Math Strategy: Skip Counting

Skip Counting: What is it?

Math Strategy:  Skip Counting

Math Strand: Number Sense and Numeration

On Lawson’s Continua:
Skip counting can be found in the Addition and Subtraction Continuum and the Multiplication and Division Continuum.

Overview: 
Skip Counting is counting by regular intervals repeatedly to reach a certain value. It is counting by a number other than one.
In early grades, students learn to skip count by 2, 5, and 10s.  They learn to skip count forwards and backwards.  Then later they learn to skip by 100s, 50s and 25s.  Skip counting is different then counting rhythmically.  To ensure students connect the values of the counts have them build the amounts with cubes or counters.  This will support students as them begin to understand that each skip count, or grouping, is a unit of a certain amount.

(5, 10, 15, 20 is 4 units of 5)

When skip counting, students learn that you can count to a certain number faster instead of counting all numbers individually.  Initially, students will solve problems like: 5 groups of 2 by creating the groups by adding 2 counters into each group.  They then count all of the counters individually to find the product.  As students learn to skip count and grasp the efficiency of skip counting, they will progress to counting by 2’s in this problem rather than 1’s.
From skip counting students learn that groups of equal sizes can be combined to form a whole quantity.  For example, when skip counting by 2’s, students will be able to see that 2, 4, 6, 8, 10 ends up being 5 groups of 2 combined to get 10.
Skip counting helps students identify patterns in numbers but also supports their ability to later think multiplicatively.  To facilitate this type of thinking, students can be asked to identify all the ways they can skip count to a certain number.  This will help them to identify multiples of that number and then the factors as well.

All the ways to skip count to 24:
2, 4, 6. 8, 10, 12, 14, 16, 18, 20, 22, 24 (12 groups of 2)
3, 6, 9, 12, 15, 18, 21, 24  (8 groups of 3)
4, 8, 12, 16, 20, 24 (6 groups of 4)
6, 12, 18, 24 (4 groups of 6)
8, 16, 24 (3 groups of 8)
12, 24, (2 groups of 12)

According to Marian Small in Making Math Meaningful,  pg. 149,
“Multiplicative thinking is thinking that focuses on how one number is made up of groups of another “unit” ...  For example, thinking of 20 as 4 fives is thinking of the 20 being made up of the units of 5.”  Knowledge of skip counting will support this type of thinking.  

Supporting Students to Skip Count:
There are many ways to support skip counting, as seen on the video. These include:
- Using 100 charts to mark the numbers they are skip counting by
- Creating amounts with base 10 blocks to skip count by 1000’s, 100’s, 10’s, or 2’s to find their totals
- Money can be used to support skip counting, such as adding up tens, loonies, quarters, dimes, or nickels.
- Number lines can be used to add up in chunks to show equal groups, which may then progress to open number lines where they don’t show all the numbers on the line
- Students may build arrays and skip count along rows or columns to find the total amounts using colour tiles.  As the amounts become difficult to skip count they will split the groups into smaller groups they are more comfortable with

Students should be encouraged to learn to skip count on from a variety of numbers.  This will support students to later solve problems by skip counting on from an addend. For example, 37 + 40:

An example of Skip Counting from Lawson's What to Look For, pg 86:

Where to next:  
Consider using activities that promote Skip Counting in real life contexts in your class.  Some suggestions can be found in the text, “What to Look For” by Alex Lawson, on page 157, specifically pages 178, 185, 190 & 195.
Additionally, “Trading Up to 1000” is another activity that supports skip counting.  This game, along with other information and activities on skip counting, can be found in the K-3 Guide to Effective Instruction in Math, Number Sense and Numeration. 

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