# Essential Math Concepts: Prime Factorization, Powers, Exponents, and Multiplication Strategies

Learn fundamental math concepts such as prime factorization, powers, exponents, multiplication patterns, and problem-solving strategies with examples and visuals. Explore topics like the distributive property, estimating products, and multiplying by one-digit numbers in an engaging manner.

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## Presentation Transcript

**Lesson 1 Prime Factorization**Prime factorization is breaking down a composite number into its prime factors. To find the prime factorization of a number, use a factor tree. Example: 18 3 x 2 x 3 The prime factorization of 18 is 2 x 3 x 3 ( 2 x 3 ). 6 x 3**Lesson 3 Powers and Exponents**3 3 is the base 4 is the exponent The base is the number that is being multiplied . The exponent tells you how many times you multiply the base. Example: 3 = 3 x 3 x 3 x 3 9 x 9 = 81**Lesson 4 Multiplication Patterns**With powers of 10 and other large numbers, you can use mental math to solve. Example: 450 x 1,000 450 x 10 (the exponent tells you how many zeros to add) 1. Multiply the numbers that are not zeros . 450 x 1,000 45 x 1 = 45 2. Count the number of zeros in the product. Put that many zeros in your answer. 1 zero + 3 zeros = 4 zeros in answer 450 x 1,000 450 x 1,000 = 450,000**Lesson 5 Problem-Solving Strategy: Make a Table**Janice is training for a marathon. She begins by running 2 miles the first week. Each week she runs double the amount of miles. How many miles will she run during week 4? Double = x 2 Week 1 2 3 4 Miles 2 4 8 16 starting # x 2 x 2 x 2 Janice will run 16 miles during week 4.**Lesson 7 The Distributive Property**You can use the Distributive Property to break numbers into smaller ones that you can easily multiply. Example: 8 x 12 10 2 Break the digit down into tens and ones Multiply and add the sums. (8 x 10) + (8 x 2) 80 + 16 = 96**Lesson 8 Estimate Products**1. Round numbers all the way to the left. Use the rules for rounding . 92 900 1 2 3 4 - round down x 12 x 10 5 6 7 8 9 round up 2. Multiply the non-zero numbers. Count the zeros. x 10 90 9 x 1 = 9 1 zero + 1 zero = 2 zeros 900**Lesson 9 Multiply by One-Digit Numbers**1. Multiply the ones. 2. Multiply the tens. Bring the digit in the tens place over to the next number. 1 873 x 2 46 873 x 2 6 3. Multiply the hundreds. Add the number you carried over. 1,746 1 873 x 2**Lesson 10 Multiply by Two-Digit Numbers**1. Multiply the ones. 2. Erase any markings. Add a zero to the next row. 3. Multiply the tens. 56 4. Add the columns. x 17 4 56 392 x 17 392 + 560 952