The document discusses patterns in division and provides examples to illustrate definitions and concepts related to division. It defines dividend, divisor, and quotient, and shows that the dividend goes inside the division bracket, the divisor goes outside, and the quotient goes above. Examples are provided to demonstrate that for larger numbers, the same patterns can be used, such as 160 divided by 8 being 20 since 16 divided by 8 is 2. Patterns are also shown for numbers with zeros, such as 32,000 divided by 8 being 4,000.

1. 5-1 Mental Math:
Patterns in Division
Math Notes
Number Sense 1.0

2. What you’re learning today...

3. What you’re learning today...
Number Sense 1.0 - Computing with
positive integers.

4. What you’re learning today...
Number Sense 1.0 - Computing with
positive integers.
Definitions of dividend, divisor, and
quotient.

5. What you’re learning today...
Number Sense 1.0 - Computing with
positive integers.
Definitions of dividend, divisor, and
quotient.
12 ÷ 3 = 4

6. What you’re learning today...
Number Sense 1.0 - Computing with
positive integers.
Definitions of dividend, divisor, and
quotient.
12 ÷ 3 = 4 54 ÷ 6 = 9

7. What you’re learning today...
Number Sense 1.0 - Computing with
positive integers.
Definitions of dividend, divisor, and
quotient.
12 ÷ 3 = 4 54 ÷ 6 = 9
3,000 ÷ 5 = 600

8. Division Review
12 ÷ 3 = 4

9. Division Review
12 ÷ 3 = 4
12 is the dividend, the
number being divided.

10. Division Review
3 is the divisor, the number
that divides into the dividend
12 ÷ 3 = 4
12 is the dividend, the
number being divided.

11. Division Review
3 is the divisor, the number
that divides into the dividend
12 ÷ 3 = 4
4 is the quotient, the
12 is the dividend, the
result of dividing the
number being divided.
dividend by the
divisor.

12. Division Review
12 ÷ 3 = 4

13. Division Review
12 ÷ 3 = 4

14. Division Review
3=4
12

15. Division Review
The dividend goes
inside the division
bracket.
3=4
12

16. Division Review
The dividend goes
inside the division
bracket.
4
3 12

17. Division Review
The divisor goes
outside the division
bracket.
The dividend goes
inside the division
bracket.
4
3 12

18. Division Review
The divisor goes
outside the division
bracket.
The dividend goes
inside the division
bracket.
4
3 12

19. Division Review
The divisor goes
outside the division
bracket.
The dividend goes The quotient goes
inside the division above the division
bracket.
4 bracket.
3 12

20. Example 1
160 ÷ 8 = n

21. Example 1
160 ÷ 8 = n

22. Example 1
160 ÷ 8 = n

23. Example 1
Think
16 ÷ 8
160 ÷ 8 = n

24. Example 1
Think
16 ÷ 8
160 ÷ 8 = n
16 ÷ 8 = 2

25. Example 1
Think
16 ÷ 8
160 ÷ 8 = n
16 ÷ 8 = 2
160 ÷ 8 = 20

26. Example 1
Think
16 ÷ 8
160 ÷ 8 = n
16 ÷ 8 = 2
160 ÷ 8 = 20
16 tens

27. Example 1
Think
16 ÷ 8
160 ÷ 8 = n
16 ÷ 8 = 2
160 ÷ 8 = 20
16 tens 2 tens

28. Example 2
30 ÷ 5 = 6
30 ÷ 5 = 6
30 ÷5=6

29. Example 2
30 ÷ 5 = 6
300 ÷ 5 = 6
30 ÷5=6

30. Example 2
30 ÷ 5 = 6
300 ÷ 5 = 60
30 ÷5=6

31. Example 2
30 ÷ 5 = 6
300 ÷ 5 = 60
3000 ÷ 5 = 6

32. Example 2
30 ÷ 5 = 6
300 ÷ 5 = 60
3000 ÷ 5 = 600

33. Example 2
60 ÷ 30 = 2
60 ÷ 30 = 2
60 ÷ 30 = 2

34. Example 2
60 ÷ 30 = 2
600 ÷ 30 = 2
60 ÷ 30 = 2

35. Example 2
60 ÷ 30 = 2
600 ÷ 30 = 20
60 ÷ 30 = 2

36. Example 2
60 ÷ 30 = 2
600 ÷ 30 = 20
6000 ÷ 30 = 2

37. Example 2
60 ÷ 30 = 2
600 ÷ 30 = 20
6000 ÷ 30 = 200

38. Example 3
140 ÷ 2

39. Example 3
Think
14 ÷ 2 = 7
140 ÷ 2

40. Example 3
Think
14 ÷ 2 = 7
140 ÷ 2 = 7

41. Example 3
Think
14 ÷ 2 = 7
140 ÷ 2 = 7
Don’t forget that 0

42. Example 3
Think
14 ÷ 2 = 7
140 ÷ 2 = 70
Don’t forget that 0

43. Example 4
32,000 ÷ 8

44. Example 4
Think
32 ÷ 8 = 4
32,000 ÷ 8

45. Example 4
Think
32 ÷ 8 = 4
32,000 ÷ 8 = 4

46. Example 4
Think
32 ÷ 8 = 4
32,000 ÷ 8 = 4
Don’t forget those 000’s

47. Example 4
Think
32 ÷ 8 = 4
32,000 ÷ 8 = 4000
Don’t forget those 000’s