Last updated: 8/15/2021

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Grade 1 - Operations and Algebraic Thinking

  Subject:   Mathematics (NYS P-12 Common Core)
  Grade:   Elementary, 1st Grade
  Unit Title:  

Grade 1 - Operations and Algebraic Thinking
  Approx. Number of Weeks:  

1st Semester

Unit Summary:

Develop an understanding of addition and subtraction of whole numbers and strategies for basic facts.

Models will be used to develop an understanding of the meanings of addition and subtraction, the relationship between them and strategies to solve problems. 

Models: manipulatives, number lines, drawings and pictures, charts and symbols

Strategies:  part-whole, adding to (counting-on), taking away from (counting back), comparing

The commutative and associative properties will be used to explain (e.g. making tens) and solve problems.

Students will develop fluency and apply single-digit addition and subtraction facts to and including 10.  (10 problems in 1 minute)

Next Generation Skills Addressed:
   Collaboration & Communication
   Creativity & Innovation
   Critical Thinking & Problem Solving
   Research & Information Fluency
   Social & Emotional Intelligence

1. What will students know and be able to do?

Standards:



1.OA.1 - 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.

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.

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.)

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.

1.OA.5 - Relate counting to addition and subtraction (e.g., by counting on 2 to dd 2).

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).

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.

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 = ?.


Essential Understandings:


Students will understand that…

 

Number relationships are used to solve problems.   

Numbers can be joined, separated and compared to solve problems.

   

   

Essential Questions:


What do you know that can help you solve the problem?

Possible ways to scaffold the question:

  • What do you know about the numbers? 
  • Is there a relationship among the numbers?       

 

How can we join, separate and compare numbers?

Possible ways to scaffold the question:

  • How does understanding teh relationship between addition and subtraction help us solve problems?
  • How can you represent the joining, separating and comparing numbers?
  • How can you find an unknown number in an equation?

Students will know:


Addition has properties; rules to solve problems.

Addition and subtraction are inverse operations.

   

Students will be able to:


Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

 •  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. (1.OA.1)

•  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. (1.OA.2)

Understand and apply properties of operations and the relationship between addition and subtraction. (1.OA.3)

•  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.)

 •  Understand subtraction as an unknown-addend problem. (1.OA.4)

For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

Add and subtract within 20.

•  Relate counting to addition and subtraction. (e.g., by counting on 2 to add 2). (1.OA.5)

FLUENCY STANDARD  !

 •  Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

Use mental 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).

Work with addition and subtraction equations.

 •  Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. (1.OA.7)

 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.

 • Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. (1.OA.8)

 For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = 􀀀 – 3, 6 + 6 = 􀀀.

Color Code Key: Gaps, Major Clusters, Supporting Clusters, Additional Clusters

2. How will we – and they – know?

Authentic Performance Task:


Common Benchmark Assessment:


3. What learning activities will students participate in?

Learning Activities:


 

Math Their Way- Center for Innovation in Education/Addison-Wesley

Box It and Bag It-The Math Learning Center

Developing Number Concepts Book 2—Addition and Subtraction by Kathy Richardson/Dale Seymour Publications

Daily Word Problems- Grade 1 Math/ Evan Moor Publications

Read It! Draw It! Solve It!—Grade 1/Dale Seymour Publications

 

Discipline Specific Considerations:


Vocabulary – Specialized and High Frequency

Adding to, Taking from, putting together, taking apart, comparing, unknown, drawing, add, subtract, +,- , sum, count-on, addition, subtraction, number sentence, count-back, decompose, make ten, difference, equal to , fact families, commutative property, associative property, equals, equal sign, equation, count, compare, number line, symbol, strategy

Common Core State Standards:  Standards for Mathematical Practice

 Standard 1:    Make sense of problems and persevere in solving them

Standard 2:    Reason abstractly and quantitatively

Standard 3:    Construct viable arguments and critique the reasoning of others

Standard 4:    Model with Mathematics

Standard 5:    Use appropriate tools strategically

Standard 6:   Attend to precision

Standard 7:  Look for and make use of structure

Standard 8:  Look for and express regularity in repeated reasoning

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