Unit 1 Number Theory (5th Grade)

Unit 1: Number Theory 5 th Grade

Learning Goals ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Even and Odd Numbers ,[object Object],[object Object],8 is even because it can be divided into two equal whole amounts. 7 is odd because it cannot be divided into two equal whole amounts.

Try it out! ,[object Object],9, 5, 7, 4, 17, 23 3, 5, 8, 21, 29, 43 3, 9, 21, 43, 5, 15

Correct! ,[object Object],Click here to return to learning goals 1 2 Even Odd 3 5 7 9 11 13 15 17 4 6 8 10 12 14 16 18

Keep Trying! ,[object Object],9, 5, 7, 4, 17, 23 3, 5, 8, 21, 29, 43 Neither one of these groups of numbers is all odd because 4 and 8 are both even numbers. Click here to return to learning goals 1 2 Even Odd 3 5 7 9 11 13 15 17 4 6 8 10 12 14 16 18

Drawing Rectangular Arrays ,[object Object],3 x 4 = 12 2 x 6 = 12 4 x 3 = 12 6 x 2 = 12 1 x 12 = 12 12 x 1 = 12

Try it out! ,[object Object],[object Object]

Correct! ,[object Object],Click here to return to learning goals 4 x 7 = 28 4 rows 7 columns 28 total

Keep Trying! ,[object Object],Click here to return to learning goals 4 x 7 = 28 Correct 2 rows 14 columns 28 total 5 rows 7 columns 35 total 4 rows 7 columns 28 total

Know Your Facts! ,[object Object],http:// www.multiplication.com / http:// www.schoolexpress.com/funtime/math_generator/index.php http:// www.multiplication.com/interactive_games.htm Find more on http:// guest.portaportal.com/renegar Click here to return to learning goals

Use a Divisibility Test Has double digits, pattern i.e. 33, 121, etc 11 Ends in 0 10 Sum of all digits is 9 (or divisible by 9) 9 Divisible by both 2 and 3 6 Ends in 5 or 0 5 Sum of the digits is divisible by 3 3 Is an even number, ends in 0, 2, 4, 6, or 8 2 Test Divisible by

Try It Out! ,[object Object],1, 3, 6, and 9 1, 3, and 9 1, 3, and 6

Correct! ,[object Object],[object Object],[object Object],[object Object],171 / 1 = 171 171 / 3 = 57 171 / 9 = 19 Click here to return to learning goals

Keep Trying! ,[object Object],[object Object],[object Object],[object Object],171 / 1 = 171 171 / 3 = 57 171 / 9 = 19 171 is not divisible by 6 because it is not divisible by 2. (It’s an odd number.) Click here to return to learning goals

Find the Factors of Numbers ,[object Object],5 x 3 = 15 factors product 15 / 3 = 5 15 / 5 = 3 Factor (5) Factor (3) Total (product) = 15

Ways to Find Factors Create arrays. Factors of 6 are: 1, 2, 3, 6 Divide. 6 / 6 = 1 6 / 1 = 6 6 / 2 = 3 6 / 3 = 2 * You already know 1 and 6 are factors, divide by each number (record only the ones that divide evenly) and stop when you begin to see repeating numbers. stop 2 3 1 6

Try It Out! ,[object Object],1, 48, 2, 4, 6, 8, 12, 24 1, 48, 2, 3, 4, 6, 8, 12, 24 1, 48, 2, 3, 4, 6, 8, 12, 16, 24

Correct! 48 48 / 48 = 1 48 / 1 = 48 48 / 2 = 24 48 / 3 = 16 48 / 4 = 12 48 / 6 = 8 48 / 8 = 6 Stop Remember to record only numbers that divide evenly! If you chose to make arrays, you would have 5 different arrays. Factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 Click here to return to learning goals

Keep Trying! 48 48 / 48 = 1 48 / 1 = 48 48 / 2 = 24 48 / 3 = 16 48 / 4 = 12 48 / 6 = 8 48 / 8 = 6 Stop Remember to divide sequentially (in order) and record only numbers that divide evenly! If you chose to make arrays, you would have 5 different arrays. Factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 Click here to return to learning goals

Identify Prime and Composite Numbers ,[object Object],[object Object]

Correct! ,[object Object],These are really the same arrangement, just rotated 90 degrees. Click here to return to learning goals

Try Again! ,[object Object],These are really the same arrangement, just rotated 90 degrees. incorrect 9, 6, and 4 are composite numbers because they can be made into other arrays. They have more than 2 factors. Click here to return to learning goals

Find the prime factorizations of numbers ,[object Object],32 2 16 2 8 2 4 2 2 = 2 x 2 x 2 x 2 x 2 These are all the prime factors of 32. A Factor String is a string of factors that equal a number. 32 = 2 x 2 x 8 A Prime Factorization is the longest possible factor string. 32 = 2 x 2 x 2 x 2 x 2

Try it out! ,[object Object],9, 5 3, 5 3, 3, 5

Correct! ,[object Object],Click here to return to learning goals 45 5 9 3 3 = 5 x 3 x 3 5, 3, and 3 are all prime factors of 45.

Keep Trying! ,[object Object],The answer is not 5, 3, because 5 x 3 = 15. In order to be the prime factorization, all of the factors multiplied together must equal the beginning number. The answer is not 9, 5, because 9 is not prime. Click here to return to learning goals 45 5 9 3 3 = 5 x 3 x 3 5, 3, and 3 are all prime factors of 45.

Rename Numbers Written In Exponential Notation ,[object Object],5^3 or 5 3 = 5 x 5 x 5 When you have an exponent, it means to multiply the base number by itself that many times. In this case, 5 is the base number and 3 is the exponent. 4 2 = 4 x 4 base exponent 4 2 = 16

Try It Out! ,[object Object],3 2 = 9 6 8

Correct! ,[object Object],[object Object],[object Object],Click here to return to learning goals

Keep Trying! ,[object Object],[object Object],[object Object],Remember that the base is the number to multiply, the exponent is the number of times to multiply it! Click here to return to learning goals

Square Numbers and Square Roots ,[object Object],4 2 means “4 squared”. It forms an array that is 4 x 4. 4 2 = 16 4 4 16 is a SQUARE NUMBER because it has a factor (4) that can be multiplied by itself.

Square Roots ,[object Object],[object Object],√ 9 = 3 To find the square root of 9, you can arrange 9 pieces into a square (equal sides). The rows and columns would both be 3, so 3 is the square root of 9. You can also find a square number by listing its factors. 9 = 1 x 9 9 = 3 x 3 9 = 3 2

Try It Out! ,[object Object],6 2 = 12 √ 12 = 6 6 2 = 36 √ 16 = 4 6 2 = 12 √ 36 = 6 4 2 = 16 √ 12 = 6

Correct! ,[object Object],[object Object],Click here to return to learning goals

Keep Trying! ,[object Object],[object Object],Click here to return to learning goals

Unit 1 Number Theory (5th Grade)

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Unit 1 Number Theory (5th Grade)