Construct Argument

Open Ended

Gayle said Arizona had more retail sales than Massachusetts because 7>3, so $13,637 > $13,533. Construct an argument to explain whether or not Gayle is correct.

​Gayle's explanation is not reasonable.

The greatest place value where the digits are different starting from the left is the hundreds place. So, Gayle needed to compare 500 and 600 instead of 7 and 3.

Although Gayle did come to the correct conclusion, she did not justify her conjecture accurately.

Open Ended

The population of Gerald's city is three hundred thousand, twenty-seven. Gerald wrote the number as 327,000. Emily lives in a city that has a population of three hundred sixteen thousand, forty-two. Gerald concluded that his city's population is greater than the population of Emily's city.

Does Gerald's explanation make sense? Identify any flaws in Gerald's thinking?

​No; Gerald did not write the population for his city correctly. He did not write the digits in the correct places.

Open Ended

The population of Gerald's city is three hundred thousand, twenty-seven. Gerald wrote the number as 327,000.

Construct a math argument that explains why Gerald did not write the population of his city correctly.

​The digits for twenty-seven belong in the ones period.

Gerald should have written 300,027.

Open Ended

Correct Gerald's argument. Explain how to compare the populations of Gerald's and Emily's cities.

The population of Gerald's city is three hundred thousand, twenty-seven. Gerald wrote the number as 327,000. Emily lives in a city that has a population of three hundred sixteen thousand, forty-two. Gerald concluded that his city's population is greater than the population of Emily's city.

​Gerald's city is 300,027 and Emily's is 316,042. The greatest place value where the digits are different starting from the left is the ten thousands place. So, Gerald needed to compare 0 and 10,000 instead of 20,000 and 10,000.

​

Emily's city has a greater population that Gerald's city.

Open Ended

What information do you have?

​What information do you have?

​The lengths of the equators of 4 planets and Nora's conjecture are given.

Open Ended

What are the possible estimates for the lengths of the equators of Jupiter and Earth?

​What are the possible estimates for the lengths of the equators of Jupiter and Earth?

​Jupiter's equator- 400,000 km. Earth's equator - 40,000 km.

​

​(rounded to the highest place value)

Open Ended

What is the relationship between estimates you found for the lengths of the two equators?

​What is the relationship between estimates you found for the lengths of the two equators?

400,000 is 10 times 40,000

Open Ended

Construct an argument justifying Nora's conjecture.

​Jupiter's equator is about 400,000 km. and Earth's equator is about 40,000 km.

​

​Since 400,000 is 10 times 40,000, Jupiter's equator is about 10 times the length of Earth's equator.

​

​Nora's conjecture is true.

​Describe at least one way you could construct an argument justifying Lee's conjecture.

​Use place value to round each distance to the nearest thousand and show the distances are the same.

Open Ended

How can you ROUND the two flight distances in Lee's conjecture?

Chicago to Sao Paolo 

Open Ended

How can you ROUND the two flight distances in Lee's conjecture?

Chicago to Istanbul

​The flight distance from Chicago to Sao Paolo is 5,252 miles which rounds to 5,000 miles.

​

​

​

​The flight distance from Chicago to Istanbul is 5,784 miles which rounds to 6,000 miles.

Open Ended

Is Lee's conjecture true? Justify your answer.

​NO.

​

​

​

​The flight distance from Chicago to Sao Paolo is about 5,000 miles and from Chicago to Istanbul is about 6,000 miles.

​5,000       6,000