Unit 1: Number Theory. Rectangular Array: An arrangement of objects in rows and columns that form a rectangle. All rows have the same number of objects.

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Presentation transcript:

Unit 1: Number Theory

Rectangular Array: An arrangement of objects in rows and columns that form a rectangle. All rows have the same number of objects and all columns have the same number of objects. Lesson 1-2: Rectangular Arrays ColumnsColumns Rows Number Model: Rows * Columns = Product 5 * 2 = 10 1 * 5 = 5 2 * 2 = 4

Practice: Draw all possible arrays for the numbers below. Write the number model to match the array * 8 = 8 4 * 2 = 8 2 * 4 = 8 6 * 2 = 12 8 * 1 = 8 1 * 12 = 12 2 * 6 = 12 3 * 4 =12 4 * 3 = * 1 = 12

Classwork: 1. Complete journal page 5 If time: 2. Complete journal p Math Box 1-2 (p. 8) 4. Extra Credit

Journal Page 5 answers Correct your work using a pen!

Factor * Factor = Product 2 * 5 = 10 Lesson 1-3: Factors NumberFactor PairsList (numerical order) *Remember to use an organized approach to find all the factors of a number. Start with the number 1, find its factor pair, then continue in numerical order 2, 3, etc. until you hit a repeat! 1, 15 3, 5 1, 12 2, 6 3, 4 1, 9 3, 3 1, 2, 3, 4, 6, 12 1, 3, 9 1, 3, 5, 15

Classwork: 1. Complete journal page 10 If time: 2. Math Box 1-3 (p. 11) 3. Extra Credit

Journal Page 10 answers Correct your work using a pen!

Lesson 1-5: Divisibility Rules A whole number is divisible by a whole number if the remainder if zero. 4 ways to write a division problem /5 = ÷ 5 = = 37 Dividend Quotient Divisor

Divisibility Rules Memorize NumberRuleExamples One (1) All numbers are divisible by one. Two (2)A number is divisible by 2 if it is even (ends in 0, 2, 4, 6, 8). Three (3)A number is divisible by 3 if the sum of the digits adds up to a multiple of three. Four (4)A number is divisible by 4 if it is even and can be divided by two twice. Five (5) A number is divisible by 5 if it ends in a five or a zero. Six (6)A number is divisible by 6 if it is a divisible by both 2 and 3. Nine (9) A number is divisible by 9 if the sum of the digit adds up to a multiple of nine. Ten (10)A number is divisible by 10 if it ends in a zero. 38, 104, 7,536 27, 603, 8,541 64, 132, 2, , 675, 3,500 72, 306, 1,548 36, 801, 6,732 70, 290, 8,940 All whole numbers

Classwork: 1. Complete journal page 14 If time: 2. Math Box 1-5 (p. 15) 3. Extra Credit

Journal Page 14 answers Correct your work using a pen!

Lesson 1-5: Divisibility Continued Using a calculator to test for divisibility Reminder: A whole number(the dividend) is divisible by a whole number (the divisor) if the remainder in the division is zero. The result(the quotient)must be a whole number. If the remainder is not zero, then the number being divided is not divisible by the second number. 135 ÷ 5 = 27 R0 135 int ÷ 5 = ÷ 4 = 33 R3 135 int ÷ 4 = 33.75

Classwork: 1. Complete journal page 13 If time: 2. Math Box 1-5 (p. 15) 3. Extra Credit

Journal Page 13 answers Correct your work using a pen!

Lesson 1-4: Factor Captor Add game directions and game boards

Memorize Lesson 1-6: Prime & Composite Numbers Prime Number : Has exactly 2 factors, one and itself Composite Number : Has exactly 3 or more factors The number 1 is not prime or composite Prime Numbers under 50 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Classwork: 1. Complete journal page 16 If time: 2. Journal page Math Box 1-6 (p. 19) 4. Extra Credit

Journal Page 16 answers Correct your work using a pen!

Lesson 1-7: Square Numbers Square Numbers are the product of a number times itself Exponential Notation Repeated Multiplication Square Number 1 1 * * * * * * * * * * * * Read these as either: “four to the power of two” or “ four squared”

3 2 Base Exponent The exponent (2) tells how many times the base (3) is used as a factor. Exponential Notation Practice: 2 8 = 2 = 3 8 =11 = 4 = 2 3 Powers Key ^

Classwork: 1.Complete journal page If time: 2. Math Box 1-7 (p. 22) 3. Extra Credit

Journal Page answers Correct your work using a pen!

Lesson 1-8: Unsquaring Numbers * = 4 = 2 81 When you unsquare a number, you have found the square root of the number. is the square root of 4 is the square root of

Practice: _ is the square root of 16 8 is the square root of _ _ is the square root of 36 7 is the square root of _

Classwork: 1.Complete journal page 23 If time: 2. Math Box 1-8 (p. 24) 3. Extra Credit

Journal Page 23 answers Correct your work using a pen!

Unit 1: Review Stations Station 1: Square Numbers Station 2: Arrays and Number Models Station 3: Divisibility Station 4: Prime and Composite Numbers Station 5: Factors