Counting Methods
Goal:
¬ To assess Students:
o Understanding of Counting methods
o Addition and Multiplication Principals
Standards:
| 7 |
IV. DATA ANALYSIS, STATISTICS AND
PROBABILITY |
A. Data and
Statistics |
Re present data and use various measur
conclusions and identify trends. |
| 7 |
IV. DATA ANALYSIS, STATISTICS AND
PROBABILITY |
B. Probability |
Calculate and express probabilities num
concepts to solve real -world and mathem |
Materials:
Application of the Multiplication and Addition Principles Worksheet
Activity:
Complete the problems on the above menti oned worksheet with a partner. Draw
diagrams and charts to
justify your findings.
As a class share your findings and discuss differences in methods and results .
Gold Lotto
Goal:
To access students in the application of Counting Principles ie. Combinations
Materials:
The game of Gold Lotto
Application of Combinations
Standard:
| 7 |
IV. DATA ANALYSIS, STATISTICS AND
PROBABILITY |
A. Data and
Statistics |
Represent data and use various measur
conclusions and identify trends. |
| 7 |
IV. DATA ANALYSIS, STATISTICS AND
PROBABILITY |
B. Probability |
Calculate and express probabilities num
concepts to solve real-world and mathem |
Activities:
Play the game of Gold Lotto with a friend until you feel you have an
understanding of how the game is
played.
Complete the Questions on the Application of Combinations with your partner and
be prepared to discuss
your results with the class.
The Colorful Houses of Tourist Town
Goal:
¬ Introduction to Graph Theory
¬ Encouraging students through Colorful Houses to ask two types of questions.
o How will this activity change if we play it on a
different graph ?
o What if we change the rules or invented a different, but similar game?
Standards:
| 7 |
I. MATHEMATICAL
REASONING |
|
Apply skills of mathematical representation ,
communication and
four content strands. |
| 7 |
IV. DATA ANALYSIS,
STATISTICS AND
PROBABILITY |
A. Data and
Statistics |
Represent data and use various
measures associated with data to draw
conclusions and identify trends. |
| 7 |
IV. DATA ANALYSIS,
STATISTICS AND
PROBABILITY |
B. Probability |
Calculate and express probabilities
numerically and apply probability
concepts to solve real-world and
mathematical problems. |
Materials:
¬ Paint your house today worksheet
¬ Colors/Colored Pencils
Activity:
In Tourist Town there is something interesting to see in every house, and
the people who live there
want the tourists to visit them all. The City Council has decided to buy enough
paint to repaint all of
the houses.
If tourists leave a house that they have just visited and
look down a street and see a house that is the
same color, they might think that it is just like the house that they just left
and not visit it. So the
City Council wants to repaint the houses so that no house is the same color as
the next house down
the street in any direction.
Discussion
How many different colors of paint will the City Council need to buy?
If you were the city council how would you want the
outside of the homes in your town painted?
What if homes could have more than one color?
What connections can you make between number of homes ,
number of colors, and how many
colors are al lowed on each house .
Connect the ideas of the classes, and create a general
rule for your town. Make conjectures about
how many colors you need…What if you could have two houses the same color next
to each other?
Town Home Idea…
Variations:
1. Start with less Houses…Look at just one circle of 6 houses
2. Add a second group of 6 houses
3. Connect several groups together..
4. Place distances between homes and calculate the shortest distance, longest
distance, etc for
someone to visit every home. (Greedy and Nearest Neighbor)z
Extensions:
More Games on Graphs
