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FTCE K-6 Math
| Question | Answer |
|---|---|
| Accuracy Automaticity Rate Flexibility | The 4 components that measure a students level of mathematical fluency are |
| Accuracy | Getting the right answer |
| Automaticity | Selecting problem solving methods and performing computations without requiring much time to think the processes through |
| Rate | how quickly computations are made |
| Flexibility | being able to solve problems in more than one way and selecting the most appropriate method |
| Fluency | the ability to solve problems quickly and accurately by knowing which methods to use and how to use them |
| Inductive Reasoning Deductive Reasoning Adaptive Reasoning | The three main types of reasoning that students should develop |
| Inductive Reasoning | reasoning in which conclusions are based on observation |
| making conclusions based on patterns you observe | conjecture |
| Deductive Reasoning | reasoning in which conclusions are based on the logical synthesis of prior knowledge of facts and truths |
| Adaptive Reasoning | The ability to think logically about the relationships between concepts and to adapt when problems and situations change |
| Concrete Model | use objects to demonstrate operations |
| semi-concrete model | use pictures (instead of actual objects) to demonstrate operations |
| abstract model | using numbers only to perform operations |
| Semi- Abstract Model | use a single symbol (such as X or a tally mark) to represent numbers of objects while performing operations |
| Reasoning | refers to students ability to hypothesize, test their theories, and draw conclusions |
| Array | is one way to model a multiplication problem visually |
| partitive division | is needed when students know how many groups there needs to be, but not how many objects will be in each group |
| Algorithms | One technique or skills used to solve problems without visual models, they are a standard step by step procedure for solving mathematical problems |
| Iteration | a computational process in which the same steps are related until a final answer is found |
| Subitizing | the ability to instantly see the number of objects in a small set without having to count them |
| Formal Assessment | Criterion, Norm, Curriculum, Diagnostic, and Teach generated instruments (tests) are all examples of what type of assessment |
| Informal Assessment | Observation, anecdotal records, running records, work samples, and portfolios are examples of what type of assessments |
| Mathematic Assessments | Timed math fact tests, computational and word problems, proofs, and project based assessments are common ______________ |
| Fluency | the ability to solve problems quickly and accurately by knowing which methods to use and how to use them |
| Flexibility | being able to solve problems in more than one way and selecting the most appropriate method |
| rational numbers | all integers and fractions |
| irrational numbers | any number that cannot be expressed as fractions, such as an infinite, no repeating decimal |
| exponents | numbers that raise another number to a power, making it multiply by itself a certain number of times (3^2) |
| roots | the root of a number x is another number such that when the number is multiplied by itself a give number of times, it equals x |
| Place Value | a way of organizing numbers based on groupings of ten |
| Commutative property (applies to addition and multiplication) | The order of the numbers being added or multplied does not affect final result |
| Place Value | a way of organizing numbers based on groupings of ten. |
| Commutative property (applies to addition and multiplication | The order of the numbers being added or multplied does not affect final result. 1+3 equals 3+1, 2x 5 equals 5 X 2. |
| Distribute property (applies to multi.) | Multiplication in front of parentheses can be distributed to each term within the parentheses, a (b + c) equals ab + ac. |
| Associative Property (addition and multi.) | If the operations are all the same ( all addition or all multiplication) the terms can be regrouped by moving the parentheses. (a + b) + c equals a + (b + c) a(bc) equals (ab)c. |
| Subitize | "Instantly seeing how many." |
| Inventive Strategies | Examples of Inventive Strategies -Useful Representations -Complete-Number Strategies -Partitioning Strategies -Compensation Strategies -Using Multiples of 10 and 100 |
| Useful Representations | Children will often use a visual model to represent the problem they are presented with. This is often shown by using arrays. |
| Complete-Number Strategie | Students who are not comfortable with breaking a number down into its tens and ones, will resort to other methods when multiplying larger numbers. For example, they may use addition (23 x 6 = 23 + 23 + 23 +23 + 23 + 23 = 138). |
| Partitioning Strategies | When given higher number to multiply, students will sometimes break the numbers down in a variety of different ways. For example, some students may divide the numbers into tens and ones |
| Compensation Strategies | Children often find ways to manipulate numbers to allow for easier calculations (48 x 3 : 50 x 3= 150; 2 x 3 = 6; 150 - 6 = 144). |
| Using Multiples of 10 and 100 | When presented with multiples of 10 and 100, students will often use the beginning part of the number to find the product. For example, for 300 x 12, students will often first multiply 3 x 12 and then use that to help them figure out 300 x 12. It is impor |
| Composite Numbers | A whole number that can be divided evenly by numbers other than 1 or itself. Example: 9 can be divided evenly by 3 (as well as 1 and 9), so 9 is a composite number. But 7 cannot be divided evenly (except by 1 and 7), so is NOT a composite number (it is a |
| Components of Math Fluency | The ability to recall the answers to basic math facts automatically and without hesitation. Fact fluency is gained through significant practice, with mastery of basic math facts accuracy, automaticity, rate, flexibility |
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