Skip-Counting Beads (Pickle Beads)

This post was inspired by a bright young lady I have "met" only online, who is affectionately known as The Pickle.  She was skip-counting 7's on her math assignment last week and not enjoying it at all. I can relate.  Some students find that skip-counting songs are very helpful when they are trying to learn the number sequences, but for those who prefer a hands-on or visual approach (my daughter loathed memory songs), I offer this activity.

A set of 10 Skip-Counting Beads

If you're unfamiliar with the term, skip-counting is a valuable step in learning to multiply.  It's basically counting by a number: 7, 14, 21, 28, 35, 42, 49, 56, and so on.  Not everyone learns to skip count, other than the usual counting by 2's, 5's and 10's, but those who do will find that later memorization of multiplication facts comes almost effortlessly.

A set of skip-counting beads is a hands-on tool for skip-counting-- helpful not only for learning to skip-count, but also for visualizing multiplication as a concept, and comparing the quantities involved.  As an added bonus, it is also a handy illustration for Least Common Multiples.

If your student is just starting out in the lower grades, it would be beneficial to have him string his own beads, perhaps one set a day.  Older children might make more strings per session.   Some students may lack the fine motor skills or patience to complete the set without a meltdown;  it's not a total loss if you end up making them yourself, as long as the student uses them when you're finished.

Materials for making the strings.

To make a set of 10 (through 10x12) or 12 (through 12x12) skip-counting bead ropes, you'll need a couple of large bags of pony beads of a single color (shown here as white)-- 530 beads for a set of ten strings, or 771 for a set of 12), plus 12 beads of a different color for each rope.  (The set above includes 10 ropes, modeling 1x12 through 10x12.)  You will need about 24 feet of string or cord (18 if you're making only ten ropes), and a pair of scissors. An extra-fine point permanent marker is optional; it allows you to write the numbers on the beads.  Numbers are helpful, and can reduce error when learning to count.  If your child is very visual, I would definitely recommend writing the numbers on the beads.

Bottom to top: One, Two, Three, Four, and Five strings.

To make the set, make the first rope by stringing 12 of the white beads.  Tie off the ends.  (If you're using para-cord, you might want to melt the ends in a flame to prevent raveling.)  Next, make a second string alternating white and a second color, using 12 of each.  The third string uses 2 whites for every one of a third color; the fourth string uses 3 whites for every bead of the fourth color.  Continue until you have made a string to count by 5's, 6's, 7's, and so forth.

To label the beads, write the numbers 1-12 on the beads of smallest string, and then write the

Labeled beads.  (Needed a finer point marker.)

appropriate numbers on the colored beads of
each string.  (Writing the numbers on all of the white beads on every string is not a bad idea, but it may take the emphasis off the colored beads. However, some children may prefer having every bead labeled, and that's okay.)

To use the beads, the student holds a string in his hands and touches the colored beads as he counts aloud.  If he needs help. he can either count up using the white beads or read the number written on the colored beads.  The student should practice until he can rattle off the numbers easily.

Later, when the student is learning his multiplication tables, you can show him how it works on the string:  for the 3 times table, for example, use the Three string on which every third bead is colored. Touch the first colored bead as you say, "Three times one is three."  Then touch the second colored bead: "Three times two is six," and so on, up the string to "Three times twelve is 36."  Then demonstrate the facts out of order: count up 5 colored beads, and say, "Three times five is fifteen."  Count up nine: Three times nine is twenty-seven."

Lining up Three and Four string.

You can show how the facts work out the same, regardless of the order of the numbers being multiplied (Commutative property of multiplication), by lining up two strings with their beginning white beads together and the rest of their beads matching up beside each other.  Here we have the Three string and the Four string. Point out to the student that 3x4 and 4x3 have the same answer: both strings have colored beads at 12.

To illustrate Least Common Multiple (LCM), explain to the student that the colored beads represent multiples of a number.  When you skip count, you are listing the multiples of a number in order.  To find the LCM of a pair of numbers, line up strings representing the numbers you are comparing.

Lining up Four and Five string.

Here we have the Four sting and the Five string. When their beads are lined up together, the first time two colored beads line up next to each other is at 20.  This is the least, or lowest, multiple that the two numbers have in common.  If you put Two and Five together, the LCM will be 10.  Two and Four have an LCM of 8.  The student may be tempted to conclude that the LCM of two numbers is the same as the product of the two numbers; however,  sometimes the LCM is less than the product:  The LCM of Ten and Five is 10, not 50.  The LCM of Nine and Six is 18.

You can use the strings to show LCM of more than two numbers; just line up three or more strings together to point out the alignment of the colored beads.  Five, Ten and Two align at 10;  Three, Six, Two, and Nine align at 18.  (Some number combinations cannot be shown given the length of the strings; for example, the LCM of 9, 5, and 10 is 90, but the Five string stops at 60.)

Once the student has mastered the use of the skip-counting beads, he is well on his way to understanding-- and mastering-- multiplication.