In 3rd grade, students transition from plotting, ordering, and comparing 3-digits numbers to performing the same skills with 4-digit numbers. This prepares them for rounding, addition, and subtraction. It also helps their number sense understanding advance in a developmentally appropriate way towards the 4th grade level expectations.
MA.3.NSO.1.3 I can plot, order, and compare whole numbers up to 10,000.
Plotting Numbers in 3rd Grade
Plotting numbers on a number line is the easiest level of comparing and ordering number in 3rd grade. Given equal intervals on a number line, 3rd graders can locate where 4-digit numbers are by examining differences between the digits in each place. Numbers plotted on a number line are always ordered from least to greatest.
In order to prepare students for rounding, they need plenty of experience with number lines with difference, equal intervals – both pre-labeled number lines and number lines they partition and label themselves.
Students should work with intervals of 1, 10, 100, and even 1,000. This gives them experience with different relative distances between quantities represented with 4 digits.
Comparing Numbers in 3rd
There are five levels of comparing two numbers in 3rd grade. The first is comparing the number of digits in both numbers. If one number has 3 digits and the other has 4, the 4-digit number will always be greater because thousands will always have a greater value than hundreds.
Students should then learn to evaluate the digits in each place, from greatest to least. If the numbers have different digits in the thousands place, the number with the larger digit is greater. If the numbers have the same digit in the thousands place, the same evaluation needs to happen in the hundreds, then the tens, and finally the ones places.
The concept of equal is important, as well. While it is fairly simple to observe that two 4-digit numbers have the same digits in each place, this skill can be easily scaled up for a challenge.
Comparing numbers in different forms will make students work to put them in the same form first. They can also work with expanded and unit form with the places out of order or that require decomposing or composing units.
Ordering Numbers in 3rd Grade
Ordering numbers in 3rd grade is a little more challenging than comparing numbers because students are working with 3 or more numbers. Ordering from least to greatest is more natural because it mirrors the concept of a number line, where numbers increase from left to right.
Numbers ordered from greatest to least have to be arranged in the other direction, which can be counter-intuitive for some 3rd graders.
The same process applied to compare two 4-digit numbers can be used to order numbers in either direction. Students should choose two numbers to compare first. They can then sort the other numbers in the list using vocabulary like “first,” “next,” “between,” and “last.”
Having students present to the class or a partner to describe their process and justify their reasoning can raise their level of metacognition about number magnitude and their order.
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