go math lesson 10 2 homework answers

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Texas Go Math Grade 6 Lesson 10.2 Answer Key Prime Factorization

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 10.2 Answer Key Prime Factorization.

List all the factors of each number.

Question 1. 21 ______________ Answer: List the factors of 21 21 = 1 × 21 21 = 3 × 7 The factors of 21 are 1, 3, 7, 21.

Question 2. 37 ______________ Answer: List the factors of 37 37 = 1 × 37 The factors of 37 are 1, 37,

Lesson 1.2 Prime Factorization Answers 6th Grade Question 3. 42 ______________ Answer: List the factors of 42

• 42 = 1 × 42
• 42 = 2 × 21
• 42 = 3 × 14

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

Question 4. 30 ______________ Answer: List the factors of 30

• 30 = 1 × 30
• 30 = 2 × 15
• 30 = 3 × 10

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The prime factors of 240 are 5 ∙ 3 ∙ 2 ∙ 2 ∙ 2 ∙ 2 or 5 ∙ 3 ∙ 2 4

The prime factors of 54 are 2 ∙ 3 ∙ 3 ∙ 3 or 2 ∙ 3 3

Question 7. Communicate Mathematical Ideas If one person uses a ladder diagram and another uses a factor tree to write a prime factorization, will they get the same result? Explain. Answer: If one person uses a ladder diagram and another uses a factor tree to write a prime factorization, they will get the same result because the prime factors of a number are identical an independent of the method used to evaluate them.

Texas Go Math Grade 6 Lesson 10.2 Guided Practice Answer Key

Use a diagram to list the factor pairs of each number.

Question 1. 18 Answer: Given number: 18

Write the given number as a product of its factors, therefore:

The factors of 18 are 1, 2, 3, 6, 9 and 18.

Question 2. 52 Answer: Given number: 52

Write the given number as a product of its factors, therefore: 52 = 2 × 26 52 = 4 × 13 The factors are of 52 are 1, 2, 4, 13, 26 and 52.

List the possible measurements of the stage based on the factors of 72.

Use a factor tree to find the prime factorization of each number.

Prime factors of 402 are 3 ∙ 2 67.

Prime factors of 36 are 3 ∙ 2 ∙ 3 ∙ 2 or 3 2 ∙ 2 2

Use a ladder diagram to find the prime factorization of each number.

Prime factors of 32 are 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 or 2 5

Essential Question Check-In

Question 8. Tell how you know when you have found the prime factorization of a number. Answer: The prime factorization of a number is verified by studying its factors. They must all be prime numbers.

Question 10. Brandon has 32 stamps. He wants to display the stamps in rows, with the same number of stamps in each row. How many different ways can he display the stamps? Explain. Answer: Given Number = 32

Write the given number as a product of its factors, therefore: 32 = 2 × 16 32 = 4 × 8 This implies that he can arrange the stamps in 4 different ways. He can make 2 columns each containing 16 stamps or 2 rows each containing 16 stamps Or he can make 4 columns each containing 8 stamps or 4 rows each containing 8 stamps.

He can arrange the stamps in 4 different ways. He can make 2 columns each containing 16 stamps or 2 rows each containing 16 stamps. Or he can make 4 columns each containing 8 stamps or 4 rows each containing 8 stamps.

Question 11. Communicate Mathematical Ideas How is finding the factors of a number different from finding the prime factorization of a number? Answer: Finding the factors of a number indicates all the factors that may be used for the number which can be a combination of prime numbers and composite numbers. Finding the prime factorization of a number breaks a composite number into product of its prime factors.

Example: 12 – factors are 1 and 12, 2 and 6, 3 and 4 12 – prime factors are 2 ∙ 2 ∙ 3 or 2 2 ∙ 3

Factors are the numbers to be multiplied. Prime factorization results to product of prime factors of the number.

Find the prime factorization of each number.

Question 12. 891 ______________ Answer: The prime factorization of a number is the number written as the product of its prime factors. For example, the prime factors of 891 are 3, 3, 3, 3 and 11.

The prime factorization of 891 is: 891 = 3 × 3 × 3 × 3 × 11 or 3 4 × 11 = 3 4 × 11

Question 13. 5.4 ______________ Answer: The prime factorization of a number is the number written as the product of its prime factors. For example, the prime factors of 504 are 2, 2, 2, 3, 3 and 7.

The prime factorization of 504 is: 504 = 2 × 2 × 2 × 3 × 3 × 7 or 2 3 × 3 2 × 7 = 2 3 × 3 2 × 7

Question 14. 23 ______________ Answer: The prime factorization of a number is the number written as the product of its prime factors. For example, the prime factors of 23 are 1 and 23.

The prime factorization of 23 is: 23 = 1 × 23

Question 15. 230 ______________ Answer: The prime factorization of a number is the number written as the product of its prime factors. For example, the prime factors of 230 are 2, 5 and 23.

The prime factorization of 230 is: 230 = 2 × 5 × 23

Question 17. Critical Thinking List five numbers that have 3, 5, and 7 as prime factors. Answer:

• 105 = 3 ∙ 5 ∙ 7
• 315 = 3 ∙ 3 ∙ 5 ∙ 7
• 525 = 3 ∙ 5 ∙ 5 ∙ 7
• 735 = 3 ∙ 5 ∙ 7 ∙ 7
• 1,575 = 3 ∙ 3 ∙ 5 ∙ 5 ∙ 7

The numbers are 105, 315, 525, 735, and 1,575.

Question 18. In a game, you draw a card with three consecutive numbers on it. You can choose one of the numbers and find the sum of its prime factors. Then you can move that many spaces. You draw a card with the numbers 25, 26, 27. Which number should you choose if you want to move as many spaces as possible? Explain. Answer: Given number: 25, 26, 27

Write the given numbers as a product of their prime factors, therefore:

• 26 = 2 × 13
• 27 = 3 × 3 × 3

Evaluate the sum of the prime factors, therefore:

• 2 + 13 = 15
• 3 × 3 × 3 = 9

It can be seen that 15 > 10 > 9 therefore the choice of the number 26 will result in the maximum number of moves.

Prime Factorization Grade 6 Pdf Lesson 10.2 Question 19. Explain the Error When asked to write the prime factorization of the number 27, a student wrote 9 3. Explain the error and write the correct answer. Answer: Given number = 27 Write the given number as a product of its prime factors, therefore: 27 = 3 × 3 × 3 Prime factors of the given number is 3 . The student’s solution is incorrect because the factor 9 ¡s not a prime factor. The student’s solution is incorrect because the factor 9 is not a prime factor.

H.O.T. Focus On Higher Order Thinking

Question 20. Communicate Mathematical Ideas Explain why it is possible to draw more than two different rectangles with an area of 36 square units, but it is not possible to draw more than two different rectangles with an area of 15 square units. The sides of the rectangles are whole numbers. Answer: Given number = 36 Write the given number as a product of its factors, therefore:

• 36 = 2 × 18 = Rectang1e 1
• 36 = 3 × 12 = Rectangle 2
• 36 = 4 × 9 = Rectangle 3
• 36 = 36 × 1 = Rectangle 4
• 36 = 6 × 6 = Square

It can be seen that 4 rectangles with different dimensions can be made each having an area of 36 square units

Given number = 15 Write the given number as a product of its factors, therefore:

• 15 = 3 × 5 = Rectangle 1
• 15 = 15 × 1 = Rectangle 2

It can be seen that only 2 rectangles can be made here because the given area is a product of prime factors or the number itself.

Question 21. Critique Reasoning Alice wants to find all the prime factors of the number you get when you multiply 17 ∙ 11 ∙ 13 ∙ 7. She thinks she has to use a calculator to perform all the multiplications and then find the prime factorization of the resulting number. Do you agree? Why or why not? Answer: It can be seen that the number itself has factors that are prime numbers, so no calculator is required and the prime factors: 17, 11, 13 and 7 can directly be deduced.

The prime factors are 7, 11, 13 and 17.

Question 22. Look for a Pattern Ryan wrote the prime factorizations shown below, If he continues this pattern, what prime factorization will he show for the number one million? What prime factorization will he show for one billion? 10 = 5 ∙ 2 100 = 5 2 ∙ 2 2 1,000 = 5 3 ∙ 2 3 Answer: If the pattern continues, the number of zeros will determine the exponent of the base 10. 1 million = 1,000,000 = 5 6 . 2 6 1 billion = 1,000,000,000 = 5 9 . 2 9

The prime factorization for 1 million is 5 6 . 2 6 The prime factorization for 1 billion is 5 9 . 2 9

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• Chapter 1 Place Value, Addition, and Subtraction to One Million
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Grade 4 Homework FL. – Answer Keys

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SOCIAL STUDIES

PROFESSIONAL DEVELOPMENT

HMH Go Math! ® K-6

Built for teacher and student success.

Go Math! for Grades K–6 combines trusted content, practice, and games with user-friendly tools aimed at guiding every learner toward mastery.

The Tools to Engage Learners at All Levels

Go Math! has provided trusted content for more than seven million students worldwide. Now we’ve incorporated more supports to ensure every teacher can feel confident teaching math. The program emphasizes ease of use, bringing together assessment, personalized and adaptive practice, and on-demand professional learning, on one manageable system.

One Time-Saving Platform

Go Math! sets teachers up for success with a practical roadmap for daily lesson planning, assessment that automatically places students into personalized, adaptive practice, and access to rich professional development resources—all on a single platform.

Dynamic Personalization

Embedded Waggle activities, available in English and Spanish, deliver dynamic personalized learning based on Go Math!’s sequence or students’ grade level.​

​Customers using NWEA ® MAP ® Growth™ with Waggle ® will benefit from automatic placement into personalized pathways. MAP Growth scores seamlessly integrate into Waggle , ensuring that students start at their appropriate grade equivalency level.

Ready-to-Go Resources

Our Tabletop Flipchart enhances small-group math instruction with ready-made mini lessons for targeted skills support. Additionally, Go Math! offers abundant resources for centers, differentiated math instruction , and the Tier 2 and Tier 3 supports teachers know and trust.

Attention, Current Go Math! Customers

Our new and improved Go Math! curriculum for Grades K–6 has arrived and is ready to meet the demands of today’s classrooms. Rest assured, we are still here to support teachers using the current version of the program.

Authentic Learning Connections

Go Math! is designed using the proven 5E instructional model , guiding students toward proficiency by building on their previous understanding of mathematical concepts. Embedded formative math assessments ensure students get the support they need.

Math Talk for Collaboration

Embedded Math Talk and collaborative activities encourage lively discourse. Students of all languages feel safe to participate in the math community. Math Talk, new Launch Lessons, Math Centers, and games offer fun opportunities for investigation and discussion.

Acceleration for Every Learner

Waggle goes beyond adaptive practice to complement daily lessons in supporting students at all proficiency levels with curated practice and learning activities that address individual skill gaps.

Streamlined Instruction

Customizable Lesson Presentations

Our streamlined lesson planning, which includes ready-made, editable Classroom Lesson Presentations, saves teachers hours of work.

Wida-Aligned Resources

Support for Multilingual Learners

Go Math! now includes extensive, WIDA-aligned supports for multilingual learners for every lesson, and additional proficiency-level support for pulled small-groups is available via the Tabletop Flipchart.

Teacher Success Pathways

Unlimited Implementation Support

Embedded on-demand training and week-by-week planning guidance build teacher confidence in just 30 days, putting them on a clear pathway to success.

The Power of Connected Teaching and Learning

Ed , HMH's learning platform, offers a connected teaching experience for Go Math! where assessment informs personalized practice, and teachers get the support they need, when they need it—all on one seamless system.

Benchmark Assessment

Personalized skill practice.

• Professional Learning

NWEA MAP Growth is the most trusted and innovative interim assessment for measuring achievement and growth in K–12 math, reading, language usage, and science. It provides teachers with accurate, actionable evidence to help inform instructional strategies regardless of whether students are performing at, above, or below grade level.​

Waggle ® aligns with Go Math! ’s scope and sequence to easily reinforce instruction. The program takes advantage of the latest research on the gamification of learning and provides students the opportunity to work on isolated skills and standards with fun, engaging activities.

Unlimited Professional Learning

Teacher’s Corner , exclusively from HMH, connects teachers across the globe in the Breakroom and in live online webinars. Teacher’s Corner also puts real-world classroom videos and best practices at teachers’ fingertips, on their schedule.

Learn how Go Math! boosts teacher and student success.

Insights & Resources

7 Strategies for Teaching Math to English Language Learners

These ELL strategies for math instruction will help you with teaching math to English language learners and supporting math learning for multilingual students.

Richard Blankman

September 10, 2021

Technology and Personalized Learning

Discover the benefits of technology and personalized learning in the classroom—and digital tools that can automate the personalized learning process.

Aoife Dempsey

April 1, 2022

Coaching for Mathematical Knowledge for Teaching

In order to teach math well, teachers need a specialized type of knowledge called mathematical knowledge for teaching.

Dr. Sue Chapman

May 13, 2022

Go Math!: Research Evidence Base

• Report Type: Research Evidence Base
• Grade Level: Elementary, Middle
• Demonstrates a Rationale

GO Math!: 2015 Elementary Grades Efficacy Study

• Report Type: Efficacy Study, Study Conducted by Third Party
• Region: Midwest, Northeast, West
• District Urbanicity: Urban, Suburban, Rural

GO Math!: Randomized Control Trial (RCT) 2-Year Study, Grades 1, 2, and 3

• Grade Level: Elementary
• Region: Midwest, Northeast, Southwest, West
• District Urbanicity: Suburban, Rural
• Moderate Evidence

GO Math!: Quasi-Experimental Design (QED) Study, Grades 3, 4, and 5

• District Urbanicity: Urban, Suburban
• Promising Evidence

GO Math!: Efficacy Study, Grades 2–4

• Region: Midwest, Northeast

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Go Math! Multilingual Support

Go Math! K–6 Teacher Tabletop Flip Chart Sampler