Basic Arithmetic Operations · 39 lessons

There are two ways to do a calculation, and fluency is mostly about choosing between them quickly. A mental method reshapes the numbers into ones that are easier — it is fast, but it depends on the numbers cooperating. A written method ignores what the numbers look like and grinds through them at a steady cost.

1. 1Number Bonds to Ten
2. 2Taking Away
3. 3Adding Within Twenty
4. Adding and subtracting within 20 (10)
5. 4Equal Groups
6. 5Rows and Columns
7. 6Sharing Equally
8. 7Multiplying and Dividing Undo Each Other
9. Multiplication and division (10)
10. 8Adding in Any Order
11. 9Adding by Splitting
12. 10Bridging Through Ten
13. 11Doubles and Near Doubles
14. 12Rounding and Adjusting
15. 13Counting Up to Subtract
16. 14The Same Difference
17. 15Adding and Subtracting Tens and Hundreds
18. Adding and subtracting in your head (14)
19. 16Lining Up the Columns
20. 17Carrying
21. 18Carrying in More Than One Column
22. 19Borrowing
23. 20Borrowing Past a Zero
24. Subtract from 1000
25. 21Two-Step Word Problems
26. Written addition and subtraction (10)
27. 22Multiplying and Dividing by 10, 100 and 1,000
28. Rule of 101
29. Rule of 99
30. 23Multiplying by Splitting
31. Multiply by 9
32. 24Doubling to Multiply
33. Multiply by 12
34. 25Halving to Divide
35. Multiply by 5
36. Multiply by 15
37. 26Dividing by Splitting
38. Divide by 5
39. 27Rounding to Estimate
40. Multiplying and dividing in your head (12)
41. 28Multiplying in Columns
42. Last Digit of Products
43. 29Two Digits by Two Digits
44. Rule of 11
45. Squaring Ends in 5
46. Cross-Multiplication
47. 30Long Division
48. 31Remainders
49. 32Interpreting the Remainder
50. Whole numbers (16)
51. 33Brackets First
52. 34Multiply and Divide Before Adding and Subtracting
53. 35Brackets with All Four Operations
54. Order of operations (10)
55. 36Subtracting Negative Numbers
56. 37Absolute Value
57. 38Multiplying and Dividing Negative Numbers
58. 39Estimating with One Significant Figure
59. Significant figures and estimation (10)