How to Determine an Equivalent Form of a 4-Digit Whole Number for the 3rd Grade

Equivalent Forms Using Number Expressions

• 1

  Construct a number line. Because 4-digit numbers are large for a number line, use estimates of the numbers to help you see what is happening as you find equivalent forms. Use the whole numbers 1 through 20 on the number line, dividing the distance between each number into four sections. The number line will vary based on the whole number for which you want to find equivalent forms. As you increase your understanding of the process, you will find you no longer need the number line.

• 2

  Plot the 4-digit number on the number line. The example uses 5,280. Because 5,280 is close to 5,250, place the number at 5,250, the first small line after 5 on the number line.

• 3

  Decide on the mathematical operation you want to use for the equivalent form. Any number expression, using any operation, with the answer 5,280 meets the criteria of an equivalent form. For example, 5,000 + 280; 6,000 -- 720; 2,640 x 2; or 10,562 ÷ 2.

• 4

  Show the jumps on the number line corresponding to the number expression you are using. This visualizes the process. For example start at 5,000 (represented by 5 on the number line) and make a jump to the right of 280 (since we are estimating, the jump will be to the first small mark after the 5).

Equivalent Forms Using Physical Models or Diagrams

• 5

  Find the Cuisenaire Rods, or a similar manipulative, needed to represent the 4-digit number. For the thousands place, you can bundle 10 flats (equal to 100 each) if you do not have a thousands manipulative. The example uses the number 5,280. You will not need any ones (cubes). You will need 8 rods (equal to 10 cubes or ones), 2 flats (equal to 100 each) and 5 bundles of 10 flats each (or 5 thousands block).

• 6

  Label the place value columns using small pieces of paper taped to the table. The order from left to right is ones, tens, hundreds and thousands.

• 7

  Place the Cuisenaire Rods in the appropriate columns (place value). The ones column will remain empty. Put 8 rods in the tens column, 2 flats in the hundreds column and 5 bundles of flats, or 5 thousand blocks, in the thousands column. The Cuisenaire Rods are an equivalent physical model of the number 5,280. Diagrams of this process can also be drawn.

Other Equivalent Forms

• 8

  Examine the 4-digit number to determine if it can be represented another way. The example, 5,280, has an alternative equivalent form.

• 9

  Think about possible equivalent forms. This requires creativity and reasoning. Some ideas to get you started thinking this way are: 32=the number of degrees F. where water freezes; 100=the number of pennies that equal a dollar; 12=the number of inches in a foot.

• 10

  Write the equivalent form, which for our example is 5,280 = the number of feet in a mile.