Standards for Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

Established Goals: 2.OA.A.1- Represent and solve problems involving addition and subtraction.
1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

2.NBT.B.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.B.6-Add up to four two-digit numbers using strategies based on place value and properties of operations.

2.NBT.B.9-Explain why addition and subtraction strategies work, using place value and the properties of operations.

Student I Can Statements:

I can use strategies to solve addition word problems. (within 100)

I can use strategies to solve subtraction word problems. (within 100)

I can use what I know about place value to add and subtract.

I can add two-digit numbers.

I can subtract two-digit numbers.

I can explain why adding and subtracting strategies work using what I know about place value.

Prerequisite Standards: 1.OA.A-Represent and solve problems involving addition and subtraction.

1.NBT.B2-Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
a. 10 can be thought of as a bundle of ten ones—called a “ten.”
b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

1.NBT.C-Use place value understanding and properties of operations to add and subtract.
4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
6. Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), 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 and explain the reasoning used.

Big Ideas: The Base-Ten Numeration System-The base-ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value.

Equivalence-Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.

Operation Meanings and Relationships-There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.

Properties-For a given set of numbers there are relationships that are always true, called properties, and these are the rules that govern arithmetic and algebra.

Basic Facts and Algorithms-There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.

Practice, Processes, and Proficiencies-Mathematics content and processes can be applied to solve problems.

Essential Questions:

What are strategies for subtracting numbers to 100?

Students will know...

To subtract, sometimes it is necessary to regroup 1 ten as 10 ones.

You can use pencil and paper to subtract and to record the regrouping in the tens and ones places.

The standard subtraction algorithm can be used to break the calculation into simpler steps, starting with the ones and then moving to the tens.

The standard algorithm for subtracting a two-digit number from a two-digit number is just an extension of the algorithm for subtracting a one-digit number from a two-digit number.

You can use pencil and paper to subtract a two-digit number from a two-digit number.

The inverse relationship between addition and subtraction can be used to solve and check subtraction.

Subtraction problems involving two-digit numbers can be solved using subtraction or the standard subtraction algorithm. When using the algorithm, if there are not enough ones to subtract, then regroup 1 ten as 10 ones subtract, then regroup 1 ten as 10 ones before subtracting the ones, and then the tens.

You can use bar diagrams, equations, and objects to help you solve one- and two-step problems, the answer to the first step problems, the answer to the first step must be found before solving the second step.

Good math thinkers know how to think about words and numbers to solve problems.

Vocabulary:

None

Students will be skilled at...

Exchange 1 ten for 10 ones.

Subtract 2-digit and 1-digit numbers using place value and models.

Subtract using place value and regrouping.

Subtract 2-digit numbers using place value and models.

Add to check subtraction.

Subtract 2-digit numbers and decide when to regroup and when not to regroup.

Solve word problems using models and equations.

Reason about word problems and use bar diagrams and equations to solve them.

## Topic Six: Fluently Subtract within 100

Pacing (Duration of Unit):## Desired Results

Transfer:Standards for Mathematical Practices1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Established Goals:2.OA.A.1-Represent and solve problems involving addition and subtraction.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

2.NBT.B.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.B.6-Add up to four two-digit numbers using strategies based on place value and properties of operations.2.NBT.B.9-Explain why addition and subtraction strategies work, using place value and the properties of operations.Student I Can Statements:Prerequisite Standards:1.OA.A-Represent and solve problems involving addition and subtraction.1.NBT.B2-Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:a. 10 can be thought of as a bundle of ten ones—called a “ten.”

b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

1.NBT.C-Use place value understanding and properties of operations to add and subtract.4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

6. Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), 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 and explain the reasoning used.

Big Ideas:The Base-Ten Numeration System-The base-ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value.Equivalence-Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.Operation Meanings and Relationships-There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.Properties-For a given set of numbers there are relationships that are always true, called properties, and these are the rules that govern arithmetic and algebra.Basic Facts and Algorithms-There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.Practice, Processes, and Proficiencies-Mathematics content and processes can be applied to solve problems.Essential Questions:Students will know...Vocabulary:Students will be skilled at...## Assessment Evidence

Performance Assessment:Other Evidence:## Learning Plan

Learning Activities:6-1-Regroup 1 Ten for 10 Ones6-2-Models to Subtract 2-Digit and 1-Digit Numbers6-3-Subtract 2-Digit and 1-Digit Numbers6-4-Models to Subtract 2-Digit Numbers6-5-Subtract 2-Digit Numbers6-6-Use Addition to Check Subtraction6-7-Practice Subtracting6-8-Solve One-Step and Two-Step Problems6-9-Math Practices and Problem Solving: ReasoningResources:Centers:File Not FoundFile Not FoundFile Not FoundTeacher Video:Student Videos: