1. Chapter 02

2. 2 | 2 Copyright © Cengage Learning. All rights reserved. The Foundation of All Math Learning: Representations of Early Number Concepts

3. 2 | 3 Copyright © Cengage Learning. All rights reserved. Mathematical Routine: Tell me Fast

4. 2 | 4 Copyright © Cengage Learning. All rights reserved. Mathematical Routine: Tell me Fast

5. 2 | 5 Copyright © Cengage Learning. All rights reserved. Mathematical Routine: Tell me Fast

6. 2 | 6 Copyright © Cengage Learning. All rights reserved. Mathematical Routine: Tell me Fast

7. 2 | 7 Copyright © Cengage Learning. All rights reserved. Mathematical Routine: Tell me Fast

8. 2 | 8 Copyright © Cengage Learning. All rights reserved. Conversation in Mathematics Discuss what the child’s misconception was around the use of tools.

9. 2 | 9 Copyright © Cengage Learning. All rights reserved. Concrete & Abstract Representations Pedagogy

10. 2 | 10 Copyright © Cengage Learning. All rights reserved. What are Mathematical Tools? Often called manipulatives “Manipulatives” can be interpreted as something to play with in your hands whereas “tools” indicate that they are to assist in the learning of a math concept.

11. 2 | 11 Copyright © Cengage Learning. All rights reserved. Issues Regarding Tools Availability Knowing how to use them Management Free choice or teacher initiated

12. 2 | 12 Copyright © Cengage Learning. All rights reserved. Constructing Meaning for Tools A tool does not have meaning inherent in it. It must be constructed by the learner.

13. 2 | 13 Copyright © Cengage Learning. All rights reserved. Moving From Concrete to Abstract Representations

14. 2 | 14 Copyright © Cengage Learning. All rights reserved. Making the Connections BuildDrawRecord 27 + 4 (3+1) 10 20+10+1=31

15. 2 | 15 Copyright © Cengage Learning. All rights reserved. Moving Toward More Efficient Strategies Students share their work Students make connections between different strategies Students decide on most efficient strategies Students try on other students’ strategies

16. 2 | 16 Copyright © Cengage Learning. All rights reserved. Early Number Concepts Content

17. 2 | 17 Copyright © Cengage Learning. All rights reserved. Emergent: Oral counting and identification of numbers Matching: Counting- by 1’s, Number relationships- more/less; relating one number to another Quantifying: Counting - on/back Skip counting Number Relationships - part/part/whole Partitioning: Tens and ones -making tens -expanded notation -ten more/less Factoring: Multiplication & Division Operating: Multiplication & Division Operations with fractions

18. 2 | 18 Copyright © Cengage Learning. All rights reserved. Emergent Phase Numbers Signify quantity Rote Count to 10 with words in order Identify by sight 1-5 objects Beginning to write numerals Know more/less/same and that a change will result in either bigger or smaller (but not by how much)

19. 2 | 19 Copyright © Cengage Learning. All rights reserved. Counting in the Matching Phase What we look for when assessing/observing 1-1 correspondence how they keep track? do they remember a quantity that they counted? can they pull out a quantity that you ask? cardinality principle direct modeling

20. 2 | 20 Copyright © Cengage Learning. All rights reserved.

21. 2 | 21 Copyright © Cengage Learning. All rights reserved. Student Interview We will assess the counting skills of two kindergarten students. Identify each of the student’s strengths What is the number range that each student should be working in?

22. 2 | 22 Copyright © Cengage Learning. All rights reserved. Counting in the Quantifying phase Counting on, counting back Counting in groups

23. 2 | 23 Copyright © Cengage Learning. All rights reserved. Number Relationships in the Matching Phase More / less - one more / one less Relating one number to another

24. 2 | 24 Copyright © Cengage Learning. All rights reserved. Number Relationships in the Quantifying Phase Part-Part-Whole (“There are numbers within numbers”) - grab bag subtraction - building 2 color trains - snap it - the tub game Number relationships (doubles/doubles plus one)

25. 2 | 25 Copyright © Cengage Learning. All rights reserved.

26. 2 | 26 Copyright © Cengage Learning. All rights reserved.

27. 2 | 27 Copyright © Cengage Learning. All rights reserved. The Continuum of Number Concepts Developing from Kindergarten to Algebra