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Unit 3: Understanding Place Value

Lessons 1-3 Overview for 2nd Grade Math

Total Time: 90 minutes per lesson
Class Size: 14 students

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Learning Objectives

By the end of these lessons, students will be able to:

• Recognize that the value of digits depends on their place (ones, tens, hundreds).
• Read and write numbers to 100 and beyond in standard form, expanded form, and word form.
• Use place value understanding to add and subtract within 100.

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Learning Standards

Aligned with Common Core State Standards (CCSS) for Mathematics:

CCSS.MATH.CONTENT.2.NBT.A.1
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.

CCSS.MATH.CONTENT.2.NBT.A.2
Count within 1000; skip-count by 5s, 10s, and 100s.

CCSS.MATH.CONTENT.2.NBT.A.3
Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

CCSS.MATH.CONTENT.2.NBT.B.5
Fluently add and subtract within 100 using strategies based on place value.

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Key Vocabulary

• Place Value
• Ones
• Tens
• Hundreds
• Expanded Form
• Standard Form
• Digit
• Value

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Lesson 1: Place Value Foundations

Hook (10 minutes)

“Number Detective” Warm-up:
Show a big number chart (1-100) and call out a number. Students use mini-whiteboards to write down the number and then break it into tens and ones (e.g., 43 = 4 tens, 3 ones). End with a quick share to reinforce the concept.

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Mini-Lesson (I Do) (15 minutes)

Interactive Teaching: Place Value Blocks
Use base-ten blocks projected on the screen (or physical blocks if available). Model how tens and ones build numbers to 100.

• Show the number 57 with 5 tens blocks and 7 ones blocks.
• Write the number 57 in standard form and expanded form (50 + 7).
• Explain why place value matters.

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Guided Practice (We Do) (20 minutes)

Hands-on Place Value Chart Activity
Students use place value mats and physical manipulatives (tens and ones blocks). Call out numbers 30-99, and students build them on the mats. Partner pairs discuss and write the numbers in expanded form on dry erase boards. Teacher circulates giving feedback.

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Independent Practice (You Do) (25 minutes)

Number Building & Writing
Students receive number cards (two-digit numbers). They:

• Use blocks to build the number
• Write the number in standard form
• Write the number in expanded form
• Draw a quick sketch to represent the number in tens and ones

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Closing (Synthesis) (10 minutes)

Class Discussion: Volunteers share their favorite number and explain how they built it using blocks and place value terms. Recap key vocabulary. End with a quick thumbs-up/thumbs-down understanding check.

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Fluency Focus

Rapid flash cards of two-digit numbers — call out, students quickly show corresponding tens and ones using fingers or blocks.

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Differentiation

• For Struggling Learners: Use smaller numbers (10-50), more guided practice with teacher or aide. Provide visual charts on desk.
• For Advanced Learners: Extend to 3-digit numbers, introduce hundreds place, and have them write expanded forms including hundreds.

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Assessment

Exit Ticket: Write two numbers you built today and write their expanded forms. Teacher reviews for understanding.

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Lesson 2: Exploring Hundreds

Hook (10 minutes)

“Hundreds Hunt” Game:
Teacher hides picture cards with numbers (under 1000) around the room. Students find a card and identify the hundreds, tens, and ones in partners.

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Mini-Lesson (I Do) (15 minutes)

Digit Place Demonstration
Model 3-digit number decomposition, e.g., 246 = 200 + 40 + 6. Use place value chart and blocks (hundreds flat, tens rods, ones cubes). Write number names and expanded form on board.

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Guided Practice (We Do) (20 minutes)

Place Value Sort
Students receive number cards and sort them by hundreds, tens, and ones. In pairs, write the numbers in expanded form and read the numbers aloud.

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Independent Practice (You Do) (25 minutes)

Build & Write
Students are given three-digit numbers. Using blocks, they build the number, write it in standard form, expanded form, and number words.

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Closing (Synthesis) (10 minutes)

Reflect on place value importance. Volunteer students explain how a digit’s place affects its value using an example from their work.

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Fluency Focus

Rapid count by hundreds, tens, and ones aloud as a class and in small groups.

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Differentiation

• For Struggling Learners: Focus on two-digit numbers with teacher support.
• For Advanced Learners: Challenge: Write numbers in expanded form with some digits zero (e.g., 305 = 300 + 0 + 5).

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Assessment

Exit Slip: Write three numbers they built and break them into hundreds, tens, and ones. Teacher confirms accuracy.

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Lesson 3: Applying Place Value to Addition & Subtraction

Hook (10 minutes)

“Number Building Challenge”:
Call out an addition or subtraction problem with two-digit numbers (e.g., 42 + 35). Students quickly model with blocks.

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Mini-Lesson (I Do) (15 minutes)

Demonstrate adding tens and ones separately using place value blocks. Show regrouping (carrying) with physical blocks and write step-by-step solution.

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Guided Practice (We Do) (20 minutes)

Problem-solving in pairs: Students solve 3-4 addition or subtraction problems using blocks, draw place value charts, and write equations.

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Independent Practice (You Do) (25 minutes)

Worksheet with addition and subtraction problems within 100 using place value strategy. Students draw pictures or use number sentences to explain their thinking.

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Closing (Synthesis) (10 minutes)

Class discussion about strategies used. Share tips on how place value helped them solve problems.

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Fluency Focus

Timed “Add and Subtract” drills: rapid recall of basic sums and differences within 100, emphasizing place value strategy.

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Differentiation

• For Struggling Learners: Use smaller numbers or focus on addition only. Allow use of manipulatives.
• For Advanced Learners: Introduce three addend problems or subtracting with regrouping.

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Assessment

End-of-lesson quiz with 5 questions:

• Write a 2-digit number in expanded form
• Identify place value of a digit
• Solve 2 addition and 2 subtraction problems using place value methods

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Teacher Note:
Incorporate movement breaks and frequent positive reinforcement. Use student names and real-life numbers (birthdays, classroom items) to personalize learning and increase engagement. Utilize visual aids, tactile tools, and collaborative learning to address multiple learning styles.

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This detailed plan balances hands-on activities, conceptual understanding, and fluency practice aligned exactly with the Common Core standards for Second Grade Number and Operations in Base Ten.