In Module 3, Topic B, students practice counting by ones and skip-counting by tens and hundreds. They start off with simple counting by ones and tens from 90 to 124 and 124 to 220. They then count by ones, tens, and hundreds from 200 to 432 and from 432 to 1,000 (2.NBT.2). They apply their new counting strategies to solve a change unknown word problem (2.OA.1). “Kinnear decided that he would bike 100 miles this year. If he has biked 64 miles so far, how much farther does he have to bike?” In counting students make use of the structure provided by multiples of ten and a hundred. Students think in terms of getting to a ten or getting to a hundred. They also identify whether ones, tens, or hundreds are the appropriate unit to count efficiently and effectively. Making this determination requires knowing and understanding structures, similar to knowing the ground on which you are going to build a house and with what materials you want to build.
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.)
In Module 3, Topic E, students transition to the more abstract number disks that will be used through Grade 5 when modeling very large and very small numbers. The foundation has been carefully laid for this moment since kindergarten when students first learned how much a number less than 10 needs to make ten. The students repeat the counting lessons of the bundles and money, but with place value disks (2.NBT.2). The three representations: bundles, money, and disks, each play an important role in the students’ deep internalization of the meaning of each unit on the place value chart (2.NBT.1). Like bills, disks are “traded,” “renamed,” or “changed for” a unit of greater value (2.NBT.2). Finally, students evaluate numbers in unit form with more than 9 ones or tens, for example, 3 hundreds 4 tens 15 ones and 2 hundreds 15 tens 5 ones. Topic E also culminates with a problem-solving exploration in which students use counting strategies to solve problems involving pencils which happen to come in boxes of 10 (2.NBT.2).
Topic G closes Module 3 with questions such as, “What number is 10 less than 402?” and “What number is 100 more than 98?” As students have been counting up and down throughout the module, these three lessons should flow nicely out of their work thus far and provide a valuable transition to the addition and subtraction of the coming module where more and less will be re-interpreted as addition and subtraction of one, ten, and a hundred (2.NBT.8). The language component of this segment is essential, too. Students need to be encouraged to use their words to make statements such as, “452 is 10 less than 462 and 100 less than 562.” This allows for a greater understanding of comparison word problems (2.0A.1) wherein the language of more and less is a constant presence.
In this activity from The Electric Company, students will review counting by tens and hundreds, discuss ways to group by tens and hundreds, and match bundles of tens and hundreds with the corresponding number. Included are simple teacher-led activities and hands-on exercises for students.