Operations and Algebraic Thinking
Unit description: In this unit, students will progress towards fluency with addition and subtraction of numbers to 10 (1.OA.6) using strategies to advance them from counting all to counting on, which leads many students then to decomposing and composing addends and total amounts. They will represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), and act out situations, verbal explanations, expressions, or equations. They will understand the relationship between addition and subtraction and the meaning of the equal sign. Applying all of this knowledge and skill, students will use problem solving structures to solve addition and subtraction word problems within 10 (using both two and three whole numbers for addition) involving all situations using objects, drawings, and equations.
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Operations and Algebraic Thinking
NY-1.OA.1 – Use addition and subtraction within 20 to solve one-step word problems involving situations of adding to, taking from, putting together, taking apart, and/or comparing, with unknowns in all positions. Note: Problems should be represented using objects, drawings, and equations with a symbol for the unknown number. Problems should be solved using objects or drawings, and equations
NY-1.OA.5 – Relate counting to addition and subtraction. e.g., by counting on 2 to add 2
NY-1.OA.6a – Add and subtract within 20. Use strategies such as: • counting on; • making ten; • decomposing a number leading to a ten; • using the relationship between addition and subtraction; and • creating equivalent but easier or known sums.
NY-1.OA.6b – Fluently add and subtract within 10.
NY-1.OA.7 – Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. e.g., Which of the following equations are true and which are false? 6 = 6 7 = 8 – 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
NY-1.OA.8 – Determine the unknown whole number in an addition or subtraction equation with the unknown in all positions. e.g., Determine the unknown number that makes the equation true in each of the equations 8 + ? = 11 ＿ – 3 = 5 6 + 6 = □
Other Standards Addressed in this Unit
Operations and Algebraic Thinking
NY-1.OA.2 – 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
NY-1.OA.3 – Apply properties of operations as strategies to add and subtract. e.g.,
- 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.)
Note: Students need not use formal terms for these properties.
NY-1.OA.4 – Understand subtraction as an unknown addend problem within 20. e.g., subtract 10 – 8 by finding the number that makes 10 when added to 8.
Essential Questions and Big Ideas
What is the relationship of addition and subtraction?
- Addition and subtraction are related/inverse operations.
Why do we take apart and put together numbers?
- Numbers are composed of other numbers.
- Taking apart and putting together are the foundation of addition and subtraction.
How can the structure of a word problem or equation help us to solve it?
- Word problems have basic problem solving structures: adding to, taking from, putting together, taking apart, comparing.
- Unknowns can be in various locations (start, change, result) in equations and develop from combinations of numbers.
Why are properties important in solving equations?
- Various strategies can be used to quickly add numbers.
What is the purpose of the equal sign?
- The equal sign is used to represent quantities that have the same value.
Prerequisite Standards:
- K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
- K.CC.4b Understand that the last number name said, tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were
- counted.
- K.CC.4c Understand that each successive number name refers to a quantity that is one larger.
- 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 writing an equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
- 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.)
- K.OA.5 Fluently add and subtract within 5.
Download the complete Grade 1 Math Unit 1 frameworks to customize for your own planning: