Provide each student with a sheet of graph paper and a pencil.
Have children use pencils to check off boxes as they count out a specific number. For example, to explain the value of seven, have children check off seven boxes while counting aloud. Explain how adding one more box to a collection of six equals seven, and how subtracting a box from a group of eight also equals seven.
Explain and demonstrate multiplication with graph paper by numbering the columns and rows. Have students make a box, using the numbers associated with the rows and columns for reference. For example, while explaining the product of 3 multiplied by 4, instruct children to draw one vertical line down the right side of the third column and one horizontal line along the bottom of the fourth row. Have children count all the squares contained in the box they've drawn to determine the answer.
Explain integers with graph paper by tracing over the top and bottom lines of the center, horizontal row and each of the vertical column lines contained within the row, forming one long box containing several smaller boxes. Place a zero in the center box and use the grid as a number line to illustrate the positive and negative distances from zero, using the grid boxes to the left and right of the zero box as examples.