Zaplify World
Tap from the home page to visit the Zaplify World.
Basics
- Press a finger on the screen to create a bolt of lightning. Press more than one finger to create more than one lightning bolt.
- Pressing the top or left of the screen creates horizontal lightning bolts; pressing the bottom or right creates vertical lightning bolts. After pressing, drag to move the lightning bolts up and down or left and right.
- Orange sparks appear wherever horizontal and vertical lightning bolts cross.
- Tap Lock to lock visible lightning bolts onscreen, so they don’t fade away when you remove your fingers from the screen.
- Tap Reset to remove any “locked” bolts of lightning.
- Tap Back to exit the Zaplify World and return to the home page.
- Visit Settings on the home page to change whether Zaplify displays the numeric product value (the number of orange sparks) or the numeric vaue of your horizontal and vertical lightning factors.
- Also use Settings to control the appearance of lightning bolts and the coloured background, which may be useful if you plan to project your iPad on to a screen, or to take screen captures for eventual printing.
Activities
How do you make orange sparks appear? How could you make 6 sparks appear? How could you make 2 sparks disappear? | |
Place 2 fingers on the left (horizontal lightning) and 3 on the bottom (vertical lightning) to produce 6 sparks. Your partner can put one more finger on the screen. Where should it go to make the spark product as large as possible? | |
Make the numeric product value count up by 5. | |
Make the numeric product value count down by 6, starting at 42. | |
Using exactly 10 fingers, how can you produce the largest product? | |
What is the largest product you make using 11 fingers? | |
Use to make a storm of exactly 20 lightning bolts (horizontal and vertical combined). How many sparks can you make? Ask some friends to try the same experiment. Who winds up with the most sparks? | |
Place 2 fingers on the horizontal side and 3 on the vertical to produce 6. Ask your partner to make a sketch of the result. Now place 3 fingers on the horizontal and 2 on the vertical. What did you produce? How is it different from the sketch? | |
Claudia used 10 fingers to produce 21. Show two different ways she could have done this. | |
Find as many ways as you can to make 24. Draw sketches or take an image capture of the screen for each. Identify which sketches seem “the same” and explain what makes them seem that way. | |
Make 5 x 5 = 25. Then add 1 vertical and 1 horizontal bolt of lightning. How does the product change? Now start with 6 x 6 and explain how the number of intersections changes when you move to 7 x 7. Predict what will happen when you go from 20 x 20 to 21 x 21. |
Teacher Notes
Arithmetically, Zaplify’s horizontal and vertical lightning bolts are multiplicative factors. Orange sparks are the multiplicative product formed by these factors.
This approach to multiplication emphasizes the commutative symmetry of multiplication with respect to its factors. (Formally, a binary operation is commutative if changing the order of its operands does not change the result of the operation. Informally, visitors to the Zaplify World learn one hand “works” much like the other!) Zaplify also provides learners with a visual grid model—or, more generally, a geometric model—for thinking about multiplication and about how changes in factors affect their product.
Some children may focus initially on the areas between lightning bolts rather than on the sparks formed by their crossing, so help draw their attention to the intersections. Developing your own name for these—sparks, or fire-bugs, or crashes—helps invest them with identity. As in the Grasplify World, multiplicative products are already computed by the environment, so the focus here should be more on patterns and relationships than on “what’s the product?”
Displaying numeric values for factors and product () can help quantify learners’ explorations. Children may also see patterns in how products change (as they add lightning bolts) that attract their attention, which can lead to new explorations.
See the Research Bibliography for additional information.