Math Concepts 1 Test 1

Figurate Numbers Example

1, 3, 6, 10, 15...

Cartesian Product

n(A) * n(B)

Line Design

⊗⊗⊗ ⊗⊗⊗ ⊗⊗⊗

Fibonacci Sequence example

1,1,2,3,5,8,13,...

Examples of Arithmetic

1,3,5,7,9,... 9, 13, 17, 21, 25, 29,...

How to Find the Rule

1. Find constant difference 2. Multiply term number by difference 3. Find what has to be added or subtracted to get the term.

Bus Ride

10 Different ways

Examples of Geometric

10, 100, 1000, 10,000, 100,000,... 3,6,12,24,48,...

Magic Square

2 9 4 7 5 3 6 1 8

How to find the number of subsets

2^n

Place the numbers 0-9 in the boxes

6 2 4 1 9 0 8 7 3 5

Family Affair

8 people

Arithmetic Sequence

A sequence in which each successive term is obtained from the previous term by the addition or subtraction of a fixed number, the difference.

Geometric Sequence

Each successive term of a geometric sequence is obtained from its predecessor by multiplying be a fixed number, the ratio.

Cooperative Learning

Form interdependent teams. Set group goals Ensure individual accountability Teach communication & problem solving skills Integrate cooperative learning with other structures.

Strategies

Look for a pattern, examine a related problem, make a table, make a diagram, guess and check, write an equation, work backwords

Fundamental Counting Principle

N! (one-to-one correspondence)

Lemke (2002,2004)

Natural Language, Visual Representation, Mathematical Expression, Manual technical operations

Communication Standard

Organize and consolidate their mathematical thinking through communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate the mathematical thinking and strategies of others Use the language of mathematics to express mathematical ideas precisely

Please Help the Farmer Problem (Fox, Goose, and Corn)

Take the goose, then the fox. Bring the goose back and take the corn. Then go back and get the goose.

Polya's Four Step Process for Problem Solving

Understand the Problem Select a strategy Carry out the strategy Looking back

Figurate Numbers

a pattern in which the numbers of the pattern can be formed into a growing shape pattern

Fibonacci Sequence

a recursive pattern, after one or more consecutive terms are given to start, each successive term of the sequence is obtained from the previous term(s).

Recursive Patterns

recursive formula always uses the preceding term to define the next term of the sequence.