2 Counting Concepts
The concept of counting on is likely developed when learning basic counting principles. It is important for learners to develop fluency in counting on, counting back, and skip counting. Counting on is a preaddition skill while counting back is a presubtraction skill.
Skip counting is another important counting skill. Skip counting is a premultiplication skill. It allows learners to count groups of the same size quickly. This is key to developing multiplication concepts and counting coins.
COUNTING ON
 Have learners reveal a number on the Nudget.
 Guide learners in continuing the counting with another quantity. Checkers move from right to left.
Start with the number 4.
Count on 3 more checkers.
“1” 

“2” 

“3” 

Learners should understand that counting starts with the next number after the beginning point. Have learners explore counting on repeatedly to ensure this concept is fully developed.
COUNTING BACK
 Have learners show a number on the Nudget.
 Guide learners in counting backwards another quantity. Checkers move from left to right.
Start with the number 4.
Count back 3 checkers.
“1” 

“2” 

“3” 

Learners should understand that counting starts with the number before the beginning number. Have learners explore counting back repeatedly to ensure this concept is fully developed.
SKIP COUNTING
 Have learners begin with 0 on the Nudget.
 Ask learners to slide 1 checker, then 1 more, and count “2.”
 Explain how by sliding 2 checkers at a time they are skip counting by 2.
Start from 0.
Slide 2 checkers and Count 2.
Slide 2 checkers and Count 4.
Slide 2 checkers and Count 6.
Slide 2 checkers and Count 8.
4. Have learners reset the Nudget.
5. Ask learners to slide 3 checkers, then count “3.”
6. Explain how by sliding 3 checkers at a time they are skip counting by 3.
Start from 0.
Slide 3 checkers and Count 3.
Slide 3 checkers and Count 6.
Slide 3 checkers and Count 9.
Learners should understand that skip counting is counting only the numbers they are counting by and skipping the numbers inbetween. If skip counting by 4, then they skip “counting” 3 numbers and only count every 4^{th} number. Have learners explore skip counting by various numbers to ensure this concept is fully developed.