4. Let’s do one together…
On average, our class earns 2 pennies per day for being
enthusiastic and actively participating. If the class continues
to earn 2 pennies per day, how long will it take the class to
earn 10 pennies?
P = r(t)
P = number of pennies
r = rate of earning pennies
t = time
5. Let’s do one together…
On average, our class earns 2 pennies per day
for being enthusiastic and actively
participating. If the class continues to earn 2
pennies per day, how long will it take the class
to earn 10 pennies?
P = r(t)
What is rate?
6. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t)
What is rate? ratio comparing two different
things (ex. things per time)
7. Let’s do one together…
On average, our class earns 2 pennies per day for being
enthusiastic and actively participating. If the class continues
to earn 2 pennies per day, how long will it take the class to
earn 10 pennies?
P = r(t)
P = number of pennies
r = rate of pennies per day
t = time
8. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t)
What do we know?
9. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t)
What do we know? r = 2 pennies per day
P = 10 pennies
10. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
What do we know? r = 2 pennies per day
P = 10 pennies
11. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
What do we want to know?
12. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
What do we want to know?how long it
will take to
earn 10
pennies
13. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
What do we want to know?how long it
will take to
earn 10
pennies
14. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Let’s rewrite our equation: R = r(t)
10 = 2(t)
15. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Let’s try a few values: t = 3 days
16. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days
17. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3)
18. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3)
= 6
19. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3)
= 6
10 = 6 ???
20. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3)
= 6
10 = 6 ??? No, t ≠ 3
21. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3) No
8 days
22. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3) No
8 days 10 = 2(8)
23. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3) No
8 days 10 = 2(8)
10 = 16 ???
24. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3) No
8 days 10 = 2(8)
10 = 16 ??? No, t ≠ 8
25. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3) No
8 days 10 = 2(8) No
5 days
26. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3) No
8 days 10 = 2(8) No
5 days 10 = 2(5)
27. Let’s do one together…
On average, our class earns 2 pennies per day for
being enthusiastic and actively participating. If the
class continues to earn 2 pennies per day, how long
will it take the class to earn 10 pennies?
P = r(t) 10 = 2 (t)
Guess Check Yes/no
3 days 10 = 2(3) No
8 days 10 = 2(8) No
5 days 10 = 2(5)
10 = 10 ??? Yes! t = 5
28. Why do we use the guess
and check method?
Complicated problems or equations
Equations with multiple variables
Less room for error, checking our work
29. Solve
A petting zoo has an animal that requires a separate
enclosure. If the zookeeper has to walk to the enclosure 3
times per day, how many days will it take him to make 12
trips?
T = r(t)
T = trips to enclosure
r = rate of trips per day
t = time
30. Solve
A petting zoo has an animal that requires a
separate enclosure. If the zookeeper has to
walk to the enclosure 3 times per day, how
many days will it take him to make 12 trips?
T = r(t)
What do we know?
31. Solve
A petting zoo has an animal that requires a
separate enclosure. If the zookeeper has to
walk to the enclosure 3 times per day, how
many days will it take him to make 12 trips?
T = r(t)
What do we know? T = 12 trips
r = 3 times per day
32. Solve
A petting zoo has an animal that requires a
separate enclosure. If the zookeeper has to
walk to the enclosure 3 times per day, how
many days will it take him to make 12 trips?
T = r(t)
What do we know? T = 12 trips
r = 3 times per day
33. Solve
A petting zoo has an animal that requires a
separate enclosure. If the zookeeper has to
walk to the enclosure 3 times per day, how
many days will it take him to make 12 trips?
T = r(t)
What do we want to know?t = how many
days
34. Solve
A petting zoo has an animal that requires a
separate enclosure. If the zookeeper has to
walk to the enclosure 3 times per day, how
many days will it take him to make 12 trips?
T = r(t)
What do we want to know?t = how many
days
35. Solve
Let’s rewrite our equation: T = r(t)
A petting zoo has an animal that requires a
separate enclosure. If the zookeeper has to walk to
the enclosure 3 times per day, how many days will it
take him to make 12 trips?
T = r(t) T = 12 trips
r = 3 times per day
36. Solve
A petting zoo has an animal that requires a
separate enclosure. If the zookeeper has to walk to
the enclosure 3 times per day, how many days will it
take him to make 12 trips?
T = r(t) T = 12 trips
r = 3 times per day
Let’s rewrite our equation: T = r(t)
12 = 3(t)
37. Solve
A petting zoo has an animal that requires a separate
enclosure. If the zookeeper has to walk to the enclosure 3
times per day, how many days will it take him to make 12
trips?
T = r(t)
Let’s try a few values: 12 = 3(t)
38. Solve
A petting zoo has an animal that requires a separate
enclosure. If the zookeeper has to walk to the enclosure 3
times per day, how many days will it take him to make 12
trips?
T = r(t)
Let’s try a few values: T = r(t)
t = 4 12 = 3(4)
12 = 12 ??? Yes!, t = 4
Which teacher
wrote this
problem?
39.
40. Solve
The Justice League of America fights 5 crimes per day. If
they were in the newspaper yesterday for fighting 30
crimes, how many days did the reporter cover?
C = r(t)
C = Crimes fought
r = rate of crime fighting per day
t = time
1. What do we
know?
2. What do we
want to know?
3. Rewrite
equation
4. Guess and
check method
41. Solve
The Justice League of America fights 5 crimes per day. If
they were in the newspaper yesterday for fighting 30
crimes, how many days did the reporter cover?
C = r(t)
C = 30
r = 5
t = time
1. What do we
know?
2. What do we
want to know?
3. Rewrite
equation
4. Guess and
check method
42. Solve
The Justice League of America fights 5 crimes per day. If
they were in the newspaper yesterday for fighting 30
crimes, how many days did the reporter cover?
C = r(t)
Let’s rewrite the equation:
30 = 5(t)
1. What do we
know?
2. What do we
want to know?
3. Rewrite
equation
4. Guess and
check method
43. Solve
The Justice League of America fights 5 crimes per day. If
they were in the newspaper yesterday for fighting 30
crimes, how many days did the reporter cover?
C = r(t)
Let’s try a few values: 30 = 5(t)
1. What do we
know?
2. What do we
want to know?
3. Rewrite
equation
4. Guess and
check method
44. Solve
The Justice League of America fights 5 crimes per day. If
they were in the newspaper yesterday for fighting 30
crimes, how many days did the reporter cover?
C = r(t)
Let’s try a few values: 30 = 5(t)
t = 6 30 = 5(6)
30 = 30 ??? Yes!, t = 6
1. What do we
know?
2. What do we
want to know?
3. Rewrite
equation
4. Guess and
check method
Which teacher
wrote this
problem?
45.
46. Solve
One of your teachers brought 16 pairs of shoes to school this
summer. If they wear 2 pairs of shoes per day, how many
days will it take them to wear all of their shoes?
S = r(t)
C = Shoes brought to school
r = rate of shoe wearing per day
t = time
1. What do we
know?
2. What do we
want to know?
3. Rewrite
equation
4. Guess and
check method
47. Solve
One of your teachers brought 16 pairs of shoes
to school this summer. If they wear 2 pairs of
shoes per day, how many days will it take
them to wear all of their shoes?
S = r(t)
1. What do we
know?
2. What do we
want to know?
3. Rewrite
equation
4. Guess and
check method
Let’s try a few values: 16 = 2(t)
t = 8 16 = 2(8)
16 = 16 ??? Yes!, t = 8
Which teacher
wrote this
problem?
48.
49. Quickcheck
The maximum speed of the USS ENTERPRISE is 30 miles per
hour. Knowing that D = r(t), where D = distance, r= rate,
and t = time, how many hours will it take the USS
ENTERPRISE to go 90 miles?
Solve using the guess and check method, using at least
three values.
Guess Check Yes/no
2 hours 90 = 30(2)
90 = 60 ??? No
1. What do we
know?
2. What do we
want to know?
3. Rewrite
equation
4. Guess and
check method
Which teacher
wrote this
problem?
