Illustrative Mathematics (IM) is a problem-based core curriculum designed to foster learning for all, preparing students to solve problems, reason, communicate, and think critically in the classroom and beyond. All elementary schools will be implementing IM this year!

Unit 1: Factors and Multiples

In this unit, students apply their understanding of multiplication and area to work with factors and multiples.

Section A

In this section, students are introduced to factors and multiples by building on area and multiplication understandings learned in grade 3. To revisit the concept of area, students build rectangles using tiles, given side lengths. For example, the rectangle below has an area of 14 square units with side lengths of 7 and 2.

They then discuss possible areas for rectangles with only one side length named. These activities help students think about factors and multiples before they learn the terminology. Students then use tiles to build rectangles given a certain area. They learn that the side lengths of the rectangles they create represent the factor pairs of the given area values. In the rectangle above, we can say that 7 and 2 are a factor pair of 14 because a rectangle with sides lengths of 7 and 2 have an area of 14 and 7×2=14

As the lessons progress, students discover that there are some numbers with many factor pairs and some with only one possible factor pair, 1 and itself. They identify these numbers as prime or composite based on the number of rectangles that can be made using the given area. An example of a prime number is 7 because the only rectangle we can build with 7 tiles is a 1 by 7 so the only factor pair of 7 is 1 and 7.

An example of a composite number is 36 because, with that number of tiles, we can make four different rectangles: 6 by 6, 9 by 4, 12 by 3, and 36 by 1.

Section B

In this section, students deepen their understanding of factors and multiples by applying what they have learned to games and different contexts. Through the tasks, students look for patterns with factors and multiples. They find all of the factor pairs of a number between 1–100 and determine whether a number within this range is a multiple of a given one-digit number.