1. Math Content PD-Session #2 Developing Number Sense Presenter: Simi Minhas Math Achievement Coach, Network 204

2. Goals and Objectives Our goal is to help students… Develop flexibility in using computational strategies for addition and subtraction. We will know we are successful when students… Solve multi-digit addition and subtraction problems using strategies other than the traditional algorithm.

3. Progression of Standards Analyze the Progressions document How do the Number and Operation in Base Ten standards progress from grades K-5? What are the instructional implications? What do we need to master as teachers, in order to help our students reach the mastery of standards? How do we address the instructional Shifts?

4. Base-ten Number System: Place Value Learning about whole number computation must be closely linked to learning about the base-ten number system The heart of this work is relating the written numeral to the quantity and to how that quantity is composed and can be decomposed.

5. The Hundreds Chart A Powerful Tool for Students

6. Computational Fluency Flexibility – Comfortable with more than one approach. – Chooses strategy appropriate for the numbers. Efficiency – Easily carries out the strategy, uses intermediate results. – Doesn’t get bogged down in too many steps or lose track of the logic of the strategy. Accuracy – Can judge the reasonableness of results. – Has a clear way to record and keep track. – Concerned about double-checking results.

7. Share What are all the different strategies that you teach for adding and subtracting multi-digit numbers? You may use the following problem to model: 245-199=

8. Addition Strategies 1.Add each place from left to right 2.Add on the other number in parts 3.Use a nice number and compensate 4.Change to an easier equivalent problem

9. Directions Consider the numbers. From the list of four strategies, select an appropriate strategy for the numbers. Solve this problem using the strategy. 581 + 397 = ? Strategies Add each place from left to right Add on the other number in parts Use a nice number and compensate Change to an easier equivalent problem

10. Add Each Place from Left to Right

11. Change to an Easier Equivalent Problem

12. Add On the Other Number in Parts

13. Use a Nice Number & Compensate

14. Use Representations and Manipulatives

15. Let’s Try The Strategies

16. No pencils allowed. Solve the problem by reasoning in your mind. 35 – 19 = ? Then turn and share your reasoning.

17. Typical Instructional Sequence Model with Objects Jump to the Standard Algorithm ? What’s missing from this sequence?

18. Developmental Approach to Computation Direct Modeling  Model the situation or action step-by-step using objects or pictures and count, usually by ones, the objects. Counting Approach  Visualize the quantities to count-on, count-up-to, count- down, usually by ones; use fingers to keep track of the counts. Numerical Reasoning Strategy  Use number relationships to strategically work with quantities; break numbers apart and find easier ways to put them back together or to find differences.

19. Solve the problem in two different ways. 674 – 328 = ?

20. Subtraction Strategies 1.Subtract each place 2.Subtract the number in parts 3.Add up from the subtracted number 4.Use a nice number then compensate 5.Change to an easier equivalent problem

21. Add Up from the Subtracted Number

22. Subtract the Number in Parts

23. Use a Nice Number then Compensate

24. Change to an Easier Equivalent Problem

25. Subtract Each Place 674-328=346 600-300=300 70-20=50 4-8=? 8 is greater than 4, so we can break apart 50, and regroup the numbers. 50=40+10 10+4=14 14-8=6 300+40+6=346

26. Pick a Question to Discuss What are some things students need to know in order to develop computational fluency for addition and subtraction? In what ways might the use of varied strategies benefit and make computation more accessible for more students?

27. Closing Thought.... The most appropriate computation method can and should change flexibly as the numbers and the context change. Traditional algorithms are “digit-oriented” and “rigid” and rely on memorizing rules without reasons, and can lead to common errors. Alternative strategies are “number-oriented” and “flexible” and rely on making sense of working with numbers, and build confidence in students.

28. Khan Academy Video https://www.khanacademy.org/math/cc-fourth- grade-math/cc-4th-add-sub-topic/cc-4th- adding/v/carrying-when-adding-three-digit- numbers

29. Number Sense Why do the students need to have a deeper number sense in order to have conceptual understanding of computations?

30. Please read the article, “Towards Developing Conceptual Understanding: Four approaches to Teaching and Learning Multi-Digit Multiplication” What approaches are mentioned in the article? How are these approaches related? How are they different? Why should students be presented with different ways of problem solving?

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