Updated 2/6/2016
Meaningful Distributed Practice Planning
Grade Level / Class
Big Idea(s)
Preview
Middle School or High School
Review
Counting Methods (Tree Diagrams, Addition Principle, & Multiplication Principle)
MDP1
MDP 2
Suppose that you have a jar that contains four colored balls – a red one, a green
one, a blue one, and a yellow one. Imagine that you take one ball from the
container, record its color, and return it to the container. Then you take a second
ball from the container, record its color.
Suppose that you have a jar that contains four colored balls – a red one, a green
one, a blue one, and a yellow one. Imagine that you take one ball from the
container, record its color, and do not return it to the container. Then you take a
second ball from the container, record its color.
How many different pairings are possible? How did you represent this situation?
How many different pairings are possible?
Some Probing Questions:
Some Probing Questions:






Can this situation be explained with a Tree diagram? Explain.
Can this situation be explained using an array model? Explain.
Can this situation be explained using a Counting Principle? Explain.
Can this situation be explained using the other Counting Principle?
Explain.
Can the way you represented the pairs be explained another way?
Explain.
Does the fact that the ball IS RETURNED to the container affect the
number of possible outcomes? Explain.
Anticipated Student Responses:
RR RG
GR GG
BR BG
YR YG
RB
GB
BB
YB
RY
GY
BY
YY
Each color has four ways to make pairs
4 + 4 + 4 + 4 = 16 (Addition Principle)
Four ways to pair each of four colors
4 x 4 = 16 (Multiplication Principle)
7030 a Counting Methods






Can this situation be explained with a Tree diagram? Explain.
Can this situation be explained using an array model? Explain.
Can this situation be explained using a Counting Principle? Explain.
Can this situation be explained using the other Counting Principle?
Explain.
Can the way you represented the pairs be explained another way?
Explain.
Does the fact that the ball IS NOT RETURNED to the container affect the
number of possible outcomes? Explain.
Anticipated Student Responses:
Red
Blue
Red
Green
Blue
Yellow
Red
Green
Blue
Yellow
Green
Yellow
Red
Green
Blue
Yellow
Red
Green
Blue
Yellow
Three ways to pair each of four colors
4 x 3 = 12 (Multiplication Principle)
Red
Each color has three ways to make pairs
3 + 3 + 3 + 3 = 12 (Addition Principle)
Blue
(4 x 4) – 4 = 12
P( 4,3) =
Green
Blue Green
Yellow
Red
Green Yellow
Yellow
Red
Blue
Yellow
Red
Green
Blue
4!
= 12
( 4 - 2)!
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Updated 2/6/2016
MDP3
MDP4
Suppose that you have a jar that contains four colored balls – a red one, a green
one, a blue one, and a yellow one. Imagine that you take one ball from the
container, record its color, and return it to the container. Then you take a second
ball from the container, record its color.
Suppose that you have a jar that contains four colored balls – a red one, a green
one, a blue one, and a yellow one. Imagine that you take one ball from the
container, record its color, and return it to the container. Then you take a second
ball from the container, record its color.
If the goal is to draw two balls and have exactly one of the balls be red, how
many different outcomes are possible?
After drawing two balls, how many different outcomes include at least one red
ball?
Some Probing Questions:
Some Probing Questions:






Can this situation be explained with a Tree diagram? Explain.
Can this situation be explained using an array model? Explain.
Can this situation be explained using a Counting Principle? Explain.
Can this situation be explained using the other Counting Principle?
Explain.
Can the way you represented the pairs be explained another way?
Explain.
Does the fact that the ball IS RETURNED to the container affect the
number of possible outcomes? Explain.






Can this situation be explained with a Tree diagram? Explain.
Can this situation be explained using an array model? Explain.
Can this situation be explained using a Counting Principle? Explain.
Can this situation be explained using the other Counting Principle?
Explain.
Can the way you represented the pairs be explained another way?
Explain.
Does the fact that the ball IS RETURNED to the container affect the
number of possible outcomes? Explain.
Note: The Multiplication Principle does not apply directly to this situation.
Note: The Multiplication Principle does not apply directly to this situation.
Anticipated Student Responses:
Anticipated Student Responses:
RR RG
GR GG
BR BG
YR YG
RB
GB
BB
YB
RY
GY
BY
YY
Red
3+ 1 + 1 + 1 = 6 (Addition Principle)
Blue
Red
Green
Blue
Yellow
Red
Green
Blue
Yellow
Green
Yellow
Red
Green
Blue
Yellow
Red
Green
Blue
Yellow
Notes:
 The Multiplication Principle does not apply directly to this situation.
 Permutations and Combinations do not apply directly to this situation.
7030 a Counting Methods
RR RG
GR GG
BR BG
YR YG
RB
GB
BB
YB
RY
GY
BY
YY
Red
4 + 1 + 1 + 1 = 7 (Addition Principle)
Blue
Red
Green
Blue
Yellow
Red
Green
Blue
Yellow
Green
Yellow
Red
Green
Blue
Yellow
Red
Green
Blue
Yellow
Notes:
 The Multiplication Principle does not apply directly to this situation.
 Permutations and Combinations do not apply directly to this situation.
2/2