Tasks
Concept #1- Understanding the relative size of numbers
+ A base ten block is 1 centimeter long. If we were to line up 1 thousand blocks end to end, how far would the line they make stretch? Would it fit inside our classroom? How about 1 million? Would it fit inside our school? Inside Chicago? Inside Illinois? 1 billion?
+ Graph the following populations on the given number line. Be as precise as possible.
Enrollment at Brentano Elementary School: 502
Population of Logan Square Neighborhood: 73,702
Population of Chicago: 2,695,598
Population of the United States: 327,996,618
+ Plot each of the numbers in the table below as a point on a number line from 1 to a billion.
The table shows how fast light waves or electricity can travel through different materials.
|
Material |
Speed (meters per second) |
|
Space |
300,000,000 |
|
Water |
(2.25) ∙ 108 |
|
Copper wire (electricity) |
280,000,000 |
|
Diamond |
124 ∙ 106 |
|
Ice |
(2.3) ∙ 108 |
|
Olive oil |
200,000,000 |
(Open-Up Resources, 2017)
Concept #2- Numbers as powers of ten and laws of exponents
+ How many times bigger is the population of the United states compared to Chicago?
+ How many pennies would it take to make a million dollars?
+ How many centimeters in 10 kilometers?
+ How many seconds old are you? How long will it take for you to get to a billion seconds old?
Concept #3- Estimating
+ Suppose that the average Chicagoan drinks 58 gallons of water per year. How much drinking water is needed every year for Chicago?
+ How many school lunches are eaten every day in Chicago?
Concept #4- Scientific Notation
+ A conservative estimate of the number of stars in the universe is 6 × 1022. The average human can see about 3,000 stars at night with his naked eye. About how many times more stars are there in the universe compared to the stars a human can actually see? (Eureka Math, 2015)
+ The average person takes about 30,000 breaths per day. Express this number as a single-digit integer times a power of 10. If the average American lives about 80 years (or about 30,000 days), how many total breaths will a person take in her lifetime? (Eureka Math, 2015)
Concept #5- Operating with Scientific Notation
+ Chicago is known as the alley capitol of the United States. If you were to line up all the alleyways from end to end it would stretch a total of 1.003 x 107 feet. If the average width of an alleyway is 16 feet, how many square feet of pavement would be needed to repave all of Chicago’s alleyways?
+ If every person in the world jumped into Lake Michigan, what would happen to the level of water?
+ Consider the cost it took to build Willis Tower. If we stacked that amount in dollar bills, would the tower of cash be as a high as the building?
+ Culminating Project- Design your own big question and show all of your steps in answering it. Explain how you know your answer is reasonable. Plot the values you used and your final answer on a number line.
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