ALEX Learning Activity

In this interactive activity, students will be introduced to the concept of the greatest common factor (GCF) in a fun and engaging way. The activity revolves around an exciting article featuring NHL hockey star Nathan MacKinnon and his remarkable achievements in the sport. As students read the article, they will encounter five intriguing questions about MacKinnon's life and career. Using GCF, students will deduce the correct answers from the given choices. The primary goal of this activity is to introduce students to the concept of GCF and spark their curiosity through real-life scenarios involving a well-known sports figure allowing students to connect mathematical concepts with their interests and experiences, creating an enjoyable and relatable learning experience.

This learning activity was created as a result of the ALEX - Alabama Virtual Library (AVL) Resource Development Summit.

Students will use their knowledge of factors and multiples to find the greatest common factor (GCF).

1. Begin by asking students if they have heard of Nathan MacKinnon or any other NHL stars. Share some interesting facts about MacKinnon's achievements, highlighting his record-breaking moments.

2. Explain that students will read an article from Alabama Virtual Library about MacKinnon and answer questions related to his life and career, incorporating the concept of the greatest common factor. After reading, they will be presented with five questions from the article, each associated with two sets of numbers representing potential answers. Students will use their knowledge of GCF to find the correct answer to each question.

3. Provide students with copies of the article, paper to write down their solutions, and ask the students to read the article independently or in pairs.

4. Display the first question on the board: "Q: How old were you when you started skating?" and the given options with GCF of two numbers.

5. Discuss how to find the GCF using the "List all the factors" method described in the article.

6. After students have attempted to find the GCF for the first question, divide them into small groups to discuss their answers. Encourage students to share their thought processes and how they arrived at their solutions.

7. Facilitate group discussions to ensure all students understand how to calculate the GCF correctly.

8. Bring the class back together and review the correct GCF for the first question as a whole group.

9. Continue displaying the next question with its respective options on the board. Repeat the process, allowing students to work in groups, discuss their answers, and review each question as a class. 

10. Summarize the key points of the activity, emphasizing the concept of GCF and its application in solving problems.

The teacher will review the students' answers to the five questions about Nathan MacKinnon's life and check if they correctly found the greatest common factor for each set of numbers. This will help assess their understanding of GCF and prior knowledge. 

Approximate Duration: The activity can be completed within a single class period, typically lasting around 30 to 45 minutes, depending on the pace of the students and the level of discussion and engagement during the activity.

Materials and Resources:

1. Interactive whiteboard or projector: Utilize an interactive whiteboard or projector to display the set of whole numbers to the whole class. This will allow for easier visualization and group discussions.

2. Manipulatives (optional): Consider using manipulatives such as counters, cubes, or other math manipulatives to provide a hands-on experience for students while exploring factor pairs. These manipulatives can help students visualize the concept of factors and make connections.

3. Pens or pencils: Ensure students have writing utensils such as pencils or pens to work on and write down their solutions.
4. Sticky notes, individual dry-erase boards, student notebooks, or index cards for students to record their factor pairs, GCFs, and LCMs.
5. Print and/or digital copies of the article

Background Information/Preparation:

For Students: 

Prior to the activity, students should have a basic understanding of multiplication and factors. They should be familiar with the concept of factors, which are numbers that divide evenly into another number without leaving a remainder. 

For the Teacher:

Print and/or digital copies of the article.

Teachers should prepare materials for the activity prior to the lesson. They should also familiarize themselves with the content and questions in the activity to facilitate classroom discussions and provide necessary guidance to students.

Acceleration Strategy: For students who grasp the concept quickly and show proficiency, provide them with a challenge extension. Assign them a set of higher-level problems that require them to find GCFs of larger numbers or solve more complex mathematical equations involving GCFs. Encourage them to explain their reasoning and strategies used to find the GCFs. This extension will deepen their understanding and provide an opportunity for advanced problem-solving skills.

Intervention Strategy: For students who need help understanding the concept, provide additional support and scaffolding. Break down the process step by step, using manipulatives or visual aids to make it more concrete. Offer extra practice problems with smaller numbers to build their confidence and gradually increase the complexity. Provide individual or small-group instruction, offering frequent opportunities for guided practice and immediate feedback. Use questioning techniques to help them think through the process and guide them toward the correct answers.

This activity is followed by Determining the Greatest Common Factor with "Who Is... The Greatest?" and Determining the Greatest Common Factor with "Jason's the Greatest." 

Suggestions for strategies to teach GCF and LCM: When finding the greatest common factor (GCF) and least common multiple (LCM) of numbers, students can use several strategies. Here are some strategies they can employ specifically when given factor pairs:

1. Listing Method: Students can list all the factors of the given numbers and identify the common factors to find the GCF. To find the LCM, they can list the multiples of the numbers until they find a common multiple.

2. Prime Factorization Method: Students can use prime factorization to find the GCF and LCM. They can break down each number into its prime factors and then identify the common factors for the GCF and multiply the highest powers of the common and uncommon prime factors to find the LCM.

3. Venn Diagram Method: Students can draw a Venn diagram with two circles and write the factor pairs of each number in the respective circles. They can then identify the common factors in the overlapping region to find the GCF. For the LCM, they can multiply the factors in both circles, including the factors in the overlapping region.

4. Division Method: Students can use the division method to find the GCF. They can divide the larger number by the smaller number and continue dividing the remainder by the smaller number until the remainder is zero. The last divisor used is the GCF. To find the LCM, they can divide the product of the two numbers by the GCF and multiply the result by the smaller number.

5. Using a Calculator: Students can use a calculator with GCF and LCM functions, if available, to find the GCF and LCM quickly. They input the numbers and use the respective functions to obtain the results.

Encourage students to choose the strategy that works best for them and practice using different methods to develop a deeper understanding of GCF and LCM concepts.