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