ESTIMATION

•  Estimation can be a powerful tool in mathematics. You can use it to check an answer when you are finished solving a problem, and it will tell you whether or not your answer is reasonable. If your answer is somewhat close to your estimate, you know that you are on the right track. If your answer is off by hundreds, thousands, or more, you know that you need to revisit the problem and check over your work. Sometimes you may have missed something simple, like not lining up place value columns, or putting a decimal point in the wrong place. Sometimes you have to go back to the beginning and start again. Your estimate tells you when that is necessary, rather than waiting until you suffer the consequences of a wrong answer, like a bad grade on a test or paying too much for materials at the hardware store.

• An estimate is also useful for finding an answer quickly when an approximate answer is good enough. If you are the host of a buffet dinner and want to know about how many people are coming so you can put out enough potato salad, and estimate will probably work. However, if it is a sit - down dinner where every guest has a steak or filet on his or her own plate, an estimate is not very practical. It may leave you with too many, or even worse, too few plates to set before your guests. Knowing when to use an estimate, and when to solve for an exact answer is a life skill that comes with practice.

• Shopping is an excellent activity to help you practice your skills of estimation. If you have twenty-three dollars, and you are buying something that costs $9.98, you can quickly change the numbers to friendly numbers in your head by rounding. Twenty-three is close to 20, and $9.98 is close to 10.  If you have $20 and spend $10, you will have $10 left. As you go into the music store, you keep in mind that you have about ten dollars to spend.  This saves you time as you look for a CD to play during your party. You know that if the CD costs more than ten dollars, you will not have enough money to buy it, so you look in the section marked $8.99 and under.  When you find a CD you think you want, you can look on the back and estimate again. If the playing time says 129 minutes, you can estimate that it plays for about two hours, since that would be 120 minutes. Yes, estimation can be a very useful tool.

 Name:__________________________________

Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm   your answers.

1)  What is one beneficial thing about using estimation?

2)  What is the difference between an approximate answer and an exact answer

3)  What is meant by the term friendly number?

4)  Describe a time when you used estimation. How was it helpful?

5) Use what you have learned. What is a good estimate for 48 + 37? Round to friendly numbers, and then estimate the sum.

THE TRANSCONTINENTAL RAILROAD

• In today’s world, travel by train is no longer a major mode of transportation. However, there was a time in our nation’s history when the   train was the biggest advancement in transportation technology. Up until that point, people had to rely on their own two feet, or on the strength of animals such as oxen and horses, when they wanted to travel any distance.

• We are accustomed to the fast-moving pace of our society. In our country’s early years, however, progress moved at a much slower rate. It was not an easy task to build a railroad. Lots of workers were required to lay the tracks, and the conditions were often very dangerous. To help clear rocks and mountains, unstable nitro-glycerine explosives were used. The glass containers of liquid had to be kept absolutely still to prevent them from exploding at the wrong time.  Often, the job of handling the crate filled with the hazardous fluid was given to a Chinese immigrant. Many Chinese who came to California seeking their fortunes during the Gold Rush of 1849 stayed behind to work on the railroad.  Unfortunately, thousands died during its construction.

• Theodore Judah was the engineer who dreamed of making a transcontinental railroad come to life in the 1850’s. There were already railroads operating in cities on the east coast, and Judah was in the process of constructing railroads in the west, but there was no service at all across the  empty middle spaces of our nation. Judah was determined to change all that. He recruited some investors: Leland Stanford, Mark Hopkins, Charles Crocker, and Collis Huntington, who were nicknamed “the Big Four”, provided the money to create the Central Pacific Railroad Company. Construction on the transcontinental railroad began in 1863.

• Thousands of railway workers laid tracks from both the west and the east at the same time. It was dangerous and difficult work. The two sections of track were finally able to be joined on May 10, 1969 in Promontory, Utah.  Its completion signaled the beginning of mass travel of both communication and people between the east and west coasts. For the first time, the country felt truly united.

Name:__________________________________

 Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers.

1) Why did the expansion of the railroad system have such an impact on the nation?  

2) What do you think motivated the Big Four to invest in the construction of the transcontinental railroad?

3) Why do you suppose the company continued railroad construction in spite of the fact that so many people were killed or injured?

4) How did the ability to move people and ideas quickly from one side of the country to the other change the United States?

5) What impact do you think the Gold Rush had on the transcontinental railroad?

HIDE AND SEEK

•  In the wild, it often comes down to predator and prey, the hunter and the hunted. As you can imagine, most organisms want to stay alive. They have developed ways of adapting to severe habitats, and hiding or escaping from those who would like to eat them. So how do they do it?

• One very helpful adaptation is called camouflage. You may have been surprised by an animal that was using camouflage in the past. It blended into its surroundings so well that you nearly missed seeing it at all. Its coloring, markings, or other physical features resemble its habitat so much that you can look directly at it without seeing it at first. This is often good enough to fool a predator that is scanning an area to look for food. This helps prey to hide from its predator. But did you know that it often works the other way around, too? Predators can use camouflage to trap their prey.  If a predator wants to eat a certain animal, and that animal cannot see it lying in wait, it can pounce on its prey unexpectedly, devouring it before it  even knows what is happening.

• Another popular adaptation is mimicry. Mimicry is when an animal has markings or other physical characteristics that allow it to look like some other kind of animal or plant. If it can make its predators believe that it is something that preys on them, or would at least be difficult or painful to catch, its predator will often go off in search of an easier target.

• Sometimes animals are able to survive when their habitat changes because they adapt to the new conditions. For example, birds that were accustomed to nesting on high cliffs or in tall trees have survived industrialization of their habitat by learning to nest in the crevices of tall buildings. Raccoons easily adapt to residential areas that have taken over their woodland homes. They often help themselves to any food they can grab, whether it is in trashcans, or inside people’s homes!

 Name:__________________________________

Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm   your answers.

1)  What is the function of camouflage in the wild?

2)  Compare and contrast camouflage and mimicry. How   are they different? How are they the same?

3) What would motivate wild raccoons to enter people’s   homes?

4) If you were a wild animal, would you rather have the ability to mimic another animal, or the ability to camouflage yourself? Why?

5) Why do you think cliff-dwelling birds feel at home on the ledges of skyscrapers?

WHAT'S EATING YOU?

• Within any ecosystem, all the living organisms have a role to play. Plants are producers. Within their green leaves, they have round discs called chloroplasts that form stacks called grana. A distinctively green substance called chlorophyll fills the chloroplasts, giving the plant its green color. The chloroplasts allow the plant to use water, sunlight, and carbon dioxide (the gas we breathe out) to make, or produce, their own food. That is why they are called producers.

• When an animal eats a plant, energy that the plant got from the sun is transferred to the animal. An animal that eats plants is called an herbivore.  Since it is the first animal in the food chain, it is also the primary consumer.  A consumer is an animal that eats plants, or other animals. Consumers that eat only other animals are called carnivores. Consumers that eat both plants and animals are called omnivores.

• Producers are critical to the survival of all living organisms in an ecosystem.  Consumers depend on producers for the food, which gives them energy. Without producers, none of the other living things in the ecosystem would survive for long. It makes sense, then, that animals sometimes help plants to reproduce, or make more plants.

• Many plants make seeds by combining pollen from their flowers with pollen from other flowers. Water or wind occasionally helps pollen get where it needs to go, but sometimes it is carried by animals, especially birds and insects.

• Animals that help plants reproduce by carrying pollen from one plant to another are called pollinators.

• Larger animals often help plants reproduce without even realizing it. They carry seeds from one place to another so plants can spread to new places.  Carrying and scattering plant seeds so they will have the opportunity to expand to new areas is called seed dispersal. Some seeds are blown by the wind or carried by water, but many are caught in the fur of animals or eaten with fruit from the plant. Carried either inside or outside of an animal, the seeds are deposited and grow in their new locations.

Name:__________________________________

Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm   your answers.

1) What is the relationship between producers and consumers?

2) What is the ultimate source of energy for all living things?

3)  How do animals help ensure that plants reproduce?

  

4)  Give an example of a pollinator.

5)  Describe a food chain with at least three links. What is the producer? What is the primary consumer? What is the secondary consumer?