As an international educator, I have learned different strategies for mathematics instruction by working with international colleagues. One in particular is partitioning. With partitioning, students learn to think flexibly about a number and visualize what numbers are inside of a given number before introducing the operations of addition and subtraction. This is a strategy used to lead to understandings about place value; it builds number flexibility to implement a variety of addition and subtraction strategies with facility. I have created activities for students to use when learning to partition from 10 - 20 in groups of 2, 3 and by ones & tens; number of the day; and sheets for numbers above 20. These can be done in pairs or individually.
Example of partitioning: A student has 10 cubes, he/she breaks it into two groups to find (7,3). Then breaks it into 2 groups again to get (2,9). Continues...
SIDENOTE: While watching, Pam Harris' free course, I saw her make a connection to partitioning for students even in high school. She plays a game called 'I have, you need' using numbers to 1000. It builds on this same concept of partitioning. I have 255, what do you need? 745. It is a great game for partitioning up to 1000 mentally for students who are ready for it. She calls it partners to 100 or to 1000. While problem solving with high school students, she uses this strategy time and time again.