Using inductive reasoning
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This document discusses inductive reasoning and using number patterns to derive mathematical rules. It introduces key concepts like number sequences, terms, arithmetic sequences with a common difference, and geometric sequences with a common ratio. It explains using a tree diagram of successive differences to identify patterns in number sequences and deduce rules. As an example, it shows deriving the formula for finding the sum of the first n odd counting numbers as n^2.
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The document discusses truth tables, which are used to determine if compound statements are true or false. It provides examples of truth tables for negation, conjunction, and disjunction. A conjunction is true only when both statements are true, while a disjunction is true when at least one statement is true. Truth tables can have more than two statements, with each additional statement doubling the number of possible cases.
Estimation
This document discusses estimation and story problems. It provides examples of estimating the number of busses needed for a field trip with 115 people where each bus holds 27 people. It recommends always rounding up when estimating. It also gives an example of estimating a baseball player's batting average by rounding his at bats to 600 and hits to 200 to get an estimated average of 0.333. Finally, it mentions using proportions to compare two different ratios.
Sets copy
This document discusses sets and their properties. It defines what a set is and the different ways to describe a set using word descriptions, listings, or set-builder notation. It discusses elements and members of sets, and whether certain values are elements of example sets. It also defines key set concepts like cardinality (the number of elements in a set), finite vs infinite sets, and why cardinal numbers cannot be determined for infinite sets.
Sets, subsets, compliments
The document defines various types of numbers and sets them in a circle chart. It then discusses concepts related to sets such as complements, proper subsets, and the formula to calculate the number of subsets in a set based on the number of elements. The key points are:
1) Natural numbers are contained within whole numbers, integers, rational numbers, real numbers, and imaginary numbers in descending order.
2) The complement of a set A is everything in the universal set that is not in A.
3) A proper subset has some but not all elements of the original set.
4) The number of subsets of a set is calculated by 2 to the power of the number of elements (2
Cells the structure of life
description of basic parts of a cell; Membrane, cytoplasm, wall, nucelus, ribosome, mitochondria, cholophyll.
For middle grades
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Using inductive reasoning
- 2. Inductive reasoning Observe a pattern and come up with general principles ( A Rule or Formula) Today we will look at how observations are turned in to Mathematical rules
- 3. First; Some Vocab Number Sequence - A list of numbers. There’s a 1st number, a 2nd number… etc Terms - The name of one of the numbers in the sequence Arithmetic Sequence - There is a common difference (you + or – a number each time) Geometric - There is a common Ratio Sequence (you x or ÷ a number each time)
- 4. Sequences Arithmetic Geometric 3,7,11,15,19… 7, 21, 63, 189… Difference from one The ration you term to another is; multiply by each time is; 101, 92, 83, 74… 276, 138, 69… Difference from one The ratio you multiply term to another is; by each time is;
- 5. Successive Differences Sometimes the differences between numbers follow a pattern Use a Tree scheme to figure out the pattern of the differences. Continue until you get a constant difference
- 6. The Sum of “n” odd counting numbers Find the sum of “n” odd counting numbers n= # of terms 1 = 12 n=1 2n-1 = n2 1+3 = 22 n=2 1+3+5 = 32 n=3 The sum of 8 odd counting 1+3+5+7 = 42 n=4 numbers 1+3+5+7+9 = 52 n=5 1, 3, 5…. (2n-1)← the last term 1+3+5+7+9+11= 62 n=6 n2 = the sum of those #s