Topic+Five

= Topic Five: Subtract Within 100 Using Strategies = 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:__**


 * Numbers and the Number Line**-The set of real numbers is infinite and ordered. Whole numbers, integers, and fractions are real numbers. Each real number can be associated with a unique point on the number line.


 * 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...**__
 * When subtracting two-digit numbers, you can add the same amount to both numbers in the problem, or you can subtract the same from both numbers in the problem to make subtraction easier.
 * You can use bar diagrams, equations, and the relationship between addition and subtraction to help you solve one- and two-step word problems. In the case of two-step problems, you need to find the answer to the first step, and then use it to solve the second step.
 * Good math thinkers use math to explain why they are right. They can talk about the math that others do, too.
 * Two-digit numbers can be broken apart using tens and ones to subtract in different ways. You can represent how you break apart and subtract numbers with hops or jumps on an open number line. You can count back or add up to subtract.
 * One digit numbers can be broken apart to make it easier to subtract them mentally.
 * Two-digit numbers can be broken apart to make it easier to subtract them mentally.
 * Two-digit numbers can be broken apart to make it easier to subtract them mentally.

__**Vocabulary:**__ None || __**Students will be skilled at...**__ 5-1-Subtract Tens and Ones on a Hundred Chart
 * Create numbers that are easier to subtract, and use mental math to find the difference.
 * Solve one- and two-step problem using addition or subtraction.
 * Critique the thinking of others by using what is know about addition and subtraction.
 * Add up to subtract using an open number line.
 * Break apart 1-digit numbers to make it easier to subtract them mentally.
 * Break apart 2-digit numbers to make it easier to subtract.
 * Make numbers that are easier to subtract, and use mental math to find the difference.
 * Solve one- and two-step problems using addition or subtraction.
 * Critique the thinking of others by using what it is known about addition and subtraction. ||
 * ~ = Assessment Evidence = ||
 * __**Performance Assessment:**__ || __**Other Evidence:**__ ||
 * ~ = Learning Plan = ||
 * __**Learning Activities:**__

5-2-Count Back to Subtract on an Open Number Line

5-3 Continue to Count Back to Subtract on an Open Number Line

5-4-Add Up to Subtract Using an Open Number Line

5-5-Break Apart Numbers to Subtract

5-6-Continue to Break Apart Numbers to Subtract

5-7-Subtract Using Compensation

5-8-Solve One-Step and Two-Step Problems

5-9-Math Practices and Problem Solving: Critique Reasoning ||
 * __**Resources:**__ ||