How can the teacher differentiate instruction when teaching number sense or mathematical operations?
The process of differentiating instruction about any subject begins with assessing the needs of the students being taught. Exact approaches to instruction, activities to be used for reinforcement and practice, and methods of assessment will all depend upon the age, abilities, and past experiences of the students in the class.
Students just beginning to acquire a sense of what numbers mean should have lots of opportunities for direct physical experience with the concept of counting and assigning number names to groups of objects. Some students will learn best if given counters to place in rows, others will benefit from counting fingers, others may be able to draw tally marks or simple pictures to count.
In the same sense, the style of teaching and learning about mathematical operations will vary, based on what operation is being taught and on the needs of the learners. When teaching subtraction, some students will be able to use counters to create a large group and then physically remove a given number. Others will work better when allowed to line up classmates and then escort some to another area of the room. Use of manipulatives is generally valuable, but allowing students to choose what they work with at time encourages involvement and sustains motivation.