Addition and

Subtraction

911 Emergency

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Math911-mm_08-10-07.wmv

What we will cover….

• Revisit Numeracy Stages

• Addition and Subtraction strategies.

• Activities and games for students at different stages.

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

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.

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.

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 =

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.

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.

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

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

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

Advanced Multiplicative

Tidy Numbers would be a smart strategy. 30 x 6 =

180180 – (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.

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) – 125 + 27 = (25 + 25) + 2 = 52

• Making 10s 5 + 4 + 5 = 10 + 415 + 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

Addition and Subtraction cont’d

• Compensation 63 – 39 = 63 – 40 + 1 = 24

• (Rounding, Tidy Numbers) 198 – 20 can be:200 – 20 – 2 = 178398 + 30 = 400 + 30 – 2 = 428

• Reversibility 63 – 39 = so 39 + ? = 63Therefore 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 = 40so 64 – 40 = 24

865 – 590 = 875 – 600 = 275

• Algorithm 865 +432

1297

Websites

•www.nzmaths.co.nz• www.rainforestmaths.com