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2015-2016 Curriculum Blueprint Grade: 4 Course: Mathematics Topic 7 – Factors and Multiples Flexible Time Line 6 days Topic Overview Students will be able to identify factors and multiples of whole numbers from 1 to 100 to determine if those numbers are prime or composite using strategies such as arrays and patterns. Vertical Progression 3rd Grade: Students develop fluency with basic multiplication and division facts. Students are given 2 factors in order to find a product. This work provided essential background for understanding factors and multiples. Students relate multiplication to area (arrays can be used to find factors). th 5 Grade: Students will learn how to use common multiples to rewrite two fractions so that they will have a common denominator. Once the fractions have a common denominator, they can be added or subtracted. Learning Goal Essential Questions Students will be able to identify factors and multiples of whole numbers. How can you use arrays or multiplication to find the factors of a number? How can you identify prime and composite numbers? Topic 7 Scale How can you find multiples of a number? Textbook Correlation Recommended Instructional Sequence Essential Vocabulary *Be selective in choosing problems aligned to the standards Step 1: Problem-Based Learning “Solve and Share” factor within the topic. Lessons and problems used for instruction Problem-Based Learning Lesson Flow Map multiple and assessment should be determined through collaborative Conceptual understanding is developed when mathematics is factor pairs unit planning. introduced in the context of solving a real problem in which generalize ideas related to the new content are embedded. Conceptual prime number understanding results because the process of solving a problem Topic 7: Factors and Multiples composite number requires students to connect their prior knowledge with the new Lesson 7-1: Understand Factors concept or procedure (Charles, R., Bay-Williams, J., et al., 2016). Lesson 7-2: Factors Lesson 7-3: Math Practices and Problem Solving: Repeated Each lesson in the book begins with a Solve and Share. See the Reasoning links below for additional tasks to be used as needed: Lesson 7-4: Prime and Composite Numbers Math Formative Assessment System (MFAS) Tasks by Standard Lesson 7-5: Multiples Illustrative Mathematics Tasks by Standard Step 2: “Visual Learning Bridge” Enhance student learning by connecting student thinking and solutions from the Solve and Share to the new ideas of the lesson through the use of the worked-out problem in the textbook. Deconstructed Standards MAFS.4.OA.2.4 (DOK 2) Investigate factors and multiples. a) Find all factor pairs for a whole number in the range 1–100. b) 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. c) Determine whether a given whole number in the range 1–100 is prime or composite. Define prime and composite numbers. Know strategies to determine whether a whole number is prime or composite. Identify all factor pairs for any given number 1-100. Recognize that a whole number is a multiple of each of its factors. Determine if a given whole number (1-100) is a multiple of a given one-digit number. Evaluate if a given whole number (1-100) is a prime or composite number. MAFS.4.NBT.2.5 (DOK 2) Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number. Multiply two two-digit numbers. Use strategies based on place value and the properties of operations to multiply whole numbers. Illustrate and explain calculations by using written equations, rectangular arrays, and /or area models. Math Practice Standard(s) Link to Mathematical Practice Standards Rubric MAFS.K12.MP.8.1 Look for and express regularity with repeated reasoning. Additional Resources & Links Higher Order Questions & Writing Connections Georgia Units Link to Webb’s DOK Guide Unit 2 *Higher order questions should be utilized to foster a deep, conceptual Factor Finding understanding of the topic. Encouraging students to express their Prime vs. Composite mathematical thinking in writing helps them solidify their learning. NOTE: all of Georgia Unit 2 pertains to this Topic. What does it mean to factor? How do I identify prime numbers? Engage New York Module 3 How do I identify composite numbers? Topic F, Lesson 22 What is the difference between a prime and a composite number? How is skip counting related to identifying multiples? www.pearsonrealize.com What is the difference between a factor and product? Home-School Connection Page How do we know if a number is prime or composite? Reteach to Build Understand Pages How can we determine whether a number is odd or even? How are factors and multiples defined? Florida Interim Assessment Item Bank and Test Platform Marzano Proficiency Scales Bank Math Formative Assessment System (MFAS) Tasks by Standard CPALMS -MFAS includes tasks and rubrics that the teacher can implement with their students. How will diagrams help us determine and show the products of twodigit numbers? How can I effectively explain my mathematical thinking and reasoning to others? What patterns do I notice when I am multiplying whole numbers that can help me? Illustrative Mathematics Tasks by Standard The site illustrates standards with impeccably crafted tasks, videos, lesson plans, and curriculum modules. Common Core Flip Books: Provides additional information and sample problems for every standard FSA Test Item Specifications Spiral Review *Consistent review of previously learned standards allows students multiple opportunities to master and build fluency with mathematical concepts and procedures. www.pearsonrealize.com Daily Review 7-1 through 7-5