Kindergarten

Our number system is a base-10 system. Every place value in our number system is greater than the place value to the right by a factor of 10. So, if you have the number 22, the 2 in the ones column is worth 2 ones. The 2 in the tens column is worth 20 (2 x 10 = 20).

Learning to read numerals as words (and convert number words into numerals) is based mostly upon understanding place value and the digits 0-9. Before learning to name two-digit numbers, students should know the numbers 0-9 perfectly.  

Sometimes students need practice forming numerals. These worksheets help students form their numbers, with lines to help them space their numbers proportionally.

Have students become somewhat comfortable with single digits before you move into double digit numbers. But, writing any double digit number provides help forming individual digits, so students don't have to have 1-10 perfect before they move on to the higher numbers.

Do make sure that students are practicing counting and understanding numbers as they learn to print them. 

We also subtract all the time, often without thinking about it.  Someone has 5 pieces of candy and then someone takes two, "Hey, I only have 3 left!"  But, teaching subtraction can be a little trickier than teaching addition.

We add all the time -- often without even realizing that we're adding.  The student who has 2 pencils, grabs another and calls out, "Now I have 3 pencils!" just did mental addition without even thinking about it!

Learning addition is a process.  Most people start that process on their fingers (any object will work... but fingers are handy and there are some cool patterns that kids can learn with fingers). 

The most basic form of finger (or object addition) is "counting all."

Example:

$3+5=8$

Ordering numbers is very similar to counting.  But, because it requires taking numbers that are out of order and reorganizing them (rather than just counting up) it's a slightly more difficult counting skill. When you have students who are struggling with counting, ordering exercises can be very helpful to reinforce the counting process. 

The worksheets below including ordering worksheets as well as ordering puzzles for younger students. 

One of the critical concepts in math is understanding which numbers represent "more" and which numbers represent "less." 

As with counting and ordering numbers, some students compare numbers easily and naturally. Other students need a lot of practice.  

One of the first steps towards advanced math includes the ability to read a (word) sentence and convert it into numbers. Once students learn to count and skip count and understand the concepts of "more" and "less," they can start to solve "more" and "less" number sentences. 

After students learn to count by 1, the next step is to learn to skip count. 

Skip counting is used in many math operations:

Counting, and understanding the base-10 number system, is the foundation of our math system.  It is critical that our students learn to count well and automatically.  For students to excel in math, it is also important that they see the patterns in the number system.  When counting, it can be hard to remember that 40 comes after 39, but any student who understands how the number system works will know that 41 comes after 40.