasis is on explanations of the relationships among organisms in terms of similarity or differences of the gross appearance of anatomical structures. Scientific genus and species level names indicate a degree of relationship. (MS-LS-4.3) Further Explanation: Emphasis is on inferring general patterns of relatedness among structures of different organisms by comparing diagrams, pictures, specimens, or fossils. Natural selection leads to the predominance of certain traits in a population, and the suppression of others. (MS-LS-4.4) Further Explanation: Emphasis is on using concepts of natural selection, including overproduction of offspring, passage of time, variation in a population, selection of favorable traits, and heritability of traits. In artificial selection, humans have the capacity to influence certain characteristics of organisms by selective breeding. One can choose desired parental traits determined by genes, which are then passed to offspring. (MS-LS-4.5) Further Explanation: Emphasis is on identifying and communicating information from reliable sources about the influence of humans on genetic outcomes in artificial selection (such as genetic modification, animal husbandry, gene therapy), and on the influence these technologies have on society as well as the technologies leading to these scientific discoveries. Adaptation by natural selection acting over generations is one important process by which species change over time in response to changes in environmental conditions. Traits that support successful survival and reproduction in the new environment become more common; those that do not become less common. Thus, the distribution of traits in a population changes. (MS-LS-4.6) Further Explanation: Emphasis is on using mathematical models, probability statements, and proportional reasoning to support explanations of trends in changes to populations over time. Examples could include Peppered Moth population changes before and after the industrial revolution.
Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: ⢠Free-falling objects do not encounter air resistance. ⢠All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs ⢠Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 ⢠a ⢠d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 ⢠(-8.00 m/s2) ⢠d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) ⢠d (16.0 m/s2) ⢠d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi ⢠t + ½ ⢠a ⢠t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) ⢠(4.1 s) + ½ ⢠(6.00 m/s2) ⢠(4.10 s)2 d = (0 m) + ½ ⢠(6.00 m/s2) ⢠(16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: ⢠An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. ⢠If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. ⢠If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. ⢠If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi ⢠t + ½ ⢠a ⢠t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) ⢠(t) + ½ ⢠(-9.8 m/s2) ⢠(t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) ⢠(t)2 -8.52 m = (-4.9 m/s2) ⢠(t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 ⢠a ⢠d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 â˘(-9.8m/s2) â˘d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) â˘d (-19.6 m/s2) ⢠d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) ⢠d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.
12 Different Behaviors in Social Media 1. The Ultras â check feeds dozens of times a day. Happily, admit their obsession. (14% of Facebook users spend at least 2 hours a day on the network) 2. The Deniers â social media do not control their lives, but gets anxious when unable to access networks. (20% of Facebook users would feel anxious or isolated if they had to deactivate their accounts. 3. The Virgins â taking first tentative steps in social media (19% of British people donât use any social networks) 4. The Peacocks â popularity contest, high numbers of followers, fans, likes and retweets. (1 out of 10 Twitter users want more followers than friends.) 5. The Lurkers â hiding in the shadows of cyberspace. Watches what others are saying, but rarely (if ever) participate themselves. (45% of Facebook users described themselves as âobserversâ) 6. The Ranters â mock and mid in face-to-face conversations. Highly opinionated online. 7. The Changelings â adopt completely new personality online so no one knows their real identities. 8. The Ghosts â create anonymous profiles, for fear of giving out personal information to strangers. .9. The Informers â seek admiration by being the first to share the latest trends with audiences. 10. The Approval Seekers â constantly check feeds and timelines after posting. Worry until people respond. 11. The Quizzers â asking questions allow them to start conversations. 12. The Dippers â access their pages infrequently, often going days, of even weeks without posting.
Create quiz for the following, keep the questions in the same order and note that option 1 is the correct for all. đ Reading Quiz: Global E-sports Industry Overview 1. Identify the main idea of the infographic. A. To present key statistics and facts about global E-sports B. To explain how to become a professional gamer C. To describe different traditional sports 2. Determine which country has the highest number of active E-sports players. A. United States B. China C. Brazil 3. Identify which country has more active players: France or Germany. A. France B. Germany C. They have the same number 4. Select the correct detail about E-sports fans. A. The average age is 26â29 years old. B. Most fans are over 40 years old. C. The average age is 15â18 years old. 5. Identify what happened in 1972. A. The first E-sports tournament took place. B. Mobile gaming was invented. C. China became number one in E-sports. 6. Determine which segment of E-sports is growing the fastest. A. Mobile E-sports B. Console E-sports C. Traditional sports 7. Explain what the statistic â76% of E-sports fans spend more time playing E-sports than traditional sportsâ suggests. A. Most fans prefer playing E-sports over traditional sports. B. Fans dislike all sports. C. Traditional sports are more popular than E-sports. 8. Compare China and the United States. What can you conclude? A. The United States has more active players than China. B. China has more active players than the United States. C. Both countries have the same number of players. 9. Analyze why the author included numbers for many different countries. A. To show that E-sports is popular around the world B. To prove only one country is important C. To criticize traditional sports 10. Infer why the infographic includes the average age of fans. A. To show that E-sports mainly attracts young adults B. To show that children are the main audience C. To prove that older adults do not like E-sports
A solution is a mixture in which one or more substances are uniformly distributed in another substance. Solutions can be mixtures of liquids, solids, or gases. For example, plasma, the liquid part of blood, is a very complex solution. It is composed of many types of ions and large molecules, as well as gases, that are dissolved in water. A solute (SAHL-YOOT) is a substance dissolved in the solvent. The particles that compose a solute may be ions, atoms, or molecules. The solvent is the substance in which the solute is dissolved. For example, when sugar, a solute, and water, a solvent, are mixed, a solution of sugar water results. Though the sugar dissolves in the water, neither the sugar molecules nor the water molecules are altered chemically. If the water is boiled away, the sugar molecules remain and are unchanged. Solutions can be composed of various proportions of a given solute in a given solvent. Thus, solutions can vary in concentra- tion. The concentration of a solution is the amount of solute dis- solved in a fixed amount of the solution. For example, a 2 percent saltwater solution contains 2 g of salt dissolved in enough water to make 100 mL of solution. The more solute dissolved, the greater is the concentration of the solution. A saturated solution is one in which no more solute can dissolve. Aqueous (AY-kwee-uhs) solutionsâsolutions in which water is the solventâare universally important to living things. Marine microorganisms spend their lives immersed in the sea, an aqueous solution. Most nutrients that plants need are in aqueous solutions in moist soil. Body cells exist in an aqueous solution of intercellu- lar fluid and are themselves filled with fluid; in fact, most chemical reactions that occur in the body occur in aqueous solutions. Copyright Š by Holt, Rinehart and Winston. All rights reserved. Liquid water Solid water Ice (solid water) is less dense than liquid water because of the structure of ice crystals. The water molecules in ice are bonded to each other in a way that creates large amounts of open space between the molecules, relative to liquid water. FIGURE 2-12 solvent from the Latin solvere, meaning âto loosenâ Word Roots and Origins CHEMISTRY OF LIFE 43 ACIDS AND BASES One of the most important aspects of a living system is the degree of its acidity or alkalinity. What do we mean when we use the terms acid and base? Ionization of Water As water molecules move about, they bump into one another. Some of these collisions are strong enough to result in a chemical change: one water molecule loses a proton (a hydrogen nucleus), and the other gains this proton. This reaction really occurs in two steps. First, one molecule of water pulls apart another water molecule, or dissociates, into two ions of opposite charge: H2O â H OH The OH ion is known as the hydroxide ion. The free H ion can react with another water molecule, as shown in the equation below. H H2O â H3O The H3O ion is known as the hydronium ion. Acidity or alkalin- ity is a measure of the relative amounts of hydronium ions and hydroxide ions dissolved in a solution. If the number of hydronium ions in a solution equals the number of hydroxide ions, the solution is said to be neutral. Pure water contains equal numbers of hydro- nium ions and hydroxide ions and is therefore a neutral solution. Acids If the number of hydronium ions in a solution is greater than the number of hydroxide ions, the solution is an acid. For example, when hydrogen chloride gas, HCl, is dissolved in water, its mol- ecules dissociate to form hydrogen ions, H, and chloride ions, Cl, as is shown in the equation below. HCl â H Cl These free hydrogen ions combine with water molecules to form hydronium ions, H3O. This aqueous solution contains many more hydronium ions than it does hydroxide ions, making it an acidic solution. Acids tend to have a sour taste; how- ever, never taste a substance to test it for acidity. In concentrated forms, they are highly corrosive to some materials, as you can see in Figure 2-13. Bases If sodium hydroxide, NaOH, a solid, is dissolved in water, it dissociates to form sodium ions, Na, and hydroxide ions, OH, as shown in the equation below. NaOH â Na OH Copyright Š by Holt, Rinehart and Winston. All rights reserved. Eco Connection onnection Acid Precipitation Acid precipitation, more commonly called acid rain, describes rain, snow, sleet, or fog that contains high levels of sulfuric and nitric acids. These acids form when sulfur dioxide gas, SO2, and nitrogen oxide gas, NO, react with water in the atmosphere to produce sulfuric acid, H2SO4, and nitric acid, HNO3. Acid precipitation makes soil and bodies of water, such as lakes, more acidic than normal. These high acid levels can harm plant and animal life directly. A high level of acid in a lake may kill mollusks, fish, and amphibians. Even in a lake that does not have a very elevated level of acid, acid precipitation may leach aluminum and magnesium from soils, poisoning water- dwelling species. Reducing fossil-fuel consump- tion, such as occurs in gasoline engines and coal-burning power plants, should reduce high acid levels in precipitation. Sulfur dioxide, SO2, which is produced when fossil fuels are burned, reacts with water in the atmosphere to produce acid precipitation. Acid precipitation, or acid rain, can make lakes and rivers too acidic to support life and can even corrode stone, such as the face of this statue. FIGURE 2-13 44 CHAPTER 2 This solution then contains more hydroxide ions than hydronium ions and is therefore defined as a base. The adjective alkaline refers to bases. Bases have a bitter taste; however, never taste a substance to test for alkalinity. They tend to feel slippery because the OH ions react with the oil on our skin to form a soap. In fact, commercial soap is the product of a reaction between a base and a fat. pH Scientists have developed a scale for comparing the relative con- centrations of hydronium ions and hydroxide ions in a solution. This scale is called the pH scale, and it ranges from 0 to 14, as shown in Figure 2-14. A solution with a pH of 0 is very acidic, a solution with a pH of 7 is neutral, and a solution with a pH of 14 is very basic. A solutionâs pH is measured on a logarithmic scale. That is, the change of one pH unit reflects a 10-fold change in the acidity or alkalinity. For example, urine has 10 times the H3O ions at a pH of 6 than water does at a pH of 7. Vinegar, has 1,000 times more H3O ions at a pH of 3 than urine at a pH of 6, and 10,000 times more H3O ions than water at a pH of 7. The pH of a solution can be measured with litmus paper or with some other chemical indicator that changes color at various pH levels. Buffers The control of pH is important for living systems. Enzymes can function only within a very narrow pH range. The control of pH in organisms is often accomplished with buffers. Buffers are chemi- cal substances that neutralize small amounts of either an acid or a base added to a solution. As Figure 2-14 shows, the composition of your internal environmentâin terms of acidity and alkalinityâ varies greatly. Some of your body fluids, such as stomach acid and urine, are acidic. Others, such as intestinal fluid and blood, are
Alright, Isti â hereâs a longer and more detailed English version of the Isaac Newton text, still written at a level thatâs accessible for Grade 4 students, but rich enough in information to meet PISA literacy expectations and EF A2-level vocabulary. Iâve kept sentences short, clear, and with explanations for new concepts so itâs easier for young learners to follow, while still including both famous facts and lesser-known stories. ⸝ Isaac Newton: The Man Who Changed the Way We See the World A Boy from a Small Village Isaac Newton was born on January 4, 1643, in Woolsthorpe, a small village in England. His life was not easy. His father died before he was born. When he was just a few months old, his mother remarried and left him to live with his grandmother. Isaac missed his parents, but he kept himself busy by making things and exploring the world around him. As a child, Isaac liked to build models and machines. He made a small windmill that could turn with the wind. He built a water clock that told the time by dripping water into a container. He even made a sundial â a clock that tells the time by using the shadow of the sun. đĄ Did you know? The sundial marks that Isaac carved as a boy can still be seen today on the wall of his old house. ⸝ School and Curiosity When Newton first went to school, he was not the top student. At first, he did not pay much attention in class. But one day, another boy teased him for not being smart. Newton decided to study hard to prove him wrong. Soon, he became the best in his class. Isaac loved asking questions. He wanted to know how and why things happened. He enjoyed watching the stars at night and thinking about how the world worked. ⸝ The Falling Apple and Gravity One of the most famous stories about Newton is the falling apple. One afternoon, Isaac sat in his motherâs garden and saw an apple drop from a tree. This made him think: âWhy does the apple fall straight down? Why doesnât it fly up into the sky?â From this question, Newton began to think about gravity â an invisible force that pulls objects toward each other. Gravity is what keeps our feet on the ground. Itâs also what keeps the Moon moving around the Earth and the planets moving around the Sun. đĄ Fun fact: The apple did not hit Newtonâs head. Thatâs just a story people made up later to make the tale more exciting. ⸝ Newtonâs Three Laws of Motion Newton studied movement and wrote three important rules: 1. Objects stay still or keep moving unless something makes them change. ⢠Example: A ball will not roll unless you push it. 2. The bigger the push, the bigger the movement. ⢠Example: If you kick a ball harder, it will go faster and farther. 3. Every action has an equal and opposite reaction. ⢠Example: When you jump off a boat, the boat moves backward as you move forward. These three laws are still used today to understand how cars, rockets, and even roller coasters work. ⸝ Discoveries in Light and Color Newton also studied light. He found that white light is not just one color â it is made of many colors. He used a glass prism to split sunlight into a rainbow. This helped scientists understand how colors work. ⸝ Inventions and New Ideas Newton made a special telescope that used mirrors instead of lenses. This type of telescope made images of planets and stars much clearer. It is still called the Newtonian telescope today. He also worked in mathematics and helped create a new type of math called calculus, which is used to study changes and movement. ⸝ Strange Experiments Newton was so curious that he sometimes tested ideas on himself. Once, he put a thin needle, called a bodkin, beside his eye to see how it would change his vision. It was very dangerous, but luckily he did not go blind. đĄ Did you know? Newton also studied alchemy â an old kind of science where people tried to turn metal into gold. He never succeeded, but it showed how wide his interests were. ⸝ Later Life and Work At the age of 27, Newton became a professor at Cambridge University. He later worked for the Royal Mint, making sure coins were made safely and stopping people from making fake money. He was very strict, and some criminals were sent to prison because of his work. Newton never married. He spent most of his life reading, writing, and doing experiments. ⸝ The End of His Life Isaac Newton died in 1727 at the age of 84. He was buried in Westminster Abbey, a famous place in London where great people of Britain are honored. His work changed the world forever. Even today, scientists, engineers, and students still use Newtonâs laws and ideas. đŹ Newton once said: âIf I have seen further, it is by standing on the shoulders of giants.â This means we can make new discoveries by learning from the work of others who came before us. give 10 questions to each passage with PISA literacy standard for kid 10 years, 1. Nikola Tesla: The Man Who Dreamed of Lightning Born: July 10, 1856 Died: January 7, 1943 When Nikola Tesla was a boy in Croatia, he saw a flash of lightning and asked his mother, âCan we catch the light?â That question never left him. As he grew older, Tesla became a brilliant inventor, especially fascinated by electricity. He believed in a future where energy could be sent wirelessly through the airâlike music through the radio! Tesla invented the alternating current (AC) system, which became the foundation of modern electricity. At the time, Thomas Edison promoted direct current (DC), and the two men had a fierce competition. Many laughed at Tesla's bold ideas, but he never gave up. He dreamed of wireless communication, flying machines, and even free energy for everyone. Though he died alone and poor, today the world honors his vision. Think About It: Why do you think people didnât believe Tesla at first? What can we learn from Teslaâs courage to dream big? 2. Charles Darwin: The Man Who Studied the Worldâs Weirdest Creatures Born: February 12, 1809 Died: April 19, 1882 When young Charles Darwin got on a ship called HMS Beagle, he didnât know he would change science forever. He sailed around the world for five years, collecting plants, animals, and fossils. On the GalĂĄpagos Islands, he noticed something curious: finches had different beaks depending on their island. Why? Darwinâs observations led him to write the theory of evolution by natural selection. It explained how animals adapt and survive. But his ideas shocked many people because they seemed to challenge religious beliefs. Despite the controversy, Darwin continued his work. His book On the Origin of Species changed how we see life on Earth. Think About It: Should scientists share their ideas even if they go against what others believe? How did traveling help Darwin make new discoveries? 3. Marie Curie: The Woman Who Glowed in the Dark Born: November 7, 1867 Died: July 4, 1934 Marie Curie was born in Poland at a time when girls were not allowed to study science. But that didnât stop her. She moved to France, worked day and night, and discovered radioactivity, a powerful energy hidden inside atoms. She and her husband, Pierre Curie, found two new elements: polonium and radium. She became the first woman to win a Nobel Prize, and the only person to win in two different sciences: physics and chemistry. Even when Pierre died in an accident, Marie continued their work. Her discoveries helped doctors treat cancerâbut working with radioactive materials also harmed her health. She died from radiation exposure, but her legacy lives on. Think About It: What challenges did Marie Curie face as a woman in science? Why is it important to balance discovery with safety? 4. Galileo Galilei: The Star Watcher Who Defied the Church Born: February 15, 1564 Died: January 8, 1642 Galileo loved looking at the stars. He built one of the first powerful telescopes and made stunning discoveries: mountains on the Moon, moons around Jupiter, and that the Earth orbits the Sunânot the other way around. This idea, called heliocentrism, went against the teachings of the Church. He was put on trial and forced to say he was wrong. But he wasnât. He spent his last years under house arrest, quietly writing. Today, Galileo is called the father of modern science for daring to question what others blindly believed. Think About It: Why do you think Galileo was punished for telling the truth? Should science always follow evidence, even if it goes against powerful beliefs? 5. Isaac Newton: The Man Who Asked âWhy?â When an Apple Fell Born: January 4, 1643 Died: March 31, 1727 One day, an apple fell from a tree, and Isaac Newton began to wonder: Why did it fall down, not sideways or up? This simple question led to his theory of gravity. Newton also invented calculus, described the laws of motion, and changed physics forever. But Newton wasnât just a geniusâhe was curious, quiet, and often worked alone. He believed everything in nature followed rules, and it was our job to discover them. Thanks to him, we understand how planets move, how rockets launch, and why you fall when you trip. Think About It: How did Newtonâs curiosity lead to great discoveries? Do you think working alone helped or hurt Newton? 6. Ada Lovelace: The First Computer Programmer Before Computers Existed Born: December 10, 1815 Died: November 27, 1852 Ada Lovelace was the daughter of the famous poet Lord Byron, but she didnât love poetryâshe loved numbers! At a time when girls were expected to sew, Ada studied mathematics. She met Charles Babbage, who designed an early computer called the Analytical Engine. Ada imagined the machine could do more than just mathâit could create music, art, and even write! She wrote what is now considered the first computer program, long before real computers were built. Think About It: How did Ada imagine something that didnât exist yet? Why do we call her a pioneer in technology? 7. Albert Einstein: The Man Who Brought Time and Space Together Born: March 14, 1879 Died: April 18, 1955 Albert Einstein wasnât always a good student. In fact, his teachers thought he was slow. But Einstein thought deeply. He asked big questions like, âWhat if you could ride a beam of light?â His theories of relativity changed how we see space, time, and gravity. He also warned the world about the dangers of nuclear weapons, even though his ideas helped create them. Einstein believed science should help people, not harm them. With his messy hair, kind smile, and brilliant mind, he remains a symbol of genius. Think About It: Can someone be bad in school but still be brilliant? Should scientists be responsible for how their inventions are used? 8. Pythagoras: The Musician Who Loved Math Born: Around 570 BC Died: Around 495 BC Long ago in ancient Greece, Pythagoras believed the universe followed numbers. He discovered the Pythagorean Theorem, a rule about triangles that helps us build houses, design computers, and navigate space. He also believed that music had math inside itâthat certain notes made perfect harmony because of mathematical ratios. Pythagoras started a secret school and taught his students to search for truth through numbers, shapes, and sound. Think About It: Why do you think Pythagoras saw math in everything? How does music relate to math? 9. Rosalind Franklin: The Woman Behind the DNA Discovery Born: July 25, 1920 Died: April 16, 1958 Rosalind Franklin loved looking closely at things. She used a special machine called X-ray crystallography to photograph molecules. One of her greatest photos, called Photo 51, showed the shape of DNA, the molecule that carries lifeâs instructions. But her work was taken without credit. Two men, Watson and Crick, used her photo to build their famous model of DNA and won the Nobel Prize. Rosalind died young and never knew how important her work became. Think About It: Why is it important to give credit in science? What can we learn from Rosalindâs quiet strength? 10. Carl Linnaeus: The Man Who Gave Names to Everything Born: May 23, 1707 Died: January 10, 1778 Have you ever wondered why a tiger is called Panthera tigris? Thatâs thanks to Carl Linnaeus, a Swedish scientist who created a way to name and organize every living thing. His system is still used today in biology. Linnaeus loved nature and spent his life collecting plants, animals, and even rocks. He believed that by organizing life, we could better understand it. Thanks to him, we now have a global âdictionary of nature.â Think About It: Why is it important to name and organize living things? How does order help us understand the world?