Last updated: 8/15/2021 ## Grade 2 - Numbers and Operations in Base Ten

 Subject: Mathematics (NYS P-12 Common Core)
 Unit Title: Grade 2 - Numbers and Operations in Base Ten
 Approx. Number of Weeks: 2nd Semester

#### Unit Summary:

Extend understanding of the base-ten numeration system and place-value concepts.

Create equivalent representations of given numbers using place value (such as; 35 represented by 35 ones, 3 tens & 5 ones or 2 tens & 15 ones, etc.) and properties of operations [such as; 35 represented by commutative 30 + 5 = 5 + 30, associative (20 + 10 )+ 5 = 20 + (10 + 5) etc.].

Write, compare and order multi-digit numbers.  Use representation; drawings, manipulatives, equations, charts, number lines, etc.

Compose and decompose multi-digit numbers.  Use benchmark numbers, skip counting, multiples of 10 & 100, equations, expressions, etc. Collaboration & Communication Creativity & Innovation Critical Thinking & Problem Solving Research & Information Fluency Social & Emotional Intelligence

### 1. What will students know and be able to do?

#### Standards:

 2.NBT.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. Understand the following as special cases: 2.NBT.2 - Count within 1000; skip-count by 5s, 10s, and 100s. 2.NBT.3 - Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 2.NBT.4 - Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 2.NBT.5 - Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.6 - Add up to four two-digit numbers using strategies based on place value and properties of operations. 2.NBT.7 - Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.8 - Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. 2.NBT.9 - Explain why addition and subtraction strategies work, using place value and the properties of operations.

#### Essential Understandings:

Students will understand that…

The placement of a digit in a number affects its value.

#### Essential Questions:

How does the pattern affect the value?

Possible ways to scaffold the question:

• What pattern do you see?
• What’s the purpose of the pattern?

#### Students will know:

Whole numbers can be grouped in units and multiples of 100s, 10s & 1s (to 1,000).

Place value notation is a short-hand for the sums of multiples of powers of 10 (e.g. 853 as 8 hundreds + 5 tens +3 ones)  ( e.g. 35, 30+5, 20 + 10+ 5)

Numbers have relationships and can be compared and ordered.

Place value and properties of operations can be used to add and subtract numbers.

Sometimes it is necessary to compose or decompose tens and hundreds when adding and subtracting three-digit numbers.

Addition and subtraction strategies can be explained using place value and properties of operations.

#### Students will be able to:

Number and Operations in Base Ten

Understand place value. (2.NBT. 1-4)

• 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.

*Understand the following as special cases:

a. 100 can be thought of as a bundle of ten tens—called a “hundred.”

b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

• Count within 1000; skip-count by 5s, 10s, and 100s.

• Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

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

Use place value understanding and properties of operations to add and subtract. (2.NBT.5-9)

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• Add up to four two-digit numbers using strategies based on place value and properties of operations.

• Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.

Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

• Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

• Explain why addition and subtraction strategies work, using place value and the properties of operations.

Color Code Key: Gaps, Major Clusters, Supporting Clusters, Additional Clusters

### 3. What learning activities will students participate in?

#### Learning Activities:

Number Talks /Mental Math and Computation Strategies K-5-- from Math Solutions K-5

Mathematics Handbook Series/Math to Learn, Math to Know- Teacher Handbook from Great Source

Mathematics Handbook Series/Math to Learn, Math to Know- Teacher’s Resource Book- Reproducibles from Great Source

#### Discipline Specific Considerations:

Vocabulary – Specialized and High Frequency

Digit, expanded form, standard form, compare, tens, ones, hundreds, strategies, relationship , models, symbol, one-digit number, two-digit number, three-digit number, four-digit number names, skip count, operation, addition, subtraction, <, >, =, value, sum, difference, equal, commutative property, associative property, compose, decompose

True statements:

Transposing place value of numbers does impact development of number sense!

Reversing written numerals is developmental!

Misconception:

That 700 represents just 7 hundreds, 0 tens, 0 ones, actually it also represents: 70 tens or 700 ones.

Common Core State Standards:  Standards for Mathematical Practice

Standard 1:    Make sense of problems and persevere in solving them

Standard 2:    Reason abstractly and quantitatively

Standard 3:    Construct viable arguments and critique the reasoning of others

Standard 4:    Model with Mathematics

Standard 5:    Use appropriate tools strategically

Standard 6:   Attend to precision

Standard 7:  Look for and make use of structure

Standard 8:  Look for and express regularity in repeated reasoning 