I was doing some spring cleaning a few weeks ago and came across a stash of old files that were “extra” ideas that never made their way into our Dynamic Number curriculum project. One concept in particular caught my attention—a “scooting” tick mark. Unlike traditional tick marks that dutifully sit in place on a number line, a scooting tick mark is much more active. If you enter a location on a number line, say, 0.4, the tick mark will rush to that exact spot and await your next destination.
The Web Sketchpad model below (and here) consists of four pages of scooting tick mark activities. Use the page navigation arrows in the lower-right corner of the websketch to move between pages. Scroll down for the activity descriptions.
Page One
The Page One model shows a 0-1 number line along with a scooting tick mark. Below are some activity suggestions.
Left or Right?: Enter a new value for the scooting tick mark and ask students to predict whether the tick mark will scoot to the left or the right. Play this game for a while, entering new values for the scooting tick mark and making predictions about which way the tick mark will move. At first, you might start with values like 0.200, 0.100, or 0.800. You might then progress to the hundredths and thousandths place by asking students to compare values like 0.640 and 0.650 or 0.302 and 0.370.
Bigger and Bigger: Ask students to enter a new value for the scooting tick mark so that it will scoot to the right. Challenge students to keep entering values that will make the tick mark move to the right. The process can end very quickly if students enter 0.700, 0.800, 0.900, 1.000. Can students find a way to slow down the growth so that the tick mark takes a long time to reach 1? If students increment the value of the tick mark by 0.001 (e.g., 0.701, 0.702, 0.703, …) then the movement they see will be so slow as to be almost imperceptible.
Smaller and Smaller: The same basic challenge as Bigger and Bigger, but now the goal is to make the tick mark’s value ever smaller each time it moves.
Page Two
This is the same as page one, but now the focus is on both negative and positive numbers.
Page Three
This scooting tick mark model is repurposed here for a Hit the Target game. The goal is to “scoot” the blue tick mark so that it lands directly on the target — the green tick mark. As students play, they try to minimize the number of estimates it takes to hit the target. Press New Target to play again.
Page Four
Now, the target is a random fraction with a denominator less than or equal to 10. Of all the activities, this is the one I would most like to test with students to analyze the strategies they use to identify the target fraction.