# ALEX Learning Activity

## Factors...Multiples...Game On!

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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This learning activity provided by:
 Author: Kimberly Dockery System: Alabama Department of Education School: Alabama Department of Education
General Activity Information
 Activity ID: 2699 Title: Factors...Multiples...Game On! Digital Tool/Resource: Illuminations: Product Game Web Address – URL: https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Product-Game/ 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 DiagramsProduct Game Reflection
Associated Standards and Objectives
Content Standard(s):
 Digital Literacy and Computer Science DLIT (2018) Grade: 6 6) Identify steps in developing solutions to complex problems using computational thinking. Unpacked Content Evidence Of Student Attainment:Students will: use the problem solving or design thinking process to think logically through a previously solved complex problem.Teacher Vocabulary:computational thinkingKnowledge: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. Mathematics MA2019 (2019) Grade: 6 7. Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. Unpacked Content Evidence Of Student Attainment:Students: Use the distributive property to write an equivalent expression for the sum of the two numbers as the product of the greatest common factor of the two numbers, and the sum of two whole numbers with no common factor. [if the two whole numbers are 36 and 8, 36+8 = 4(9+2)].Teacher Vocabulary:Greatest common factor Distributive property Parentheses DecomposeKnowledge:Students know: Distributive property of multiplication over addition. Strategies to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor by decomposing the numbers.Skills:Students are able to: Use and model the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor by decomposing the numbers.Understanding:Students understand that: Multiplication is distributive over addition. Composing and decomposing numbers provides insights into relationships among numbers. Quantities can be represented using a variety of equivalent expressions.Diverse Learning Needs: Essential Skills:Learning Objectives: M.6.7.1: Define greatest common factor, least common multiple, and the distributive property. M.6.7.2: Design problems using greatest common factor and the distributive property. M.6.7.3: Show an understanding of how to solve a problem using the distributive property, with or without the use of a calculator. Prior Knowledge Skills:Identify factor and product. Explain why addition and subtraction strategies work, using place value and the properties of operations. Apply properties of operations as strategies to multiply and divide.
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.
Strategies, Preparations and Variations
 Phase: During/Explore/Explain Activity: 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: 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. Advanced 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. Variation Tips (optional): 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. Notes or Recommendations (optional): If multiple days are available, create a class tournament using the Product Game. Depending on the class size, use single or double elimination.
Keywords and Search Tags
 Keywords and Search Tags: Factor, Factors, Game, Interactive, Multiple, Multiples