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[quote=Anonymous][quote=Anonymous]There is a huge leap to the next set of math standards which require algebraic thinking.  For kids who start school without being able to count, that is a pretty big leap.  Sure, some could do it, but most could not.[/quote]

Do you mean the standards that come next in Kindergarten?

Either these (The rest of the Kindergarten Counting and Cardinality standards)

Compare numbers.

CCSS.MATH.CONTENT.K.CC.C.6
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1

CCSS.MATH.CONTENT.K.CC.C.7
Compare two numbers between 1 and 10 presented as written numerals.

Or these (The Operations and Algebraic Thinking  Standards for K)

Understand addition, and understand subtraction.

CCSS.MATH.CONTENT.K.OA.A.1
Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

CCSS.MATH.CONTENT.K.OA.A.2
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

CCSS.MATH.CONTENT.K.OA.A.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).

[b]CCSS.MATH.CONTENT.K.OA.A.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.
[/b]
CCSS.MATH.CONTENT.K.OA.A.5
Fluently add and subtract within 5.

Or do you mean what comes after them in first grade?

I've bolded the most "Algebraic" standard above.  Here's what a related lesson might look like in my class:

[i]This is probably closest to Algebraic Thinking of the K standards.  Here's how I'd teach this lesson in a mixed group with some kids who had already mastered the counting and cardinality standards, and some who were still working on this.

Step 1:  Give each kid in the group a 10's frame.  Kids who are at grade level (e.g. still working on counting) or below (don't get counting even though it's February) get an egg carton with 2 sections cut off.  Higher kids might get an egg carton too, or they might get a piece of paper with a rectangle sectioned into 2 rows of 5.

Step 2:  Show the kids a number less than 10, let's say 4.

Step 3:  Have each kid count out 4 of the same color counters (could have a different color than their neighbor, but all 4 in a set should be the same), and put 1 counter in 1 hole/space on their 10's frame.  Help kids below grade level.

Step 4: Have a quick conversation about how we know that's 4.  Lower level kids might give, or be prompted to give an answer like "because I can see it's 4" (subitizing) or "I can count it again to check".  Kids above grade level might come up with "I only have 1 space left in the top 5, so I know it's 4" or "I counted them before I put them in, and I didn't change the set".

Step 5: Ask the kids how many spaces are empty.  Kids on grade level will solve by counting.  Kids above grade level may notice that you have a whole row of 5 and 1 more.  Either way, they should come to the idea that there are six left.

Step 6: Pick new colors, make sets of 6, drop them in one hole at a time.  Count to confirm.  Help kids below grade level.

Step 7: Look at what you've made!  You've shown that 4 and 6 make 10.  Good for you!  Let's write this down so we can remember it.

Step 8: Give kids a paper 10's frame (a piece of paper with a black rectangle divided into 10 boxes) have them choose a crayon or dot marker the same color as their first set, and draw 4.  Switch colors draw six more.  Let kids above grade level work independently, give support to kids on grade level and below, and then let them color the last 2 or 3 independently, while they're doing that help the above grade level kids write an equation (not a K standard, but nice to introduce for kids who are ready) under their 10's frame.

Step 9: Repeat one more time with a different starting number.
[/i]

On a different day, we might cook fruit salad.  Each kid can choose 10 pieces of fruit to add (e.g. 3 blueberries, 4 grapes, and 3 cutie orange sections), and then draw a picture recipe to show what they cooked.  [/quote]

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