This document discusses numeracy development stages and strategies for addition and subtraction. It outlines 8 stages of development from emergent to advanced proportional reasoning. For each stage, it provides examples of the skills, knowledge, and strategies students at that stage typically use. It also lists and describes common addition and subtraction strategies like counting on, making 10s, partitioning, compensation, and the standard algorithm. Finally, it provides websites for additional math resources.

1. Addition and Subtraction

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3. What we will cover…. Revisit Numeracy Stages Addition and Subtraction strategies. Activities and games for students at different stages.

4. Stage 0 Emergent Stage 1 1 – 1 counting Stage 2 Counting from 1 on Materials Stage 3 Counting from 1 by Imaging Stage 4 Advanced Counting Stage 5 Early Additive Stage 6 Advanced Additive/Early Multiplicative Stage 7 Advanced Multiplicative/Early Proportional Stage 8 Advanced Proportional Stages of Development

5. Strategy is about how children solve number problems, in particular the mental processes they use. Creates new knowledge through use Strategy Knowledge Provides foundation for strategies Knowledge considers the key items of knowledge that children need to acquire.

6. Emergent Movie Clip 1,2,3,5,8...? Can you get me 7 counters from the pile please? The child can not consistently count a collection of objects.

7. One to One Counting 1,2,3,4,5,6,7,8. Can you get me 7 counters from the pile please? The child can count a set of objects up to ten but can’t join and separate sets like 4 + 3 =

8. Count From One on Materials 1,2,3,4,5,6,7. There are 4 counters and another 3 counters. How many are there altogether? The child solves the problem by using their fingers or other materials and counts from one.

9. Count From One By Imaging Counts in head 1,2,3,4,5,6,7,8. There are 4 counters and another 3 counters. How many are there altogether? The child counts all the objects from one by imaging visual patterns of the objects in their mind.

10. Advanced Counting Counts on 9, 10, 11, 12, 13. There are 9 counters under there and another 4 counters under there. How many are there altogether? The child counts on from the largest number

11. Early Part-Whole “ I know that If I take one off the 6 and put it on the 9 it =10. 10 + 5 = 15” There are 9 counters under there and another 6 counters under there. How many are there altogether? The child uses simple strategies to solve addition and subtraction problems mentally

12. Advanced Part-Whole I think tidy numbers would be smartest. 63 – 40 = 23 23 + 1 = 24 63 people are on the bus and 39 people get off the bus. How many people are left on the bus? The child can select from a wide range of strategies to solve various addition and subtraction problems mentally

13. Advanced Multiplicative Tidy Numbers would be a smart strategy. 30 x 6 = 180 180 – (2 x 6) = 168 There are 28 fruit trees in each aisle of the orchard. There are 6 aisles. How many trees are there altogether? The child can select from a wide range of strategies to solve various multiplication and division problems mentally.

14. Addition and Subtraction Strategies Counting All Objects 5 + 4 = 1,2,3,4,5,6,7,8,9 Counting On 8 + 5 = 9, 10, 11, 12, 13 Counting Backwards 37 – 4 = 36, 35, 34, 33 Doubles 8 + 7 = (8 + 8) – 1 25 + 27 = (25 + 25) + 2 = 52 Making 10s 5 + 4 + 5 = 10 + 4 15 + 18 + 5 +2=10+10+10+10 = 40 Place Value 43 + 25 = (40 + 20) + (3 + 5) Partitioning 69 – 43 = (60 – 40) + (9 – 3) so 20 + 6 = 26

15. Addition and Subtraction cont’d Compensation 63 – 39 = 63 – 40 + 1 = 24 (Rounding, Tidy Numbers) 198 – 20 can be:200 – 20 – 2 = 178 398 + 30 = 400 + 30 – 2 = 428 Reversibility 63 – 39 = so 39 + ? = 63 Therefore 39 + 20 + 4 =63 so answer is 24 Compatible Numbers 247 + 243 = (247–2)+(243 +2) =245+245=490 Equal Additions 63 – 39 = 63 + 1 = 64, 39 + 1 = 40 so 64 – 40 = 24 865 – 590 = 875 – 600 = 275 Algorithm 865 +432 1297

16. Websites www.nzmaths.co.nz www.rainforestmaths.com