School Improvement in Maryland

Using the State Curriculum: Mathematics, Grade 4

Algebra | Geometry | Measurement | Statistics | Probability | Number | Processes
Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic

Topic A. Knowledge of Number and Place Value

Indicator 1. Apply knowledge of whole numbers and place value

Objective d. Compare, order, and describe whole numbers

  • Use no more than 4 whole numbers with or without using the symbols (<, > , =) and whole numbers (0 - 1,000,000)

Clarification

To compare numbers, determine how their values differ—which is greater, which is less, which is the least. Then, in some instances, the numbers can be put in order from the greatest to the least, or from the least to the greatest. To compare numbers, look at the digits in each of the places within the number (thousands, hundreds, tens and ones) and take note of how those in the same place differ. Each digit in a number represents a certain value. For example, 13,452 in terms of place value means:

Ten -thousands Thousands Hundreds Tens Ones
1 3 4 5 2

or 1 ten-thousand + 3 thousands + 4 hundreds + 5 tens + 2 ones
which is 10,000 + 3,000 + 400 + 50 + 2

This is the expanded form of the number 13,452 and it shows the value each digit represents.

  • To compare numbers, write each number in expanded form and compare the values in each place, beginning with the largest place value.

    Compare 3,467 and 3,572. Rewrite each number in expanded form.

    3,467 = 3,000 + 400 + 60 + 7
    3,572 = 3,000 + 500 + 70 + 2

    Each number has the same value in thousand's place. Look at hundred's place.

    3,467 = 3,000 + 400 + 60 + 7
    3,572 = 3,000 + 500 + 70 + 2

    Because 500 > 400, 3,572 > 3,467. Or 3,467 < 3,572.

  • To order numbers, write each number in expanded form and compare the values in each place, beginning with the largest place value.

    Order 12,566, 12,452, 11,673 and 13,451 from the least to the greatest. Rewrite each number in expanded form.

    12,566 = 10,000 + 2,000 + 500 + 60 + 6
    12,452 = 10,000 + 2,000 + 400 + 50 + 2
    11,673 = 10,000 + 1,000 + 600 + 70 + 3
    13,451 = 10,000 + 3,000 + 400 + 50 + 1

    Each number has the same value in ten-thousand's place. Look at thousand's place.
    13,451 has the greatest thousand's value and 11,673 has the least. The least and greatest numbers are shown.

    11,673, _________, ________, 13,451

    Now compare the remaining two numbers. 12,566 and 12, 452 have the same thousand's value. Look at their hundred's value. 500 > 400, so 12,566 > 12,452. Complete the ordering.

    11,673, 12,452, 12,566, 13,451

As students become more proficient in comparing numbers written in expanded form, they will begin to mentally compare the numbers in each place without writing out the expanded form.

Classroom Example 1

The following table has the greatest depths recorded for each ocean.

Ocean Greatest Depth (in feet)
Arctic 17,881
Atlantic 28,232
Indian 23,376
Pacific 35,840
  1. Which ocean has the greater depth, the Indian or Atlantic?
    The Atlantic has the greater depth.
    Using the expanded form of the numbers:
    28,232 = 20,000 + 8,000 + 200 + 30 + 2
    23,376 = 20,000 + 3,000 + 300 + 70 + 6

Since the digits are the same in the ten-thousand's place, we compare the thousand's place and see that 8,000 > 3,000 so 28,232 is greater than 23,376.

  1. List the oceans in order from the greatest depth to the least depth.
    Using the expanded form of the numbers:
    17,881 = 10,000 + 7,000 + 800 + 80 + 1
    28,232 = 20,000 + 8,000 + 200 + 30 + 2
    23,376 = 20,000 + 3,000 + 300 + 70 + 6
    35,840 = 30,000 + 5,000 + 800 + 40 + 0

Starting with the ten-thousand's place, the 3 is the largest digit value so 35, 840 is the greatest number.
Again in ten-thousand's place, the 1 is the least digit value so 17, 881 is the smallest number.

The other two numbers are the same in ten-thousand's place (2). Go to thousand's place. Since 8,000 > 3,000, 28, 232 > 23, 376. The numbers in order from the greatest to the least are:

Pacific Atlantic Indian Artic
35,840 28,232 23,376 17,881

Classroom Example 2

Using the U.S. Census Bureau's "2006 American Community Survey", the following table shows the estimated population for counties in Maryland.

County Est. Population
Anne Arundel 509,300
Howard 272,452
Montgomery 932,131
Prince George's 841,315
  1. Does Anne Arundel County or Montgomery County have a greater population?
    509,300 = 500,000 + 00,000 + 9,000 + 300 + 00 + 0
    932,131 = 900,000 + 30,000 + 2,000 + 100 + 30 + 1

    Montgomery County has the greater population.

  2. Which county has a seven in the ten-thousand's place? What does this number represent? Howard County has a 7 in ten-thousand's place. The 7 represents 70,000.
  3. List the counties from the least population to the greatest population.
Hundred- thousands Ten- thousands thousands hundreds tens ones
Anne Arundel 500,000 00,000 9,000 300 00 0
Howard 200,000 70,000 2,000 400 20 2
Montgomery 900,000 30,000 2,000 100 30 1
Prince George's 800,000 40,000 1,000 300 10 5

Howard, Anne Arundel, Prince George's and Montgomery
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