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Rational Numbers

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Cards (163)

Section 1

(50 cards)

Rational Numbers

Front

Numbers that can be expressed as fractions that do not equal 0. Denoted by Q Any number that can written as a fraction or a ratio. Rationale's root word "ratio"

Back

Isosceles triangle

Front

Two equal sides and two equal angles

Back

Obtuse triangle

Front

has one angle more than 90 degrees

Back

Reflex angle

Front

angle that is more than 180 degrees

Back

Scalene triangle

Front

No congruent sides

Back

Concrete

Front

Using real objects

Back

Inductive reasoning

Front

When teaching with inductive reasoning, the teacher introduces a concept and the students then make inferences from the data and develop generalizations. For example, the teacher might show several examples of subtraction problems with two places and ask the students to identify the rule. Here the students have to solve the three problems and then make a general rule about fractions and decimals.

Back

Tessellation

Front

Tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

Back

Level 1

Front

Recalls information Facts, definitions, terms

Back

Mean

Front

All numbers added up divided by the amount of numbers

Back

Level 2

Front

Basic application of concepts and skills Reads and interprets info from a simple graph

Back

Integers

Front

All positive natural numbers, negative natural numbers, and zero Examples: -1,-1,-3,0,1,2,3

Back

Semi-abstract

Front

Symbols such as tally marks

Back

Supplementary angles

Front

two angles add up to 180 degrees

Back

Acute angle

Front

angle that is less than 90 degrees

Back

Real Numbers

Front

All numbers that can be found on a number line. Example: 5,-17,0.312, 1/2

Back

Deductive reasoning

Front

When a teacher instructs from the general to the specific, she is teaching with deductive reasoning. She would teach the general rules and then have the students apply them to specific problems.

Back

Translation

Front

Same distance, same direction

Back

Right angle

Front

angle that is exactly 90 degrees

Back

Obtuse angle

Front

angle that is greater than 90 degrees but less then 180 degrees

Back

Subitizing

Front

See a small amount of objects and know how many there are without counting

Back

Identity property Addidtive

Front

a+0=a

Back

Scope

Front

Main topics

Back

4^0

Front

Any power raised to the zero power is 1

Back

1^6

Front

One raised to any power is 1

Back

Mode

Front

Most amount of the same number

Back

Semi-concrete

Front

Visual representations or pictures

Back

Transitivity

Front

Whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c

Back

Complex number

Front

Denoted by C

Back

Identity property Multiplicative

Front

a X 1=a

Back

Right triangle

Front

Has one 90 degree angle

Back

Reasonableness

Front

Help students decide which operation is necessary to solve a word problem

Back

Inverse property Additive

Front

a+ (-a)=0

Back

Natural numbers

Front

Numbers used for counting Always start from 1 1,2,3,4,5 Denoted by N

Back

Level 3

Front

Strategic Thinking and Complex reasoning Requires reasoning

Back

Complementary angles

Front

add up to 90 degrees

Back

Inverse property Multiplication

Front

a X (1/a)=1

Back

7^1

Front

Any number raised to the first number is that number

Back

Abstract

Front

Symbols operations, and numerals to solve

Back

Commutative property Multiplication

Front

ab=ba

Back

Kite

Front

2 congruent 2 consecutive sides

Back

0^6

Front

Zero raised to any power is 0

Back

Commutative property Addition:

Front

a+b=b+a

Back

Median

Front

Middle number, unless, even amount of numbers, add numbers in middle and divide by two

Back

Range

Front

Lowest number subtracted from highest number

Back

Whole numbers

Front

Starts from 0 and includes all natural numbers Denoted by W A number with no fractional part or decimal part. Examples: 0, 1,2,3,4

Back

Reversibility

Front

Counting objects from left to right, then again from right to left. Verify that the number of objects in the set are the same

Back

Level 4

Front

Extended thinking and complex reasoning Derives mathematical model explaining complex phenomenon or make predictions

Back

Equilateral triangle

Front

Three equal sides and three equal angles

Back

Straight angle

Front

angle that is exactly 180 degrees

Back

Section 2

(50 cards)

Factors

Front

Factors are numbers you can multiply together to get another number: Example: 2 and 3 are factors of 6

Back

Best way to teach place value

Front

Repeating place values

Back

When it comes to multiplication what is not the right method to use when learning multiplication facts?

Front

Memorization

Back

24 oz of hamburger meat makes 8 servings. How much meat makes twenty eight servings?

Front

84oz

Back

Rate

Front

How quickly computations are made

Back

Triangle

Front

3 sides, 3 vertices

Back

Unknown partner problems

Front

One of the partners is not given

Back

What can help students understand multiplying fractions

Front

Area models

Back

Accuracy

Front

Getting the correct answer

Back

Unknown partner: Put together

Front

Unknown Partner: Put Together Stacy invited 9 girls and some boys to her party. 16 children were invited in all. How many boys were invited? Adding

Back

Teacher buys tablecloth what is is most likely measured answer

Front

24 yards squared

Back

Composite Number. more

Front

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),

Back

Tiling

Front

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps Can be used to relate to calculating the area of rectangles wherein a rectangle is divided into unit squares and counted to find the area

Back

Pentagon

Front

5 sides, 5 vertices

Back

Place Value

Front

Back

Volume of rectangular prism

Front

V=length X width X height

Back

Itteration

Front

Repetition

Back

Parity

Front

Parity is a mathematical term that describes the property of an integer's inclusion in one of two categories: even or odd

Back

100,000 best represented by exponent

Front

10^5

Back

Irrational numbers

Front

Real numbers that cannot be written as the ratio of two integers

Back

Regular polygon

Front

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

Back

Part-part-whole

Front

How numbers can be split into parts.

Back

Hexagon

Front

6 sides, 6 vertices

Back

Rectangle

Front

4 sides, 4 vertices

Back

Polygon

Front

Plane shape (two-dimensional) with straight sides. Examples include triangles, quadrilaterals, pentagons, hexagons and so on.

Back

Conceptual Understandin

Front

Conceptual understanding is knowing more than isolated facts and methods. The successful student understands mathematical ideas, and has the ability to transfer their knowledge into new situations and apply it to new contexts.

Back

Place value misconceptions

Front

1) Inadequate part-part-whole knowledge for the numbers 0 to 10 and/or an inability to trust the count 2)An inability to recognise 2, 5 and 10 as composite or countable units (often indicated by an inability to count large collections efficiently) 3)Little or no sense of numbers beyond 10 (eg, fourteen is 10 and 4 more 4)A failure to recognise the structural basis for recording 2 digit numbers (eg, sees and reads 64 as "sixty-four", but thinks of this as 60 and 4 without recognising the significance of the 6 as a count of tens, even though they may be able to say how many tens in the tens place)

Back

Face

Front

A face is an individual surface.

Back

Cube root

Front

Cube root of a number x is a number such that a3 = x

Back

Octagon

Front

8 sides, 8 vertices

Back

Vertex

Front

Corner

Back

Quadrilateral

Front

Four sided figure

Back

Set model

Front

Snap cubes, 2 color counters, concrete model

Back

Array

Front

Array is an arrangement of a set of objects organized into equal groups in rows and columns. An array is a model for multiplication. Arrays are a good model for teaching area also using squares.

Back

Edge

Front

An edge is a line segment that joins two vertices

Back

Measurement division

Front

Needed when students know how many objects are in each group but do not know how many groups there are

Back

Compensation strategy .

Front

One number is rounded to simplify the calculation then the answer is adjusted to compensate for the original change

Back

Automaticity

Front

Selecting problem solving methods and performing computations without requiring much time to think the processes through

Back

Grid box of 100 with 12 shaded, what is the number represented?

Front

12%

Back

Circle in a square with the radius of 3 what is the area of the square?

Front

A=πr2

Back

Flexibility

Front

student's ability to recognize strategies necessary to complete a mathematical task, and a student's ability to apply learned strategies to alternative mathematical tasks'.

Back

What strategy is used when making belts and you have 66 inches and you want 22 yards

Front

part measure part divide

Back

Unknown Partner: Take Apart

Front

There were 15 people at the park. 7 were playing soccer. The others were playing softball. How many people were playing softball? Subtracting

Back

Square

Front

4 sides, 4 vertices

Back

Prime number

Front

A natural number (i.e. 1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it has exactly two positive divisors, 1 and the number itself.

Back

Cube

Front

6 congruent sides, 12 edges, 8 vertices

Back

Trapezoid

Front

4-sided flat shape with straight sides that has a pair of opposite sides parallel.

Back

Area

Front

The amount of surface that a shape covers

Back

Multiple

Front

Anumber that can be divided by another number without a remainder. "15, 20, or any other multiple of five"

Back

Using a times table, what is the teacher testing?

Front

Automaticity

Back

Section 3

(50 cards)

Multiplicative Inverse or Reciprocal.

Front

When the product of two numbers is one, they are called reciprocals or multiplicative inverses of each other.

Back

Divisibility rule for 3

Front

An integer is divisible by 3 if then sum of it's digits are divisible by 3. Example: 42 is divisible by 3 because 4+2=6, and 6 is divisible by 3

Back

Prime Number

Front

Number that has only 2 factors, the number itself and 1. Examples: 2,3,7,13

Back

Mixed numbers

Front

There is a whole number and a fraction Example: 2 2/3, 18 1/8, -9 5/7

Back

Average

Front

The sum of a set of quantities divided by the total number of quantities; also known as mean

Back

Divisibility rule for 9

Front

An integer is divisible by 9 if the sum of the digits is divisible by 9 Example: 297 is divisible by 9 because 2+9+7=18, and 18 is divisible by 9

Back

Improper fraction

Front

The numerator is bigger than or equal to the denominator Example: 10/3, 8/8, -25/5

Back

Proportion

Front

Number sentence where two ratios are equal.

Back

Divisibility rule for 5

Front

An integer is divisible by 5 if it ends in 0 or 5 Example: 10, 65, 2,320 are all divisible by 5 because they end either 0 or 5

Back

Multiplying fractions

Front

Multiply straight across

Back

Capacity

Front

1 tablespoon=2 teaspoons 1 fluid oz= 2 tablespoons 1 cup= 8 fl oz 1 pint= 2 cups 1 quart= 2 pints 1 gallon= 4 quarts

Back

Congruent

Front

Exactly the same; congruent figures are the same shape and same size

Back

Greatest Common Factor GCF

Front

In a set of numbers, the largest whole numbers that is a factor of all of the given numbers. For example the GCF of 30 and 20 is 10. The largest whole number common factor that divides both numbers evenly.

Back

Subtracting fractions

Front

Denominator must be the same (Find LCM)

Back

Rate

Front

Special kind of ratio where the two amounts being compared have different units.

Back

Webb's Depth of Knowledge: Level Three

Front

Strategic Thinking: Why can the knowledge be used? Why did it happen? How can you use it? Why can you use it?

Back

Cone

Front

A three dimensional shape figure that has one circular base and a separate face that comes to a vertex point; similar to a pyramid, but with a circular base

Back

Webb's Depth of Knowledge: Level Two

Front

Basic application of skills and knowledge: How can the knowledge be used? How does/did it happen? How does/did it work? How is/was it used?

Back

Computation algorithm

Front

A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly.

Back

Attributes

Front

Aspects of a shape that are particular to a specific shape

Back

Adding fractions

Front

Denominator must be the same (Find LCM)

Back

Multiples

Front

When we multiply a number by any whole number (that is'nt 0) that is a multiple. Example: What are the multiples of 4? 4x1=4 4x2=8 4x3=12 4x4=16 (and so on) The multiples of 4 are 4,8,12, 16

Back

Length

Front

12 inches= 1 foot 3 feet= 1 yard 1760=1 mile

Back

Irrational number

Front

A number that cannot be written as a simple fraction (because the decimal goes on without repeating)

Back

Dilation

Front

Shrinking or expanding of a figure

Back

Absolute value bars

Front

Grouping symbols, you must complete the operation inside them first, then take the absolute value Example: |5-3|=|2|=2

Back

Divisibility rule for 2

Front

An integer is divisible by 2 if it ends in an even number Example: 10, 92, 44, 26, and 8 are all divisible by 2 because they end in an even number

Back

Greatest Common Factor (GCF)

Front

Largest factor that both numbers share

Back

Heptagon

Front

7 sided polygon

Back

Positive Numbers

Front

Used to describe quantities greater than zero Example: 4, +4

Back

Webb's Depth of Knowledge: Level Four

Front

Extended Thinking: What else can be done with the knowledge? What is the impact? What is the relationship?

Back

Webb's Depth of Knowledge: Level One:

Front

Recall and Reproduction; What is the knowledge? Who?, What?, When, Where, How?

Back

Learning progressions

Front

Involve narrative documents describing progressions of a topic across a number of grade levels, which are informed by research on students' cognitive development and logical structure of mathematics. Also, they can be used to explain why standards are sequenced in a given manner, point out cognitive difficulties and pedagogical solutions, and give more detail on particular challenging areas of mathematics.

Back

Least Common Multiple

Front

Smallest multiple that goes into two numbers Example: What is the LCM of 2 and 5? 10

Back

Set

Front

A set is a real or imagined collection of objects which may or may not be related.

Back

Rhombus

Front

4 sides that are the same length

Back

Divisibility rule for 10

Front

An integer is divisible by 10 if it ends in 0 Example: 50,110, 31,330 are all divisible by 10 because they end in zero

Back

Weight

Front

1 pound= 16oz 1 ton= 2000 pounds

Back

Unit Rate

Front

Rate that has 1 as its denominator. To find a unit rate, set up a ratio as a fraction and then divide the numerator by the denominator

Back

Fractions

Front

Real numbers that represent a part of a whole. A fraction bar separates a part from a whole Example: Part/Whole The part is the numerator and the whole is the denominator

Back

Opposites of Opposites property

Front

The opposite of -16 is 16. The opposite of 16 is -16

Back

Decagon

Front

Ten sided polygon

Back

Computation strategy

Front

Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another

Back

Negative Numbers

Front

Used to describe quantities less than 0 Example: -4

Back

Absolute Value

Front

The distance of the number from zero on the number line. Absolute value is always positive. Absolute value is indicated by |4| two bars placed around the number

Back

Common Factors

Front

Any factors that are the same for 2 or more numbers

Back

Fluency

Front

Ability to recall facts with speed, accuracy, and automaticity

Back

Base Ten

Front

In base 10, each digit in a position of a number can have an integer value ranging from 0 to 9 (10 possibilities). The places or positions of the numbers are based on powers of ten (e.g., hundredths, tenths, tens, hundreds, thousands). As you move to the right, each place value is one-tenth the place value to the left

Back

Variable

Front

A letter or symbol used in place of a quantity we don't know yet

Back

Proper fraction

Front

The numerator is smaller than the denominator Example: 5/6, 2/3, 1/1000, -4/27

Back

Section 4

(13 cards)

Distance formula

Front

speed x time= distance

Back

Teacher graphs (5, -4) what is graphed five places above it

Front

(5,1)

Back

5665 yards into feet?

Front

5665 yard /1 = 3ft/1 yard cross multiply. Make sure to cancel out like terms

Back

When multiplying fractions you should use what manipulative?

Front

Area modelsf

Back

Simple Interest formula

Front

I=p x r x t

Back

Geometry is which critical component of the mathematics curriculum?

Front

Content strand

Back

Inverse property of addition adding

Front

equals 0 a+-a=0

Back

Three Basic Number Properties

Front

Distributive property, associative property, and commutative property

Back

Partitive division

Front

- Number of groups is known and you are trying to find the number in each group.

Back

Conceptual understanding

Front

Take numbers apart rearrange and still get the same sum

Back

Inverse bread question

Front

doubles

Back

Person makes 18.50 per hour for 40 hrs. Get 1.5 for every hour overtime if a person works 48 hours how much do they make? highest answer

Front

$1702

Back

Measurement or subtraction concept

Front

Subtracting or measuring off as many sets as possible

Back