Question 1: Partition the number 3,456,789 into hundreds of thousands, ten thousands, thousands, hundreds, tens, and units.

Answer: 3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9

Question 2: Write 987,654 as the sum of its place value parts.

Answer: 900,000 + 80,000 + 7,000 + 600 + 50 + 4

Question 3: Partition 2,345,678 into its components.

Answer: 2,000,000 + 300,000 + 40,000 + 5,000 + 600 + 70 + 8

Question 4: A number is partitioned as 4,000,000 + 800,000 + 30,000 + 5,000 + 600 + 70 + 8. What is the number?

Answer: 4,835,678

Question 5: Using partitioning, add the numbers 1,234,567 and 2,345,678 by separately adding their parts.

Answer: Sum of parts: (1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7) + (2,000,000 + 300,000 + 40,000 + 5,000 + 600 + 70 + 8) = 3,234,567 + 2,345,678 = 5,580,245

Question 6: Construct a number with the following partition: 5 million, 200 thousand, 30 thousand, 4 hundred, and 5 units.

Answer: 5,230,405

Question 7: Identify and correct the mistake: The partition of 4,567,890 was written as 4,000,000 + 500,000 + 6,000 + 700 + 80 + 9.

Answer: The mistake is missing the 60,000 and 30,000 parts; it should include 4,000,000 + 500,000 + 60,000 + 7,000 + 800 + 90.

Question 8: Partition the number 6,789,123 into its place value components.

Answer: 6,000,000 + 700,000 + 80,000 + 9,000 + 100 + 20 + 3

Question 9: Explain how partitioning helps in adding two large numbers.

Answer: Partitioning separates numbers into manageable parts, allowing addition of each place value independently, reducing errors and simplifying calculations.

Question 10: Plot the graph of y=2x for x values from 0 to 5 on the grid.

Answer: Students draw the line passing through (0,0), (1,2), (2,4), (3,6), (4,8), (5,10).

Question 11: Challenge: Partition 9,876,543 into parts such that the sum of the parts is 9,876,543 and each part is a multiple of 10,000.

Answer: Possible partition: 9,000,000 + 800,000 + 70,000 + 6,000 + 500 + 40 + 3