Provide children with a choice of manipulatives to use when solving a math problem. This choice will allow them to have as much or as little help as they need. When asked to solve a two-digit addition problem, one child may be able to solve it in his head or by writing the algorithm on paper. Another may be able to find the answer with the help of base ten blocks. A student, who is still struggling to understand place value may be able to solve the problem by counting out the two numbers with cubes or beans and then counting the total.
When giving students a math problem to solve, give them three choices of the numbers to use in the problem. If your problem reads "There were 9 green apples and 12 red apples in the bowl. How many apples in all?" allow the children to replace the numbers with "2 and 3" or "19 and 27" to make the problem easier or harder. You may need to model how to choose the appropriate set of numbers and nudge a few students in the right direction, but with practice students will learn to choose the numbers that provide them with the right challenge.
Most mat problems can be approached in a variety of ways. Allow children to choose a strategy when solving these math problems. Drawing pictures, using manipulatives, inventing algorithms are a few of the strategies that different children may choose. Once all of the children have solve the problem, allow them to share their strategies with each other.
Present students with problems that have more than one answer. A problem, such as " There were 13 marbles in the jar. Some were red and some were blue. How many of each could there have been?" has a many possible answers. One students may struggle just to find one answer, while another may be able to find all of them. Allow the children to find as many answers as they can, instead of requiring a set amount.
Give all of the students the same problem but provide a few extension questions for those who need more of a challenge. Your main problem might ask the students to figure out how many legs there would be if 4 children were sitting at a table. As an extension, ask them to find out how many fingers and how many fingers and toes together.
When giving children a set of problems to solve, include a few that are more of a challenge and place a star by them. Make the starred problems optional.