From stones, sticks and caves for a few of us 
. to . 
smart factories and nice houses for millions of us?? 


>>> 
SUBJECT: – Mathematics: Grades K5 Counting and Place Value  from the beginning
INSTRUCTIONAL GOAL: Students should be able to appreciate the value of counting, grouping and place values in number systems to civilization, through history and into the future.
OBJECTIVE:
To
help students learn about and appreciate how, from ancient times our
ancestors began to use the concepts of units, counting,
grouping and, with the smart assistance of objects, symbols, and
number systems as tools to measure,
record and keep track of quantities in the
environment, use them to improve our
lives from the cavedwelling times to the present, and into the
future.
CA Common Core K5 Mathematics Standards: Common CoreMathematics Standards (DOCUMENT) Conceptual understanding: The standards call for conceptual understanding of key concepts, such as Numbers, Place Values and Operations in Base Ten.

Grade K 
Work with numbers 1119 to gain foundations for place value.CCSS.Math.Content.K.NBT.A.1 


Grade 1 
Extend the counting sequence.CCSS.Math.Content.1.NBT.A.1 Understand place value.
CCSS.Math.Content.1.NBT.B.2
CCSS.Math.Content.1.NBT.B.2.a
CCSS.Math.Content.1.NBT.B.2.b
CCSS.Math.Content.1.NBT.B.2.c CCSS.Math.Content.1.NBT.B.3 Use place value understanding and properties of operations to add and subtract.
CCSS.Math.Content.1.NBT.C.4
CCSS.Math.Content.1.NBT.C.5 CCSS.Math.Content.1.NBT.C.6 


Grade 2 
Understand place value.
CCSS.Math.Content.2.NBT.A.1
CCSS.Math.Content.2.NBT.A.1.a
CCSS.Math.Content.2.NBT.A.1.b
CCSS.Math.Content.2.NBT.A.2
CCSS.Math.Content.2.NBT.A.3 CCSS.Math.Content.2.NBT.A.4 Use place value understanding and properties of operations to add and subtract.
CCSS.Math.Content.2.NBT.B.5
CCSS.Math.Content.2.NBT.B.6
CCSS.Math.Content.2.NBT.B.7
CCSS.Math.Content.2.NBT.B.8 CCSS.Math.Content.2.NBT.B.9 


Grade 3 
Use place value understanding and properties of operations to perform multidigit arithmetic.¹
CCSS.Math.Content.3.NBT.A.1
CCSS.Math.Content.3.NBT.A.2 CCSS.Math.Content.3.NBT.A.3 


Grade 4 
Generalize place value understanding for multidigit whole numbers.
CCSS.Math.Content.4.NBT.A.1
CCSS.Math.Content.4.NBT.A.2 CCSS.Math.Content.4.NBT.A.3 Use place value understanding and properties of operations to perform multidigit arithmetic.
CCSS.Math.Content.4.NBT.B.4
CCSS.Math.Content.4.NBT.B.5 CCSS.Math.Content.4.NBT.B.6 




Grade 5 
Understand the place value system.
CCSS.Math.Content.5.NBT.A.1
CCSS.Math.Content.5.NBT.A.2
CCSS.Math.Content.5.NBT.A.3
CCSS.Math.Content.5.NBT.A.3.a
CCSS.Math.Content.5.NBT.A.3.b CCSS.Math.Content.5.NBT.A.4 Perform operations with multidigit whole numbers and with decimals to hundredths.
CCSS.Math.Content.5.NBT.B.5
CCSS.Math.Content.5.NBT.B.6 CCSS.Math.Content.5.NBT.B.7 



MATERIALS AND AIDS (what you will need in order to teach this lesson)
An audiovisual computer classroom allowing each individual student to access the Internet at a reasonable speed for moderatetofast multimedia content.
Each station (teacher and student) should have installed the most recent Mozilla Firefox, Google Chrome, or Microsoft Explorer browser, or Apple Safari browser that includes a fullfunctioning Adobe Flash media player.
PROCEDURE
This lesson uses a "seethinkanddo" approach, supported with focused interactive multimedia minilesson activities related to the Common CoreMathematics Standards Number base ten representations and Operations. The content is guided by a narrative webpage Its a Binary world, and the New Generation Science Standards for 35 th grades. This lesson is proposed for convenient delivery of context and including sufficient handson opportunities for students to experience additional, expanded, focused activity sessions.
INSTRUCTIONAL GOAL Students should be able to begin to appreciate the purpose and value of defining "units" of substance and work with them and integrating (counting) them as parts of larger amounts of the same substance (measurement). Students should also be able to see and experience diverse number systems as smarter ways to represent and manipulate larger amounts of substance integrated in consistent groups (number base grouping of quantity).
PERFORMANCE OBJECTIVE In the end, students should be able to identify and represent correctly various common, small and large numbers in different base systems over 90% of the time . In particular, students should be able to represent and manipulate (add, subtract and multiply) Decimal, base Ten numbers into their corresponding Binary, Base Two equivalents 100% of the time.
RATIONALE An understanding of the nature and form of the Decimal and Binary number representations is helpful in providing a strong foundation and confidence in students for understanding present and future tools of computing, telecommunications and automation we see today and in the future.
LESSON CONTENT: This lesson includes participatory physical and virtual demonstration activities that stimulate the students perceptual and tactile abilities and common sense through reallife objects, coherent animation and computer interactivities. The narrative includes:
PART 1: An initial introduction to ancient and present base number systems
PART 2: Representation of FRACTIONS in different base number systems
PART 3: An introduction to basic manipulation (ADDITION,
SUBTRACTION and MULTIPLICATION) for quantities represented in
different base number systems. The focus is on the mastering of the
humanfocused Decimal and the computerfocused Binary, base 2 number
systems.
INSTRUCTIONAL PROCEDURES:
SESSION 1 : An introduction to Number Systems Structures  Counting and Place Value, from ancient times. Students will be presented first with access from their individual computer stations to the main narrative: Its a Binary world (DOCUMENT). The narrative INTRODUCTION presents a series of preliminary ideas and includes links to the most relevant number and base systems in human history:
HindiArabic, Small decimal numbers, Counting Pennies, Counting Weights, Guess the Number, Rounding and Truncating, Rounding Practice Worksheet , Comparing small block counts , Comparing numbers in Decimal , Play skipcount , Addition and subtraction
Binary, Coding numbers in binary , Interactive practice , Worksheet
To conclude their reading, students should fill in the worksheet Multiple representation of numbers.
The INTRODUCTION section includes also a reference to the
optimality of the Binary system (Shannons's Information Entropy
Theorem), and lowest error probabilities due to minimal ambiguity in
the physical definition of its only TWO distinguishable states (0, 1
or OFF, ON) for each of the place value positions. This allows for
extraordinary efficiencies and further reliability through datablock
integrity checks (Checksum) implemented in current electronic and
electromagnetic information technologies .
After
completing the review and practice work in the INTRODUCTION, students
wil be asked to explore through the REPRESENTATION
and FRACTIONS sections of the narrative.
SESSION 2 : The Concept of FRACTIONS, Why? How?  Free Fractioning and Base Fractioning, From Ancient times. In this session, the students will be invited to access section 4 FRACTIONS of the narrative (Its a Binary world) from their individual computer stations to explore the basic concept and applications of fractions. Students will also be asked to explore the various displays and activities in the section FRACTIONS AND DECIMALS of the Animated Math activities.
SESSION 3 : An introduction to Number Systems Operations  Counting and Place Value, from ancient times. Students will be requested to explore the ADDITION, SUBTRACTION and MULTIPPLICATION section of the main narrative (Its a Binary world).
ADDITION and SUBTRACTING Decimal: Adding by Counting up, Blocks, Right to Left, Blocks, Lefttoright , Subtracting by Counting Down , Adding with Mechanical Pinions
ADDITION: Binary practice with symbols, Binary addition and subtraction animation, Worksheet. For example, try the following: a) 12 + 8, b) 1250 + 875, and c) 2014 + 100.
MULTIPLICATION DECIMAL: Basic tables and Division , With symbols , With fractions
MULTILICATION BINARY: With symbols , Animation
A view of devices and instruments for the various number bases. Students will be requested to explore the THE PAST, THE PRESENT, AND THE FUTURE section of the main narrative (Its a Binary world), and offer their own thoughts and conclusion about the evolution and usefulness of the various number Bases and devices that helped civilizations though history, and the possible future with the Binary, or possible new number systems. Students write down their thoughts and submit the papers for teacher review.