Math Curriculum

Trinity Area School District

Template for Curriculum Mapping

 

Course:  Math

Grade:  K

Designer(s):  Math Committee

 

Overview of Course:

 

Overarching Big Ideas, Enduring Understandings, and Essential Questions

  • Make sense of problems and persevere in solving them.                       
  • Reason abstractly and quantitatively. 
  • Construct viable arguments and critique the reasoning of others.                     
  • Model with mathematics.  
  • Use appropriate tools strategically.           
  • Attend to precision.
  • Look for and make use of structure.           
  • Look for and express regularity in repeated reasoning.

Big Idea

(A Big Idea is typically a noun and always transferable within and among content areas.)

 

Standard(s) Addressed

(What Common Core Standard(s) and/or PA Standard(s) addresses this Big Idea?)

 

Enduring Understanding(s)

(SAS refers to Enduring Understandings as “Big Ideas.”  EUs are the understandings we want students to carry with them after they graduate.  EUs will link Big Ideas together.  Consider having only one or two EUs per Big Idea.)

Essential Question(s)

(Essential Questions are broad and open ended.  Sometimes, EQs can be debated.  A student’s answer to an EQ will help teachers determine if he/she truly understands.  Consider having only one or two EQs per Enduring Understanding.)

 

 

  • Order

 

PA Standards:

CC.2.1.K.A.1 Know number names and write and recite the count sequence

  1. Numbers are counted in a specific sequence. 

 

  1. Why do numbers need to be in a sequential order? 
  2. What would happen if numbers were out of order?

 

 

  • Correlations

PA Standards:

CC.2.1.K.A.2 Apply one-to-one correspondence to count the number of objects.

CC.2.1.K.A.3 Apply the concept of magnitude to compare numbers and quantities.

 

  1. There is a unique symbol that goes with each number word.
  2. Numerals represent a set of objects.
  3. Counting tells how many are in a set not matter which order the objects are counted or arranged.
  4. The last number said when counting a set is the total.
  5. Counting is cumulative.
  6. Benchmarks can be used to estimate quantities of groups.
  7. In a pair of numbers, the number that shows more is greater.  The number that shows fewer is less.  If two numbers are exactly the same amount, they are equal.

 

 

 

  1. When can you use number symbols to tell about a set of objects?
  2. How does counting tell how many?
  3. When can you use number symbols to tell about a set of objects?
  4. How can you determine if a number is greater than, less than, or equal to another number?
  • Production

PA Standards

CC.2.1.K.B.1 Use place value to compose and decompose numbers within 19.

.  

 

  1. There is more than one way to show a number.
  2. Numbers can be decomposed in different ways.

 

  1. Why can you show the same number in different ways?
  2. How can number decompositions be represented?
  3. How can decomposing numbers help build better number sense?
  • Relationships

PA Standards:

CC.2.2.K.A.1 Extend the concepts of putting together and taking apart to add and subtract within 10.

  1. Addition is putting together and adding to.
  2. Subtraction is taking apart and taking from.
  3. Addition and subtraction scenarios can be represented in a variety of ways.
  4. Different combinations of number pairs can produce the same sum.
  5. A knowledge of the base ten system is key to a strong foundation in both addition and subtraction.
  6. Automaticity of addition and subtraction facts is an important foundation for the building of more complex mathematical concepts.
  7. Problems can be solved by using objects to act out the actions in a problem.
  1. How can you represent addition and subtraction scenarios in a variety of ways?
  2. How can you use base ten knowledge to fluently solve both addition and subtraction scenarios?
  3. Why is automaticity of basic addition and subtraction facts important?
  • Characteristics

 

PA Standards:

CC.2.3.K.A.1 Identify and describe two- and three dimensional shapes.

 

CC.2.3.K.A.2 Analyze, compare, create, and compose two- and three-dimensional shapes

 

CC.2.4.K.A.1 Describe and compare attributes of length, area, weight, and capacity of everyday objects.

 

CC.2.4.K.A.4 Classify objects and count the number of objects in each category.

  1. Basic shapes can be used to describe objects in the environment.
  2. Shapes have attributes.
  3. Shapes can be formed and drawn using knowledge of their specific attributes.
  4. Two-dimensional shapes are flat.
  5. Three dimensional shapes are solid.
  6. Many everyday objects closely approximate standard geometric solids.
  7. Solid figures can be compared in different ways.
  8. Some solid figures can be compared by their flat surfaces and vertices.
  9. The flat surfaces of many solid figures have specific shapes.
  10. Shapes can be combined to make other shapes.
  11. Measurement is a process of comparing a unit to the object being measured.
  12. Objects can be compared and ordered by length, capacity, and weight.
  13. Attributes can be used to compare objects.
  14. Attributes such as color, shape, or size can be used to sort the same set of objects in different ways.
  15. A set of objects can be sorted according to a combination of attributes.
  16. Data can be collected and represented in various ways.
  17. Graphs can be used to answer questions.
  18. The position of objects can be determined in relation to surrounding objects and described using words.

 

  1. How do you know when shapes are exactly the same?
  2. What do you look for when you describe and match shapes?
  3. What kinds of figures roll, slide, and stack?
  4. How can you describe flat surfaces of solids?
  5. What do you need to know about a shape’s attributes in order to recreate that shape?
  6. How can you use smaller shapes to make a larger shape?
  7. How can you use smaller shapes to make a different shape?
  8. How does making and reading a graph help to answer questions?
  9. How can you decide which object is larger and which object is smaller?
  10. How can you compare and order the length of three objects?
  11. How can you tell if a container holds the same or more or less than another?
  12. How can you compare the weights of two objects?
  13. What does looking at the color, shape, and size of objects help you know about them?
  14. What are some ways you can sort objects?
  15. In order to make a group of objects that are exactly alike in two ways, what should you notice about the objects?
  16. How does matching objects in two groups help you know which group has more, fewer, or as many as the other group?
  17. How can data be represented?
  18. What data can you gain from looking at a graph?
  19. How can you describe where something is using the words, inside, and outside, over,  under, and on, top, middle, and bottom, or left and right.
  20. How can you describe objects in the environment using shapes?
  21. How can you tell if a shape is a rectangle, square, circle, triangle, or hexagon?
  22. How can you tell if a shape is flat or solid?

 

Big Ideas, Enduring Understandings, and Essential Questions Per Unit of Study

(These do NOT “spiral” throughout the entire curriculum, but are specific to each unit.)

 

Month of Instruction

(In what month(s) will you teach this unit?)

 

Title of Unit

Big Idea(s)

(A Big Idea is   a noun and always transferable within and among content areas.)

 

Standard(s) Addressed

(What Common Core Standard(s) and/or PA Standard(s) addresses this Big Idea?)

Enduring Understanding(s)

(SAS refers to Enduring Understandings as “Big Ideas.”  EUs are the understandings we want students to carry with them after they graduate.  EUs will link Big Ideas together.  Consider having only one or two EUs per Big Idea.)

 

Essential Question(s)

(Essential Questions are broad and open ended.  Sometimes, EQs can be debated.  A student’s answer to an EQ will help teachers determine if he/she truly understands.  Consider having only one or two EQs per Enduring Understanding.)

 

Common Assessment(s)*

(What assessments will all teachers of this unit use to determine if students have answered the Essential Questions?)

Common Resource(s)*

Used

(What resources will all teachers of this unit use to help students understand the Big Ideas?)

Aug - Sept

 

Understanding Numbers 1-10

 

 

Order

Correlations

Production

Relationships

Characteristics

 

PA Standards:

CC.2.1.K.A.1 Know number names and write and recite the count sequence

 

CC.2.1.K.A.2 Apply one-to-one correspondence to count the number of objects.

 

CC.2.1.K.A.3 Apply the concept of magnitude to compare numbers and quantities.

 

CC.2.2.K.A.1 Extend the concepts of putting together and taking apart to add and subtract within 10.

 

CC.2.3.K.A.1 Identify and describe two- and three dimensional shapes.

 

CC.2.3.K.A.2 Analyze, compare, create, and compose two- and three-dimensional shapes

 

  1. Numbers are counted in a specific sequence. 
  2. There is a unique symbol that goes with each number word.
  3. Numerals represent a set of objects.
  4. Counting tells how many are in a set not matter which order the objects are counted or arranged.
  5. The last number said when counting a set is the total.
  6. Counting is cumulative.
  7. Benchmarks can be used to estimate quantities of groups.
  8. In a pair of numbers, the number that shows more is greater.  The number that shows fewer is less.  If two numbers are exactly the same amount, they are equal.
  9. Addition is putting together and adding to.
  10. Subtraction is taking apart and taking from.
  11. Addition and subtraction scenarios can be represented in a variety of ways.
  12. Different combinations of number pairs can produce the same sum.
  13. A knowledge of the base ten system is key to a strong foundation in both addition and subtraction.
  14. Automaticity of addition and subtraction facts is an important foundation for the building of more complex mathematical concepts.
  15. Problems can be solved by using objects to act out the actions in a problem.
  16. Basic shapes can be used to describe objects in the environment.
  17. Shapes have attributes.
  18. Two-dimensional shapes are flat.
  19. Two-dimensional shapes have width and length.
  20. Shapes can be formed and drawn using knowledge of their specific attributes.

 

 

 

  1. Why do numbers need to be in a sequential order? 
  2. What would happen if numbers were out of order?
  3. When can you use number symbols to tell about a set of objects?
  4. How does counting tell how many?
  5. When can you use number symbols to tell about a set of objects?
  6. How can you determine if a number is greater than, less than, or equal to another number?
  7. How can you represent addition and subtraction scenarios in a variety of ways?
  8. How can you use base ten knowledge to fluently solve both addition and subtraction scenarios?
  9. Why is automaticity of basic addition and subtraction facts important?
  10. How do you know when shapes are exactly the same?
  11. What do you look for when you describe and match shapes?
  12. What do you need to know about a shape’s attributes in order to recreate that shape?
  13. How can you use smaller shapes to make a larger shape?
  14. How can you use smaller shapes to make a different shape?
  15. How can you tell if a shape is a rectangle, square, circle, triangle, or hexagon?
  16. How can you tell if a shape is flat or solid?

Unit 1 Test

 

Performance Task

 

Quick Quizzes

 

Formative Assessments

 

Fluency Check

 

*Text

*Manipulatives

*Online

Resources

*Vocabulary:

 

 

Oct.– Nov.

5-Groups in Numbers 6-10

 

 

PA Standards:

CC.2.1.K.A.1 Know number names and write and recite the count sequence.

 

CC.2.1.K.A.2 Apply one-to-one correspondence to count the number of objects.

CC.2.1.K.A.3 Apply the concept of magnitude to compare numbers and quantities.

 

CC.2.1.K.B.1 Use place value to compose and decompose numbers within 19.

 

CC.2.2.K.A.1 Extend the concepts of putting together and taking apart to add and subtract within 10.

 

CC.2.3.K.A.1 Identify and describe two- and three dimensional shapes.

 

CC.2.3.K.A.2 Analyze, compare, create, and compose two- and three-dimensional shapes.  

 

  1. Numbers are counted in a specific sequence. 
  2. There is a unique symbol that goes with each number word.
  3. Numerals represent a set of objects.
  4. Counting tells how many are in a set not matter which order the objects are counted or arranged.
  5. The last number said when counting a set is the total.
  6. Counting is cumulative.
  7. Benchmarks can be used to estimate quantities of groups.
  8. In a pair of numbers, the number that shows more is greater.  The number that shows fewer is less.  If two numbers are exactly the same amount, they are equal.
  9. There is more than one way to show a number.
  10. Numbers can be decomposed in different ways.
  11. Addition is putting together and adding to.
  12. Subtraction is taking apart and taking from.
  13. Addition and subtraction scenarios can be represented in a variety of ways.
  14. Different combinations of number pairs can produce the same sum.
  15. A knowledge of the base ten system is key to a strong foundation in both addition and subtraction.
  16. Automaticity of addition and subtraction facts is an important foundation for the building of more complex mathematical concepts.
  17. Problems can be solved by using objects to act out the actions in a problem.
  1. Basic shapes can be used to describe objects in the environment.
  2. Shapes have attributes.
  3. Shapes can be formed and drawn using knowledge of their specific attributes.
  4. Two-dimensional shapes are flat.
  1. Why do numbers need to be in a sequential order? 
  2. What would happen if numbers were out of order?
  3. When can you use number symbols to tell about a set of objects?
  4. How does counting tell how many?
  5. When can you use number symbols to tell about a set of objects?
  6. How can you determine if a number is greater than, less than, or equal to another number?
  7. How can you represent addition and subtraction scenarios in a variety of ways?
  8. How can you use base ten knowledge to fluently solve both addition and subtraction scenarios?
  9. Why is automaticity of basic addition and subtraction facts important?
  10. How do you know when shapes are exactly the same?
  11. What do you look for when you describe and match shapes?
  12. What do you need to know about a shape’s attributes in order to recreate that shape?
  13. How can you use smaller shapes to make a larger shape?
  14. How can you use smaller shapes to make a different shape?
  15. How can you tell if a shape is a rectangle, square, circle, triangle, or hexagon?
  16. How can you tell if a shape is flat or solid?

Unit 2 Test

 

Performance Task

 

Quick Quizzes

 

Formative Assessments

 

Fluency Checks

 

*Text

*Manipulatives

*Online

Resources

*Vocabulary:

 

 

Dec. – Jan.

Teen Numbers as Tens and Ones

Order

Correlations

Production

Relationships

Characteristics

 

PA Standards:

CC.2.1.K.A.1 Know number names and write and recite the count sequence.

 

CC.2.1.K.A.2 Apply one-to-one correspondence to count the number of objects.

 

CC.2.1.K.B.1 Use place value to compose and decompose numbers within 19.

 

CC.2.2.K.A.1 Extend the concepts of putting together and taking apart to add and subtract within 10.

 

CC.2.3.K.A.1 Identify and describe two- and three dimensional shapes.

 

CC.2.3.K.A.2 Analyze, compare, create, and compose two- and three-dimensional shapes

 

CC.2.4.K.A.4 Classify objects and count the number of objects in each category.

 

  1. Numbers are counted in a specific sequence. 
  2. There is a unique symbol that goes with each number word.
  3. Numerals represent a set of objects.
  4. Counting tells how many are in a set not matter which order the objects are counted or arranged.
  5. The last number said when counting a set is the total.
  6. Counting is cumulative.
  7. Benchmarks can be used to estimate quantities of groups.
  8. In a pair of numbers, the number that shows more is greater.  The number that shows fewer is less.  If two numbers are exactly the same amount, they are equal.
  9. There is more than one way to show a number.
  10. Numbers can be decomposed in different ways.
  11. Addition is putting together and adding to.
  12. Subtraction is taking apart and taking from.
  13. Addition and subtraction scenarios can be represented in a variety of ways.
  14. Different combinations of number pairs can produce the same sum.
  15. A knowledge of the base ten system is key to a strong foundation in both addition and subtraction.
  16. Automaticity of addition and subtraction facts is an important foundation for the building of more complex mathematical concepts.
  17. Problems can be solved by using objects to act out the actions in a problem.
  18. Basic shapes can be used to describe objects in the environment.
  19. Shapes have attributes.
  20. Shapes can be formed and drawn using knowledge of their specific attributes.
  21. Two-dimensional shapes are flat.
  22. Shapes can be combined to make other shapes.
  23. Attributes can be used to compare objects.
  24. Attributes such as color, shape, or size can be used to sort the same set of objects in different ways.
  25. A set of objects can be sorted according to a combination of attributes.
  26. Data can be collected and represented in various ways.
  27. Graphs can be used to answer questions.
  1. Why do numbers need to be in a sequential order? 
  2. What would happen if numbers were out of order?
  3. When can you use number symbols to tell about a set of objects?
  4. How does counting tell how many?
  5. When can you use number symbols to tell about a set of objects?
  6. How can you determine if a number is greater than, less than, or equal to another number?
  7. Why can you show the same number in different ways?
  8. How can number decompositions be represented?
  9. How can decomposing numbers help build better number sense?
  10. How can you represent addition and subtraction scenarios in a variety of ways?
  11. How can you use base ten knowledge to fluently solve both addition and subtraction scenarios?
  12. Why is automaticity of basic addition and subtraction facts important?
  13. How do you know when shapes are exactly the same?
  14. What do you look for when you describe and match shapes?
  15. What do you need to know about a shape’s attributes in order to recreate that shape?
  16. How can you use smaller shapes to make a different shape?
  17. How does making and reading a graph help to answer questions?
  18. What does looking at the color, shape, and size of objects help you know about them?
  19. What are some ways you can sort objects?
  20. In order to make a group of objects that are exactly alike in two ways, what should you notice about the objects?
  21. How does matching objects in two groups help you know which group has more, fewer, or as many as the other group?
  22. How can data be represented?
  23. What data can you gain from looking at a graph?
  24. How can you describe objects in the environment using shapes?
  25. How can you tell if a shape is a rectangle, square, circle, triangle, or hexagon?

 

Unit 3 Test

 

Performance Task

 

Quick Quizzes

 

Formative Assessments

 

Fluency Checks

 

*Text

*Manipulatives

*Online

Resources

*Vocabulary:

 

 

Feb.

-

March

Partners, Problem Drawings, and Tens

Order

Correlations

Production

Relationships

Characteristics

 

PA Standards:

CC.2.2.K.A.1 Extend the concepts of putting together and taking apart to add and subtract within 10.

 

CC.2.1.K.B.1 Use place value to compose and decompose numbers within 19.

CC.2.3.K.A.1 Identify and describe two- and three dimensional shapes.

 

CC.2.3.K.A.2 Analyze, compare, create, and compose two- and three-dimensional shapes

 

CC.2.4.K.A.4 Classify objects and count the number of objects in each category.

 

  1. There is more than one way to show a number.
  2. Numbers can be decomposed in different ways.
  3. Addition is putting together and adding to.
  4. Subtraction is taking apart and taking from.
  5. Addition and subtraction scenarios can be represented in a variety of ways.
  6. Different combinations of number pairs can produce the same sum.
  7. A knowledge of the base ten system is key to a strong foundation in both addition and subtraction.
  8. Automaticity of addition and subtraction facts is an important foundation for the building of more complex mathematical concepts.
  9. Problems can be solved by using objects to act out the actions in a problem.
  10. Basic shapes can be used to describe objects in the environment.
  11. Shapes have attributes.
  12. Shapes can be formed and drawn using knowledge of their specific attributes.
  13. Three dimensional shapes are solid.
  14. Many everyday objects closely approximate standard geometric solids.
  15. Solid figures can be compared in different ways.
  16. Some solid figures can be compared by their flat surfaces and vertices.
  17. The flat surfaces of many solid figures have specific shapes.
  18. Shapes can be combined to make other shapes.
  1. Why can you show the same number in different ways?
  2. How can number decompositions be represented?
  3. How can decomposing numbers help build better number sense?
  4. How can you represent addition and subtraction scenarios in a variety of ways?
  5. How can you use base ten knowledge to fluently solve both addition and subtraction scenarios?
  6. Why is automaticity of basic addition and subtraction facts important?
  7. How do you know when shapes are exactly the same?
  8. What do you look for when you describe and match shapes?
  9. What kinds of figures roll, slide, and stack?
  10. How can you describe flat surfaces of solids?
  11. What do you need to know about a shape’s attributes in order to recreate that shape?
  12. How can you describe where something is using the words, inside, and outside, over,  under, and on, top, middle, and bottom, or left and right.
  13. How can you describe objects in the environment using shapes?
  14. How can you tell if a shape is flat or solid?

Unit 4 Test

 

Performance Task

 

Quick Quizzes

 

Formative Assessments

Fluency Checks

 

*Text

*Manipulatives

*Online

Resources

*Vocabulary:

 

 

April - May

Consolidation of Concepts

Order

Correlations

Production

Relationships

Characteristics

 

PA Standards:

CC.2.2.K.A.1 Extend the concepts of putting together and taking apart to add and subtract within 10.

 

CC.2.1.K.A.2 Apply one-to-one correspondence to count the number of objects.

 

CC.2.1.K.A.3 Apply the concept of magnitude to compare numbers and quantities.

 

CC.2.4.K.A.1 Describe and compare attributes of length, area, weight, and capacity of everyday objects.

 

 

  1. Addition is putting together and adding to.
  2. Subtraction is taking apart and taking from.
  3. Addition and subtraction scenarios can be represented in a variety of ways.
  4. Different combinations of number pairs can produce the same sum.
  5. A knowledge of the base ten system is key to a strong foundation in both addition and subtraction.
  6. Automaticity of addition and subtraction facts is an important foundation for the building of more complex mathematical concepts.
  7. Problems can be solved by using objects to act out the actions in a problem.
  8. There is a unique symbol that goes with each number word.
  9. Numerals represent a set of objects.
  10. Counting tells how many are in a set not matter which order the objects are counted or arranged.
  11. The last number said when counting a set is the total.
  12. Counting is cumulative.
  13. Benchmarks can be used to estimate quantities of groups.
  14. In a pair of numbers, the number that shows more is greater.  The number that shows fewer is less.  If two numbers are exactly the same amount, they are equal.
  15. Measurement is a process of comparing a unit to the object being measured.
  16. Objects can be compared and ordered by length, capacity, and weight.
  1. How can you represent addition and subtraction scenarios in a variety of ways?
  2. How can you use base ten knowledge to fluently solve both addition and subtraction scenarios?
  3. Why is automaticity of basic addition and subtraction facts important?
  4. When can you use number symbols to tell about a set of objects?
  5. How does counting tell how many?
  6. When can you use number symbols to tell about a set of objects?
  7. How can you determine if a number is greater than, less than, or equal to another number?
  8. How can you decide which object is larger and which object is smaller?
  9. How can you compare and order the length of three objects?
  10. How can you tell if a container holds the same or more or less than another?
  11. How can you compare the weights of two objects?
  12. How does matching objects in two groups help you know which group has more, fewer, or as many as the other group?

Unit 5 Test

 

Performance Task

 

Quick Quizzes

 

Formative Assessments

 

Fluency Checks

 

*Text

*Manipulatives

*Online

Resources

*Vocabulary:

 

 

June

Review of Previously Taught Units

Order

Correlations

Production

Relationships

Characteristics

 

 

 

All Common Core Standards

 

 

All Essential Understandings

 

 

All Essential Questions

End of the Year Assessment

 

 

*Text

*Manipulatives

*Online

Resources

*Vocabulary:

 

 

                     

* Some teachers may need to think about the assessments and resources used in order to determine the Big Ideas, Enduring Understandings, and Essential Questions embedded in their courses.  At this point in your curriculum mapping, you might want to ignore the “Common Assessments” and “Common Resources Used” columns.  However, you may use them if you wish.