Bridging the gap - moving children from counting to breaking up numbers

1. Bridging the gap - moving children from counting to breaking up numbers

2. With a deck of cards • Share all the cards out amongst the group • Take turns to put a card face up in the middle • As you put the card up say: • 1 more than the number on the card • 1 less than the number on the card • 10 more than the number on the card • 9 more than the number on the card (10-1) • 11 more than the number on the card (10+1) • 100 more than the number on the card • 99 more than the number on the card (100-1) • 101 more than the number on the card (100+1) • 1000 more than the number on the card • 999 more than the number on the card (1000-1) • The Number on the card plus/minus? = 10

3. Objectives of Session: • To develop an understanding of common place value misconceptions and how these can be addressed. • To explore key activities, equipment and resources that will help support the development of place value knowledge.

4. Understanding Place Value: In your groups discuss: • What is Place Value? • Why is it so important?

5. Teaching Place Value: What equipment should we use to teach place value? Why? • Use the ‘representation of 28’ sheet • Order the equipment from least to most abstract -group as necessary

7. Language vs. Understanding? • The construction of the English number words from 1 to 60 is a mixture of strange rules which often cause confusion for children. • Correcting these initial place value problems is a language issue not a mathematical one. • The “ty” and the “teen” words need to be unpacked for children.

8. Decoding the Numbers: • Children need to make connections between the numeral symbols, the way they are read, and their representations in materials. For example the number 65: • See ‘65’ • Say in one way: sixty-five • Say in the other way: six tens and five ones • Do show 6 bundles and 5 loose sticks • Do 65 singles sticks Give children experiences at connecting these 3 forms. For example: Twenty + 31 = 58 + 4 tens = Seventy two + 14 =

9. Grouping: • The key idea is that students practice bundling and connecting this to symbols. For example, 17 is read as seventeen, and one ten and seven ones, and modeled as one ten and seven and also seventeen singletons. • Students need to group materials so they eventually understand that one ten and ten ones are the same.

10. Stage 5 Grouping/Place Value and Basic Facts knowledge: • Basic Facts: • Addition facts to 20 and subtraction facts to 10. • Multiplication facts for the 2, 5 and 10 times tables and corresponding division facts. • Multiples of 100 that add to 1000. • Place Value: • Groupings within 100, e.g., 49 and 51. • Groupings of two, five and ten that are within numbers. • The number of hundreds in centuries and thousands. • Rounding 3 digit numbers to the nearest 10 or 100.

11. Misconceptions with Place Value: • Donald is in Year 2. He thinks that the number following fifty-nine is fifty-ten. What are his misconceptions? How would you teach him? What equipment would you use?

12. Days at School Watch your place value understanding develop using the ‘Days at School’ strategy. Have a celebration when you hit 100 days at school! Thanks to Waterloo School

13. Misconceptions with Place Value: • Jane is given 6 bundles of ten sticks. When asked how many groups of ten, Jane replies 60. What are Jane’s misconceptions? What are her next learning steps?

14. Misconceptions with Place Value: • Sam is very good at counting. He can orally count up to 199 without any trouble. His teacher sets the class the task of writing down the numbers following 98. Sam writes 99, 100, 1001, 1002, 1003. What does Sam need to learn? What learning experiences would he benefit from?

15. The Ten for One Swap Frog Swamp game (Adapted from Bev Dunbar Exploring 0-100 Numeration)

16. Activities for Stage 4: • Children also need experience adding and subtracting numbers using place value. • Use a mixture of words and numbers. This is a powerful indicator as to whether a student understands meaning. 60 + twenty-seven = 3 tens + sixteen = Seventy - 3 tens =

17. Entering into Stage 5: • Problems that scaffold children part-whole thinking: 26 + 4 = Importance of Place Value Cannon There are ten ones which need to be swapped for one ten. This produces three tens which is coded as 30. Other eg: 4 + 66 = ? + 48 = 50 43 + ? = 50 • Children should have mastered the above examples in their heads at number properties.

18. Misconceptions with Place Value: • Juliet works out 73 – 27 by saying … “I can’t take 7 from 3 so I borrow a 1 from the 7. 13 – 7 = 6 6 – 2 = 4 The answer is 46” Is Juliet correct? How would you respond? What questions may you ask? What equipment would you use?

19. Key Place Value Concepts to Develop: • The fundamental place value issue is that ten units must be interchanged for one new unit. The zero place holder idea is significant but not the main problem. • Students need experiences initially making groups of tens by bundling and unbundling ten ones for one ten. • It is important that students know how to write a numeral; how to say the numeral in two ways; as well as how to model in two ways both as singletons and objects grouped as tens and ones.

20. Place Value Activities: What is the key purpose? • Card Games • Target • Frog Swamp • Close to Hundred (Bk.4 Pg.24) • Squeezy Boxes • Place Value Dice Game How could this activity be adapted or modified? How would I use this activity? Independent, whole class, Group Box??

21. Place Value Dice Game Place Your Values: • Roll a 0-9 dice. • Make the number using the popsticks. • Roll the dice again. Add this total to the previous using the popsticks - remember the “canon of place value” • Once you’ve reached a three digit number, STOP. • How can we now use our digit cards to model this understanding?

22. Tips for Teaching Knowledge: • Knowledge teaching is tailored to the children’s gaps and what they require to move to the next stage. • Equipment is essential. • Key mathematical language is being developed. • Practice activities develop quick and accurate recall of knowledge.