Operations and Algebraic Thinking: Represent and Solve Problems Involving Addition And

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Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings and equations with a symbol for the unknown number to represent the problem. Essential Skills/Concepts Teaching Notes/Strategies Resources - Understand addition and - Have students explain, write subtraction concepts and reflect on their problem www.cde.ca.gov Mathematics - Understand symbols +, -, = solving strategies. Partner Framework, Appendix F (more Symbols are introduced in 1st Share defined methods for solving single- grade, add/sub concepts were digit addition and subtraction learned in kinder - Board Math Stems: Compare: problems) - Understand that there are How many more, how many less, different types of addition and how many fewer… Board Math Frames subtraction problems (see Number Line framework, p. 9) Methods for solving single digit Hundreds Chart - Understand that there are addition/subtraction problems Math Workmats different strategies to solve (Framework, p. 7): District Problem-Solving Poster addition and subtraction Level 1 (kinder): Direct Modeling by problems (counting on, making Counting All or Taking Away: Use ten, doubles, doubles plus one objects, drawings or fingers to etc.) represent a problem Level 2 (1st grade): Counting on: Use -Comparing problems are introduced one addend and count on. Some in first grade. Ex. Sam has 9 balls. method of keeping track (fingers, Jake has 3 balls. How many more objects, mentally imaged objects, balls does Sam have than Jake? body motions) is used to monitor the count Caution: Comparing problems are Level 3 (1st/2nd grade): Convert to an difficut because many students easier problem “hear” the part of the sentence of who has “more” but do not initiatlly Example: Compare Problems. hear the part about how many more”. Using objects to represent two sets of balls Abel has 5 balls. Susan has 3 balls. How many more balls does Abel have than Susan?

Teachers can also ask the related question, “How many fewer balls does Susan have than Abel?”

Comparison Bars: Rather than representing the actual objects with manipulatives or drawings, they use the numbers in the problem to represent the quantities.

?? balls

Number Bond Diagrams:

Operations and Algebraic Thinking: Represent and solve problems involving addition and subtraction. Standard: 1. OA. 2 Cluster: major (m)

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

(Similar to 1.OA.1… just with three numbers.)

Essential Skills/Concepts Teaching Notes/Strategies Resources - Understand addition concepts - Have students explain, write Board Math Frames - Understand symbols +, = and reflect on their problem Number Line - Understand that there are solving strategies. Partner Hundreds Chart different types of addition Share Math Workmats problems District Problem-Solving Poster - Understand that there are different strategies to solve addition problems

Example: Mrs. Smith has 4 oatmeal raisin cookies, 5 chocolate chip cookies, Focus on Level 2/3 Methods: and 6 gingerbread cookies. How many st cookies does Mrs. Smith have? Level 2 (1 grade): Counting on: Use one addend and count on. Some method of keeping track (fingers, objects, mentally imaged objects, body motions) is used to monitor the count. Level 3 (1st/2nd grade): Convert to an easier problem Operations and Algebraic Thinking: Understand and apply properties of operations and the relationship between addition and subtraction. Standard: 1. OA. 3 Cluster: major (m)

Apply properties of operations as strategies to add and subtract. 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).

Essential Skills/Concepts Teaching Notes/Strategies Resources Board Math Frames - Understand the concept of Students build a tower of 8 green Number Line related facts: 4 + 6 = 10, 6 + 4 = cubes and 3 yellow cubes, and Hundreds Chart 10, 10- 4 = 6, 10 – 6 =4 another tower of 3 yellow and 8 Math Workmats green cubes to show that order Ten Frame - Apply properties of operations does not change the result in the as strategies to add and operation of addition. subtract (students don’t need to know the names, but need to Students can also use cubes of 3 understand the concepts) different colors to demonstrate - Commutative: 4 + 5 = 5 + 4 that (2 + 6) + 4 is equivalent to 2 + (6 - Associative (it doesn’t + 4) and then to prove 2 + (6 + 4) = 2 matterwhich numbers you add + 10. together first) 3 + (9+1) = (3+9) + 1 = 12 + 1 = 13 Board Math Stems Make Ten

Operations and Algebraic Thinking: Understand and apply properties of operations and the relationship between addition and subtraction. Standard: 1. OA. 4 Cluster: major (m) Understand subtraction as an unknown-addend problem. For example, subtract 10-8 by finding the number that makes 10 when added to 8.

Essential Skills/Concepts Teaching Notes/Strategies Resources See 1. OA. 3 See 1. OA. 3 See 1.OA. 3 Teacher Share (games) - Understand the connection Subtraction problems are missing between addition and addend problems: Restate subtraction subtraction as an unknown addend - Think-Addition: uses known and solve by counting on: “7-3 means addition facts to solve for the 3+ ? = 7, so 4,5,6,7, I counted on 4 unknown part or quantity within more to get to 7, so 4” a problem. When students use this strategy, they think, “What Board Math examples: goes with this part to make the - What number sentence can you total?” The think-addition use to check the answer for 12 strategy is particularly helpful + 6 = 18 for subtraction facts with sums - What is the inverse of 9 + 6 = of 10 or less 15 - Write the related facts for 3, 5, 8

Games: “Figure out how many I took away” Ten frame partially filled in… Operations and Algebraic Thinking: Add and subtract within 20 Standard: 1. OA. 5 Cluster: major (m) Relate counting to addition and subtraction (e.g., by counting on 2 to add 2)

Essential Skills/Concepts Teaching Notes/Strategies Resources - Connect “Counting on” and - Hold the start number in your See Above “counting back” to adding and head and count forward. subtracting - Subtraction problems are missing addend problems: Restate subtraction as an unknown added and solve by counting on: “7-3 means 3+ ? = 7, so 4,5,6,7, I counted on 4 more to get to 7, so 4”

- Board Math Stems

Operations and Algebraic Thinking: Add and Subtract within 20. Standard: 1. OA. 6 Cluster: major (m) 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).

Essential Skills/Concepts Teaching Notes/Strategies Resources Math facts timed quizzes See above - Understand addition/subtraction Flash Cards Computer and number concepts within 20 Partner practice www.commoncoresheets.com - Understand concept of fluency Student success charts - Understand different strategies Homework Practice for adding/subtracting: Addition/Subtraction games *decomposing a number Computer Games to make ten *related facts Examples of different strategies: (relationship between addition and Sam has 8 red marbles and 7 green subtraction), marbles. How many marbles does Sam have in all? *creating equivalent but easier known sums (doubles, doubles Making 10 and Decomposing a Number plus one etc.) I know that 8 plus 2 is 10, so I broke up (decomposed) the 7 up into a 2 and a 5. First I added 8 and 2 to get 10, and then added the 5 to get 15. 7 = 2 + 5 8 + 2 = 10 10 + 5 = 15

Creating an Easier Problem with Known Sums I broke up (decomposed) 8 into 7 and 1. I know that 7 and 7 is 14. I added 1 more to get 15.

8 = 7 + 1 7 + 7 = 14 14 + 1 = 15

There were 14 birds in the tree. 6 flew away. How many birds are in the tree now?

Relationship between Addition & Subtraction I thought, ‘6 and what makes 14?’. I know that 6 plus 6 is 12 and two more is 14. That’s 8 altogether. So, that means that 14 minus 6 is 8. 6 + 8 = 14 14 – 6 = 8

Board Math Stems: “Use the strategy of ‘Making a Ten’ to solve this addition problem.

8 + 6 = Operations and Algebraic Thinking: Work with addition and subtraction equations. Standard: 1. OA. 7 Cluster: major (m)

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. Essential Skills/Concepts Teaching Notes/Strategies Resources Board Math Stems: See Above - Understand that the - Find the difference. 15 – 6 = quantity on one side of the - Is this equation true? Why or equal sign must be the Why not? same quantity on the other 5 + 6= 2 + 8 side of the equal sign. - What operation will make this number sentence true?

- Interchange language: 13 _ 5 = 8 - Which of these equations are “equal to”, “is the same as” true or false? Explain your “not equal to” “is not the thinking. same as” 10 = 3+7 12-2=4+6 4 + 5 + 1 = 5 + 4 + 1 - Number talks (mental math, explain reasoning) - Estimation may be used as a strategy: 3 + 4 = 3 + 3 +2 “There are 3s on both sides, but the right side has 3 + 2 and the left side has 4, which is less than 3+ 2” Operations and Algebraic Thinking: Work with addition and subtraction equations. Standard: 1. OA. 8 Cluster: major (m)

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 = __

Essential Skills/Concepts Teaching Notes/Strategies Resources See above Use skills and concepts from 1.OA.4 Board Math Stems: and 1.OA.6 - What number makes this equation true? 7 = ____ - 5 - Determine the unknown number. 5 = ____ - 2 ___ + 9 = 17

- Use symbol for unknown/ Unknown in different spots 4 + = 5 + 4

+ 3 = 2 + 3