Math Action Goes Both Ways

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. ||Common Core Mathematics||Kindergarten||Mathematical Practices|||K.NBT.1. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.||Common Core Mathematics||Kindergarten||Number And Operations In Base Ten||Work With Numbers 11-19 To Gain Foundations For Place Value|||K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||K.OA.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||K.OA.4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||K.OA.5. Fluently add and subtract within 5.||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||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. ||Common Core Mathematics||Grade 1||Mathematical Practices|||1.OA.3. Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Understand And Apply Properties Of Operations And The Relationship Between Addition And Subtraction|||1.OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 ? 8 by finding the number that makes 10 when added to 8.||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Understand And Apply Properties Of Operations And The Relationship Between Addition And Subtraction|||1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 ? 4 = 13 ? 3 ? 1 = 10 ? 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 ? 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Add And Subtract Within 20|||1.OA.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 ? 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Work With Addition And Subtraction Equations|||1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? ? 3, 6 + 6 = ?.||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Work With Addition And Subtraction Equations|||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. ||Common Core Mathematics||Grade 2||Mathematical Practices|||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.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.NBT.6. Add up to four two-digit numbers using strategies based on place value and properties of operations.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||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.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||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.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations.3||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.||Common Core Mathematics||Grade 2||Operations And Algebraic Thinking||Add And Subtract Within 20|||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. ||Common Core Mathematics||Grade 3||Mathematical Practices|||3.OA.5. Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 ? 4 = 24 is known, then 4 ? 6 = 24 is also known. (Commutative property of multiplication.) 3 ? 5 ? 2 can be found by 3 ? 5 = 15, then 15 ? 2 = 30, or by 5 ? 2 = 10, then 3 ? 10 = 30. (Associative property of multiplication.) Knowing that 8 ? 5 = 40 and 8 ? 2 = 16, one can find 8 ? 7 as 8 ? (5 + 2) = (8 ? 5) + (8 ? 2) = 40 + 16 = 56. (Distributive property.)||Common Core Mathematics||Grade 3||Operations And Algebraic Thinking||Understand Properties Of Multiplication And The Relationship Between Multiplication And Division