### Grade 4/Chapter 5: Factors, Multiples & Patterns

Resources:

- When you find the factors of a number you can skip count by that number
**multiple**times and arrive at the number you were finding the factors of. - Factors refer to whole numbers only.

Online Resource:

- Illustrative Mathematics: Locker Task (4.OA.4), Multiples of 3, 6, 7 (4.OA.5)
- Dr. Math: Different Types of Numbers, Zero & One, Divisibility Rules

Thoughts on Lessons:

**Tools**: number grids and tables, Venn Diagrams**Models**: ratio table, factor rainbow, number line- Center ideas: Divisibility Rules, Numeric & Geometric Patterns,
- Lesson 5.1: Group or partner work. Provide students with whole number products (1 – 100). Ask them to make all possible rectangular arrays each number. Have them determine which ones will take a lone time and which ones won’t. Ask them to explain why? For later use…color code your
**primes**and**composites**. Make this into a center. Develop a series of questions that allow students to look for patterns. For example, ask students: “Well if we know that 3 is a factor of 12, then what else do we know?” Expected response: “12 can be divided by 3.” - Lesson 5.2: Have students discover the divisibility rules. Expect fluencies with: 1) All numbers are divisible by 1. 2) All even numbers are divisible by two. 3) All numbers ending in 0 or 5 are divisible by five. 4) All numbers ending in 0 are divisible by ten. The focus should not be to memorize divisibility rules, but to note patterns and number relationships.
- Lesson 5.3: Other than an exploration – DO NOT TEACH. Common factors is a 6th grade standard (CCSS.MATH.CONTENT.6.NS.B.4) – Look at EngageNY – Topic F.
- Lesson 5.4/5.5: Adjust this lesson. Centers for “Find the Multiples of…” and then guided groups to determine if a number is a factor of another number and if the number is prime or composite (Lesson 5.5). Use different strategies to determine factors and multiples. a) Make an array. b) Make a list of the multiples. 3) Use equal groups. 4) Use a divisibility rule. 5) List the factors. 6) Make a Venn Diagram. Turn exercise 17 – 20, pg. 301, into a game. Use the Venn Diagram Idea, pg. 302. Spend 2 – 3 days on this idea or build into a routine and do daily. Introduce concept of prime and composite (Lesson 5.5). Look at the Advanced Learner on pg. 306. Makes a great center. Extension: Find My Match – Same number of factors, primes or composites. Mix, Freeze, Group: Make a groups based upon the number of factors a number has, i.e. students would make a group of 6 for the number 12, because 12 has 6 factors.
- Lesson 5.5: The Sieve of Eratosthenes – Main focus: Explain using precise mathematical language the rational behind each step. Define the word “sieve” as a strainer to filter out something. Other prime number sieves exist. Have students discover this algorithm, by asking the question how can we use the number grid to determine the prime numbers to 100. Have students come up with the questions that can be asked. See sidebar, pg. 308.
- Lesson 5.6: Determine if growth or repeating pattern. Use geometric objects, but focus on the numbers. Use the idea of the Advanced Learners on pg. 312, as a center activity. Have students create a pattern given a rule, and someone else has to continue the pattern. Make the “One Your Own” into a game or center activity. Extend the ideas on pg. 314. in the student generated work. Possible card game: Labels (composite, prime, even, square, etc.). Students are given cards that they have to get rid of by placing under a category and justifying the placement.
- Examples of Repeating (same group over and over again) and Growing Patterns (pattern increased or deceases additively or multiplicatively). Growth and Repeating patterns can happen in either direction (shrinking or decreasing or enlarging or increasing). You need a sequence of three terms to determine a pattern.

Activities:

- Make an Anchor Chart of strategies for finding factor pairs. See Gr. 6 strategies for GCF
- What is the relationship between factors and multiples?
- Mix, Freeze, Group – Make a groups based upon the number of factors a number has, i.e. students would make a group of 6 for the number 12, because 12 has 6 factors.