Students begin module 2 by using visual models and an understanding of divisibility to find the greatest common factor and least common multiple of pairs of numbers. Then, students apply their previous understanding of multiplication and division to divide fractions by fractions. They model fraction division expressions with tape diagrams and double number lines, use common denominators to divide fractions by fractions, and then develop and apply the invert and multiply strategy. Students use standard algorithms to fluently add, subtract, and multiply decimals, and apply those skills in real-world applications. They extend their understanding of division from prior grades to use the standard division algorithm to divide multi-digit numbers and decimals.
In topic A, students first explore visual models involving square and rectangular tiles to determine common factors and common multiples of pairs of numbers. Students learn strategies for determining divisibility by 3 and 6, use number sense to reason about divisibility of any given number, and explore the connection between divisibility and factors. They learn the definitions for greatest common factor (GCF) and least common multiple (LCM) and use a variety of strategies to find GCF and LCM, including organized lists of factors and multiples, prime factorization, and Venn diagrams. In an optional lesson, students learn and apply the Euclidean algorithm to find the GCF of two numbers and use the GCF to find the LCM.
6.NS.7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers from 1 to 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.
I can...
Use visual models to determine common factors and common multiples of pairs of numbers.
Lesson at a Glance
In this digital lesson, students identify the differences between factors and multiples. They first play a game and develop strategies for finding factors and multiples of numbers. Students then explore two interactive visual models to discover common factors and common multiples of two numbers.
Use the digital platform to prepare for and facilitate this lesson. Students will also interact with the lesson content and activities via the digital platform.
I can...
Determine whether numbers are divisible by other numbers.
Lesson at a Glance
In this lesson, students work in groups to make conjectures about divisibility. They defend their reasoning, agree or disagree with their classmates’ conjectures, and give counterexamples as necessary. Students review divisibility rules for 2, 5, and 10 and establish divisibility rules for 3 and 6. Students learn that they can skip-count as a general method to determine divisibility by other numbers, such as 4, 7, 8, and 9.
I can...
Determine the greatest common factor of two whole numbers less than or equal to 100.
Lesson at a Glance
In this lesson, students list factor pairs of two numbers to find their greatest common factor. They work in groups to write the prime factorizations of numbers and recognize that each number has a unique prime factorization. Students use the prime factorizations of two numbers to find their greatest common factor. Working in pairs, students find the greatest common factor in real-world contexts. This lesson introduces the terms greatest common factor and prime factorization.
I can...
Find the least common multiple of two whole numbers less than or equal to 12.
Lesson at a Glance
To begin this lesson, students watch a video about a situation, which leads them to ask questions that they can answer by finding common multiples. Students list multiples of two numbers to identify the least common multiple. Working in pairs, students create a Venn diagram with the prime factors of two numbers. They realize that the least common multiple of the two numbers is the product of all the prime factors shown in the Venn diagram. This lesson introduces the term least common multiple.
I can...
Find the greatest common factor of large numbers by using the Euclidean algorithm.
Find the least common multiple of large numbers by using the greatest common factor.
Lesson at a Glance
In this optional lesson, students work in pairs to solve a new puzzle. They find the side length of the square that remains after repeatedly removing the largest squares from rectangles. Students use the Euclidean algorithm to calculate the greatest common factor of two large numbers and compare that method to how they solved the puzzle. Students then calculate the least common multiple of two large numbers by using the greatest common factor and a Venn diagram.