Operations and Algebraic Thinking: Represent and Solve Problems Involving Addition And
1234567891234567891234567891234567891231234567891234567891234567891234567891231234567891234567891234567891234567891231234567891234567891234567891234567891231234567891234567891234567891234567891231234567891234567891234567891234567891231234567891234567891234567891234567891231234567891234567891234567891234567891231234567891234567891234567891234567891231
Operations and Algebraic Thinking: Represent and solve problems involving addition and subtraction.
Standard: 1. OA. 1
Cluster: major (m)
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 subtraction concepts
- Understand symbols +, -, = Symbols are introduced in 1st grade, add/sub concepts were learned in kinder
- Understand that there are different types of addition and subtraction problems (see framework, p. 9)
- Understand that there are different strategies to solve addition and subtraction problems (counting on, making ten, doubles, doubles plus one etc.)
-Comparing problems are introduced in first grade. Ex. Sam has 9 balls. Jake has 3 balls. How many more balls does Sam have than Jake?
Caution: Comparing problems are difficut because many students “hear” the part of the sentence of who has “more” but do not initiatlly hear the part about how many more”.
/ - Have students explain, write and reflect on their problem solving strategies. Partner Share- Board Math Stems: Compare: How many more, how many less, how many fewer…
Methods for solving single digit addition/subtraction problems (Framework, p. 7):
Level 1 (kinder): Direct Modeling by Counting All or Taking Away: Use objects, drawings or fingers to represent a problem
Level 2 (1st 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
Example: Compare Problems.
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:
/ www.cde.ca.gov Mathematics Framework, Appendix F (more defined methods for solving single-digit addition and subtraction problems)
Board Math Frames
Number Line
Hundreds Chart
Math Workmats
District Problem-Solving Poster
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
- Understand symbols +, =
- Understand that there are different types of addition problems
- Understand that there are different strategies to solve addition problems
Example: Mrs. Smith has 4 oatmeal raisin cookies, 5 chocolate chip cookies, and 6 gingerbread cookies. How many cookies does Mrs. Smith have?
/ - Have students explain, write and reflect on their problem solving strategies. Partner ShareFocus on Level 2/3 Methods:
Level 2 (1st 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 / Board Math Frames
Number Line
Hundreds Chart
Math Workmats
District Problem-Solving Poster
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- Understand the concept of related facts: 4 + 6 = 10, 6 + 4 = 10, 10- 4 = 6, 10 – 6 =4
- Apply properties of operations as strategies to add and subtract (students don’t need to know the names, but need to understand the concepts)
- Commutative: 4 + 5 = 5 + 4
- Associative (it doesn’t matterwhich numbers you add together first) 3 + (9+1) = (3+9) + 1 = 12 + 1 = 13 /
Students build a tower of 8 green cubes and 3 yellow cubes, and another tower of 3 yellow and 8 green cubes to show that order does not change the result in the operation of addition.
Students can also use cubes of 3 different colors to demonstrate that (2 + 6) + 4 is equivalent to 2 + (6 + 4) and then to prove 2 + (6 + 4) = 2 + 10.
Board Math Stems
Make Ten / Board Math Frames
Number Line
Hundreds Chart
Math Workmats
Ten Frame
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 / ResourcesSee 1. OA. 3
- Understand the connection between addition and subtraction
- Think-Addition: uses known addition facts to solve for the unknown part or quantity within a problem. When students use this strategy, they think, “What goes with this part to make the total?” The think-addition strategy is particularly helpful for subtraction facts with sums of 10 or less / See 1. OA. 3
Subtraction problems are missing addend problems: Restate subtraction as an unknown addend 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 examples:
- What number sentence can you use to check the answer for 12 + 6 = 18
- What is the inverse of 9 + 6 = 15
- Write the related facts for 3, 5, 8
Games: “Figure out how many I took away”
Ten frame partially filled in… / See 1.OA. 3
Teacher Share (games)
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 “counting back” to adding and subtracting / - Hold the start number in your head and count forward.- 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 / See Above
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- Understand addition/subtraction and number concepts within 20
- Understand concept of fluency
- Understand different strategies for adding/subtracting:
*decomposing a number to make ten
*related facts (relationship between addition and subtraction),
*creating equivalent but easier known sums (doubles, doubles plus one etc.)
/ Math facts timed quizzes
Flash Cards
Partner practice
Student success charts
Homework Practice
Addition/Subtraction games
Computer Games
Examples of different strategies:
Sam has 8 red marbles and 7 green marbles. How many marbles does Sam have in all?
Making 10 and Decomposing a Number
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 = / See above
Computer
www.commoncoresheets.com
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- Understand that the quantity on one side of the equal sign must be the same quantity on the other side of the equal sign.
- Interchange language: “equal to”, “is the same as” “not equal to” “is not the same as”
/ Board Math Stems:
- Find the difference.
15 – 6 =
- Is this equation true? Why or Why not?
5 + 6= 2 + 8
- What operation will make this number sentence true?
13 _ 5 = 8
- Which of these equations are true or false? Explain your thinking.
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” / See Above
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 / ResourcesUse skills and concepts from 1.OA.4 and 1.OA.6
/ Board Math Stems:
- 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 / See above