Curriculum / Math / 6th Grade / Unit 3: Multi-Digit and Fraction Computation / Lesson 15
Math
Unit 3
6th Grade
Lesson 15 of 17
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Find the greatest common factor of two numbers. Solve application problems using the greatest common factor.
The core standards covered in this lesson
6.NS.B.4 — 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 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
The foundational standards covered in this lesson
4.OA.B.4 — Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Understanding the greatest common factor of two numbers will support students in their work in Unit 5, Numerical and Algebraic Expression, where they will use common factors and the distributive property to write expressions in factored form.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Find the greatest common factor by listing out factors.
a. Find the greatest common factor of 12 and 18.
b. Use this same method to find the greatest common factor of 48 and 56.
Grade 6 Mathematics > Module 2 > Topic D > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Find the greatest common factor by using prime factorization.
c. Use this same method to find the greatest common factor of 8 and 25. What happens in this example?
Jasmine’s family is having a family picnic. Jasmine is planning on ordering enough pizza to have 96 slices and a tray of 72 cookies. She wants to make sure each family member gets the same number of cookies and slices of pizza. Based on this food order, what is the greatest number of family members Jasmine can invite to the picnic? How many slices of pizza and cookies will each family member get?
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Complete each of the following:
a. List all the factors of 48.
b. List all the factors of 64.
c. What are the common factors of 48 and 64?
d. What is the greatest common factor of 48 and 64?
Factors and Common Factors, accessed on Sept. 28, 2017, 4:31 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 14
Lesson 16
Topic A: Dividing with Fractions
Interpret division problems as the number of items in each group or the number of groups of a given number of items. Write corresponding multiplication and division problems.
6.NS.A.1
Divide a fraction by a whole number using visual models and related multiplication problems.
Divide a whole number by a fraction using visual models.
Use visual models and patterns to develop a general rule to divide with fractions.
Solve and write story problems involving division with fractions.
Solve problems involving division with fractions.
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Topic B: Computing with Decimals
Add and subtract decimals using the standard algorithm.
6.NS.B.3
Multiply decimals using strategies, and develop an understanding of the standard algorithm.
Multiply decimals using the standard algorithm.
Divide multi-digit whole numbers using the standard algorithm.
6.NS.B.2
Divide numbers with decimal quotients. Divide decimals by whole numbers.
6.NS.B.2 6.NS.B.3
Divide decimals by decimals using the standard algorithm.
Solve problems involving decimals using all four operations.
Topic C: Applying the Greatest Common Factor and the Least Common Multiple
Use prime factorization to represent numbers as products of prime factors.
6.NS.B.4
Find the least common multiple of two numbers. Solve application problems using the least common multiple.
Solve mathematical and real-world problems using the greatest common factor and least common multiple.
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