I have been learning how important it is for kids to use manipulatives as they learn new math concepts. To be able to tangibly see what they're doing and work out problems with different objects it helps make sense of things to them, so they can actually see what's really happening as they solve problems, and why certain algorithms work.
One of the best tools to help kids with all sorts of math problems is using counters such as these. With these kids can be given a word problem and by using counters, can come up with a more complicated math question. For example: "Mary had some toys. She gave away 5 toys. Now she has 4 left. How many toys did she start out with?" Have the students put a group of 5 together representing the toys given away, and have them put a group of 4 together representing the toys that Mary had left in the end. Now have them look at the total of them all to find out how many she had started out with in the beginning.
This type of manipulative works best when teaching negative numbers to students. Let the yellow side of the disk represent a positive number, and the red side of the disk represent a negative number. Give a student a problem such as: 5+(-4)= Have the students place out 5 yellow disks and 4 red disks. Let them see that one red negative disk will cancel out one yellow positive disk. Each of the 4 red disks will cancel out 4 of the yellow disks leave one yellow disk left over, making the answer to the problem a positive 1.
This is a great idea for teaching fractions, and how different fractions are equal to, greater than, or less than others. These can easily be made out of paper or cardboard or craft paper. Have each color represent a different denominator. For example, let all the green pieces be fourths of a circle, the pinks be halves of a circle, etc. This is a great tool to help kids see that 1/2 is equal to 2/4 and 4/8. Ask them questions to have them figure the problems out on their own: "What is greater? 2/3 or 3/5?" Or these can also be used to teach them adding and subtracting fractions: "What is 2/4 + 1/4?" Have them use only the green pieces that represent the fourths to figure out this answer.
The ideas for manipulatives are endless, here are some Pinterest boards made for collecting ideas to use: