Prime Time
Goals of Prime Time
Students should...
Students should...
- Understand relationships among factors, multiples, divisors, and products
- Classify numbers as prime, composite, even, odd, or square
- Recognize that factors of a number occur in pairs
- Recognize situations that call for common factors and situations that call for common multiples
- Recognize situations that call for the greatest common factor and situations that call for the least common multiple
- Develop strategies for finding factors and multiples
- Develop strategies for finding the least common multiple and the greatest common factor
- Recognize and use the fact that every whole number can be written in exactly one way as a product of prime numbers
- Use exponential notation to write repeated factors
- Relate the prime factorization of two numbers to the least common multiple and greatest common factor of two numbers
- Solve problems involving common factors or common multiples.
Prime Time Objectives and Standards | |
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Investigation 1
Investigation 1 Vocabulary | |
File Size: | 233 kb |
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We will begin the year with the book entitled "Prime Time." In this unit we will be looking at factoring, prime and composite numbers, finding multiples, factor pairs, common multiples and factors, factor strings, prime factorization, even and odd numbers, distributive property, and operations.
In Prime Time 1.3 students will be learning about products and multiples. Students can use the button on the right to practice their products using the product game.
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Investigation 2
Investigation 2 Vocabulary | |
File Size: | 156 kb |
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Investigation 2 uses real-life situations to motivate student interest in common factors and common multiples. The concepts of least common multiple and greatest common factor occur naturally within the context of the problems. The context of the problems and questions helps make it clear to students whether a solution involves finding a common multiple, a common factor, the least common multiple, or the greatest common factor.
Investigation 3
Vocabulary Investigation 3 | |
File Size: | 158 kb |
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In previous Investigations, students found the factors and factor pairs of a number and the common factors and common multiples of two or more numbers. This Investigation provides opportunities for students to think about factorizations of whole numbers as the products of several whole numbers.Finding longer and longer factor strings of a number leads students to the Fundamental Theorem of Arithmetic, which states that “a whole number can be written as a product of primes in exactly one way, disregarding order.” The number 1 is not a prime number.
The intent of the Investigation is to help students see that every string shorter than the longest has at least one factor that is not prime. These non-prime factors can be broken down to make longer strings. The process ends when every number in the string is prime and no further decomposition can occur. This is the unique string of primes that can be multiplied to produce the original number—the prime factorization of the number.
Students use the prime factorization to find the least common multiple and greatest common factor of two numbers. Exponents are introduced as an efficient way to write repeated factors in the factorization of a number.
The intent of the Investigation is to help students see that every string shorter than the longest has at least one factor that is not prime. These non-prime factors can be broken down to make longer strings. The process ends when every number in the string is prime and no further decomposition can occur. This is the unique string of primes that can be multiplied to produce the original number—the prime factorization of the number.
Students use the prime factorization to find the least common multiple and greatest common factor of two numbers. Exponents are introduced as an efficient way to write repeated factors in the factorization of a number.
Investigation 4
Vocabulary Investigation 4 | |
File Size: | 227 kb |
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Throughout this Unit, students have been looking at the multiplicative structure of a number. This Investigation explores the relationship between the multiplicative and additive structures of numbers. That is, numbers can be written as a product of factors or as a sum of terms.Multiplicative and additive structures are explored through the introduction of the Distributive Property. The Distributive Property states that for any numbers a, b, and c, a(b+c)=ab+ac. The factored form, a(b+c), and the expanded form, ab+ac, are equivalent expressions. They represent the same quantity.
Working with equivalent numerical expressions provides an opportunity to introduce the Order of Operations convention. The Investigation ends with several applications in which the students have to decide which operations are needed to solve problems.
Working with equivalent numerical expressions provides an opportunity to introduce the Order of Operations convention. The Investigation ends with several applications in which the students have to decide which operations are needed to solve problems.