1. 3 Chapter Whole Numbers and Their Operations
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2. 3-4 Algorithms for Whole-Number Multiplication and Division
Multiplication Algorithms
Division Algorithms
Division by a Two-Digit Divisor
Multiplication and Division in Different Bases
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3. Algorithms for Whole-Number Multiplication and Division
They select appropriate methods and apply them accurately to estimate products or calculate them mentally, depending on the context and numbers involved.
They develop fluency with efficient procedures, including the standard algorithm, for multiplying whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.
NCTM grade 4 Focal Points, p. 16
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4. Properties of Exponents
Definition of an for whole numbers If a, the base and n, the exponent, are whole numbers and n  0, then
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5. Properties of Exponents
Theorem 3-9 For any whole number a and natural numbers m and n: Theorem 3-10
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6. Properties of Exponents
Theorem 3-11 For any whole number a and natural numbers m and n: Theorem 3-12 If a, m, and n are natural numbers with m > n, then
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Example 3-4
Write each of the following with only one exponent. a. b. a. b.
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8. Multiplication Algorithms
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9. Multiplication Algorithms
Multiplication by 10n
To multiply by 10, replace each piece with a base-ten piece that represents the next higher power of 10. Replace each unit with a long, and replace each long with a flat.
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10. Multiplication Algorithms
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11. Multiplication Algorithms
Multiplication using expanded addition
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12. Multiplication Algorithms
Multiplication with Two-Digit Factors
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13. Multiplication Algorithms
Lattice Multiplication
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Division Algorithms
Using Repeated Subtraction to Develop the Standard Division Algorithm or
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Division Algorithms or
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Division Algorithms
Using Base-Ten Blocks to Develop the Standard Division Algorithm
1. Represent 726 with base-ten blocks.
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2. Determine how many sets of 6 flats (hundreds) there are. There is one set of 6 flats with 1 flat, 2 longs, and 6 units left over.
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3. Convert the one leftover flat to 10 longs.
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4. Determine how many sets of 6 longs there are in the 12 longs. There are 2 set of 6 longs and 6 units left over.
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5. Now determine how many sets of 6 units there are. There is 1 set of 6 units with no units left over.
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21. Division Algorithms Short Division Decide where to start.
Divide the hundreds. Write the remainder by the tens.
Divide the tens. Write the remainder by the ones.
Divide the ones.
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22. Division by a Two-Digit Divisor
Four step method:
1. Estimate
2. Multiply
3. Subtract
4. Compare (check)
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23. Division by a Two-Digit Divisor
Divide
1. Estimate the quotient. The quotient is between 10 and 100.
2. Find the number of tens in the quotient.
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3. Find the number of units in the quotient.
4. Check. 32 · = 2618
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25. Multiplication and Division in Different Bases
Base-Five Multiplication Table
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26. Multiplication and Division in Different Bases
Multiply 21five · 3five.
Fives
Ones 2 1  3 → → →
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27. Multiplication and Division in Different Bases
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Example 3-4a
Multiply:
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