Topic+Four

= Topic Four: Fluently Add Within 100 = Pacing (Duration of Unit): 1. Make sense of problems and persevere in solving them. 2. Reason abstractly 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. || 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.
 * ~ = Desired Results = ||
 * __**Transfer:**__
 * Standards for Mathematical Practices**
 * __**Established Goals:**__
 * 2.OA.A.1-** Represent and solve problems involving addition and subtraction.


 * 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.

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.B2-**Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

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. ||
 * 1.NBT.C-**Use place value understanding and properties of operations to add and subtract.
 * __**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 the strategies for adding numbers to 100? ||
 * __**Students will know...**__
 * When adding two-digit numbers, you can add the ones and tens separately and then add these partial sums to find the total sum. Partial sums addition provides a bridge between mental addition and the standard algorithm.
 * The standard addition algorithm for two-digit numbers breaks the calculation using place value, starting with ones and then tens. Answers to the simpler calculations are used to find the partial sum.
 * The standard addition algorithm for two-digit numbers breaks the calculation into simpler calculations using place, starting with ones and then tens. Answers to the simpler calculations are used to find the final sum.
 * Addition algorithms and addition strategies can be used to add more than two 2-digit numbers; and numbers can be added in any order.
 * Addition algorithms and addition strategies can be used to add more than two numbers; and numbers can be added in any order.
 * Some problems can be solved in one step. Other problems can be solved in two steps-first by solving a sub-problem or by answering a hidden question, and then, by using that answer to solve the original problem.
 * Good math thinkers use math they know to show and solve problems.

__**Vocabulary:**__ partial sum regroup compatible numbers || __**Students will be skilled at...**__ || **Other Evidence:** || 4-1-Add with Partial Sums
 * Add using place value and partial sums.
 * Create models to add 2-digit numbers and then explain their model.
 * Add 2-digit numbers and then explain their strategies for calculations.
 * Add three or four 2-digit numbers.
 * Add more than two numbers using mental math strategies and models.
 * Solve one- and two-step problems using drawings,models, and equations.
 * Create models to help solve math problems. ||
 * ~ = Assessment Evidence = ||
 * __**Performance Assessment:**__
 * ~ = Learning Plan = ||
 * __**Learning Activities:**__

4-2-Continue to Add with Partial Sums

4-3-Models to Add 2-Digit Numbers

4-4-Add 2-Digit Numbers

4-5-Add More than Two 2-Digit Numbers

4-6-Practice Adding

4-7-Solve One-Step and Two-Step Problems

4-8-Math Practices and Problem Solving-Model with Math ||
 * __**Resources:**__


 * Games:** ||