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Mathematical Task 2.3A

Mathematical Task 2.3A. What is a Number String?.

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Mathematical Task 2.3A

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  1. Mathematical Task 2.3A

  2. What is a Number String? A number string is a set of related math problems, crafted to support students to construct big ideas about mathematics and build their own strategies (Fosnot & Dolk, 2002). Typically, a teacher gathers her students near the board and presents the problems — one at a time — providing plenty of time for students to think. Students first solve the problems mentally, then share their strategies with the class while making sure they understand others’ thinking. Meanwhile, the teacher is representing students’ strategies on a model and facilitating conversation among students about the sense they are making within and between the problems. Strings are not a rigid recipe but a flexible classroom routine — used by teachers daily or weekly with both small groups and entire classes. Numberstrings.com

  3. What is a Number String?

  4. The Hindu-Arabic Numeration System • The Hindu-Arabic numeration system that we use today was developed about 800 c.e. The following list features the basic numerals and various attributes of this system. • 1. Digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9: These symbols, or digits, can be used in combination to represent all possible numbers. • Grouping by tens (decimal system): Grouping into sets of 10 is a basic principle of this system, probably because we have 10 “digits” on our two hands. (The word digit literally means “finger” or “toe.”) Ten ones are replaced by 1 ten, 10 tens are replaced by hundred, 10 hundreds are replaced by 1 thousand, and so on. The number of objects grouped together is called the base of the system; thus our Hindu-Arabic system is a base ten system. • Place value (hence positional): Each of the various places in the numeral 6523 , for example, has its own value. • Additive and multiplicative: The value of a Hindu-Arabic numeral is found by multiplying each place value by its corresponding digit and then adding all the resulting products.

  5. Mathematical Task 2.3B

  6. Figure 2.31

  7. Algebraic Reasoning The process described for converting 97 to a base five number is really solving the equation 97 = 25x + 5y + z where x , y and z are less than 5 .

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