Question for Christina: Why is skip counting so hard?

I often get emails from teachers asking for advice on how to teach a certain concept and it is difficult for me to effectively discuss it with them via an email….I try my best but I’ve decided to use my blog as a way to elaborate in ways that I cannot in my emails.  So here is the first installment in this new series, Question for Christina, and if you have a question for me just send me an email:

“I am a kindergarten teacher…My daughter is in 2nd grade and her most recent challenge has been with skip counting and number lines.  Do you have any recommendations on good activities/apps to help her better understand this concept??”

Kids who have not developed the beginning stages of counting/early numeracy will not be able to transition into skip counting with deep understanding.  If we want kids to understand skip counting instead of just memorizing a sequence of numbers, then we are really asking them to:

1) Understand how to join sets (aka addition),

2) Stop counting one-by-one to join those sets, and

3) Start counting groups of items rather than individual items.

This picture from One Day at a Time illustrates this perfectly. The children are practicing skip counting but they need to see the sets of three within each new count.  Some kids are still needing to count one-by-one when they add on each new set of 3…they don’t just instantly know it is going to be 3, 6, 9, 12, etc.

Skip counting is the switch from counting individual items when adding to counting a set as one whole group of a particular amount and adding that to the same amount.  If your students are skip counting but are not solid in early numeracy and addition, then they aren’t skip counting…they are just parroting back a number sequence.

If your students are not there yet, and they are only ‘learning’ skip counting through memorization.  They may be having trouble memorizing the skip counting sequences and the only way to increase our capacity to know from memory (instead of just memorizing) is to build LOTS of connections…which guess what, that takes me back to helping kids see how skip counting is like addition only we are adding on the same amount every time so we can skip those numbers in between.

Check out this video from The Teaching Channel.  It shows how the foundation of counting built in kindergarten through 1st grade builds the understandings needed in order to skip count.

And not to ignore the other portion of the question…what about Number Lines?  First off, we start using number lines way before kids are ready to understand them and instead we should be using number paths.  Read this document to get a better understanding of why Number Paths are more appropriate for Kindergarten and 1st grade.  Also, most everything kids do around counting is putting the objects in piles.  Number paths, and then number lines, put quantities into a linear fashion.  Start by having them place objects onto a number path while they are counting.  As they get older, you can cut apart the 100s (or 120s) chart to form an even longer number path.  It is essential that children get lots of opportunities to see quantities arranged in a linear fashion before we throw a number line at them.

So here is my incomprehensive list of ideas to help you all in developing skip counting (and number line understanding):

1. Lots and Lots of Counting

Video(s)

Watch this video from the Teaching Channel for a nice lesson that connects Counting Collections to skip counting and addition/subtraction, or check out THIS VIDEO that I took last night when my daughter was trading in her coins for dollar bills.  Money gives us a natural context to help address many important math concepts.

Activity

Counting Collections. Most teachers do this a lot around the 100th day of school but kids need constant counting practice (like every day!).  However, we want to encourage them to start organizing and grouping their counts.  When students organize their counts into groups of 2, 5, or 10 it gives them practice counting one-by-one but then gives them an opportunity to come back and skip count that same group of items.  Check out my Pinterest board full of counting and skip counting activities.

Apps

TallyTots: This simple app deals with numbers 1-20.  It shows the numeral, then counts up to that number, and shows a visual picture of that amount.  There is also a screen to have them practice counting up to 100.

100 Butterflies: Kids tap on sleeping caterpillars and turn them into butterflies.  Each time they tap the app says the next number in the counting sequence.  I LOVE how there is only 10 butterflies or each screen and then they go up the tree to the next decade of counting numbers.

2. Lots and Lots of Subitizing

Video(s)

Here is a quick video to show you how young children can and should be encouraged to subitize or check out this video of kids using one of my favorite math tools, a rekenrek, which gives children opportunities to subitize.

Activity

I don’t think I can pick just one to share!  Here is a link to my blog posts pertaining to Subitizing, but basically any activity you do with Ten Frames, Rekenreks, Dot Patterns, and Dice can encourage children to subitize.  Here is a popular activity from my blog, where kids roll a die to determine how many pom poms they get to place on their picture:

Apps

Quick Images: My favorite subitizing app!  It creates Quick Images (that disappear after a set time) using dot patterns, finger patterns, ten frames, and a rekenrek.

Pattern Sets: This app displays “Quick Images” of dots and then covers them.  The child has to determine how many were shown and then select the correct numeral to correspond with that amount.  This app builds subitizing for kids and helps them visualize the patterns.

3. Lots and Lots of Joining of Sets

Video(s)

I am a big believer in Cognitively Guided Instruction, which centers around using story problems to teach math.  You can check out my blog post about their book Children’s Mathematics, but here are some videos of kindergarten kids modeling contextual problems.

Activity

Addition problems are best done in context.  They naturally occur in our students’ lives and we need to bring those situations into the classroom.  Find natural ways to incorporate addition using contexts your students care about…if your school is collecting items, then use that as a context for creating problems, “Sierra brought 7 Box Tops today and Camden brought 5.  How many Box Tops do we get to add to our collection?”  Also, check out this blog post from the Math Learning Center.  It has samples of story problems to go with some of their units in 1st grade.

Apps

Hungry Guppy: Kids practice subitizing and addition in this fun game where children drag bubbles together to create the amount the fish wants to eat.

Fast Facts Early Add: This app has children practice subitizing and then moving into addition, but for each ‘fact’ they are practicing it provides a ten frame visual for each addend in case children still need to count or find other strategies (like making a 10) to solve the problem.

4. Lots and Lots of Investigating Patterns

Video(s)

Most of the videos out there are showing the kids the patterns, I like this video because it shows how to use a virtual manipulative that you can use to help your students explore the patterns.

Activity

Building the 100s chart (which should now be a 120s chart) is an excellent way to encourage kids to use the patterns to help them place numbers.  I love 120s charts to help investigate patterns, but if you are going to use them a lot or plan to have children model addition and subtraction using the chart, please check out this post by Graham Fletcher first about how we should be rearranging the order.

Once kids have had a chance to explore the 100s chart (or 120s chart), try turning it into a Number Path.  This gives you the opportunity to start moving towards a Number Line and then the size of numbers becomes endless.

Apps

Line ’em Up: This app gives kids an introduction into a number path.  It gives them part of a number path started and then they have to finish it.  Great for getting kids to understand the order of numbers and sets it up into a linear model so that kids can then understand a number line.

Math Adventures: Number Find : This app centers on finding numbers on the 100s chart.  However I highly suggest using the ‘Advanced’ section of the app because this is where they move around the starting spot of the numbers, so children have to rely on their understanding of the patterns of the numbers not just memorizing where the 10, 20, 30, etc sit on the chart.

Zoom: This app helps kids place numbers on a number line.  They can Zoom in, to look at a small piece of the number line, or Zoom out to see an extended number line.

Do any of you have some fun ways to develop the understanding of numbers that is needed for skip counting? 

So, in summary, children can learn to recite skip counting sequences, just like they learned to recite the normal counting sequence….but the true understanding of counting, whether one-by-one or skip counting, comes when kids learn to attach meaning to the numbers they are counting.