Essential Math Concepts: Prime Factorization, Powers, Exponents, and Multiplication Strategies
Multiply Whole Numbers
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
↓ ↓
6 x
3
↓ ↓ ↓
3
x
2
x
3
The prime factorization of 18 is 2 x 3 x 3 ( 2 x 3
²).
Lesson 3 – Powers and Exponents
3⁴
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 ⁴ = 3 x 3 x 3 x 3
↓
↓
9 x 9 = 81
Lesson 4 – Multiplication Patterns
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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
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 .
9
2
→ 90
0 1 2 3 4 - round down
x 1
2
→
x 10
5 6 7 8 9 – round up
2.
Multiply the non-zero numbers. Count the zeros.
90
9 x 1 =
9
x 10
1 zero + 1 zero =
2 zeros
900
Lesson 9 – Multiply by One-Digit Numbers
1. Multiply the ones.
87
3
x
2
6
2. Multiply the tens. Bring the digit in the tens place over to the
next number.
1
8
7
3
x
2
4
6
3. Multiply the hundreds. Add the number you carried over.
1
8
73
x
2
1
,
7
46
Lesson 10 – Multiply by Two-Digit Numbers
1. Multiply the ones.
4
56
x 1
7
392
2. Erase any markings. Add a zero to the next row.
3. Multiply the tens. 56
x
1
7
392
+
560
4. Add the columns.
952
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
