The document discusses various topics related to teaching mathematics concepts like numbers, place value, and numeration systems. It provides information on strategies for teaching cardinality using models like number lines. It also describes the evolution of number systems from ancient civilizations to modern systems and compares features like place value across different numeration systems.

1. Fill in all squares of the grid with single digits Each column, each row, each 3x3 grid contains all the digits from 1-9 with no repeats. Sudoku Let’s play …

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3. Fill in all squares of the grid with single digits Each column, each row, each 3x3 grid contains all the digits from 1-9 with no repeats. Sudoku Let’s play … Where’s The Math?

4. Number Sense and Numeration

5. Number Sense permeates all aspects of mathematics teaching and learning …. Make sense of Numerical situations Intuitive feeling for numbers Develops with experience NSN PA M GSS DMP

6. Part Part Whole 7 7 Complex / Multifaceted / Relationships Spatial Recognize sets of objects in patterned 1 and 2 more 1 and 2 less Anchors 5 and 10

7. 7 3 15 Counting Of course, that only makes sense…

8. Benchmark: A Point of Reference Ministry Document: K - 3 Strategies Grade 1 lesson: Ten in the Nest - Page 125

9. 1 2 3 4 5 6 1 2 3 4 5 6 Cardinality Principle

10. Cardinal Nominal Ordinal “ How Many” “ Which One?” “ Which Position?” Sara is 6 years old Please come to her 6 th birthday party It’s at 4:00 pm On Thursday Sept. 11 th It’s at 355 Third Avenue Call 519-453-4161 to R.S.V.P

11. Use of More / Less / Same in their language is a benchmark for the teacher that changes over time. Key Language Development: Game Facts: Ms. Brooks won by 15 points. In one quarter they scored the same number of points. In another quarter, Mr. Adams scored 10 more points. In yet another quarter, Mr. Adams was outscored by 5 points. Mr. Adams Ms. Brooks Final 4 th 3 rd 2 nd 1 st Player

12. Number Models – visual representations What techniques (lessons) might a teacher use to model cardinality? Number Lines – a single dimensional model ‘ BIG” number lines (ropes and strings) Build a Model Strategy 1: To Compare and Order Numbers ….

13. Use 'Intelligent' Guess and Check “ I’m thinking of a number between ….” Strategy 2: To Compare and Order Numbers …. 25 72 Numberline Game .... Fish Bowl

14. Strategy 3: Doubles and Near Doubles …. double 3 is the 'bug' double ... double 4 is the 'spider' double ... double 5 is the 'hand' double ... double 6 is the 'egg carton' double ... double 7 is the 'two week' double ...

15. There has to be a better way!

16. How did number systems evolve?

17. Engage all of your learners ... A Brief Comparison of Ancient Number Systems Technique: Jigsaw Class is divided into 4 teams. Each group member is given a letter. (A-D) Each letter group assembles into specialist groups. Specialist group becomes the expert group. Parent group reassembles with each member responsible for their topic.

18.  Place Value  Zero as a Place Holder  International 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Hindu-Arabic Numeration System Characteristics of Base 10 System Will this Numeration System evolve too?

19. Japanese Numeration System … 15 14 13 12 11 Jugo Go 5 Jushi Shi 4 Jusan San 3 Juni Ni 2 Juichi Ichi 1

20. Language …A Bump In The Road Tenty-one Tenty-two Tenty-three Tenty-four Tenty-five 15 14 13 12 11 Fifteen Five 5 Fourteen Four 4 Thirteen Three 3 Twelve Two 2 Eleven One 1

21. the value of a digit is determined by its position in a number. 275 Place Value Most Significant Digit

22. PV Blocks (pre-grouped) “ Count by…” Start / Dir / Skip 8 U 2 24 D 5 15 U 3 108 D 4 Model Building: Proportional Place Value Sticks (‘groupable’)

23. PV Blocks (pre-grouped) Sticks (‘groupable’) Model Building: Non-Proportional Place Value Issues 1 10 100

24. Trading Equivalent Values 1 10 100 1 10 100

25. The Hundreds Chart Sieve of Eratosthenes: Primes and Composites Think / Pair / Share Find 1 more patterns. 45 36 34 35 27 15 13

26. Expanded Notation A Critical skill 'Lost in the Wilderness' Multiple Representations 275 = 200 + 70 + 5 275 = 100 + 170 + 5