In Module 3, Topic C, the teaching sequence opens with students counting on the place value chart by ones from 0 to 124, bundling larger units as possible (2.NBT.1a). Next, they represent various counts in numerals, designating and analyzing benchmark numbers (e.g., multiples of 10) and numbers where they bundled to count by a larger unit (2.NBT.2). Next, students work with base ten numerals representing modeled numbers with place value cards that reveal or hide the value of each place. They represent three-digit numbers as number bonds and gain fluency in expressing numbers in unit form (3 hundreds 4 tens 3 ones), in word form, and on the place value chart. Students then count up by hundreds, tens, and ones, leading them to represent numbers in expanded form (2.NBT.3). The commutative property or “switch around rule” allows them to change the order of the units. They practice moving fluidly between word form, unit form, and expanded form (2.NBT.3). Students are held accountable for naming the unit they are talking about, manipulating, or counting. Without this precision, they run the risk of thinking of numbers as simply the compilation of numerals 0–9, keeping their number sense underdeveloped. The final Application Problem involves a found suitcase full of money: 23 ten dollar bills, 2 hundred dollar bills, and 4 one-dollar bills, in which students use both counting strategies and place value knowledge to find the total value of the money.
In Module 3, Topic D, students will further build their place value understanding. Students count by $1 bills up to $124, repeating the process done in Lesson 6 with bundles. Using bills, however, presents a new option. A set of 10 ten dollar bills can be traded or changed for 1 hundred dollar bill, driving home the equivalence of the two amounts, an absolutely essential Grade 2 place value understanding (2.NBT.1a). Next, students see that 10 bills can have a value of $10 or $1,000 but appear identical aside from their printed labels (2.NBT.1, 2.NBT.3). A bill’s value is determined by what it represents. Students count by ones, tens, and hundreds (2.NBT.2) to figure out the values of different sets of bills. As students move back and forth from money to numerals, they make connections to place value that help them see the correlations between base-ten numerals and corresponding equivalent denominations of one, ten, and hundred dollar bills. Word problems can be solved using both counting and place value strategies. For example: “Stacey has $154. She has 14 one-dollar bills. The rest is in $10 bills. How many $10 bills does Stacey have?” (2.NBT.2). Lesson 10 is an exploration to uncover the number of $10 bills in a $1,000 bill discovered in great grandfather’s trunk in the attic. (Note that the 1,000 dollar bill is no longer in circulation.)
Part of using base-ten numbers correctly is understanding how to express the same number in different forms. This video demonstrates how to express base-ten numerals written in standard form, unit form, expanded form, and number name.