Sample Quiz

Each symbol and term has only one meaning, which avoids confusion

It helps us describe patterns, relationships, and real-world problems.

Math allows us to express complex ideas in a short and simple way.

A combination of numbers, variables, and operations without an equal sign.

A statement that can be true or false because it contains a relation symbol like =, >, or <.

A _______ in mathematics refers to an accepted rule, notation, or method used to ensure clarity and uniformity in mathematical communication. These help avoid ambiguity and make problem-solving more systematic

Order of Operations

A rule that assigns each input exactly one output.

A connection between numbers in two sets

A collection of numbers or objects.

Operations that take two inputs to produce a result.

Words like “and” (^), “or” (∨), and “if…then” (→) connect statements

It help us describe how many things the statement applies to. -are used to express quantities without giving an exact number

(∃) “There exists”

(∀) – “For all”

______ is when we make a statement the opposite of its original meaning.

It uses specific observations to form a general rule. It identifies patterns and trends, but the conclusion is not always guaranteed to be true.

It starts with a general rule and applies it to specific cases. If the general rule is true, then the conclusion must also be true.

is an instinctive understanding of patterns, relationships, or solutions before formal proof.

Noticing trends and relationships before proving them.

Using mental images to understand concepts, such as imagining geometric shapes or number patterns.

Testing small cases or real-world examples to develop a general understanding.

Real world application

Mathematicians and programmers use intuition to identify trends before running algorithms.

Real world application

– Investors rely on mathematical intuition to predict market movements.

Real world application

Many scientific breakthroughs start with intuitive ideas before being formally tested.

Real world application People use intuition in estimating distances, time management, and decision-making.

In mathematics, _____means being sure that a statement is true.

We achieve this certainty through _____, which are logical explanations showing why a statement is true

We start with a known fact and use logical steps to show that another fact must be true.

1. Known Fact: All birds have wings.
2. Given Statement: A sparrow is a bird.
3. Conclusion: Since a sparrow is a bird and all birds have wings, a sparrow must have wings.

We disprove a general statement by providing an example where it doesn't hold. Ex. "All numbers can be evenly divided by two.”

Instead of proving a statement directly, we prove that if the statement were false, it would lead to a contradiction. Example: "If it is raining, then the ground is wet.”

We assume the opposite of what we want to prove and show that this assumption leads to an impossible situation. Ex. Nothing is Faster than the Speed of Light

This format lists each step of the proof along with its justification in a structured manner.

This format presents the proof as integrating each step into complete sentences.

George Pólya (1887-1985) - he is most well-known for his contributions to problemsolving and mathematics education. His book "______________" introduced a four-step

THE 4 STEPS

Done for recreation or as a hobby and intended to be fun. Typically it involves games or puzzles that relate to mathematics, although the term can cover other material.

Chinese puzzle made out of geometric shapes

a classic mathematical puzzle involving three pegs and a set of disks of varying sizes,

• regular, repeated, or recurring forms or designs • anything that is not random

a sense of harmonious and beautiful proportion of balance or an object is invariant to any of various transformations

2 types of symmetry, pick 2

• curve or geometric figure, each part of which has the same statistical character as the whole • a class of highly irregular shapes that are related to continents, coastlines, and snowflakes • 'never-ending' patterns that repeat indefinitely as the pattern is iterated on an infinitely smaller scale

• also known as growth spiral • a self-similar spiral curve that often appears in nature • was first described by Rene Descartes and was later investigated by Jacob Bernoulli

created when a shape is repeated covering a plane without any gaps or overlaps • another word for a tessellation is a tiling

_________ratio can be found in the beauty of nature, the growth patterns of many plants, insects, and the universe

• the oldest example of a periodic chain of numbers • developed by Leonardo de Pisa formed by adding the preceding two numbers, beginning with 0 and 1 ratios of two Fibonacci numbers approximate the golden ratio, which is considered the most aesthetically pleasing proportion _____ sequence