Learning Resource Type

Learning Activity

Factors...Multiples...Game On!

Subject Area

Digital Literacy and Computer Science
Mathematics

Grade(s)

6

Overview

The Illuminations tool, Product Game, is an excellent resource for students to gain a deeper understanding of factors and multiples. This tool challenges students to make offensive and defensive moves to obtain four products in a row by selecting factors ranging from one to nine. The challenge comes when one of the factors must be from your opponent’s last move. Students can either play against the computer or with a partner in their class.

GCF Venn Diagrams

Product Game Reflection

    Mathematics (2019) Grade(s): 6

    MA19.6.8

    Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

    Unpacked Content

    UP:MA19.6.8

    Vocabulary

    • Greatest common factor
    • Least common multiple
    • Exponential Form
    • Prime Factorization
    • Factors
    • Multiples
    • Prime
    • Relatively Prime
    • Composite

    Knowledge

    Students know:
    • Strategies for determining the greatest common factor of two or more numbers,
    • Strategies for determining the least common multiple of two or more numbers,
    • Strategies for determining the prime factorization of a number.

    Skills

    Students are able to:
    • Apply strategies for determining greatest common factors and least common multiples.
    • Apply strategies for determining the product of a number's prime factors in multiple forms which include exponential form and standard form.

    Understanding

    Students understand that:
    • Determining when two numbers have no common factors other than one means they are considered relatively prime.
    • Composing and decomposing numbers provides insights into relationships among numbers.
    Digital Literacy and Computer Science (2018) Grade(s): 6

    DLCS18.6.6

    Identify steps in developing solutions to complex problems using computational thinking.

    Unpacked Content

    UP:DLCS18.6.6

    Vocabulary

    • computational thinking

    Knowledge

    Students know:
    • how to define the problem.
    • how to plan solutions.
    • how to implement a plan.
    • how to reflect on the results and process.
    • how to iterate through the process again.

    Skills

    Students are able to:
    • identify the steps involved with formulating problems and solutions in a way that can be represented or carried with or without a computer.

    Understanding

    Students understand that:
    • computational thinking is formulating problems and solutions in a way that can be represented or carried out with or without a computer.

    Phase

    During/Explore/Explain
    Learning Objectives

    Learning Objectives

    Students will:

    • find common factors of two given whole numbers.
    • explain offense and defense steps to win the Product Game.
    • demonstrate the difference between factors and multiples.
    • identify the steps in their offensive and defensive moves during gameplay to demonstrate computational thinking.

    Activity Details

    Prior to completing this activity, students need to understand the difference between multiples and factors. A multiple of a number is the product of that number and any nonzero whole number. A factor is a whole number that divides another whole number with a remainder of zero. Any number is always divisible by all its factors.

    Pass out the GCF Venn Diagrams. There are ten different combinations. You have the flexibility to have students complete one or all of the Venn Diagrams. Some are more challenging than others to accommodate student’s different ability levels. Students will then list all the factors of the two numbers and complete the Venn Diagram by placing common factors in the middle. Understanding common factors between two numbers is an important step to be successful in the Product Game. Then students will discover the GCF by identifying the largest number in the middle. 

    Have students access the Product Game and play a few rounds. One student will move one marker to make their first move. The resulting multiple will be identified on the gameboard. The next player can only move one of the two markers to create another multiple as their move on the gameboard. The object is for each player to get four moves in a row either horizontally, vertically, or diagonally. Students can either play against the computer or with a partner. Finally have students complete the Product Game Reflection. This will require them to think about how the game works and connect how to make strategic moves to win the game.

    Assessment Strategies

    Assessment Strategies

    3-2-1: Have students list 3 new things they learned, 2 questions they still have, and 1 connection they made while playing the Product Game.

    Teacher observation of students while using the digital tool Product Game.

    Review students' responses to the Venn Diagram and/or Product Game reflection to assess student understanding.

     

    Variation Tips

    • The GCF Venn Diagrams could be set up around the classroom as stations to allow students the opportunity to move.
    • Have students play after they complete the reflection task thinking about strategic moves.
    • Change the settings within the game to include more factors. This can be done with the customize button on the left of the game board.

    Background and Preparation

    Background / Preparation

    Each student or pair of students will need an electronic device.

    Ensure Internet access is available.

    Make copies of the GCF Venn Diagrams.

    Make copies of the Product Game Reflection.

    Digital Tools / Resources

    ALSDE LOGO