Common Core Standards Curriculum Map

Mathematics - Grade 1

 

 

Trimester

Unit

Title

Instructional Days

1

1

Exploring Numbers

19

2

Exploring Addition and Subtraction

5

3

Developing Addition Strategies

9

4

Developing Subtraction Strategies

9

5

Developing Addition and Subtraction to Solve Story Problems

9

6

Investigating Numbers

9

 

 

 

60

2

1

Exploring Place Value

10

2

Understanding Place Value

12

3

Interpreting Data

5

4

Using Data

5

5

Measurement & Applying Time

8

6

Developing & Applying Measurement

8

7

Exploring Attributes of Shapes

5

8

Developing Numbers to 120

7

 

 

 

60

3

1

Finding Tens to Add and Subtract

10

2

Applying Addition and Subtraction to Solve Story Problems

10

3

Applying Numbers from 1 to 20

10

4

Developing Equal Shares of Circles and Rectangles

12

5

Reasoning with Shapes and their Attributes

9

6

Applying Addition and Subtraction Strategies

9

 

 

 

60

 

 

Common Core Standards Curriculum Map - Grade 1

Trimester One

                                        

Unit One - Exploring Numbers  (19 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Extend the counting sequence.

1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Understand place value.

1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

 

  • Count to 100.
  • Read and write numerals to 100.
  • Represent a number of objects with a written numeral.
  • Compare 2 two-digit numbers (10-99) using concrete models.
  • Record the results of comparisons with the equal (=) symbol.

Notes from the NC Unpacking Document:

-  Knowing those numbers out of sequence (teens in particular because they don’t follow the pattern)

-  Place value connection to the number that is important

-  Student example A is based on place value (focus where the standards focus).  

-  Decade numbers are groups of tens with none left-over.

-  Don’t say “and” such as one hundred AND ninety.... just say one hundred ninety.  

-  Develop comparisons with language first and then layer in >, <, =

How can you use symbols to show the relationship between two numbers?

-  greater than (>) symbols to show that one number is more than

-  less than (<) symbols to show that one number is less than

-  equal signs (=) to show that numbers are the same

-  this tower is taller than this tower so I know it is greater

-  we build with unifix cubes to see what has more

-  matching

-  we use the number line to see how far

-  we look at hundred charts/number grids to see where the numbers are

-  we used the scales to see which one weighs more or less or is equal

How do you know when two numbers are equal?

-  my towers are the same size

-  using the word same as a synonym

-  when I see it in number sentences I know that both sides are the same

-  when the scale is level

-  balance

How is ______ related to ______? (<, >, = )

What are the next ____numbers after ____?

How many are in this set? How can you write the numeral?

 

What number comes before ______?

If you continued this pattern what numbers will be next?

SMP 6  Attend to precision.

Mathematically proficient students try to communicate precisely with others by...

   -  Stating the meaning of the symbols they choose (greater than, less than, equal...).

   -  Using the equal sign consistently and appropriately to represent balance.

-  Use more and less appropriately

-  Difference between a digit in a place vs. the value (5 is in the tens place in 59, but its value is 50.

SMP 7  Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure by...

   -  Notice repeating patterns on a number line or hundreds chart.

   -  If the tens place is equal, know to look to the ones when comparing numbers.

-  Decade numbers, the zero represents that there are zero ones.  The zero represents zero no matter where it is located.

   -  Teen numbers represent one group of ten with a certain amount of ones.

-  Position of numbers determines the value of the number.  (17 vs. 71)

Prior Learning:

In Kindergarten, students counted to 100 by 1s and 10s.  They began at any given number within the known sequence.  They wrote and represented numbers from 0-20 and represented a number of objects with a written numeral from 0-20.  Students compared the number of objects in one group to the number of objects in another group.  Students also compared two numbers between 1 and 10 presented as written numerals.

Current Learning:

This is a critical area in Grade One.  Read the overview of K-5 Number and Operations in Base 10 Learning Progressions for background information for this unit.  Teachers may create numeral lists and visual supports as teaching tools (p.6).

Throughout the year, students write and read numerals up to 120.  The reading, writing and representing numerals are being taught at a developmental level in this unit.  Also, students compare two 2-digit numbers using concrete models and oral discussion.  

The emphasis for students is on understanding the concept of equality, not limited to the appropriate use of the equal symbol in comparing numbers.  See CCSS Glossary p.90 Table 4 for the properties of equality, in particular the Reflexive Property of Equality.

Future Learning:

In grade two, students will read and write numbers up to 1,000.  They will compare three-digit numbers using symbols for greater than, less than and the equal symbol.

Notes from Progressions Document:

Kindergarten:

-  The English language causes students to struggle with teen numbers - can use both.

-  Number bond diagrams

-  Layered place value (sometimes called arrow cards)

Grade Two:

-  Comparing 3-digit numbers (viewing 10 tens as a hundred)

-  Don’t differentiate until they can justify two numbers like Student A from the NC document

Home

Unit Two - Exploring Addition and Subtraction  (5 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Represent and solve problems involving addition and subtraction.

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

 

  • Use addition and subtraction to solve word problems (adding to, taking from, putting together, taking apart and comparing) by using objects, drawings and equations to represent the problem.
  • Understand how addition and subtraction are strongly related to counting.

North Carolina Unpacking the Standards & Progression Documents:

-know what a number looks like to be able to

  • add and subtract
  • visualize and solve an equation
  • compare numbers using a concrete model
  • decompose a number
  • where the number falls on the number line or grid
  • add and subtract and relate it and use counting
  • count on to find a sum
  • express understanding of the equal sign as two quantities that are the same
  • articulate how the student arrived at the answer

How many do I have? How do I know?

How can you use what you know from the story to solve this problem?

How can you show me the number that is ____ more/less than _____?

How many more/less do I need to make  _______? How do you know?

How is 4 related to 6? (It is 2 more.)

How can you solve this problem?

How is addition/subtraction like counting?

How do you know when you are
adding/subtracting?

When adding/subtracting 2, how is that like counting?

SMP 1  Make sense of problems and persevere in solving them.

   -  Understand the meaning of the problem.

   -  Use concrete objects or pictures to solve a problem.

    -   Know and flexibly use different properties of operations and objects.

SMP 2  Reason abstractly and quantitatively.

   -  Decontextualize and recontextualize.

  -  Use concrete objects or pictures to solve a problem.

   -  Attend to the meaning of quantities.

   -  Use objects, drawings or equations to represent the problem.

Prior Learning:

In Kindergarten, students represented addition and subtraction word problems with pictures, sounds and mental images or equations.  Students also decomposed numbers ten and less into pairs more than one way.  They used pictures or objects and recorded the decomposition by a drawing or equation.  When given any number 1-9, students found the number that made 10 by using objects or drawings.  Students fluently added and subtracted within 5.

Current Learning:

This is a critical area in Grade One.  Subtraction is a developmental concept as this is the first experience students will have this year.  They use subtraction to solve word problems - refer to p.88, Table 1 in the CCSS for addition and subtraction situations and problem types.  Another developmental skill with a strong connection to Unit One is understanding the meaning of the equal sign involving addition and subtraction.

Later in the year, students will demonstrate fluency with addition and subtraction within 10.  They will determine if equations are true or false.  They will work with unknowns in all positions and the associative property of addition.

Future Learning:

In grade two, students will use addition and subtraction within 100 in all situations to solve one- and two-step word problems with unknowns in all positions.  Students will fluently add and subtract within 20 using mental strategies.  They will know, from memory, all sums of two one-digit numbers.

Home

Unit Three - Developing Addition Strategies  (9 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

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.2 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.)

 

Add and subtract within 20.

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).

 

Work with addition and subtraction equations.

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 +

  • Apply the commutative property to add and relate this to subtraction using the idea of fact families.
  • Add and subtract within 10 using counting on as a strategy.
  • Understand the meaning of the equal sign involving addition and subtraction.

What is the relationship between addition and subtraction?

Explain with pictures, words, or equations: What are the Fact Families?

How does a Fact Family help you solve math problems?

Use manipulatives to commute a number sentence for: Addition    

and Subtraction

SMP 8 Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts.

   -  Notices that 3+7 and 7+3 are equal

   -  Notices that 2+3+5=8+2

   -  Composes and decomposes numbers to 20 using pictures and objects

Prior Learning:

In kindergarten, students solved addition word problems within 10 using objects, fingers, mental images, simple drawings, sounds, acting out, verbal explanations, or equations. Students used drawings or equations to decompose numbers less than or equal to 10 (5 = 2 + 3; 5 = 4 + 1). For any number 1–9, students found the number that made 10 when added to a given number by using objects or drawing and recorded answers with an equation or drawing. Students became fluent adding and subtracting within 5. Kindergarten students were exposed to equations and the equals sign symbol (=), and were encouraged to

write equations, but writing equations was not required.

Current Learning:

This is a critical area of learning in Grade 1.

In this unit, students relate counting to addition to solve word problems within 20 using strategies involving adding to and putting together using objects, drawings, and equations with a symbol for the unknown number. Working with the commutative property of addition (8 + 3 = 11; 3 + 8 = 11) encourages students to use counting on strategies when combining quantities. As the year goes on students will add within 20 using a variety of strategies to include: counting on, making a ten, and creating equivalent, but easier known sums. They develop understanding of the meaning of the equals sign (=). This is taught at the developmental level.

Future Learning:

In second grade, students will develop understanding of odd and even within 20 and will fluently add within 20 using mental strategies. Students will add and subtract within 1,000 using concrete models, drawings, and strategies based on the properties of operations, place value, and the relationship between addition and subtraction; they will fluently add and subtract within 100 using these strategies. Third grade students will generalize these strategies to larger numbers, and in fourth grade students will be expected to fluently apply the standard algorithm for addition and subtraction.

Home

Unit Four - Developing Subtraction Strategies  (9 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

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.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.

 

Add and subtract within 20.

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).

• Apply the commutative property to add and

subtract (e.g., if 8 + 3 = 11 is known, then 3 + 8 = 11, 11 – 3 = 8 and 11 – 8 = 3 is also known—“fact family”).

-  Apply the associative property to add (e.g, if 3+4+7 is the given expression, than students can rearrange the addends to (3+7) + 4 or 4 + (7+3) to take advantage of the 10 and simplify the calculation).

• Understand subtraction as an unknown addend

problem. (e.g., subtract 10 – 8 by finding a number that makes 10 when added to 8.)

• Relate counting to addition and subtraction.

• Add and subtract within 20 using multiple efficient strategies (e.g., counting on, making ten, relating addition to subtraction, etc.)

What strategies can we use to add?

What strategies can we use to subtract?

Show me how you know:

8+3=11

3+8=11

How do you know _____+______=_____?

SMP 7  Look for and make use of structure

Mathematically proficient students look closely to discern a pattern or structure by...

  • Noticing that 10-7=3 is 10- ____ =3
  • Composing or decomposing numbers to 20 using pictures and objects.
  • Using ten to simplify calculations and become more procedurally fluent when adding and subtracting within 20.

Prior Learning:

In kindergarten, students decomposed numbers ten and less into pairs more than one way. They used pictures or objects and recorded the decomposition by a drawing or equation. When given

any number 1–9, students found the number that made ten by using objects or drawings. Students fluently added and subtracted within 5.

Current Learning:

This is a critical area in Grade 1.

Subtraction is a developmental concept as this is the first experience students will have this year. They use subtraction to solve problems and understand subtraction as an unknown addend problem. Refer

to p. 88, Table 1 in the Common Core State Standards Mathematics for addition and subtraction situations and problem types going forward. In the CCSS, strategies such as counting on, making ten, decomposing a number leading to a ten, and using the relationship between addition and subtraction are used. Students create equivalent but easier known sums.    (Students do not need to know/use formal names for commutative and associative properties, however, modeling appropriate math language and connecting it to student-friendly language is always optimal).

Future Learning:

In grade 2, students will use addition and subtraction within 100 in all situations to solve one- and two-step word problems with unknowns in all positions. Students will fluently add and subtract within 20 using mental strategies. They will know, from memory, all sums of two one-digit numbers.

Home

Unit Five - Developing Addition and Subtraction to Solve Story Problems  (9 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning,

Current Learning and Future Learning

Represent and solve problems involving addition and subtraction.

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,

-  Use addition and subtraction within 20 to solve

word problems (adding to, taking from, putting

together, taking apart, and comparing).

-  Use objects, drawing, and equations with symbols for the unknown number to represent the problem.  (See CCSS glossary, Table 1.)

-  Solve word problems adding three whole

numbers whose sum is less than or equal to 20

(using objects and drawings).

How can we decide if we need to add or subtract to solve a story problem?

What strategies can we use to solve addition and subtraction problems?

Can you show 3 + 2?

How many do you have all together?

Can you show me another way (to show 3 + 2)?

Listen to this number story.  Can you tell me how many ___ in all?

SMP 1  Make sense of problems and persevere in solving them.

• Understand the problem and look at how to

begin to solve the problem.

• Plan a solution instead of jumping right into

the problem.

SMP 3  Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments...

  • They understand the reason for for using a given strategy for an answer.  
  • They can decide whether answers make sense by looking at a picture, diagram, and manipulatives.
  •  They can ask questions about using strategies.

Prior Learning:

In kindergarten, students represented addition and subtraction word problems with pictures, sounds and mental images, or equations. They also decomposed numbers 10 and less into pairs more than one way. Students used pictures or objects and recorded the decomposition by a drawing or equation. When given any number 1–9, they found the number that made 10 by using objects or drawings. Students fluently added and subtracted within five.

Current Learning:

This is a critical area of instruction for grade 1.

In this unit, students solve word problems involving situations of adding to, taking from, putting together,taking apart, and comparing by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (See CCSS glossary, Table 1.) Comparing is taught at the developmental level, and all other strategies are reinforced in this unit.  Also, they will determine the unknown whole number in an addition or subtraction equation relating three whole numbers. These skills are taught at the developmental level. Research suggests using a variety of problem situations (see Table 1) and exploiting everyday situations to introduce and discuss addition and subtraction.** To understand student difficulties with language in comparison problems refer to K–5 Operations and Algebraic Thinking Learning Progressions, page 12.

Future Learning

In grade 2, students will use addition and subtraction within 100 in all situations to solve one- and two step word problems with unknowns in all positions. Reference CCSS, page 88, Table 1: Common addition and subtraction situations. Students will fluently add and subtract within 20 using mental strategies. They will know from memory all sums of two 1-digit numbers.

Home

Unit Six - Investigating Numbers (9 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning a

nd Future Learning

Understand place value.

1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

-  Read and write numerals to 120.

-  Represent a number of objects with a written numeral up to 120.

-  Compare two 2-digit numbers 10–99

-  Record the results of comparisons using correct mathematical symbols     (<, >, =).

How can we decide if a number is greater than, less than or equal to another number?

Identify tens and ones that are in (a given number)?

Write the number (______) and draw a picture to show that number.

Name a numeral greater than (____)

Name a numeral less than (____).

SMP 7  Look for and make use of structure.

• Use the structure of the  base ten system to compare numbers.

SMP 8  Look for and express regularity in repeated reasoning.

• Look for general methods and shortcuts when counting

• Continually evaluate the reasonableness of intermediate results.

Prior Learning:

In kindergarten, students counted to 100 by ones and tens. They began at any given number within a known sequence. Students wrote and represented numbers 0–20 and represented the number of objects with a written numeral 1–20.  They compared objects from 0-10 using the words greater than, less than and equal.

Current Learning:

This is a critical area in grade 1.

Reading and writing numerals 0–60 and the concept of equality are taught at the reinforcement level.

Skills taught at the developmental level are as follows:

• Students read and write numbers 61–120 and use the symbols for greater than and less than to compare numbers up to 120.

-  Students compare numbers using inequality symbols and the equal sign.

Future Learning:

In grade 2, students will understand that the digits of a three-digit number represent hundreds, tens, and ones. They will count, read, and write numbers up to 1,000 using base-10 numerals and expanded form.  Students will compare three-digit numbers using the symbols for greater than, less than, or equal.

Home

Trimester 2

Unit One -Exploring Place Value  (10 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Understand place value.

1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones — called a “ten.”

c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

 

• Understand that the two digits of a two-digit number are made up of tens and ones.

• Understand that 10 is a bundle of 10 ones

called a “ten.”

• Understand that the decade numbers (10, 20, 30, 40 …) refer to 1, 2, 3, 4 tens and zero ones.

Given a two-digit number, how many tens and ones does this number represent?

How many tens and ones are there in the number (10, 20, … 90)? (Answers would be one ten and zero ones, etc.)

How many tens can you make from these materials (snap cubes, craft sticks, etc.)?

Show me how to build _______ using base ten blocks.

In the number ______ which number represents tens? ones? hundreds?

SMP 1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution by...

  •  Continually ask themselves, “Does this make sense?”
  •  Use concrete objects or pictures to help conceptualize and solve problems.
  •  Understand the approaches of others.
  •  Making sense of the value of a number

SMP 7  Look for and make use of structure.

• Recognize the structure of two-digit numbers (understand two-digit numbers as composed of tens and ones).

• Detect the pattern in a counting sequence.

• Detect patterns in word names and their numeral representations.

Prior Learning:

In kindergarten, students counted to 100 by 1s and 10s. They began at any given number within the known sequence. Students also wrote numbers 0–20 and represented a number of objects with a written numeral 0–20. Students began to build the foundation for place value by composing and decomposing numbers from 11–19 into ten ones and some further ones by using objects or drawings or equations.  Students compared the number of objects in one group to the number of objects in another group. Students also compared two numbers between 1 and 10 presented as a written numeral.

Current Learning:

Place value is a critical area of instruction in first grade. Students understand that the two digits of a 2- digit number represent bundles of tens and some ones. This is taught at the developmental level. They understand that 10 is a bundle of ten ones called a “ten.” Students understand that decades (10, 20, 30, etc.) refer to a number of tens and no additional ones. This is taught at the reinforcement level. Students are at the discrete stage of development and solid place-value rods may promote confusion. As students gain experience with countable bundles, they may be able to transition to place-value rods and other more abstract visuals and models.

Future Learning:

In second grade, students will learn that 100 is a bundle of ten 10s. The numbers (100, 200, 300, etc.) refer to the number of hundreds (and 0 tens and 0 ones). They will count within 1,000.. Students will read and write numbers to 1,000 using base-ten numerals,number names, and expanded form.

Home

Unit Two - Understanding Place Value  (12 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Understand place value.

1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones — called a “ten.”

b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

 

• Understand that the two digits of a two-digit number are made up of tens and ones.

• Understand that 10 is a bundle of 10 ones called a “ten.”

• Understand that the numbers 11–19 are composed of a ten and ones.

• Understand that the decade numbers (10, 20, 30, 40 …) refer to 1, 2, 3, 4 tens and zero ones.

Prior Learning:

In kindergarten, students counted to 100 by 1s and 10s. They began at any given number within the known sequence.  Students also wrote numbers 0–20 and represented a number of objects with a written numeral 0–20.  Students began to build the foundation for place value by composing and decomposing numbers from 11–19 into ten ones and some further ones by using objects or drawings or equations. Students compared the number of objects in one group to the number of objects in another group. Students also compared two numbers between 1 and 10 presented as a written numeral.

Current Learning:

Place value is a critical area of instruction in first grade. Students understand that the two digits of a 2-digit number represent bundles of tens and some ones. This is taught at the developmental level. They understand that 10 is a bundle of ten ones called a “ten.” Students understand the teen numbers (11–19) are composed of a ten and additional ones, and the decades (10, 20, 30, etc.) refer to a number of tens and no additional ones. This is taught at the reinforcement level. At this time of year, students need to develop this understanding by using bundles, such as snap cubes and linking chains, that are easy to count and separate into ones. Students are at the discrete stage of development and solid place-value rods may promote confusion. As students gain experience with countable bundles, they may be able to transition to place-value rods and other more abstract visuals and models. Later in the year, students record the results of these comparisons using <, >, and =, and increase the number range to 120. Students will use their understanding of place value to compute sums within 100.

Future Learning:

In second grade, students will learn that 100 is a bundle of ten 10s. The numbers (100, 200, 300, etc.) refer to the number of hundreds (and 0 tens and 0 ones). They will count within 1,000. Students will skip count by 5s, 10s, and 100s. Students will read and write numbers to 1,000 using base-ten numerals, number names, and expanded form. They will compare 2- and 3-digit numbers and use symbols <, >, and = to record results.

Home

Unit Three - Interpreting Data (5 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

1.MD.4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

 

• Interpret data with up to three categories.

• Answer questions about the data

What does this graph show?

 

What questions can you ask about this graph?

How many (boys, girls, sneakers, etc.) does this graph show?

 

SMP 4  Model with mathematics.

• Apply mathematics known to everyday life.

• Analyze and interpret data mathematically to

draw conclusions.

SMP 6  Attend to precision.

• Communicate precisely to others.

• Specify units of measure to clarify the quantity.

• Calculate/count accurately.

Prior Learning:

Students classified objects into given categories.  and sorted the categories by count. They compared two numbers between 1 and 10.  No formal “graphing” is in the Kindergarten Standards.

Current Learning:

In this unit, students interpret data with up to three categories.

Students ask and answer questions about the data. This is taught at the developmental level.

Future Learning:

In second grade, students will generate data by measuring line plots. They will draw a picture graph and a bar graph to represent data with up to four categories. They will solve word problems using information presented in a bar graph.

Home

                                        

Unit Four - Using Data (5 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Represent and interpret data.

1.MD.4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 

• Interpret data with up to three categories.

• Answer questions about the total number of data points.

• Tell how many data points are in each category.

What does this graph/chart/table show?

What questions can you ask about this graph/chart/table?

How many _______ does this _____ show?

How many more/less _________ are there?

How many ________ and _________ are there altogether?

SMP 4  Model with mathematics.

• Apply mathematics known to everyday life.

• Analyze and interpret data mathematically to

draw conclusions.

SMP 6  Attend to precision.

• Communicate precisely to others.

• Specify units of measure to clarify the quantity.

• Calculate/count accurately.

Prior Learning:

Students classified objects into given categories.  and sorted the categories by count. They compared two numbers between 1 and 10.  No formal “graphing” is in the Kindergarten  Standards.

Current Learning:

In this unit, students interpret data with up to three categories. Students ask and answer questions about the total number of data points. This is taught at the developmental level.

Students organize and represent data with up to three categories . They ask and answer

questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Future Learning

In second grade, students will use and select appropriate tools to measure objects using standard units. Students will generate data by measuring line plots. They will draw a picture graph and a bar graph to represent data with up to four categories. They will solve word problems using information presented in a

bar graph.

Home

Unit Five - Measurement & Applying Time  (8 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Tell and write time.

1.MD.3. Tell and write time in hours and half-hours using analog and digital clocks. 

• Tell and write time in hours using analog and digital clocks.

How can you use this clock to represent the time?

How many hours are in a day?

How many minutes are in an hour?

How many seconds are in a minute?

Identify the clock hands?

What time is this (show clock)?-- use 1/2 hour and hour?

4 Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace by...

  • Understand math is used in everyday life
  • Use clocks to understand a daily schedule (to the hour and half hour)
  • Use tools (clocks) appropriately

Mathematically proficient students consider the available tools when solving a mathematical problem.

Prior Learning:

In kindergarten, students did not work on telling time.

Current Learning

Students in grade one tell and write time in hours and half-hours using digital and analog clocks. These skills are taught at the developmental level.

Future Learning

In grade 3, students will solve problems involving elapsed time.

Home

Unit Six -Developing & Applying Measurements  (8 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Measure lengths indirectly and by iterating length units.

1.MD.1. Order three objects by length; compare the lengths of two objects indirectly by using a

third object.

1.MD.2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a

whole number of length units with no gaps or overlaps.

• Compare the lengths of two objects indirectly

by using a third object (if a > b and b > c then

a > c; transitivity).

• Express the length of an object as a whole

number of length units (by laying multiple

copies of a shorter object end to end).

• Understand that the length measurement of an

object is the number of same-size length units

that span it with no gaps or overlaps.

Which one of these three objects is the  longest/shortest? How do you know?

What is the length of this object? How do you know? (Use familiar materials.)

Explain how to use this measuring tool (ruler, blocks, etc.)

5.  Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a measurement problem.

Prior Learning

In kindergarten, students did direct comparisons by comparing two objects with a measurable attribute in common (taller/shorter). They classified objects into given categories, counted the numbers in each category (up to 10) and sorted the categories by count.

Current Learning

Students order three objects by length.. In this unit, these concepts are taught at the reinforcement level. In this unit, students compare the lengths of two objects indirectly by using a third object (see Additional Findings below on transitivity). Refer to CCSS (p. 90), Table 4 for further information on the transitive property of equality (if a = b and b = c then a = c) and Table 5 for the properties of inequality (if a > b and b > c then a > c). Students express the length as a whole number of length units. These skills are taught at the developmental level.

Future Learning

In grade 2, students will select and use appropriate tools to measure objects. They will be measuring to determine how much longer one object is than another, expressing the difference in terms of a standard length unit. Students will also estimate lengths using inches, feet, centimeters, and meters. Students will

measure the same object using different units of measure.

Home

Unit Seven-Exploring Attributes of Shapes (5 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

 

• Understand defining attributes (e.g., triangles are closed and three-sided).

• Understand non-defining attributes (e.g., color, orientation, overall size).

• Distinguish between defining and non-defining attributes.

• Build shapes to understand defining attributes.

• Draw shapes to understand defining attributes.

What are some attributes that don’t define

shapes?

What shape is this? How do you know?

 

How do you draw a ______?

 

How did you sort these shapes? (What is your sorting rule?)

 

What do all _______ have that are not the same? (Example: Triangles are closed and three-sided.)

7.  Look for and make use of structure.

Make connections by sorting shapes according to defining and non-defining attributes.

Make connections using manipulatives.

Prior Learning

Students named objects in the environment using names of shapes. They also named shapes correctly regardless of orientation. Students analyzed and compared two- and three-dimensional shapes describing their similarities and differences using informal language. Students built and drew shapes as well as composing simple shapes to form larger ones.

Current Learning

In this unit, students distinguish between defining (number of sides, number of vertices) and non-defining (color, size, orientation) attributes and use this formal language to describe shapes. They expand knowledge of two-dimensional shapes (square, circle, triangle, hexagon, rectangle, and trapezoid) using defining attributes and they draw and build shapes to distinguish defining attributes (draw/build closed shape with four equal sides). This is being taught at the developmental level. Later in the year, students will compose two-dimensional and three-dimensional shapes to make composite shapes.

Future Learning

In second grade, students will use their knowledge of attributes to recognize and draw shapes having specified attributes (number of angles or faces).

Home

Unit Eight -Developing Numbers to 120  (7 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Extend the counting sequence.

1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write

numerals and represent a number of objects with a written numeral.

Understand place value.

1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits,

recording the results of comparisons with the symbols >, =, and <.

• Count to 120, starting at any number less than 120.

• Read and write numerals to 60.

• Represent a number of objects with a written numeral.

• Compare 2 two-digit numbers (10–60) using concrete models.

• Record the results of comparisons with the equal (=) symbol.

How do you know when two numbers are equal?

Which number is greater than/less than?  How do you know?

How is _____ related to ______?

What are the next 3 numbers before or after ______?

How many numbers are in this set?

What comes before or after _____?

8 Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general

methods and for shortcuts by...

  • Notice repeating patterns (hundreds grid and number line)
  • Make connections or relationships in number patterns
  • Compare numbers using greater than, less than, and equal to.

Prior Learning

In kindergarten, students counted to 100 by 1s and 10s. They began at any given number within the known sequence. They wrote and represented numbers from 0–20 and represented a number of objects with a written numeral 0–20. Students compared the number of objects in one group to the number of objects in another group. Students also compared two numbers between 1 and 10 presented as written numerals.

Current Learning

This is a critical area in Grade 1.

Read the overview of the K–5 Number and Operations in Base 10 Learning Progressions for background information for this unit. Teachers may create numeral lists and visual supports as teaching tools (p. 6). Earlier in the year, students write and read numerals 0 to 30. The reading, writing, and representing of numerals 31–60 are being taught at the developmental level in this unit. Also, students compare two 2-digit numbers up to 30 using concrete materials and oral discussion. In this unit, students compare two 2-

digit numbers up to 60 at the developmental level. Continue to reinforce comparing numbers within the range of 0–30.

The emphasis for students is on understanding the concept of equality, not limited to the appropriate use of the equal symbol in comparing numbers. The concept of equality is reinforced, but using the equal symbol to compare two 2-digit numbers is at the developmental level. See CCSS Glossary p. 90 Table 4 for the properties of equality, in particular the Reflexive Property of Equality. Later in the year, students use the symbols for greater than and less than to compare numbers up to 120. Students also read, write, and represent numbers up to 120 based on meanings of tens and ones.

Future Learning

In grade 2, students will read and write numbers up to 1,000. They will compare three-digit numbers using the symbols for greater than, less than, and the equal symbol.

Home

Trimester 3

Unit One - Finding Tens to add and Subtract (10 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Add and subtract within 20.

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).

• Relate counting to addition and subtraction.

• Add and subtract within 20 using multiple efficient strategies (e.g., counting on, making ten, relating addition to subtraction, etc.)

• Understand the meaning of the equal sign involving addition and subtraction.

What is the relationship between addition and subtraction?

Add _____ to ____.  What is the sum?

Find the difference between ______ and ______.

Find a pattern (odds/evens, 5's, 2's, 10's) on the number grid.

1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution by...

  • using objects and/or pictures to understand and solve problems
  • check their work to be sure it makes sense.

Reason abstractly and quantitatively

attend to meaning of quantities

Identify which operations will be used

Use objects, equations,  and/or drawings to solve problems.

Prior Learning

In kindergarten, students represented addition and subtraction word problems with pictures, sounds, and mental images or equations. Students also decomposed numbers ten and less into pairs more than one way. They used pictures or objects and recorded the decomposition by a drawing or equation. When given any number 1–9, students found the number that made ten by using objects or drawings. Students fluently added and subtracted within 5.

Current Learning

This is a critical area in Grade 1.  In the CCSS, strategies such as counting on, making ten, decomposing a number leading to a ten, and using the relationship between addition and subtraction are used. Students create equivalent but easier known sums. Another developmental skill is to understand the meaning of the equal sign involving addition and subtraction.

Future Learning

In grade 2, students will use addition and subtraction within 100 in all situations to solve one- and two-step word problems with unknowns in all positions. Students will fluently add and subtract within 20 using mental strategies. They will know, from memory, all sums of two one-digit numbers.

Home

Unit Two - Applying Addition and Subtraction to Solve Story Problems (10 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Represent and solve problems involving addition and subtraction.

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.

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.6 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.)

• Use addition and subtraction within 20 to solve word problems (adding to, taking from, putting together, taking apart, and comparing) by using objects, drawing, and equations with symbols for the unknown number to represent the problem. (See CCSS glossary, Table 1.)

• Solve word problems adding three whole numbers whose sum is less than or equal to 20 by using objects and drawings.

• Apply the Associative Property of Addition as a strategy to add and subtract (e.g., To add 2 + 6 + 4, the second two numbers can be added to make a 10, so 2 + 6 + 4 = 2 + 10 = 12).

Draw a picture and write an equation to solve this number story.

What is the relationship between addition and subtraction?

How do you know that:

8+3=11

3+8=11?

1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.

  • Use objects, pictures, and/or equations to understand and solve problems
  • Check their work to be sure their solution makes sense

Prior Learning

In kindergarten, students represented addition and subtraction word problems with pictures, sounds and mental images, or equations. They also decomposed numbers 10 and less into pairs more than one way.  Students used pictures or objects and recorded the decomposition by a drawing or equation. When given any number 1–9, they found the number that made 10 by using objects or drawings. Students fluently

added and subtracted within five.

Current Learning

This is a critical area of instruction for grade 1.

Students use strategies such as counting on, making 10, doubles, near doubles, fact families, etc. They understand the meaning of the equal sign involving addition and subtraction.

In this unit, students solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (See CCSS glossary, Table 1.)

Future Learning

In grade 2, students will use addition and subtraction within 100 in all situations to solve one- and two-step word problems with unknowns in all positions. Reference CCSS, page 88, Table 1: Common addition and subtraction situations. Students will fluently add and subtract within 20 using mental strategies. They will know from memory all sums of two 1-digit numbers.

Home

Unit Three- Applying Numbers from 1 to 20  (10 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Work with addition and subtraction equations.

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 = o – 3, 6 + 6 = o.

Number and Operations in Base Ten 1.NBT

Use place value understanding and properties of operations to add and subtract.

1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

• Determine the unknown whole number in an addition or subtraction equation

• Add a two-digit number and one-digit number within 100 using concrete models or drawings and strategies based on place value.

• Add a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value.

• Mentally find 10 more or 10 less than a two-digit number without having to count, and explain the reasoning used.

How do you find the missing value in these equations?

____ + 6 = 15

4 + 9 = ____

____ - 6 = 3

Explain what a fact family is.

Create an addition or subtraction problem using manipulatives.

6 Attend to precision.

Mathematically proficient students try to communicate precisely to others.

  • Communicate precisely
  • Interpret the meaning of symbols on an equation

8 Look for and express regularity in repeated reasoning.

  • Notice repeated addition and subtraction patterns
  • Notice patterns within their work
  • Understand if and why an answer is reasonable

Prior Learning

In kindergarten, students added and subtracted within 10 and did so fluently within 5.

Current Learning

This is a critical area in grade 1.

Skills taught at the developmental level are as follows:

• Students add within 100, including adding a two-digit number and a one-digit number and a two-digit number and a multiple of 10 (using open number lines, 10 frames, number grid, bundles). They should relate their strategies to a written method and explain the reasoning used.

• Students mentally find 10 more or 10 less without counting, given a two-digit number, and explain the reasoning used.

Future Learning:

In grade 2, students will add and subtract within 100 using strategies based on place value and properties of operations and/or relationships between addition and subtraction. In addition, they will mentally add and subtract 10 or 100 to a given number 100–900.

Home

Unit Four - Developing Equal Shares of Circles and Rectangles  (12 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Reason with shapes and their attributes.

1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

• Partition circles into two and four equal shares.

• Partition rectangles into two and four equal shares.

• Describe the shares using the word halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.

• Describe the whole as two of or four of the shares.

• Understand that decomposing into more equal shares creates smaller shares.

How do you know shares are equal?

Break this shape into:

halves

quarters

How many squares can fit into this rectangle?

3.  Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.

Use concrete objects, pictures, diagrams, and actions to solve and understand problems and solutions.

  • Listen to others work and solutions and tell whether they make sense and why.

Prior Learning

In kindergarten, students composed simple shapes to form larger shapes. They identified shapes as two or three-dimensional. They also built and drew shapes.

Current Learning

Earlier in grade 1, students compose simple shapes to form larger shapes, so they understand that a whole can be composed of smaller parts. This is taught at the reinforcement level. In this unit, students build on this concept by recognizing that fractional parts of a whole must be equal in size. They can decompose these shapes into two or four equal shares. Students use mathematical terms to describe the whole and its fractional parts (half of, fourth of, quarter of, halves, fourths, equal share, whole). This is taught at the developmental level. These skills are not considered a critical area of focus for grade 1. According to A Research Companion to Principles and Standards for School

 

Mathematics, a conceptual breakthrough for students is to understand that the magnitude of a quantity (e.g., the whole) is unchanged when the size of the shares changes. (p. 101) conceptualizing fractions is based on conceiving two quantities as being in a reciprocal relationship of relative size. For example, if a share is one half of the size of the whole, then the whole is twice as large as the share. (p. 107)

Future Learning

In grade 2, students will decompose circles and rectangles into thirds and describe the whole as three of the shares. The shares are equal and smaller. Students will partition a rectangle into rows and columns of same-size squares and count to find the total number of them. In addition, students will partition circles and rectangles into three equal shares and describe the shares using the words thirds and a third of, and they will describe the whole as three thirds.

Finally, they will recognize that equal shares of identical wholes need not have the same shape. Grade 3 will be the first time students represent equal shares of a figure using fraction notation (e.g., 1/2, 1/3, 1/4, 3/4).

Home

Unit Five - Reasoning with Shapes and their Attributes  (9 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Reason with shapes and their attributes.

1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

• Build and draw shapes possessing defining attributes.

• Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half circles and quarter circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular

cones and right circular cylinders) to create a composite shape.

• Compose new shapes from the composite shape.

What is this shape called?  How do you know?

How can these shapes fit together to form larger shapes (i.e., 2-D shapes such as tangram puzzles, or paper shapes)?

Now, how can you use this new shape to form more (2-D) shapes?

How can these shapes fit together to form larger shapes (i.e., 3-D shapes)?

Now how can you use this new shape to form more (3-D) shapes?

3 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.

  • Use concrete objects, pictures, diagrams, and actions to solve and understand a problem/solution.
  • Listen to other work solutions and whether they make sense and why

Prior Learning

In kindergarten, students composed simple shapes to form larger shapes (e.g., Can you join these two triangles with full sides touching to make a rectangle?) They also identified shapes as two-dimensional or three-dimensional.

Current Learning

In grade 1, students put together 2-D shapes (such as triangles) to compose other geometric shapes (such as a trapezoid). They put together 2-D shapes (such as a square and a rectangle) to create a composite shape (such as a house). These are being taught at the reinforcement level in grade 1. At the developmental level, students take apart a 2-D composite shape to make a new shape.

Also, students put together 3-D shapes (such as cubes) to compose other geometric shapes (such as rectangular prisms). They put together 3-D shapes (such as cubes and a cone) to create a composite shape (such as a rocket). Students take apart a 3-D composite shape to make a new shape. These skills are being taught at the developmental level. Teachers can reference van Hiele Theory of Geometric Thought for the levels of understanding. Also, reference Elementary and Middle School Mathematics (p. 353) by John A, Van De Walle for the four types of tangram puzzles that illustrate the range of difficulty levels.

Future Learning

In second grade, students will recognize and draw shapes having specified attributes (e.g., number of angles or a given number of equal faces). They will identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

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Unit Six - Applying Addition and Subtraction Strategies (9 days)

North Carolina Unpacking Document - Grade One

Progressions Document -  Number and Operations in Base Ten (NBT)

Progressions Document - Operations and Algebraic Thinking (OA)

Progressions Document - Geometry (G)

Progressions Document - Measurement and Data (MD) - Measurement Part

Progressions Document - Measurement and Data (MD) - Data Part

Common Core Standards/ 

Content to Be Learned

Essential Questions/

Instructional Questions

Mathematical Practices/Prior Learning, Current Learning and Future Learning

Add and subtract within 20.

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).

Work with addition and subtraction equations.

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 = o – 3, 6 + 6 = o.

Number and Operations in Base Ten 1.NBT

Use place value understanding and properties of operations to add and subtract.

1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 

• Determine the unknown whole number in an addition or subtraction equation

• Add a two-digit number and one-digit number within 100 using concrete models or drawings and strategies based on place value.

• Add a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value.

• Mentally find 10 more or 10 less than a two-digit number without having to count, and explain the reasoning used.

How do you find the missing value in these equations?

____ + 6 = 15

4 + 9 = ____

____ - 6 = 3

Explain what a fact family is.

Create an addition or subtraction problem using manipulatives.

6 Attend to precision.

Mathematically proficient students try to communicate precisely to others.

  • Communicate precisely
  • Interpret the meaning of symbols on an equation

8 Look for and express regularity in repeated reasoning.

  • Notice repeated addition and subtraction patterns
  • Notice patterns within their work
  • Understand if and why an answer is reasonable

Prior Learning

In kindergarten, students added and subtracted within 10 and did so fluently within 5.

Current Learning

This is a critical area in grade 1.

Skills taught at the developmental level are as follows:

• Students add within 100, including adding a two-digit number and a one-digit number and a two-digit number and a multiple of 10 (using open number lines, 10 frames, number grid, bundles). They should relate their strategies to a written method and explain the reasoning used.

• Students mentally find 10 more or 10 less without counting, given a two-digit number, and explain the reasoning used.

Future Learning:

In grade 2, students will add and subtract within 100 using strategies based on place value and properties of operations and/or relationships between addition and subtraction. In addition, they will mentally add and subtract 10 or 100 to a given number 100–900.

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Adapted from the Charles A. Dana Center work with SORICO 2012