# Algebra 2 Lesson Plan 3 - Matrices

**Learning Outcomes:**

1. Key vocabulary for matrices

2. Adding and subtracting of matrices. Standard Course of Study goal 1.04 for
Algebra 2 will be taught.

3. Applying a real life scenario using the Olympic medaling as a matrix –
project with research and testing outcomes/data analysis. SCOS Goal 2.10.

4. Students will learn more about the world through the Olympics, working in
groups, synthesizing data and evaluating the project.

**Evidence of Student Success:**

1. Project applying matrices to the Olympics over a two
week time period.

2. Students will demonstrate usage of vocabulary in their projects along with
creating matrices. Students will practice adding and subtracting matrices.

3. Students will use their researching skills to do the project and hypothesize.

4. Students will summarize and reflect on the project so critical thinking
skills will shine through. Materials Needed: Handout with Olympics project,
sources to find data about outcomes from Olympic

**Materials Needed:** Handout with Olympics project,
sources to find data about outcomes from Olympic games.

**Time:** Lesson will take a two-three weeks time
period to fully complete.

What the Teacher will do | What the Student will do |

Introduce matrices. Define vocabulary words: | Copy down definitions. Talk through meanings , |

Matrix (matrices plural), element, dimensions, | Ask questions if do not understand |

square matrix, row matrix, column matrix, scalar | |

product | |

Present examples of matrices . Explain rules for | Listening and absorbing. Asking questions? |

adding matrices, must be same dimension. Same | copying examples. |

for subtraction. Then multiplying by a constant c. | |

Guided practice of adding, subtracting, and | Practicing sample problems at their seat |

multiplying by a constant. | Independently. |

Present handout with project assignment. | Creating an hypothesis, thinking of ways to |

See attached. | Research the medal counts daily |

Process of setting up matrices, manipulating | |

the matrices for final results. Learning to work | |

in a group and analyzing data. | |

Continue to use class time to work on projects | Students must turn in hypotheses for approval. |

Walk around to help students and check on | They must clearly demonstrate what |

progress. Make sure their hypotheses are sound | they are comparing and that it is thorough. |

and will result in accurate data. | |

After papers are turned in, talk about the project | |

share findings and compare results as a class. | |

Evaluate the project. |

Olympics Project

Purpose/objectives: To use matrices in real life scenarios, to practice researching skills, to test hypotheses and outcomes, and to learn about other countries and sports.

We will have class time to work on this and use the computer lab, newspaper, and television. You will work in groups of 3, but each person must write their own reflection at the end of the project. However, you will turn in one summary of your findings per group.

Over a two week period, follow the Olympic medal counts. Pick 3 sports to follow and 3 teams to follow in that sport throughout the Olympics. Hypothesize which teams in your chosen sports will end up with the highest total medal count and also most gold medals. You should have 6 hypotheses, two for each sport since within each sport you will hypothesize what country will have the highest total medal count and then the most gold medals. Make sure to be specific in what sports you are choosing. There are several competing categories within each sport including different distances, relays, men or women, team or individual, etc. Research your sports to make sure you have a grasp of all the competitions. Investigate previous Olympics and countries so you can make a sound hypothesis.

**Example:
**1) I feel that Russia will have the most gold medals in the men and women
gymnastics competition for the team competitions. 2) I think the United States
will have the most medals in the overall gymnastics sport including men and
women, individual and team competitions.

3) I feel that New Zealand will take the most medals in relay swimming for men and women and all distances.

4) I feel that Germany will have the most gold medals in swimming for all women’s competitions – team and individual.

After collecting the data for your sport the first week, create a matrix for each sport of the winning teams by total medals earned.

**Example** Swimming:

Gold | Silver | Bronze | |

Team | |||

New Zealand | 3 | 0 | 1 |

Germany | 2 | 1 | 0 |

Sri Lanka | 0 | 2 | 0 |

Create another matrix of that sport the next week to include trials of the sport that week. You should have at least 2 matrices per sport. Add the matrices to get your final medal count for the end of the Olympics. (If your sport is completed in the first week, break your matrices up to reflect two sets of data – one matrix the first few trials and the next matrix the final trials). Be careful not to have your second matrix reflect the running total of the medal counts. Show your work.

Once your matrices are totaled and added, test your hypotheses by using the matrices. Were they true or false? As a group write a summary of your findings. This should address all of your hypotheses so a minimum of three paragraphs, one per sport. Compare the overall Olympics and how each team faired. What do you think it means if a country/team did not receive a gold medal but had several other medals? What if a team only had 1 gold medal and no other medals? Did the matrices help you evaluate your hypotheses and the data? How? What sources did you find useful in finding your data. Were there any flaws or possible errors in your data? Make sure the use your vocabulary words for matrices when writing. Look at the larger picture and Olympics as whole. Did some teams do better in one sport than another? Are some countries well-rounded in the summer/winter Olympics?

After the end of your group summary, each person will write a reflection of project: Was there a sport you enjoyed watching more than another – why? What about it made you enjoy it or not enjoy it. Name 3 new things you learned about the Olympics as an organization, teams competing, Beijing, or individual players. What did you like about this project? What would you change? Reflection should not be longer than a page, double spaced.

What you will turn in:

A list of all your hypotheses – due early for approval

3 matrices per sport so 9 total as a group.

A group summary of your findings evaluating all of your hypotheses

A personal reflection