Grade 2 Number Concepts

2.NBT.A.4

About the Math

Full Standard

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**2nd Grade Students Learning 2nd Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of number concepts and relationships

**1st Grade Students Learning 2nd Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of number concepts and relationships

About the Math

Skills and concepts below are learning goals for this standard.

Students need a strong understanding of place value to compare numbers. Connect their understanding to two-digit numbers and make connections to three-digit numbers. Avoid jumping to the symbols for >, <, and = too quickly. Encourage students to use the terms greater than, less than and equal to when they discuss the numbers. Then move to how to record this using symbols.

Explain how numbers are compared using representations including base ten models and number lines.

Make connections to comparison ideas used with smaller (two-digit numbers). Extend this reasoning to three-digit numbers. Use multiple representations to confirm comparisons including base ten blocks, modified hundred charts, and number lines.

Estimate and compare numbers to benchmarks (i.e. 198 is close to and less than 200, 163 is close to and greater than 150).

Have students compare and/or related numbers to benchmarks. This will be especially helpful for estimating sums and differences later in the year.

Explain a process for comparing numbers using the meaning of place value.

We compare numbers by first examining their greatest place value. This is done simply because more of any place value will be greater than less of a place value. Moreover, a greater place value is automatically greater than a less place value (eg hundreds are greater than tens, so 578 is greater than 99). Note that students often hold the misconception that the greatest digit (anywhere in the number) is how to determine the greater value. When the greatest place value of two numbers is the same, we then move to the next greatest place value to compare.

Record comparisons using the symbols >, <, and =.

Incorporate symbols as students make sense of the concept. For example, as students consider comparing 234 and 576 with base ten blocks, record the result as 234 < 576. Connect the recording to the representation. Avoid jumping to the symbols for >, <, and = too quickly. That is, avoid jumping to simply comparing via 234 < 576 without a conceptual understanding of place value/number lines. Encourage students to use the terms greater than, less than and equal to when they discuss the numbers. Then move to how to record this using symbols.

Essential vocabulary and symbols for this standard include: greater than, less than, equal, <, >, and =. Visit the online dictionary for vocabulary support.

Progression of Standard within Grade 2

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Explain how numbers are compared using representations including base ten models and number lines. Estimate and compare numbers to benchmarks (i.e. 198 is close to and less than 200, 163 is close to and greater than 150). Explain a process for comparing numbers using the meaning of place value. Record comparisons using the symbols >, <, and =.	*Revisit this standard throughout the year through routines, independent practice, discussions, and other activities.	*Revisit this standard throughout the year through routines, independent practice, discussions, and other activities.	*Revisit this standard throughout the year through routines, independent practice, discussions, and other activities.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map. Information is not the complete standard.

Progression Across Grades
Grade 1	Grade
Understand that the two digits of a two-digit number represent amounts of tens and ones (1.NBT.2)	This concept is not taught after Grade 2. Students are expected to apply the standard proficiently.

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Instructional Tasks

Tasks

These tasks can be used with small group or whole group instruction.

Group students into pairs. Have each student pick three digit cards and represent a three-digit number using base ten blocks. Have the pair of students compare their models and record their comparisons in their journals. You can also group students into triads to order the numbers from least to greatest. Pose a question such as what do you notice about the digits in your comparisons.
Group students into pairs. Have each student pick three digit cards, create a three-digit number and write the number in expanded form. Have the pair of students compare their expressions and record their comparisons in their journal. Pose a question such as what role does place value have in comparing numbers.
Draw a number line with endpoints 0 and 1,000 and label every multiple of 100 on the number line. Have students identify where 392 would be placed and place that number on the number line. Have students identify three numbers greater than 392 and three numbers less than 392. This could also be represented using a string and placing folded index cards on the number line to label points. Pose a question such as how can we use benchmark numbers such as 400 to compare numbers.
Summer and Tara are comparing numbers. Summer wrote 59 and Tara wrote 112. Summer says you start at left when comparing numbers, so she says her number is largest because 5>1. Tara says her number is largest because it has more digits. Who is correct and why? Use what you know about place value to explain your answer.
Using the digits 4, 6, and 2, create three different three-digit numbers and then order them greatest to least.
Write three numbers that are even and greater than 300. Write three numbers that are odd and less than 300 and have a 5 in the tens place.
Sue and Julie each have a 3-digit number that contains the digits 2, 8, and 6. Sue’s number is larger. What could Sue and Julie’s numbers be? What are two other numbers they could be?
432 > 423 even though each number has the same digits. Using place value vocabulary, explain why this is true.

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 2 • Place Value

Compare two-digit numbers:

Additional Tasks

These links provide instructional ideas connected to this standard.

Ordering 3-digit numbers (Illustrative Math)
Comparisons 1 (Illustrative Math)
Digits 2-5-7 (Illustrative Math)
Number Line Comparisons (Illustrative Math)
Using Pictures to Explain Number Comparisons (Illustrative Math)
Twenty Questions (Math Solutions Lesson Seed)
The Great Stuff Cafe (Utah Core Academy Lesson)
Pokemon Cards (Utah Core Academy Lesson)
M&Ms and Skittles (Utah Core Academy Lesson)
Carol's Numbers (Georgia Department of Education, pgs. 113-118)
Fish Food More or Less (NCTM Illuminations Lesson)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Teaching Student-Centered Mathematics	K-3	140 (Say It/Press It, Activity 5.14)
Hands On Standards	1-2	20-21 (Greater Than and Less Than) 42-43 (Comparing Two-Digit Numbers)
Hands-On Standards	3-4	18-19 (Comparing and Ordering Numbers)
Nimble With Numbers	1-2	21-32, 73-95, 102, 108, 117-118, 123-124
Groundworks Reasoning with Data and Probability	2	48-55 (Out of Order)
Brain Compatible Activities for Mathematics,	K-1 2-3	19-21 (Number Slap) 7-10 (Order Up!)
Number Sense	1-2	138-142 164
Developing Number Concepts	2	68-77
SuperSource Base Ten Blocks	K-2	18-21 (Balance of Values) 26-29 (Build a Bughouse) 38-41 (How Many Can You Hold?)
Math In Practice Teaching Second-Grade Math	2	Module 5

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Greatest? Least? Equal? (HCPSS-adpated resource)
Recycle It (HCPSS-adpated resource)
Layers of Numbers (HCPSS-adapted resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

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Assessment

Full Standard

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Measurement Topic

The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.

2nd Grade Students Learning 2nd Grade Standards by Measurement Topic

Demonstrates understanding of number concepts and relationships

Quarter 1

Accurately compare three-digit numbers.
Explain number comparisons using representations.
Record comparisons using the symbols >, <, and =.

1st Grade Students Learning 2nd Grade Standards by Measurement Topic

Demonstrates understanding of number concepts and relationships

Quarter 1

Accurately compare three-digit numbers.
Explain number comparisons using representations.
Record comparisons using the symbols >, <, and =.

2NBT4 Anecdotal Data Collection Tool

Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification.

Rubric (for thinking and reasoning evidence)

Use this rubric for observation and constructed responses (tasks that require explanation, justification, and/or representation).

Rubric for Tasks (pdf)

Exemplars for this standard (if available)

These samples are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.

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