Subtizing, addition, subtraction, numeration

1. Prenumeration, Number Operations, Addition and Subtraction

4. How many of each color did you see?

9. Discuss a forward sequence and a backward sequence for the flow of action.

10. Have students make up their own sequence. What happened “ first ”? What happened “ next ”? What happened “ last ”?

12. Another type of sequence involves size relationships.

14. The student’s task would be to match this original set, but use a different manipulative, like a soccer ball. It is not the manipulative it self that is being matched but the number of items. This emphasis upon the number, not the form, is essential for later number development.

17. Name to Number and Number to Name to “ONE” “ ONE” to As this become routine for the students try to extend this activity to assigning the numeral, i.e., 1, 2, 3,…, to both the object and the oral name for the object.

20. With 1-1 Correspondence 1 2 3 4 5 6 Without 1-1 Correspondence 1 2 3 4 5 6

21. Expanding Subtizing

25. Basic Number System, Base 10 , 10 0 10x1 10 1 10x10 10 2 10x10x 10 10 3 10x10x 10x10 10 4 10x10x 10x10x 10 10 5

26. Basic Number System, Base 8 , 8 0 8x1 8 1 8x8 8 2 8x8x8 8 3 8x8x8x8 8 4 8x8x8x 8x8 8 5

30. Basic Operations On Objects

32. Change Result Initial Change Result Initial Join Separate Part Part Whole Part-Part-Whole Larger Small Set Set Difference Compare

34. Change Result Initial Separate Separate: Result Unknown Sandra had 12 pennies. She gave 4 pennies to George. How many pennies does Sandra have now? Separate: Change Unknown Sandra had 12 pennies. She gave some to George. Now she has 8 pennies. How many did she give to George? Separate: Initial Unknown Sandra had some pennies. She gave 4 to George. Now Sandra has 8 pennies left. How many pennies did Sandra have to begin with? 12 – 4 = 8 12 – 4 = 8 12 – 4 = 8

35. Part-Part-Whole: Whole Unknown George has 4 pennies and 8 nickels. How many coins does he have? George has 4 pennies and Sandra has 8 pennies. They put their pennies into a piggy bank. How many pennies did they put into the bank? Part-Part-Whole: Part Unknown George has 12 coins. Eight of his coins are pennies, and the rest are nickels. How many nickels does George have? George and Sandra put 12 pennies into the piggy bank. George put in 4 pennies. How many pennies did Sandra put in? Part Part Whole 4 + 8 = 12 4 + 8 = 12

36. Compare: Difference Unknown George has 12 pennies and Sandra has 8 pennies. How many more pennies does George have than Sandra? George has 12 pennies. Sandra has 8 pennies. How many fewer pennies does Sandra have than George? Compare: Larger Unknown George has 4 more pennies than Sandra. Sandra has 8 pennies. How many pennies does George have? Sandra has 4 fewer pennies than George. Sandra has 8 pennies. How many pennies does George have? Compare: Smaller Unknown George has 4 more pennies than Sandra. George has 12 pennies. How many pennies does Sandra have? Sandra has 4 fewer pennies than George. George has 12 pennies. How many pennies does Sandra have Difference Larger Small Set Set 12 – 8 = 4 12 – 8 = 4 12 – 8 = 4

38. Part-Part-Whole Model for 5 + 3 = 8 and 8 – 3 = 5 Addition Models

39. Models for 9 – 4 as a Missing-Part Problem

40. Models for the difference between 8 and 5.

45. Join or part-part-whole problems in which one of the addends is a 1 or 2 are easy to make up. For example: When Tommy was at the circus, he saw 8 clowns come out in a little car. Then 2 more clowns came out on bicycles. How many clowns did Tommy see in all? Can you think of a word problem using this method?

52. Make-Ten Extended Three of the six facts have 7 as one the addends. The make-ten strategy is frequently extended to the facts as well. For 7 + 4, the idea is 7 and 3 more makes 10 and 1 left is 11. You may decide to suggest this idea at the same time you initially introduce the make-ten strategy. It is interesting to note that Japan, mainland China, Korea, and Taiwan all teach an addition strategy of building through 10 and do so in the first grade. Counting On Counting on is the most widely promoted strategy. It is generally taught as a strategy for all facts that have 1, 2, or 3 as one of the addends and thus, includes the one and two-more-than facts. For the fact 3 + 8, the child starts with 8 and counts three counts, 9, 10,11. There are several reasons this approach is downplayed in this text. First, it is frequently applied to facts where it is not efficient, such as 8 + 5. It is difficult to explain to young children that they should count for some facts but not others. Second, it is much more procedural than conceptual. Finally, if other strategies are used, it is not necessary.

53. Ten-Frame Facts The ten-frame model is so valuable in seeing certain number relationships that these ideas cannot be passed by in thinking about facts. The ten-frame helps children learn the combinations that make 10: 5 + 6, 5 + 7, and 5 + 8 are quickly seen as two fives and some more when depicted with these powerful models.