An appropriate cutting activity can be introduced that is fun for children, builds small-motor co-ordination and, once learned, can use up a block of time when an independent activity is desirable:
Start with a half-sheet of paper (easy to handle, but really, any size will do) and with age-appropriate scissors, start cutting at one corner. Cut, parallel with the edge of the paper, the thinnest strip that the child can manage. With practice, children become more skilled at cutting a thin strip. When the child reaches the paper’s corner, have the child carefully turn the corner with the scissors, being careful to not break the cut piece. Continue around and around the sheet of paper, allowing the cut strip to get longer and longer. The goal is to have it remain in one continuous strip until your child has cut all the way to the center of the paper and cannot turn the paper to cut it again because the uncut part is too small. With a partner, very carefully stretch the long strip of paper out just as far as possible to reveal its length. It won’t be perfectly straight (all those rounded corners!) but it will be possible to measure how long the strip is. (This is a lot of “work” for a child, so if the paper breaks, fasten with tape so the activity can continue.) Very likely your child will be very surprised at the length of the strip he/she has been able to produce. Try it again, using different sizes of paper, trying to cut thinner and thinner strips, estimating before measuring whether or not the new strip is longer than a previous attempt, etc. Measurements can be made using different tools and scale—tape measures, rulers, carpenter/household measuring tapes, etc. in either centimeters or inches. If you have a household measuring tape (they usually pull out from the center of a metal case) introduce your child to the concept of a measuring tool that is marked in both inches and feet.