Curriculum / Math / 6th Grade / Unit 3: Multi-Digit and Fraction Computation / Lesson 14
Math
Unit 3
6th Grade
Lesson 14 of 17
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Lesson Notes
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Use prime factorization to represent numbers as products of prime factors.
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
While prime factorization is not explicitly mentioned in the standards, understanding how numbers can be represented as a product of prime factors can support students in understanding concepts like greatest common factor and least common multiple.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Four numbers are shown below. Each number has something unique about it that is unlike the other three numbers. What makes each number different from the others?
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For each number below, use a factor tree to write the number as a product of prime factors.
48 140
The pictures shown below are composed of dots, organized in various ways to represent numbers.
a. These pictures represent numbers 1–7. What do you notice? What patterns do you see? How are these pictures related to the prime factorization of the numbers?
b. These pictures represent numbers 8–14. What do you notice? What patterns do you see? How are these pictures related to the prime factorization of the numbers?
c. What number does the picture below represent? What would the picture look like for the number 28?
d. Optional: Play factor dominoes using the cards for numbers 1–60.
New Math Game: Factor Dominoes! by Malke Rosenfeld is made available on The Math in Your Feet Blog under the CC BY-NC-SA 4.0 license. Accessed Sept. 28, 2017, 4:19 p.m..
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
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
5-10 minutes
Find the prime factorization of the numbers below. Show your work.
200 56 91
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.
Next
Find the greatest common factor of two numbers. Solve application problems using the greatest common factor.
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.
Standards
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.26.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
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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