One of my favorite SIMPLE resources is one-inch graph paper.
I renew my supply every year as we use it for all ages and stages.
Graph Paper Patterning. Littles, markers in hand, enjoy making colorful patterns. For the very youngest we start with simple ABABABA patterns and work up to harder ABBCBBABBCBB patterns. They love creating their own patterns or copying patterns I give them. Patterning is a prenumber skill needed for numeration, counting and even language arts skills.
One-to-One Correspondence and Counting. One-inch graph paper (or larger) is perfect for learning one object to one number. The child counts, writing a number in each square.
Column Guide. Graph paper can be a gentle guide, keeping columns in math problems aligned. For example, the problem 32 x 21 can be written on graph paper, one digit per square, to keep children on process (in other words, which number or column is added, multiplied, subtracted or divided next) and digits in line (making the last steps of problems easy and natural, not swinging and swaying between ones, tens and hundreds). Graph paper can be helpful for all number operations (addition, subtraction, multiplication and division) keeping problems neat and organized.
Concept of Multiplication. Rows and columns not only provide a visual picture of a multiplication equation, but also prepare a student for learning the concept of area: length times width. Once the multiplication concept is mastered, begin learning the multiplication facts.
Concept of Area. A natural next step to the column/row concept of multiplication above, graph paper allows the concept of area visual. I begin by drawing a large square on graph paper. Then, I teach area as length times width, tracing my finger along the square while speaking "length times width". I then write the corresponding numbers and operational symbols (squares along the length x squares along the width) under the square and solve the multiplication equation. Lastly, I count the number of squares inside the large square to check.
Algebraic Graphing. Graph paper helps big learners, too. My bigs have drawn x- and y- axis graphs on quarter-inch graph paper to solve slope intercept problems. Some learners cut out their graphs and pasted them into their regular math notebooks while others have me purchase a graph paper notebook to work their lessons, both graph and not-graphing problems.
More than Math. We have also used graph paper for spelling, writing one letter per square. When comparing word lengths, we have cut and placed words strips side-by-side providing a visual tool for word comparison. For children who have difficulty with letter and word spacing in sentences, use quarter-inch graph paper to spell words one letter per square, leaving a square empty between words.
Valuable Visual. Many children need a visual reference to file in the brain, especially when learning a new concept. Graph paper has provided this colorful visual for my children and many others to whom I have made this recommendation. Try it! See if graph paper presents the visual tools necessary for your child to master foundational concepts.
Graph paper is an education staple in our home. For some children it has kept columns straight, for others graph paper offered opportunities for patterning and geometric design creation. As we look forward to the coming school year and inventory our back-to-school needs, graph paper will be a must-have resource.