Thinking Flexibly About Numbers to 1,000 Unit of Study 2: Place Value Concepts to 1,000 Global Concept Guide: 2 of 4
Content Development • Students’ experiences, not memorization, of place value positions are essential in understanding and applying concepts within this GCG. • Experiences should include a variety of manipulatives including but not limited to : base ten blocks, virtual manipulatives, secret code cards, place value mats, etc. • This GCG focuses on having students flexibly represent 3-digit numbers by building concrete models, drawing pictorial representations, and connecting those models with more abstract representations such as standard form, expanded form, and word form. • Examples of critical conceptual understandings which serve as a foundation for regrouping are: • 238 has the same value as 23 tens and 8 ones or 2 hundreds and 38 ones, not just 2 hundreds, 3 tens, and 8 ones. • There are 23 tens in 238 not just 3 tens.
Day 1 • Essential Question: How do you record a 3-digit number that is shown by a set of base-ten blocks? • Students should be able to add hundreds, tens, and ones onto a number and state the new sum. (e.g. “If I have 2 hundreds, 4 tens, and 8 ones and I add 3 tens, what is my new number?”) • An example of a common error students make is when writing the number six hundred four in standard form they write it as “6004”. When students have this misconception it is important to reteachto develop conceptual understanding. • By the end of Day 1, students should to be able to move fluently between concrete representations, expanded form, and standard form of three-digit numbers.
Day 2 • Essential Question: How can you use base-ten blocks or quick pictures to show the value of a number in different ways? • The focus of Day 2 is to combine lessons 2.6 and 2.7 to reinforce the connections between word form, base-ten blocks, and expanded form. This Graphic Organizer can be used to represent numbers multiple ways: Number Representation • During instruction students should have multiple experiences moving between concrete representations with base-ten blocks and expanded form as they move toward the standard form of a number. It is important that students should experience numbers with zeroes to address place value misconceptions. • Reinforce vocabulary and precision in reading numbers. Students should be reminded to notinsert the word “and”when reading three-digit numbers. For example, the number 132 should be read as “one hundred thirty-two,” not “one hundred and thirty-two.” • By the end of Day 2, students should be able to represent a number in multiple ways using base-ten blocks and quick pictures.
Day 3 • Essential Question: How can you represent 3-digit numbers in multiple ways? • The focus of Day 3 is to extend the concept of composing and decomposing numbers using tens and hundreds. Students have prior experiences composing and decomposing two-digit numbers. • Students should be able to represent three-digit numbers in multiple ways. For example, 235 can be represented as 23 tens and 5 ones which is the same as 22 tens and 15 ones (or 2, 3 tens, and 5 ones). • As students are gaining experiences, facilitate discussions that help them make connections between concrete, pictorial, and abstract representations of three-digit numbers. The ultimate goal is to move students away from concrete models/manipulatives toward true conceptual understanding of three-digit numbers in standard form. • By the end of Day 3, students should be able to represent numbers flexibly, in multiple ways
Example of base-ten blocks representing a number flexibly. The concept serves as a foundation for regrouping.
Day 4 • Essential Question: What strategy can you use to organize the different ways to represent a number? • The focus of Day 4 extends the previous day by using an organized list. The lesson supports students in communicating their understanding of patterns and structures in composing and decomposing three-digit numbers (example on next slide, from TE p. 85B). • Recognizing familiar structures in place value will support students as they move toward the development of algorithms for regrouping. • Additionally, students should experience expanded form problems represented out of order (e.g. 5 + 20 + 300 or 20 + 5 + 300 is the same as 325). If the order is always presented in the traditional way with hundreds, tens, and ones appearing “in order,” we may be creating and/or reinforcing a misconception for students. • By the end of Day 4, students will be able to use an organizational strategy to represent numbers multiple ways.
Enrich/Reteach/Intervention Reteach: • For students who need further support with two-digit numbers, use Vocabulary Builder on TE 77A - Word Forms of Numbers. • For students who need further support with different forms of a number - TE 81B – Differentiated Instruction Activities. • Utilize Reteach p. R17 to help students represent numbers. Enrich: • For enrichment regarding place value, use TE p. 70 (Enrich 2.4) and TE p. 82 (Enrich 2.7). • Challenge students to represent the number 324 using 45 pieces. • Challenge students to use base ten blocks to make five hundred thirty-four” without using exactly five flats, three rods, and four unit cubes.