My math professor is a genus.
I sometimes wonder is she invented math itself.
She showed us how to make this amazing bead manipulative at our last math ed. club meeting.
She came up with this idea as a cheap alternative to traditional counters, which we all know can get lost and dropped and can even be loud and annoying. The students make them and then keep them in their desks for when they are needed.
It's nylon string (so the ends can be melted), with 20 bead, 10 in two colors.
There are about a million ways to use this thing.
You can use it to add. Here we have 2+2 = 4.
Reverse the steps to subtract. Push all you need to one side, then take from that group.
Check numbers to see if they are even or odd. Alternate pushing beads to the center, then fold and check to see if each bead has a partner.
Here I did 5. So I pushed to the center a yellow, then green, yellow, green, yellow. Then split the colors in half and folded over my finger. Looks like I have an extra yellow with no partner, so 5 must be an odd number.
Add another green to make 6, and check. Looks like 6 is an even number.
You can find different ways to make numbers (part-part-whole). Here I made 7 using 2 and 5.
And here I made 7 using 4 and 3.
Here is multiplication. I'm multiplying 2 x 7, so I made 7 groups of 2, or 2, 7 times
Push them all together and I get 14. The trick is however, the students should know that there are 10 of one color, and thus, should not be counting all the yellow beads. Instead they should count on, starting with the first green (11,12,13,14), or should just know that 10 plus 4 more is 14.
The possibilities are endless, and this cost change to make, especially if you buy in bulk and either save it for the next years students, or split the supplies with other teachers.
3 yards of nylon string, ends melted (use a match/lighter to burn the ends)
20 beads, 10 each in 2 colors
Fold the string in half and knot the top so that there is a little loop above the knot.
String the beads on using a basic macrame stitch, illustrated in my bad diagram below. Basically both strings cross each other inside the bead.
String on all 20 beads, and then knot and melt together the ends.
And you're done!