Math Message Lesson 1 . 1

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Math Message Lesson 1 . 1

• Browse through your journal. Then read Welcome
  to Fifth Grade Everyday Mathematics, on page 1
  in your journal.

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L.G.

• Familiarize yourself with your Student Reference
  Book

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Math Message Lesson 1 . 2

• Read page 10 in your SRB. Then draw a
  rectangular array made up of 12 dots. You may
  use counters to help you.

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Rectangular Arrays

• Each row has the same number of parts
• Each column has the same number of parts
• Each array has a rectangular shape.

5

• Take out six counters (rainbow cubes)
• Arrange the six counters in a rectangular array

??? ???
Number model - 2 3 6 2 rows by 3 columns 6
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Commutative Property

• The order in which two numbers are multiplied
  makes no difference.
• For example, 2 3 6 and 3 2 6
• Also called the turn around rule

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Math Message Lesson 1 . 3

• Take a sheet of dot paper. Use counters (rainbow
  cubes) to make all possible arrays of 15 objects.
  Record the arrays on the dot paper. Write a
  number model for each array.

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Factors

• Factor
• Product
• Factor Pair

3 5 15
Product
Factors
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Find all of the factors for 18

• 1 18 18
• 18 1 18
• 2 9 18
• 9 2 18
• 3 6 18
• 6 3 18

Factors of 18 are (1, 2, 3, 6, 9, 18)
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Math Message Lesson 1 . 4

• Which of the following number are factors of 36?
• 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

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Finding Factors of a Number

• Multiplication and division are related
• They are opposites
• If you know your multiplication facts, you know
  your division facts
• We can find factors of a number by checking for
  divisibility

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Divisibility a number is divisible by another
number if the result of division is a whole
number.

• Is 54 divisible by 9?
• Is 25 divisible by 6?
• Is 8 a factor of 48?
• Is 4 a factor of 30?

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Math Message Lesson 1 . 5

• Solve problems 1 and 2 at the top of journal
  page 12.

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Divisibility

• A number is divisible by a whole number is the
  remainder in the division is zero and the
  quotient is a whole number.
• We can use a calculator to test for divisibility
• Example 27 is not divisible by 5 because 5.4 is
  not a whole number.

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Divisibility Tests - 2

• A number is divisible by 2 if it ends in 0, 2, 4,
  6, or 8.
• We also call those numbers even numbers.

44, 12, 28, 62, 108, 256, 80
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Divisibility Tests - 3

• A number is divisible by 3 if the sum of its
  digits is divisible by 3.
• Example

237 2 3 7 12 1 2 3
410 4 1 0 5
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Divisibility Test - 6

• A number is divisible by 6 if it is divisible by
  both 2 and 3.

426 Is it even? Yes 4 2 6 12 1 2 3
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Divisibility Test - 9

• A number is divisible by 9 if the sum of its
  digits is divisible by 9.
• Example

198 1 9 8 18 1 8 9
429 4 2 9 15 1 5 6
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Divisibility Tests 5

• A number is divisible by 5 if it ends in a 5 or a
  0.
• Example 25, 30, 105, 1260

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Divisibility Tests 10

• A number is divisible by 10 if it ends in a zero.
• Example 10, 20, 1450, 370

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Math Message Lesson 1 . 6

• Draw all the arrays possible for these numbers
  4, 10, 16.
• Draw all the arrays possible for these numbers
  2, 5, 11.

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Prime and Composite Numbers

• A prime number has exactly two factors 1 and
  the number itself.
• A composite number has more than two factors.
• The number one is neither prime nor composite.
  (It has only one factor.)

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Prime or Composite?

• 25
• 17

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Math Message Lesson 1 . 7

• Use the rainbow cubes. Try to make a
  rectangular array that has an equal number of
  rows and columns for each of the following
  numbers
• 14 16 18

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Square Numbers

• Has the same number of rows and columns
• Has an odd number of factors
• Can be written using an exponent
• 42
• 4 4 16

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Exponents and Base Numbers

• exponent
• 42
• base number

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Math Message Lesson 1 . 8

• Find the numbers n and m that make these
  statements true
• n n 4 m2 81

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Unsquaring Numbers

• Solving m281 is unsquaring a number.
• What number multiplied by itself is equal to 289?
• After unsquaring a number, the result is called
  the square root.

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Unsquaring More Numbers

• What number when multiplied by itself equals 49?
• What number when multiplied by itself equals 25?
• What number when multiplied by itself equals 36?

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Unsquaring More Numbers (calculator)

• 196
• 441
• 676
• 900
• 1024
• 1849

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Math Message Lesson 1 . 9

• 8 8 and 4 4 are two names for the number 16.
  Write at least five other names for 16.

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Factor Strings and Prime Factorization

• Factor Strings
• 24 3 2 4
• 12 2 3 2
• How can we make the longest factor strings?

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180
34
180
35
180
18
10
36
180
18
10
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Prime Factor String
180 2 5 2 3 3
Prime Factorization using Exponential Notation
180 22 32 5
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Math Message Lesson 1 . 10

• Please complete the Time to Reflect questions on
  journal page 27. ?