Improving Mathematical Understanding Deepening Number Sense

1. Improving Mathematical Understanding Deepening Number Sense

3. How do kids represent number? • Level 0- Subitizing numbers up to 3, raises fingers sequentially. • Level 1- Subitizing regular patterns up to 6 and irregular patterns up to 5, raises fingers simultaneously up to 5. • Level 2- Recognize 5-wise and pair-wise structures, create finger patterns, combine and partition numbers up to 10.

4. Level 3- Uses the sub-base of 5 to combine and partition numbers up to 10 without counting. • Level 4- Combines and partitions numbers up to 20 using 10-plus and doubles. • Level 5- Uses sub-base of 5, base of 10, and doubles to combine and partition numbers up to 20 without counting.

5. 81 – 79 = 11 – 8 =

6. Number Sense vs. Teaching the Standard Algorithm

7. Fact Fluency

8. Number Line 13 14 15 16 17 18 19 20 Open Number Line

9. Ten Frames

10. Dot Cards Subitizing

16. Task 1 Flashed Dot Patterns What interventions should we do to support this?

17. Task 2 What interventions should we do to support this? Finger patterns

18. 1 2 3 4 5 6 7 8

19. 1 2 3 4 5 6 7 8 9 10 11 12 13 It is important to know what type of thinkers your students are. Interval thinkers like the number line. Discrete thinkers don’t understand the number line. They need concrete objects. Interval Thinkers think in terms of jumping on the number line. Example: 12 remove 3 I have 12 so 11, 10, 9-I have 9 left. (12…. 11, 10, 9) 10 9 11 I have 9 left.

20. Johnny had 12 heart cookies. He gave his friend Mr. 12, Mr. 11, and Mr. 10, so he had 9 left. Discrete Thinkers think in terms of counting individual objects. Example: 12 remove 3 I removed 12, 11, and 10 so I have 9 left. (12, 11, 10……9) 11 I have 9 left. 10 12

21. What interventions should we do to support this? Task 3 Name and visualize quantities on a pair-wise ten frame

22. What does the Investigations curriculum do to develop number sense? What are your next steps?