## Virginia Standards of Learning Kindergarten v Peano Axioms

http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/sol_ccss_comparison_mathematics.pdf

Page 7 to 9

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and Cardinality K.CC
Know number names and the count sequence.
1. Count to 100 by ones and by tens. K.4 The student will
a) count forward to 100 and backward from 10;
b) identify one more than a number and one less than a number;
and
c) count by fives and tens to 100.
2. Count forward beginning from a given number within the
known sequence (instead of having to begin at 1).
K.4 The student will
a) count forward to 100 and backward from 10;
b) identify one more than a number and one less than a
number; and
c) count by fives and tens to 100.
3. Write numbers from 0 to 20. Represent a number of objects
with a written numeral 0‐20 (with 0 representing a count of no
objects).
K.2 The student, given a set containing 15 or fewer concrete
objects, will
a) tell how many are in the set by counting the number of
objects orally;
b) write the numeral to tell how many are in the set; and
c) select the corresponding numeral from a given set of
numerals.
1.1 The student will
a) count from 0 to 100 and write the corresponding numerals;
and
b) group a collection of up to 100 objects into tens and ones and
write the corresponding numeral to develop an understanding
of place value.
Count to tell the number of objects.
4. Understand the relationship between numbers and quantities;
connect counting to cardinality.
a. When counting objects, say the number names in the
standard
K.1 The student, given two sets, each containing 10 or fewer
concrete objects, will identify and describe one set as having

..

CCSS for Mathematics – Kindergarten Mathematics SOL
subtract within 10, e.g., by using objects or drawings to
represent the problem.
K.6 The student will model adding and subtracting whole
numbers, using up to 10 concrete objects.
1.6 The student will create and solve one‐step story and picture
problems using basic addition facts with sums to 18 or less and
the corresponding subtraction facts.
3. Decompose numbers less than or equal to 10 into pairs in
more than one way, e.g., by using objects or drawings, and
record each decomposition by a drawing or equation (e.g., 5 = 2
+ 3 and 5 = 4 + 1).
K.6 The student will model adding and subtracting whole
numbers, using up to 10 concrete objects.
1.18 The student will demonstrate an understanding of equality
through the use of the equal sign.
1.18 CF
• Model an equation that represents the relationship of two
expressions of equal value.
4. For any number from 1 to 9, find the number that makes 10
when added to the given number, e.g., by using objects or
drawings, and record the answer with a drawing or equation.
K.6 The student will model adding and subtracting whole
numbers, using up to 10 concrete objects.
1.5 The student will recall basic addition facts with sums to 18
or less and the corresponding subtraction facts.
5. Fluently add and subtract within 5. 1.5 The student will recall basic addition facts with sums to 18
or less and the corresponding subtraction facts.
Number and Operations in Base Ten K.NBT
Work with numbers 11–19 to gain foundations for place value.
1. Compose and decompose numbers from 11 to 19 into ten
ones and some further ones, e.g., by using objects or drawings,
and record each composition or decomposition by a drawing or
equation (e.g., 18 = 10 + 8); understand that these numbers are
composed of ten ones and one, two, three, four, five, six, seven,
eight, or nine ones.
1.1 The student will
a) count from 0 to 100 and write the corresponding numerals;
and
b) group a collection of up to 100 objects into tens and ones and
write the corresponding numeral to develop an understanding
of place value.
1.5 The student will recall basic addition facts with sums to 18
or less and the corresponding subtraction facts.

==

http://www.doe.virginia.gov/testing/common_core/index.shtml

==Compare to

http://newmathdoneright.com/2012/05/14/peano-axioms-number-line/

1. Zero is a unique tick on the number line.
2. For each tick on the number line, there exists a unique tick immediately to the right of it.
3. Zero is not a tick to the right of another tick.
4. If the ticks to the right of two ticks are equal, then said two ticks are equal.
5. If a set contains zero and each tick to the right of a tick, then it contains all the ticks on the number line.

http://newmathdoneright.com/2012/08/16/lucky-duck-induction/

Zero is a lucky duck.

Each lucky duck is a mom lucky duck.

Zero is not a baby lucky duck.

Each baby lucky duck has exactly one mom lucky duck.

If a farm has the zero lucky duck and the baby lucky duck of
each mom lucky duck on the farm, then the farm has all the lucky ducks.

http://newmathdoneright.com/2012/08/13/peano-axioms-in-21-words-126-characters/

1. Zero a tick.
2. A tick then a tick.
3. Zero no mom.
4. Not zero, one mom.
5. Zero green, green transfers, all green.

21 words 126 letters

http://newmathdoneright.com/2012/08/13/the-principle-of-math-induction-is-common-sense/

http://newmathdoneright.com/2012/08/13/the-principle-of-green-tree-induction/

http://newmathdoneright.com/2012/08/13/the-principle-of-green-induction/

The Principle of Green Induction is

1) If the first is green

2) If stage n is green then stage n’ is green

Then

All stages are green.

Another version of this is

The Principle of Green Induction is

1) If the first stage is green

2) If green transfers for any stage

Then

All stages are green.

http://newmathdoneright.com/2012/08/13/the-marie-antoinette-principle-of-induction/

http://newmathdoneright.com/2012/08/13/the-principle-of-tweet-induction/

http://newmathdoneright.com/2012/05/13/pair-of-number-lines-and-successor-identities/