THINKING WITH NUMBERS
Common Core Alignment
Common Core State Standards
For Mathematical Practice
1.   Make sense of problems and persevere in solving them.
2.   Reason abstractly and quantitatively.
3.   Construct viable arguments and critique the reasoning of others.
4.   Model with mathematics.
5.   Use appropriate tools strategically.
6.   Attend to precision.
7.   Look for and make use of structure.
8.   Look for and express regularity in repeated reasoning.
The Standards For Mathematical Practice are an integral part of
Thinking With Numbers Lessons.
Thinking With Numbers Lessons Aligned To
Common Core State Standards For Mathematics

Lessons
Chapter 1: The Ten Frame
Part 1: How Many Dots Did You See?
Part 2: How Many Empty Boxes Are There?
Part 3: Challenge: How Many Dots Were There?

This chapter is important because children will develop a mental structure that enables them to solve addition and subtraction problems. For example, it will not take long for children to recognize that when the top row is filled and one box in the bottom row is filled, there are 6 boxes filled (5 and 1 more is 6), or when there is one empty box, 9 boxes are filled (1 less than 10 is 9). Using 5 and 10 as benchmarks prepares them for more sophisticated reasoning strategies with larger numbers.

Content Standards

Kindergarten:
K.CC.A Know number names and the count sequence

K.CC.B Count to tell the number of objects

K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Chapter 2: Making Sense of Addition
Part 1: Joining: How Many In All?
Part 2: Describing: How Many In All?

This chapter will help children make sense of addition problems they encounter in school. By providing enough time for children to make sense of these problems with the ten frame structure, they will not need to count from 1 each time to answer addition problems. They will begin to develop more sophisticated strategies, which will help them later with larger numbers.

Content Standards

Kindergarten:
K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

This chapter will enable children to understand equals and the use of the equals sign. It will eliminate common misunderstandings of children who believe that it is incorrect to write 6 = 2 + 4 or that the answer to 3 + ? = 5 is 8.

Content Standards

Kindergarten:
K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

1.OA.D Work with addition and subtraction equations.

Chapter 4: Parts of Numbers
Part 1: Number Patterns
Part 2: What Parts Do You See?
Part 3: More Parts

This chapter will encourage children to look for patterns that will help them decompose numbers into parts that make sense to them. These skills are particularly helpful to children as they begin to make sense of subtraction.

Content Standards

Kindergarten:
K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

1.OA.D Work with addition and subtraction equations.

Chapter 5: Making Sense Of Subtraction
Part 1: Separating: How Many Are Hidden?
Part 2: Describing: What Is The Other Part?

This chapter will help children make sense of the first subtraction problems they encounter in school. By providing enough time for children to make sense of these problems with the ten frame structure, they will not need to count from 1 each time to answer subtraction problems. They will begin to develop more sophisticated strategies, which will help them later with larger numbers.

Content Standards

Kindergarten:
K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

Chapter 6: Equals With Subtraction

This chapter will enable children to understand equals and the use of the equals sign. It will eliminate common misunderstandings of children who believe that it is incorrect to write 2 = 6 - 4 or that the answer to ? - 3 = 7 is 4.

Content Standards

Kindergarten:
K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

1.OA.D Work with addition and subtraction equations.

Chapter 7: Equalizing

This chapter will encourage children to decompose numbers in different ways, then adding and/or subtracting can change one or both numbers to make them equal. These lessons will help children develop flexibility in their thinking, especially if they look for more than one solution.

Content Standards

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

1.OA.D Work with addition and subtraction equations.

Chapter 8: Relating Addition and Subtraction
Part 1: Joining: How Many More?
Part 4: Separating: How Many Moved?

This chapter will help children make sense of relationships between addition and subtraction (part + part = whole and whole - part = other part) so they can make sense of a variety of problem structures they will encounter in everyday life. The problems is this chapter include start numbers and change numbers unknown for both joining and separating.

Content Standards

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

1.OA.D Work with addition and subtraction equations.

2.OA.A Represent and solve problems involving addition and subtraction.

Chapter 9: The Number Line
Part 1: How Many Boxes Did You See?
Part 2: How Long Is This Box?

This chapter meaningfully introduces the number line by connecting the number of boxes shown to the units on the number line itself. It also helps children make sense of units of length. This different way of representing numbers is extremely using for problems with larger numbers.

Content Standards

Kindergarten:
K.CC.A Know number names and the count sequence

K.CC.B Count to tell the number of objects

Chapter 10: Making Sense Of Comparison
Part 1: What Is The Difference?
Part 2: What Is The Large Set?
Part 3: What Is The Small Set?

This chapter will help children make sense of comparison situations in everyday life. By providing enough time for children to make sense of these problems with the number line, they will comfortably be able to use addition and subtraction to solve a variety of comparison situations in everyday life, including large set unknown and small set unknown.

Content Standards

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

1.OA.D Work with addition and subtraction equations.

2.OA.A Represent and solve problems involving addition and subtraction.

Chapter 11: Reasoning Strategies For Addition
Part 1: Counting On
Part 2: Using Ten
Part 3: Using Known Facts
Part 4: Flexible Use Of Strategies

This chapter formally introduces addition reasoning strategies. Practice using these strategies, not drill on fact answers, is very important because flexible and fluent use of these strategies will enable children to very quickly solve addition facts and provide ways of thinking that will enable them to solve problems with larger numbers. These strategies are key to helping children make progress with the mathematics curriculum in the middle grades.

Content Standards

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

1.OA.D Work with addition and subtraction equations.

1.NBT.A Extend the counting sequence.

1.NBT.B Understand place value.

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

2.OA.A Represent and solve problems involving addition and subtraction.

2.OA.B Understand place value.

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

Chapter 12: Reasoning Strategies For Subtraction
Part 1: Counting Back
Part 2: Counting Up
Part 3: Using Ten
Part 4: Using Known Facts
Part 5: Flexible Use Of Strategies

This chapter formally introduces subtraction reasoning strategies. Practice using these strategies, not drill on fact answers, is very important because flexible and fluent use of these strategies will enable children to very quickly solve subtraction facts and provide ways of thinking that will enable them to solve problems with larger numbers. These strategies are key to helping children make progress with the mathematics curriculum in the middle grades.

Content Standards

1.OA.A Represent and solve problems involving addition and subtraction.

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.C Add and subtract within 20.

1.OA.D Work with addition and subtraction equations.

1.NBT.A Extend the counting sequence.

1.NBT.B Understand place value.

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