# activity leap frog by ZCjoRh

VIEWS: 22 PAGES: 21

• pg 1
```									LEAP FROG
How many slides, jumps,
and moves must be
pairs of frogs in the leap
frog game?
How to Play

Set up your two colors of “frogs”
on a playing board like the one
below:
3 2 1 space 1 2 3
Free
How to Play
• Begin with 1 pair of frogs of different
colors.
• Place one frog to the left and one frog to
the right of the free space in the 1 position.
• Your goal is to get all the frogs of one
color to the other side of the free space.
Rules
• Only one frog can occupy a space at one
time.
• Frogs can only move forward (toward the
opposite side), never backward.
• You can slide a frog to the empty space
beside that frog. This includes the free
space.
• You cannot jump the same-color frog.
Rules
• There must be a space on the other side
of a frog before you can jump that frog.
You cannot jump 2 frogs next to each
other without a space in between the
frogs.
As you perform this investigation,
organize your data in a table like the
one below:
# of    Sequence of moves    # of    # of # of
frog                        slides jumps moves
pairs
Recording Data
• As you move your frogs, record your
slides and jumps using a method you
develop. Write this data in the
• Count the number of slides, the
number of jumps, and the total
number of moves needed to solve the
game and record these numbers in
After you have solved the
game with 1 pair of frogs,
repeat the game with 2 pairs of
frogs, 3 pairs of frogs, etc.,
until you see a pattern.
complete sentences.
1. What is the relationship
between the number of frog
pairs and the number of slides?
2. What is the relationship
between the number of frog
pairs and the number of jumps?
3. What is the relationship
between the number of slides
and jumps and the number of
moves?
4. How did you determine the
number of slides, jumps, and
moves for 30 pairs of frogs?
5. What are the variable
expressions for slides,
jumps, and moves?
6. What labels would you give
to the x-axis and the y-axis
in a graph of this data?
Drawings of frog      Table with variable
Place the           pairs              expressions
following    (at least 4 steps)   (include expressions
at bottom of table)
items on
paper:       expressions and       (include at least 4
word                data points)
representations

Answers begin on the next slide.
# of frog      Sequence of moves          # of    # of # of
pairs                                  slides jumps moves
1                  S-J-S               2     1      3
2             S-J-S-J-J-S-J-S          4     4       8
3        S-J-S-J-J-S-J-J-J-S-J-J-S-    6     9      15
J-S
4        S-J-S-J-J-S-J-J-J-S-J-J-J-    8     16     24
J-S-J-J-J-S-J-J-S-J-S
n                                      2n    n2   2n + n2
1.   What is the relationship between the
number of frog pairs and the number of
slides?
• Answer: The number of slides is double
the number of frog pairs.
2.   What is the relationship between the
number of frog pairs and the number of
jumps?
• Answer: The number of jumps is the
square of the number of frog pairs.
3.   What is the relationship between the number
of slides and jumps and the number of
moves?
jumps, you will get the number of moves.
4.   How did you determine the number of slides,
jumps, and moves for 30 pairs of frogs?
•   Answer: For 30 frog pairs, you double the
number of frog pairs for the slides, square the
number of frog pairs for the jumps, and add the
slides and jumps together to get the number of
moves (2 ∙ 30 + 302 = 60 + 900 = 960).
slides   jumps moves
5.   What are the variable expressions for slides,
jumps, and moves?
•   Answer: The variable expression for slides is 2n,
for jumps is n2, and for moves is 2n + n2.
6.   What labels would you give to the x-axis and
the y-axis in a graph of this data?
•   Answer: Since you choose the number of frog
pairs, you would label the x-axis # of frog pairs.
Since you will have 3 sets of dots on your graph
for slides, jumps, and moves, you would label the
y-axis # of. In this case, you will need a legend
or key to explain the different dots.

Drawings
2 slides, 1 jumps, 3 moves

4 slides, 4 jumps, 8 moves

6 slides, 9 jumps, 15 moves

8 slides, 16 jumps,
24 moves
Variable expressions and word
representations:
The number of slides is twice the
number of frog pairs (2n). The
number of jumps is the number of
frog pairs squared (n2). The number
of moves is the number of slides and
jumps added together (2n + n2).
20

16

Graph                 14

12

10

Legend         8
# of slides    6
# of jumps
4
# of moves
2

00   2         4      6    8   10
# of frog pairs
TEACHER NOTES
•   Materials:
Snap cubes, cm cubes, or any type of manipulative to represent the two colors
of frogs; you could have students be the frogs by laying colored paper on the
floor and giving students the same colored paper to hold
Chart paper
Markers/crayons/colored pencils
Pencil/paper
•   Pair students for this activity.
•   Have students copy the table onto their paper.
•   As students work, circulate to ask questions to guide students during their
investigation.
•   If chart paper is not available, you can substitute newsprint or butcher paper.
•   For the drawings of the frog pairs, students should include at least 4 steps in
the sequence.
•   For the graph, students may or may not include (0,0). Students should
include at least 4 data points. Discuss with students the fact that you do not
connect the dots because you can’t have a partial pair of frogs; you can only
have whole number pairs of frogs.
•   Have students present their chart papers to the class. Post chart papers on
the wall after each presentation, provided that all groups and classes are
finished with the construction of their chart papers.

```
To top