1
Jump, Frog, Jump
Freddie, the frog, loves to jump! Today he has decided to put numbers on the lily pads in the pond and do
a lot of jumping.
1. If Freddie starts on zero, jumps to the right and takes hops
of size 1, what numbers will he land on? Use the table to
help organize your answers.
Hop #
Landing
0
1
2
3
4
5
2. If he starts on zero, jumps to the right and takes hops of size
2, what numbers will Freddie land on?
Hop #
Landing
0
1
2
3
4
5
3. If Freddie starts on 1, jumps to the right and takes hops of size 2, what numbers will he land on?
Hop #
Landing
0
1
2
3
4
5
Jump, Frog, Jump
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4. If Freddie starts on 5, jumps to the right and takes hops of size 4, what numbers will he land on?
Hop #
Landing
0
1
2
3
4
5
STOP
5.
Discuss the problems with your partners! Teacher Check_____
Using the grid below, graph all four tables from questions 1 – 4 using a different coloring pencil to
label each line.
28
26
24
22
Landing Number
20
18
16
14
12
10
8
6
4
2
0
0.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
Number of Hops
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7
7.5
6. Compare similarities and contrast differences between your graphs using the table below.
Compare (Similarities among the graphs)
Contrast (Differences between the graphs)
STOP
Discuss the problems with your partners!
Teacher Check_____
7. If Freddie starts on 3, jumps to the right and takes hops of size 2, where will he land on the 7th hop?
a. If Freddie’s friend Frieda starts on 3, jumps to the right and takes hops of size 3, where will
she land on the 7th hop?
b. How do Freddie’s and Frieda’s final landing numbers compare? Explain your thinking.
Jump, Frog, Jump
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8. If Freddie starts on 2, jumps to the right and takes hops of size 3, where will he land on the 7th hop?
a. If Freddie’s friend Frieda starts on 2, jumps to the right and takes hops of size 6, where will
she land on the 7th hop?
b. How do Freddie’s and Frieda’s final landing numbers compare? Explain your thinking.
9. Can you figure out a mathematical shortcut to predict where Freddie, the frog, will land on the 7 th
hop?
If he starts on 3 and takes hops of size 2, Freddie will land on _____ on the 7th hop.
10. Test your shortcut again
If he starts on 1 and takes hops of size 3, Freddie will land on _____ on the 7 th hop.
STOP
Discuss the problems with your partners! Teacher Check_____
11. What about the 10th hop? If Freddie starts on 0 and takes hops of size 2, where will he land on the
10th hop?
a. If Frieda starts on 2 and takes hops of size 2, where will she land on the 10 th hop?
b. How do the final landing numbers for Freddie and Frieda compare? Explain your thinking.
12. Freddie starts on 5 and takes hops of size 3, where will he land on the 10 th hop?
Jump, Frog, Jump
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13. Can you figure out a mathematical shortcut to predict where he will land on the 10th hop?
If he starts on 1 and takes hops of size 2, Freddie will land on _____ on the 10th hop.
STOP
Discuss the problems with your partners! Teacher Check _____
14. If he starts on 0 and takes hops of +2, where will Freddie land?
Hop #
Landing
1
2
3
4
5
15. If he starts on 1 and takes hops of 4, where will Freddie land?
Hop #
Landing
0
1
2
3
4
5
16. Given the following landings, determine where Freddie would have to start and the hop size he
would have to take.
Hop #(X)
Landing (Y)
Start: ________
0
Jump, Frog, Jump
1
5
2
8
3
11
4
14
5
17
Hop Size: _________
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17. Given the following landings, determine where Freddie would have to start and the hop size he
would have to take.
Hop #(X)
Landing (Y)
Start: ________
0
STOP
1
4
2
8
3
12
4
16
5
20
Hop Size: _________
Discuss the problems with your partners! Teacher Check ______
18. Freddie has been challenged to a race. He has decided to start at 0 and take hops of size 3 while his
friend Frieda starts at 3 and takes hops of size 2. Your job is to show a table for each frog, the set
of ordered pairs for each frog, the graph (put both frogs on the same graph), and then decide who
will win the race if both frogs take 5 hops during the race.
Ordered Pairs:
Landing
Landing
Hop #
Hop Number
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Challenge Problems
19. Freddie wonders how many hops he can take before he lands on 11 if he starts on 3 and takes a hop
size of 2.
20. If Freddie starts on 7 and takes a hop size of 3, what are the hops he can take and still be on a lily
pad less than 21?
21. If Freddie starts on 5 and takes hops of size 4, how many hops does it take to land on a lily pad
more than 18?
22. Freddie has a new problem. This time he wants to predict how many hops it will take him to get to
a particular lily pad. If he starts on 5 and takes hops of size 2, how many hops will it take to get to
13?
23. If Freddie starts on 3 and takes hops of size 4, how many hops will it take to get to 23?
24. If Freddie starts on 2 and takes hops of size 3, how many hops will it take to get to 20?
25. Can you find a mathematical shortcut to predict the number of hops to take to land on a certain
number?
Shortcut:
a. If Freddie starts on 3 and takes hops of size 2, he will have to take _____ hops to land on 19.
b. If Freddie starts on 4 and takes hops of size 3, he will have to take _____ hops to land on 25.
STOP
Discuss the problems with your partners! Teacher Check ______
Jump, Frog, Jump
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