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Number and Operation in Base Ten

Narrative for the (NBT) Number and Operation in Base Ten

Students’ work in the base-ten system is intertwined with their work on counting and cardinality, and with the meanings and properties of addition, subtraction, multiplication, and division. Work in the base-ten system relies on these meanings and properties, but also contributes to deepening students’ understanding of them.

In Kindergarten, teachers help children lay the foundation for understanding the base-ten system by drawing special attention to 10. Children learn to view the whole numbers 11 through 19 as ten ones and some more ones. They decompose 10 into pairs such as 1 9, 2 8, 3 7 and find the number that makes 10 when added to a given number such as 3. Students use objects, math drawings, and equations to describe, explore, and explain how the “teen numbers,” the counting numbers from 11 through 19, are ten ones and some more ones.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-00.NBT.01

 MAT-00 Targeted Standards(NBT) Domain: Number and Operation in Base Ten Cluster: Work with numbers 11­-19 to gain foundations for place value. MAT-00.NBT.01 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 (such as 18 = 10 + 8);.

Student Learning Targets:

Reasoning Targets

• I can understand numbers 11-19 are made of a group of ten ones plus some more ones.

Skills (Performance) Targets

• I can show how many tens and how many ones make a written number.
• I can show you how many ones make a ten.
• I can break a number apart to show tens and ones.
• I can write the number a base ten picture shows.

Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Student is able to compose and decompose numbers, identify the number of tens and ones, and identify the value of digits in a number within 100. (1st grade) - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 Student is able to correctly decompose numbers 11-19 into a group of ten and ones. I can show how many tens and how many ones make a written number. I can break a number apart to show a ten and ones. - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to correctly write numbers 11-19 given a base ten model (objects or drawings) of the number. I can write the number a base ten picture or model shows. - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to identify objects or drawings that represent a ten and some more ones, but may have a simple counting error. I can show the picture or objects that tell how many tens and how many ones are asked for. I can show how many ones make a ten. - 0.5 Limited or no understanding of the skill is demonstrated.

Resources

Vocabulary

• number words (one - nineteen)
• left overs
• 10 = ten ones
• tens
• ones

Operations and Algebraic Thinking

Narrative for the (OA) Operations and Algebraic Thinking

Counting and Cardinality and Operations and Algebraic Thinking are about understanding and using numbers. Counting and Cardinality underlies Operations and Algebraic Thinking as well as Number and Operations in Base Ten. It begins with early counting and telling how many in one group of objects. Addition, subtraction, multiplication, and division grow from these early roots.

In Kindergarten, students develop meanings for addition and subtraction as they encounter problem situations, and they extend these meanings as they encounter increasingly difficult problem situations in Grade 1. They represent these problems in increasingly sophisticated ways. And they learn and use increasingly sophisticated computation methods to find answers. Students learn and use mathematical and non-mathematical language, especially when they make up problems and explain their representation and solution.

Students in Kindergarten work with the following types of addition and subtraction situations: Add To with Result Unknown; Take From with Result Unknown; and Put Together/Take Apart with Total Unknown and Both Addends Unknown.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-00.OA.02

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.02 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Student Learning Targets:

Reasoning Targets

• I can decide when I need to add or subtract in a problem.

Skills (Performance) Targets

• I can solve addition word problems.
• I can solve subtraction word problems.
• I can use drawings or objects to show the problem.

Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Advanced criteria under development. In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content. - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 Student is able to correctly solve addition and subtraction word problems within 10 and correctly represent the problems using drawings or objects.  I can solve addition word problems when the answer is 10 or less with no mistakes. I can solve subtraction word problems for numbers up to 10 with no mistakes. I can use drawings or objects to show the problem with no mistakes. - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to correctly solve and represent addition word problems within 10. and Student is able to correctly solve and represent subtraction word problems within 5. I can solve addition word problems when the answer is 10 or less with no mistakes. I can solve subtraction word problems for numbers up to 5 with no mistakes. I can use drawings or objects to show the problem. - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to demonstrate beginning understanding of solving addition word problems within 5 but may have an error when finding the solution. I can solve addition problems when the answer is 5 or less, but I may have a mistake. I can use drawings or objects to show the problem. - 0.5 Limited or no understanding of the skill is demonstrated.

Resources

Vocabulary

• join
• put together
• add
• separate
• take away
• take apart
• take from
• subtract
• plus
• minus
• equal to
• same as
• less
• total
• sum
• difference

MAT-00.OA.05.a

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.05.a Fluently add basic facts within 5

Student Learning Targets:

Knowledge Targets

• I can say the answer for addition facts to 5 quickly (within 5 seconds).

Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Student is able to add facts to 10 with at least 90% accuracy given 5 seconds per fact. (1st grade) I can say almost all the answers for addition facts to 10 quickly. 3.5 Student answers facts to 10 with 80% accuracy given 5 seconds per fact. (1st grade) I can say most the answers for addition facts to 10 quickly. 3.0 Student is able to add facts to 5 with at least 85% accuracy given 5 seconds per fact. I can say almost all the answers for addition facts to 5 quickly. - 2.5 Student is able to add facts to 5 with at least 70% accuracy given 5 seconds per fact. I can say many of the answers for addition facts to 5 quickly. 2.0 Student is able to add facts to 5 with at least 50% accuracy given 5 seconds per fact. I can say some of the answers for addition facts to 5 quickly. - 1.5 Student is able to add facts to 5 with at least 40% accuracy given 5 seconds per fact. 1.0 Student is able to add facts to 5 with at least 10% accuracy given 5 seconds per fact. I can say at least one of the answers for addition facts to 5 quickly. - 0.5 Limited or no understanding of the skill is demonstrated.

Resources

Vocabulary

• add
• addition facts
• sum

MAT-00.OA.05.b

 MAT-00 Targeted Standards(OA) Domain: Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. MAT-00.OA.05.b Fluently subtract basic facts within 5

Student Learning Targets:

Knowledge Targets

• I can say the answers to subtraction facts within 5 quickly (within 5 seconds).

Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Student is able to demonstrate understanding of subtraction facts to 10 with at least 90% accuracy given 5 seconds per fact. (1st grade) I can say the answer for almost all subtraction facts to 10 quickly. - 3.5 Student answer subtraction facts to 10 with 80% accuracy given 5 seconds per fact. (1st grade) I can say the answer for most subtraction facts to 10 quickly. 3.0 Student is able to answer subtraction facts within 5 with at least 85% accuracy given 5 seconds per fact. I can answer almost all subtraction facts to 5 quickly. - 2.5 Student is able to answer subtraction facts within 5 with at least 70% accuracy given 5 seconds per fact. I can answer many subtraction facts to 5 quickly. 2.0 Student is able to answer subtraction facts within 5 with at least 50% accuracy given 5 seconds per fact. I can answer some subtraction facts to 5 quickly. - 1.5 Student is able to answer subtraction facts within 5 with at least 40% accuracy given 5 seconds per fact. 1.0 Student is able to answer subtraction facts within 5 with at least 10% accuracy given 5 seconds per fact. I can answer at least one subtraction fact to 5 quickly. - 0.5 Limited or no understanding of the skill is demonstrated.

Resources

Vocabulary

• subtract
• subtraction facts
• difference
• minus

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