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Grade 4 Mathematics Module 3, Topic F: Reasoning With Divisibility

  Classroom Resource Information  

Title:

Grade 4 Mathematics Module 3, Topic F: Reasoning With Divisibility

URL:

https://www.engageny.org/resource/grade-4-mathematics-module-3-topic-f-overview

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 3, Topic F, armed with an understanding of remainders, students explore factors, multiples, and prime and composite numbers within 100 (4.OA.4). Students gain valuable insights into patterns of divisibility as they test for primes and find factors and multiples, at times using their new skill of dividing double-digit dividends. This prepares them for Topic G’s work with dividends of up to four digits. Lesson 22 has students find factor pairs for numbers to 100 and then use their understanding of factors to determine whether numbers are prime or composite. In Lesson 23, students use division to examine numbers to 100 for factors and make observations about patterns they observe, for example, “When 2 is a factor, the numbers are even.” Lesson 24 transitions the work with factors into a study of multiples, encouraging students to notice that the set of multiples of a number is infinite while the set of factors is finite. In Lesson 25, the Sieve of Eratosthenes uses multiples to enable students to identify and explore the properties of prime and composite numbers to 100.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 4
4. For whole numbers in the range 1 to 100, find all factor pairs, identifying a number as a multiple of each of its factors.

a. Determine whether a whole number in the range 1 to 100 is a multiple of a given one-digit number.

b. Determine whether a whole number in the range 1 to 100 is prime or composite.

Unpacked Content
Evidence Of Student Attainment:
Students:
When given a number in the range 1-100,
  • Find all factor pairs and recognize that a whole number is a multiple of each of its factors.
  • Determine whether the whole number in the range 1-100 is a multiple of a given one-digit number.
  • Determine whether a whole number in the range 1-100 is prime or composite.
Teacher Vocabulary:
  • Multiple
  • Factor
  • Prime
  • Composite
  • Whole number
  • Factor pair
Knowledge:
Students know:
  • Factor pairs include two numbers that when multiplied result in a particular product.
  • Multiples are the result of multiplying two whole numbers.
  • How to identify a prime or composite number.
Skills:
Students are able to:
  • Find all factor pairs of a given number.
  • Identify a number as a multiple of each of its factors.
  • Determine whether a number is prime or composite.
Understanding:
Students understand that:
  • A whole number is a multiple of each of its factors.
  • Numbers can be classified as prime, composite, or neither, based on their properties and characteristics.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.4.4.1: Define factors, prime number, and composite number.
M.4.4.2: Apply properties of operations as strategies to multiply and divide.
M.4.4.3: Identify all factor pairs for a whole number in the range 1-20.
M.4.4.4: Name the first ten multiples of each one-digit natural number.
M.4.4.5: Recall basic multiplication facts.
M.4.4.6: Count within 1000; skip-count by 5s, 10s, and 100s.

Prior Knowledge Skills:
  • Represent equal groups using manipulatives.
  • Identify and define the parts of a multiplication problem including factors, multiplier, multiplicand and product.
  • Use multiplication to find the total number of objects arranged in rectangular arrays based on columns and rows.
  • Write an equation to express the product of the multipliers (factors).
  • Relate multiplication to repeated addition and skip counting.
  • Define pair, odd and even.
  • Recall doubles addition facts with sums to 20.
  • Apply sign+ and = to actions of joining sets.
  • Model written method for composing equations.
  • Skip count by 2s.
Tags: composite, divisibility, factor, multiple, prime, whole number
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Comments

There are four lessons in this topic.

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  This resource provided by:  
Author: Hannah Bradley