Module Overview: (K-2) Math Foundations
Session
Type
Time (Hours)
- (K-2) Intro to Number Sense
- (K-2) Counting and Cardinality
- (K-2) Tens and Ones
- (K-2) Place Value
- (K-2) Math Foundations
Session 1 (K-2) Overview: Introduction to Number Sense
Session Objectives
The teacher will describe the history and development of the base-ten system
The teacher will analyze how numbers are built from a system of ten units
The teacher will define number sense and explain the progression of number sense understanding in elementary school
Key Ideas
The creation of our base-ten system was an important and remarkable jump in mathematics for humanity.
Ten ones compose a new unit called a ten. Ten tens make a unit called a hundred. Because ten units make a unit of the next highest value, only ten digits are needed to represent any quantity in base-ten.
Students develop number sense gradually through exploring numbers, visualizing them in a variety of contexts, and relating them to real world situations.
1.1 (K-2) Welcome
1.1 (K-2) Welcome
Welcome to Introduction to Number Sense! By the end of this module, you will be able to define number sense, understand the base-ten number system, and explain how number sense understanding progresses in elementary school. You’ll accomplish this by watching a video about the history of the base-ten system, reading about the components of number sense, and analyzing student work for evidence of number sense understanding and misunderstanding.
In this session, you’ll…
Learn about the history of our base-ten number system. The base-ten number system emerged as civilizations became more advanced and needed a more sophisticated way to count and keep track of goods (Blitzer, 2011). By learning about the history of the base-ten number system, you will deepen your understanding of number sense and place value.
Read about number sense development. Children are born with an intuitive sense of numbers and the concepts of more and less. Most children by the age of two years old can accurately and confidently identify one, two, or three objects (Gelman & Gellistel, 1978). Although very young children might be able to identify small quantities, they lack a critical counting understanding. You’ll learn about the six different components of number sense, and you’ll practice looking at student work samples for evidence of number sense understanding and misunderstanding.
(K-2) History of the Base-Ten Number System
“Numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession. ”
– Hermann Weyl
As Weyl stated, we have given meaning to numbers through our number system. As such, it is important to clearly communicate the idea of numbers and the number system to your students. Understanding the foundations of our number system helps students understand how we’ve created and applied the “simple rule of straight succession.” In these videos, you will learn about the history of our numeration system – the Hindu-Arabic system – and learn how numerals were created to count and keep track of quantities.
Use your handout to take notes as you watch the videos. You can click here Download here to download the online handout. You’ll use this handout for sessions one through four.
Note: Depending on your browser, to view the videos in full-screen, you may see the full-screen icon on the lower right of the video player on the CP or need to right-click on the video to open in a new window.
HISTORY OF THE BASE TEN SYSTEM: PART I
As you watch, answer the following guiding questions:
(Please ignore the reference to the old course code, MATH-101, on the title slide of this video.)
Where was the base-ten system created?
How was the base-ten system spread to the modern world?
What is the role of zero in the base-ten system?
HISTORY OF THE BASE TEN SYSTEM: PART II
As you watch, answer the following guiding questions:
(Please ignore the reference to the old course code, MATH-101, on the title slide of this video.)
What are the guiding principles of the base-ten number system?
How is the base-ten system different from other systems?
1.4 (K-2) What is Number Sense?
This page is part of the module MODULE 6: K-2 Math Foundations and hasn’t been unlocked yet.
Completion Prerequisites
The following requirements need to be completed before this page will be unlocked:
MODULE 6: K-2 Math Foundations
1.3 (K-2) Check Your Understanding
must submit the assignment
1.4 (K-2) What is Number Sense
1.5 (K-2) Components of Number Sense
This page is part of the module MODULE 6: K-2 Math Foundations and hasn’t been unlocked yet.
Completion Prerequisites
The following requirements need to be completed before this page will be unlocked:
MODULE 6: K-2 Math Foundations
1.3 (K-2) Check Your Understanding
must submit the assignment
1.4 (K-2) What is Number Sense?
must view the page
1.5 (K-2) Components of Number Sense
must view the page
1.6 (K-2) Number Sense Analysis
This page is part of the module MODULE 6: K-2 Math Foundations and hasn’t been unlocked yet.
Completion Prerequisites
The following requirements need to be completed before this page will be unlocked:
MODULE 6: K-2 Math Foundations
1.3 (K-2) Check Your Understanding
must submit the assignment
1.4 (K-2) What is Number Sense?
must view the page
1.5 (K-2) Components of Number Sense
must view the page
1.6 (K-2) Number Sense Analysis
must view the page
Completion Prerequisites
The following requirements need to be completed before this page will be unlocked:
MODULE 6: K-2 Math Foundations
1.3 (K-2) Check Your Understanding
must submit the assignment
1.4 (K-2) What is Number Sense?