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# Unit 1: Overview | FACTORS AND MULTIPLES

Duration

(8-11) Days

Unit Learning Goal

Students apply understanding of multiplication and area to work with factors and multiples.

Essential Questions

• What is the difference between multiples and factors?

• How can patterns and properties be used in finding factor pairs for whole numbers in the range of 1-100?

• How are multiples and factors useful in our daily lives?

• How are multiples and factors connected to the area of rectangles?

• How can one determine whether a number is prime or composite?

• How can the relationship between the side lengths of a rectangle and its area tell us if the value of the area is prime or composite?

Enduring Understandings

• Multiplication and division have an inverse relationship. The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.

• Real world situations involving equal groups and area can be represented with multiplication and division equations and models.

• Area is a real-life application of multiplication and division.

• Basic multiplication facts with 3, 4, 6, 7, and 8 as a factor can be found by breaking apart the unknown fact into known facts.

• Every counting number is divisible by 1 and itself, and some counting numbers are also divisible by other numbers.

• Some numbers have exactly two factors, 1 and itself. These are prime numbers.

• Some numbers have more than two factors. These are composite numbers.

Unit Overview

In this unit, students extend their knowledge of multiplication, division, and the area of a rectangle to deepen their understanding of factors and to learn about multiples.  In grade 3, students learned that they can multiply the two side lengths of a rectangle to find its area, and divide the area by one side length to find the other side length.  To represent these ideas, they used area diagrams, wrote expressions and equations, and learned the terms “factors” and “products.”  Diagram. Rectangle partitioned into 2 rows of 3 of the same size squares.   In this unit, students return to the concept of area to make sense of factors and multiples of numbers. Given a rectangle with a particular area, students find as many pairs of whole-number side lengths as they can. They make sense of those side lengths as factor pairs of the whole-number area, and the area as a multiple of each side length.  Students also learn that a number can be classified as prime or composite based on the number of factor pairs it has.  Throughout the unit, students encounter various contexts related to school, gatherings, and celebrations. These contexts are intended to invite conversations about students’ lives and experiences. Consider them as opportunities to learn about students as individuals, to foster a positive learning community, and to shape each lesson based on insights about students.

The warm-up activities in this unit allow students to build on multiplication and division fluency from grade 3 and prepare to work with factors and multiples. Number Talks are used to help further develop multiplication fluency and mental math strategies. These Number Talks focus on multiples of 6 and 7, and the factor 3, and allow students to use the distributive and associative properties to mentally find the value of expressions.

Section

Learning Goals

Section A

• Determine if a number is prime or composite.

• Explain what it means to be a factor or a multiple of a whole number

• Relate the side lengths and area of a rectangle to factors and multiples

Section B

• Apply multiplication fluency within 100 and the relationship between multiplication and division to find factor pairs and multiples.

NJSLS

4.OA.B.4, 4.OA.C.5

4.OA.A.3, 4.OA.B.4