1. 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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2. L.G. Familiarize yourself with your Student Reference Book
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3. 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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4. L.G. Rectangular Arrays Each row has the same number of parts
Each column has the same number of parts
Each array has a rectangular shape.
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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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6. 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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7. 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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8. L.G. Factors Factor Product Factor Pair 3 * 5 = 15 Factors Product
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9. 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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10. 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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11. L.G. 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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12. Divisibility – a number is divisible by another number if the result of division is a whole number.
Is 8 a factor of 48?
Is 4 a factor of 30?
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13. Solve problems 1 and 2 at the top of journal page 12.
Math Message Lesson 1 . 5
Solve problems 1 and 2 at the top of journal page 12.
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14. Divisibility
L.G.
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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15. 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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16. Divisibility Tests - 3
A number is divisible by 3 if the sum of its digits is divisible by 3.
Example:
237
= 12
1 + 2 = 3
410
= 5
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17. Divisibility Test - 6
A number is divisible by 6 if it is divisible by both 2 and 3.
426
Is it even? Yes
= 12
1 + 2 = 3
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18. Divisibility Test - 9
A number is divisible by 9 if the sum of its digits is divisible by 9.
Example:
198
= 18
1 + 8 = 9
429
= 15
1 + 5 = 6
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19. 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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20. Divisibility Tests – 10
A number is divisible by 10 if it ends in a zero.
Example: 10, 20, 1450, 370
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21. 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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22. L.G. 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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23. Prime or Composite?
25 17
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24. 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:
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25. L.G. 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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26. Exponents and Base Numbers42
base number
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27. 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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28. L.G. Unsquaring Numbers Solving m2=81 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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29. 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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30. Unsquaring More Numbers (calculator)
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31. 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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32. L.G. 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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33. 180 10 18

34. 180 10 18

35. 180 18 10 5 2 6 3

36. 180 18 10 5 2 6 3 3 2

37. 180 = 2 * 5 * 2 * 3 * 3 180 = 22 * 32 * 5 Prime Factor String
Prime Factorization using Exponential Notation
180 = 22 * 32 * 5
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38. Please complete the Time to Reflect questions on journal page 27. 
Math Message Lesson
Please complete the Time to Reflect questions on journal page 27. 
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