Whole Numbers
512, 345
Practise saying this number. How many words does it take to say?
8
Calculate 430 times 100
43,000
Plot the following numbers on a single number line: -6, +3, -2, 0, +7. Order them from least to greatest.
Visual answers
A factory packaged 30,000 crayons into boxes of 100. How many total boxes were filled?
300 boxes
1 + 4000 + 300 + 20,000 + 500,000 =
524, 301
Maya puts 840 into a function machine that multiplies the input by 10 and then multiplies the result by 100. What is the final number output? Show your work.
Work:
Step 1: 840 times 10 = 8,400
Step 2: 8,400 times 100 = 840,000
The temperature at midnight was -8 degrees Celsius. By noon, the temperature rose by 12 degrees Celsius. Use a number line to show the change and determine the temperature at noon.
4 degrees Celsius
A stadium holds 50,000 people. About how many stadiums would be needed to seat 1,000,000 fans?
20 stadiums
Write this number in words:
6, 345, 231
six million, three hundred forty-five thousand, two hundred thirty-one
A factory produces 2,400,000 paperclips. If they pack them into boxes that hold 1,000 paperclips each, how many boxes are needed? Show or explain your reasoning.
2,400 boxes
What number is exactly halfway between 0 and 900,000?
450,000
Suppose you wanted to estimate the number of elementary school teachers needed for 1,000,000 students in a state or province.
a) What assumptions must you make to solve this problem?
b) Solve the problem based on your assumptions. Show all your thinking.
a) Assumptions: Assume an average class size of 25 students per teacher (and that each classroom has 1 primary teacher).
1,000,000 / 40,000 = 25
(Calculator allowed)
Here is why:
One "ten thousand" is equal to 10,000.
Multiplying 35×10,000 gives 350,000.
When you look at place value, 35 ten thousands means you have a 3 in the hundred thousands place and a 5 in the ten thousands place, which equals 350,000.
A student claims that multiplying any whole number by 10,000 simply means "adding four zeros to the end." Explain why this rule works for whole numbers using place value shifts, and discuss whether this rule would still work if the starting number contained a decimal point.
Why it works for whole numbers: Multiplying by 10,000 shifts every digit 4 places to the left on the place value chart. For whole numbers, the 4 empty places created in the ones, tens, hundreds, and thousands columns are filled with placeholder zeros.
Decimal numbers: The rule fails for decimals. For example, 3.5 times 10,000 does not equal 3.50000. Shifting the digits 4 places to the left gives 35,000. Adding zeros to the end of a decimal does not change its value (3.5 = 3.5000).
Point A is halfway between 200,000 and 300,000. The section between 200,000 and 300,000 is divided into 10 intervals. Point C is located 3 intervals to the right of Point A. What value does Point C represent?
Answer: 280,000
A local stadium has a seating capacity of 420,000 people. Maya claims that 420,000 is the same as 42 ten-thousands, while Leo claims that 420,000 is the same as 420 thousands.
Who is correct? Explain your answer using place value models or multiplication.
Both Maya and Leo are correct!
Maya: 42 x 10,000 = 420,000 (42 ten-thousands is 420,000).
Leo: 420 times 1,000 = 420,000 (420 thousands is 420,000).