Grasplify World

Tap from the home page to visit the Grasplify World.

Basics

Press one or more fingers on either side of the screen (the “first side”) to create a number of “pips.”
With fingers from one hand grasping a number of pips on the first side, tap one or more fingers on the other side of the screen to create “pods,” each of which contains that number of pips.
After a brief pause, all pod pips appear as a single product, in white.
Lift fingers from, or add fingers to, the first side of the screen to increase or decrease the number of pips in each pod.
Tap again on the second side to create more pods.
Drag pods to the Trash to remove them from the screen.
Press Array to rearrange your pods temporarily into an evenly-spaced grid.
Lift all fingers from the first side to remove all pips. When there are no more pips, there are no more pods, and you can start again.
Change direction: create your pips on the other side of the screen, then add pods opposite them.
Tap Back to exit the Grasplify World and return to the home page.
Visit Settings on the home page to control the display of the numerical value of the factors (the number of pips in each pod, and the number of pods) or the product (the total number of pips in all pods)..
Also use Settings to access a white background (which may be useful for projecting your iPad on to a screen, or taking screen captures for printing), or to show the Image Capture button in each World. (Image Capture takes a screen shot and adds it to your Photo Roll.)

Activities

How can you make a single pod of 5?
Skip count (change the white product value) by 3s by changing the number of pods. Then skip count by 3s by changing only the number of pips.
Make a product of 12. Find different ways of doing it. Which way uses the least number of fingers? Which way uses the most?
Starting at 20, make TouchTimes count down by 5s while keeping the pod-count the same and slowly changing the number of pips.
Make 1 x 3 = 3 using one pip and three pods. Changing only the number of pips, double the product so that it is 6. Double it again to make 12. Double it again to make 24.
Make 4 x 5 = 20. Can you halve 20 to produce 10? Then halve 10?
Make 3 x 5 = 15. Your partner can put one more finger on the screen. Where should it go to make the largest product possible?
Make 6 x 4 = 24. What would happen if you’d used one less finger on the first side of the screen, and one more on the second? Would the product become bigger or smaller?
Using exactly 10 fingers, how can you produce the largest product?
Make 5 x 5 = 25 and press Array. On paper, draw what you see on the iPad. Now make two other products that use exactly 10 fingers and draw what you see displayed. Compare the drawings you’ve made. How are they the same? How are they different?

Teacher Notes

The Grasplify World emphasizes a distinct role for each factor in a multiplication, rather than emphasize the interchangability of these roles. (Contrast the Zaplify World.) In Grasplify, learners first create the things to multiply (pips, or more formally: the multiplicand), and then create the number of times by which to multiply them (which is to say, the pods, or the multiplier). The software displays the total number of pips in all pods as the product of these factors.

Grasplify's ordering of multiplicand-then-multiplier fits naturally the physical nature of “pips in pods” of the software’s design. In more algebraic settings, however, the multiplier frequently appears before the multiplicand, as when we read “5x” as “five groups of x.” Each approach makes sense in its context. Thus “5 x 3” can be correctly seen as either “5 groups, each of which contains 3 things” or “5 things, in each of 3 groups.” Your choice of language can help support a specific interpretation of such statements in a particular context. Some teachers adopt language like “5 pips in each of 3 pods”—or more simply “5, 3 times”—to describe Grasplify’s physical model.

(Grasplify’s order follows approaches to early mathematics that are grounded in measurement and ratio, where one wants to identify the unit quantity before asking "how many units?" In research circles, this is known as a Davydovian approach.)

The tasks above encourage learners to see that varying the number of pips alters each and every pod. This observation in turn leads to a conception of multiplication as involving spread or change in scale, rather than simply as repeated addition (“adding more groups”).

See the Research Bibliography for further information.