Factors...Multiples...Game On!
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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:
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
Associated Standards and Objectives
Content Standard(s):
Digital Literacy and Computer Science 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:
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.
Mathematics 8. Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.
a. Use factors and multiples to determine prime factorization.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given any two or more whole numbers,
Strategically select and apply strategies for finding the greatest common factor of the two numbers and justify that the strategy used does produce the correct value for the greatest common factor.
Strategically select and apply strategies for finding the least common multiple of the two numbers and justify that the strategy used does produce the correct value for the least common multiple.
Use the relationship between factors and multiples to determine prime factorization. Teacher 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. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.6.8.1: Identify the least common multiple of a given set of numbers, with or without the use of a calculator.
M.6.8.2: List multiples of any given whole number, with or without the use of a calculator.
M.6.8.3: Identify the greatest common factors of a given set of numbers, with or without the use of a calculator.
M.6.8.4: Define prime factorization.
M.6.8.5: List common factors of given whole numbers, with or without the use of a calculator.
M.6.8.6: Identify the prime factorization of a single digit number, with or without the use of a calculator.
M.6.8.7: Identify the prime factorization of any two digit whole number, with or without the use of a calculator.
Prior Knowledge Skills:
Define Multiple.
Name the first ten multiples of each one-digit natural number.
Name the first 10 multiples of each one-digit natural number.
Count within 1000; skip-count by 5s, 10s, and 100s.
Recall basic multiplication facts.
Name the first ten multiples of each one-digit natural number.
Identify all factor pairs for a whole number in the range 1-20.
Apply properties of operations as strategies to multiply and divide.
Define factors, prime number, and composite number.
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
