Compare Two Two-Digit Numbers Based on Meanings of the Tens and Ones Digits, Recording

1. NBT.B.3

Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Unpacked

When teaching students to compare numbers, teachers often approach this entire skill from the symbolic perspective. They may teach the strategy of stacking the two numbers and comparing the digits in each place to determine which is the larger, or smaller, number. Teachers often state that numbers in which the numerals are the same, but the order is changed are the most troublesome to their students. When students are given ample opportunities to build multi-digit numbers with manipulatives, they will be much more likely to grasp the concept of place value. A student who can form a concrete mental image of 2 tens and 4 ones will readily be able to compare it with 4 tens and 2 ones.

Teachers may consider introducing comparisons by requiring that students build the numbers and discuss their reasoning for indicating which is the larger number. Teachers would then explicitly teach representational drawings, perhaps using straight lines to represent ten rods, and dots to represent ones cubes. Students should spend some time using these drawings to clarify/justify their thinking when comparing numbers. Consider having students draw each number and circle the part of the drawing that proves which one is greater (or less).

This standard builds on the work of 1.NBT.1 and 1.NBT.2 by having students compare two numbers by examining the amount of tens and ones in each number. Students are introduced to the symbols greater than (>), less than (<) and equal to (=). Students should have ample experiences communicating their comparisons using words, models and in context before using only symbols in this standard.

Once students are able to decompose a two-digit number into bundles of tens

and remaining ones, they can use that knowledge to compare two-digit

numbers with one another. From here, they are then able to put numbers in

order from least to greatest or vice versa, followed with the use of the >, =,

and < symbols.

Provide students with a variety of opportunities to compare two-digit

numbers, beginning with numbers that have different values in the tens and ones positions. This exploration should include the use of base 10 models, manipulatives, technologies and other visual media that will enhance a student’s understanding that the amount of bundles of tens(i.e., the tens digit) will determine how it can be compared with another two-digit number.

Provide students with problems/opportunities to compare numbers with

the same tens digits, but with different ones digits. Once students recognize

that two numbers have the same tens digit, then they can explore how those

numbers can be compared using the ones position. Manipulatives, pictures,

technologies, drawings and concrete models will enrich a student’s

understanding of this concept (e.g., base 10 blocks, ten frames, unifix

cubes).

Provide students with the opportunity to practice the use of mathematical symbols <, =, >, and to write an inequality or equality to record the result of a comparison.

Example: 42 __ 45