Students apply understanding of multiplication and area to work with factors and multiples.
Unit Narrative
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, students used area diagrams, wrote expressions and equations, and learned the terms “factors” and “products.”
In this unit, students return to the concept of area to make sense of factors and multiples of numbers. Students find as many pairs of whole-number side lengths as they can given a rectangle with a specific area. 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. They 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.
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 Narrative
In this section, students revisit the ideas of area and factors from grade 3 and encounter the idea of multiples. They begin by building rectangles given specific side lengths and identifying possible areas when only one side length is known. Students use tiles and diagrams to build their understanding before learning new terminology.
Next, students build rectangles given a certain area. They see that the side lengths of the rectangles represent the factor pairs of the given area value. Students also observe the commutative property of multiplication when they see that rectangles with the same pair of side lengths have the same area, regardless of their orientation.
Build 5 different rectangles with the given width. Record the area of each rectangle in the table.
area of rectangle
2 tiles wide
3 tiles wide
4 tiles wide
Students discover that for some whole-number values of area, only one rectangle can be built, and for other values, more than one rectangle is possible. Likewise, some numbers have only one factor pair (the number itself and 1) and other numbers have more than one factor pair. Students learn that we call the former “prime numbers” and the latter “composite numbers.”
The section closes with an optional game day, which is an opportunity to see students' fluency with multiplication and division within 100.
Apply multiplication fluency within 100 and the relationship between multiplication and division to find factor pairs and multiples.
Section Narrative
In this section, students apply and deepen their understanding of the ideas of factors and multiples as they play games and solve problems in context. The activities prompt students to look for patterns in factors, multiples, and prime and composite numbers, and use them to make predictions and generalize their observations.
Twenty students are playing a game with 20 lockers in a row.
The first student starts with the first locker and opens all the lockers.
The second student starts at the second locker and shuts every other locker.
The third student stops at every third locker and opens it if it is closed or closes it if it is open.
Which locker numbers does the third student touch?
How many students touch locker 17?
In the last lesson, students have a chance to use the ideas from this unit to create geometric art.