Children who develop a solid understanding of small numbers are able to grow into an understanding of larger numbers. A child that is able to decompose and then compose the number five is then able to use the same process to decompose and compose ten, then twenty, fifty, one hundred, one thousand and so on.
Students develop a deeper conceptual learning when given the opportunity to learn through projects (investigations) when they can: use literature, solve open-ended problems, participate in group discussions, experience hands-on exploration, and build representations.
When children are given time to think, time to exchange ideas, time to show proof or to prove their thinking, and time to write about their thinking students will have a greater understanding of numbers. Then students develop a flexibility of thinking that allows them to understand connections between mathematical ideas. With the right opportunity students will become a collaborative community of mathematical thinkers engaged in inquiry.