Unit 1, Lesson 3
Prime and Composite Numbers
Grade 4
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The purpose of this Choral Count is to invite students to practice counting by 2 and 5 and notice patterns in each count. These understandings help students develop fluency and will be helpful later when students find factor pairs. In the Activity Synthesis, students are also invited to notice numbers that are in both counts and begin to reason why this may happen based on their emerging understanding of factors and multiples.
When students identify and predict common multiples for 2 and 5 based on the numbers recorded from the count and what they know about multiplication, they look for and express regularity in repeated reasoning (MP8).
This is the first time students experience the Choral Count routine in IM Grade 4. Students are familiar with this routine from a previous grade. However, they may benefit from a brief review of the steps involved.
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Card Sort
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The purpose of this activity is for students to learn about prime numbers and composite numbers. Students are given a set of cards with rectangles on them. They sort the rectangles by area and then attempt to draw an additional rectangle for each category. They notice that some areas can be represented by more than one rectangle and some areas can only be represented by one rectangle.
During the Activity Synthesis, highlight that the side lengths of each rectangle represent one factor pair (each pair of side lengths should be used only once), and that the area of each rectangle represents a multiple of each side length. Students learn that a number with only one factor pair—1 and the number itself—is a prime number, and a number with more than one factor pair is a composite number.
Your teacher will give you a set of cards that show rectangles.
For each group of cards that have the same area, think of at least one more rectangle. Record its length and width. Be prepared to explain your reasoning.
We used our understanding of the area of rectangles to learn about factors, multiples, factor pairs, prime numbers, and composite numbers.
If we know the side length of a rectangle, we can find the areas that the rectangle could have. For instance, a rectangle with a side length of 3 could have an area of 3, 6, 9, 12, 15, or other numbers that result from multiplying 3 by a whole number. We call these numbers multiples of 3.
If we know the area of a rectangle, we can find the side lengths that it could have. For example, a rectangle with an area of 24 square units could have side lengths of 1 and 24, 2 and 12, 3 and 8, or 4 and 6. We call these pairs of side lengths the factor pairs of 24.
We also learned that a number that has only one factor pair—1 and the number itself—is called a prime number. For instance, 5 is prime because its only factor pair is 1 and 5.
A number that has two or more factor pairs is a composite number. For instance, 15 is composite because its factor pairs are 1 and 15, and 3 and 5.
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