ALEX Classroom Resource

  

Grade 6 Mathematics Module 2, Topic D: Number Theory--Thinking Logically About Multiplicative Arithmetic

  Classroom Resource Information  

Title:

 Grade 6 Mathematics Module 2, Topic D: Number Theory--Thinking Logically About Multiplicative Arithmetic

URL:

 https://www.engageny.org/resource/grade-6-mathematics-module-2-topic-d-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 2, Topic D, students think logically about multiplicative arithmetic. Students apply odd and even number properties and divisibility rules to find factors and multiples. They extend this application to consider common factors and multiples and find the greatest common factors and least common multiples. Students explore and discover that Euclid’s Algorithm is a more efficient way to find the greatest common factor of larger numbers and see that Euclid’s Algorithm is based on long division.   

Content Standard(s):
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
  • Decompose
Knowledge:
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.
Mathematics
MA2019 (2019)
Grade: 6
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.
    Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.
  • 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.
Tags: distributive property, factor, greatest common factor, least common multiple, sum
License Type: Custom Permission Type
See Terms: https://www.engageny.org/terms-of-use
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityText Resources: Content is organized under headings and subheadings
Comments

There are four lessons in this topic.

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site.

  This resource provided by:  
Author: Hannah Bradley
This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
Copyright © 2017, Alabama Learning Exchange
Alabama State Department of Education
Alabama State Department of Education