number systems
b is selected for the base and symbols for 1, b, b^2, b^3, b^4, etc. are used. These values do not depend on their location in a number because they are added up to be the value of the number.
What is an additive number system?
.77777.... may be rational or irrational.
What is a rational number?
Sally saw that John had no cookies, so she gave him one of hers. Now Sally has one cookie. How many cookies did Sally originally have?
What is take from, start unknown?
Suppose the set is A = {1, 2, 3, 4}.
This is a word that can define both B and C, but not D and E.
B = {1, 2, 3, 4} C = {1, 2, 3}
D = {{1,2}, 3} E = {1, 2, 5}
What is a subset?
b is selected for the base and 0, 1, 2, 3, . . . , b-1 are the symbol values. These values dependent on their location in a number.
What is a positional multiplicative number system?
This is any number with a non-ending and non-repeating decimal.
What is an irrational number?
The farmer has 5 boxes and 50 peaches. How many peaches can be put in the boxes?
What is put together/take apart, both addends unknown?
Classify 3 + 0i.
What are counting numbers, whole numbers, integer numbers, rational numbers, and real numbers?
In this process, you take a number system in base b and you want to convert it to base 10. The values of this number system are w = 0, x = 1, y = 2, z = 3. To convert the number xyz to a value in base 10, you do the following calculation: (3x10^0) + (2x10^1) + (1x10^2) = 3 + 20 + 100 = 123
What is the process of converting a number from base 4 to base 10?
Classify 3 (looking for 5 answers)
What are counting numbers, whole numbers, integer numbers, rational numbers, and real numbers?
Rachel got 100% on the exam. Justin got 90% on the exam. How much higher was Rachel’s score than Justin’s?
What is compare, difference unknown?
The counting numbers are a ____ of the whole numbers, which are a ____ of the integers, which are a ____ of the rational numbers, which are a ____ of the real numbers. (All of these blanks have the same word.)
What is a subset?
The Egyptian, Mayan, and Roman numeral number systems were an examples of this type of number system.
What is an additive number system?
This is any number that can be expressed in decimal form.
What are real numbers?
These models most clearly reflect the relationship of ones and tens. An example would be: Laura is picking apples. She has 4 baskets to fill. She can place 10 apples in each basket. How many apples must Laura pick to fill the baskets?
What is groupable?
Three methods that children can use to solve problems.
What is Direct Modeling, Counting Strategies, and Derived Number Fact Strategies?
The Arabic number system and Babylonian number system are examples of this type of number system. This number system was very rare in history.
What is a positional number system?
1000^0
What is 1?
These models are trading/exchanging models. An example of this would be: Laura organizes her apples by placing 10 in 7 baskets and the 4 left over in a bowl. How many apples does Laura have?
What is pre-grouped?
2^k where k is the number of elements in set A.
example:
A = {1, 2, 3} 2^3 = 8
A1 = { }
A2 = {1} A3 = {2} A4 = {3}
A5 = {1, 2} A6 = {2, 3} A7 = {1, 3}
A8 = {1, 2, 3}
How many subsets can you make from set A?