EC-6 Math
'Solution' of an inequality
A number which when substituted for the variable (ex. X) makes the inequality a true statement.
Find 25% of 360 books.
25%→0.25 x 360 = 90 books.
How many grams make 1 ounce?
28 grams
Is 2ab-cd a monomial or binomial? Label the parts.
2ab-cd is a BINOMIAL. 2 is the coefficient of ab and -1 is the coefficent of cd.
What is the algebraic expression of 2, 4, 6, 8?
2n (n=1, 2, 3, 4) 2(1)=2, 2(2)=4, etc.
Change 2¾ to a fraction.
2¾→2X4+3/4= 8+3/4= 11/4.
How many feet make up 1 yard?
3 feet
Triangles
3 sided polygons whose angles all measure to 180°.
f(x) = 3x² - 4x + 1 X=2
3(2)² - 4(2) + 1 12 - 8 + 1 f(2) = 5
Find the measures of the angles of a right triangle if one of the angles measures 30°.
30°, 60°, and 90°. Right angle =90; all angles must add up to 180; 30+90=120; 180-120=60.
Temperature water freezes at (both in °F and °C)
32°f or 0°c
What is the algebraic expression which represents 4, 7, 10, 13?
3n+1 (n=1, 2, 3, 4) 3(1)+1=4, 3(2)+1=7, etc.
Transversal Line
3rd line that crosses through parallel lines.
How many lines of symmetry do squares have?
4 lines
How many liters make 1 gallon?
4 liters
How many quarts (qt) are in 1 gallon?
4 quarts
What is the prime factorization of 48 using exponents?
48= 3x16 48= 3x2x8 48= 3x2x2x4 48= 3x2x2x2x2 The prime factorization of 48 is 3x2⁴.
Change 9/4 into a mixed number.
4÷9= 2, 1 is left over. Answer would be 2¼.
How many feet make up 1 mile?
5, 280 feet
How many weeks are in 1 year?
52
7 9/12 - 5 4/12 = ??
7 9/12 - 5 4/12 = 2 5/12. 9-4=5; homogenious denominator; 7-5=2.
7/9 - 5/9 = ?
7/9 - 5/9 = 2/9
How many fluid ounces (oz.) are in 1 cup?
8 fluid ounces (oz.)
8(5+2)=??
8(5+2) = (8 x 5) + (8 x 2) = 56
Solve: (2x + x) (5 + 3x) using FOIL Method
9x² + 15x (2x + x) (5 + 3x) → (2x X 5)+(2x X 3x)+(x X 5)+(x X 3x) → 10x+6x²+5x+3x² → 9x² + 15x [or 3(3x²+5x)].
Cube
A 3-dimensional solid figure that has 6 faces, 12 edges, and 8 vertices.
Equation for the area of a trapezoid
A = 1/2 (b₁+ b₂)h A = (b₁+ b₂)h / 2
Equation for the area of a triangle
A = 1/2 bh A = bh / 2
Equation for the area of a rectangle
A = lw A = bh
Equation for the area of a square
A = s²
Equation for the area of a circle
A = π r²
Scientific Notation
A form of writing a number as the product of a power of 10 and a decimal number greater than or equal to 1 and less than 10 [2,400,000 = 2.4 X 10⁶].
Parallelogram
A four sided polygon with 2 pairs of parallel sides.
Point
A fundamental concept of geometry. A specific location, taking up no space, having no area, and frequently represented by a dot. Considered to have no dimensions. It has neither length nor breadth nor depth.
Edge
A line segment where two faces of a three-dimensional figure meet.
Algebraic Expression
A mathematical phrase that is written using one or more vaiables and constants, but which does not contain a relatoin symbol [5y+8].
Axiomatic Structure
A mathematical rule. The basic assumption about a system that allows theorems to be developed.
Equation
A mathematical sentence stating that two expressions are equal.
Degree
The unit of measure of the angle created
Mode
The value (or values) that appear in a set of data more frequently than any other value. If all the values in a set of data appear the same number or times, the set does not have a mode.
How do you teach money to children?
They need to understand base 10. They relate each denomination to pennies to understand the relationship between other coins. Associate the value for each of the coins and make equivalences.
Algebraic Relationship
To express the relationship between two or more numbers using an algebraic expression.
3 sided polygons
Triangles
Steps to follow when solving problems
Understand the problem, choose a strategy and/or make a plan, carry out the plan, check your answer.
Conservation
Understanding that quantity, length, or number of items is unrelated to the arrangement or appearance of the object or items. Can affect a childs ability to measure volume and understand the value of money (think a nickle is worth more because it is larger).
Front-End Estimation
Use the leading or the left-most digit to make an estimate. [Estimate the sum of 594, 32, 221→600+0+200= 800].
Fahrenheit Scale
Used in the United States to measure temperature.
Pie Charts
Used to help visualize relationships based on percentages of a subject. The figure is divided based on the percentages out of a possible 100%. Requires an understanding of percentages, which makes it inappropriate for children in early grades.
Bar Graphs
Used to represent two elements of a single subject [ex: amount of books (number) read by a person (letter)].
Analog clocks
Uses two hands to represent the hours and minutes based on 60 minutes for an hour and 60 seconds for a minute. Students must have a mathematical understanding of each of the numbers on a face when using these clocks.
Find the volume of a cylinder where l= 2 liters, w= 3 liters, h= 5 liters
V=l x w x h → V=2 liters x 3 liters x 5 liters → V = 30 liters³
Why do ELLs have a difficult time with American nomenclature of math?
We tend to assume prior knowlege of specialized terms (denominator, subtract, divisor). Terms that have one meaning in one subject can mean something different in math (quarter, column, even). Vocabulary tends to have a variety of homophones (even, faces, mean, right).
Why might learning subtraction be difficult for ELLs?
We use language such as 'left over' and 'how many more are needed' and minus, take away, decrease, reduce, deduct, remove, and less than. We are not consistant with how we ask for subtraction.
Slope of the line
What M was solved for during the linear equation.
Run
What happens on the x-intercept during a linear equation.
Rise
What happens on the y-intercept during a linear equation.
How do you add or subract homogeneous fractions?
When adding or subtracting fractions with the same denominator (homogenious fraction), add or subtract the numerators. The denominator stays the same [1/9 + 4/9 = 5/9].
FOIL Method
When multiplying binomials, "first, outer, inner, last" then add the products. [(2x + x) (5 + 3x) → (2x X 5)+(2x X 3x)+(x X 5)+(x X 3x)
Nonlinear Functional Relationships
When the graph of pairs result in points not lying on a strait line, it is said to be nonlinear.
Congruent
When two angles have the same size (regardless of how long their rays may be drawn).
Decentering
Where the child can take into account multiple aspects of a problem to solve it. Can form conclusions based on reason rather than perception.
Elimination of Egocentrism
Where the child is able to view things from anothers perspective. Can retell a story from another child's perspective.
Reversibility
Where the child understands that the objects can be changed, then retruned to its original state [8-4=4; 4+4=8].
Prime Factorization
Writing every composite number as a product of prime numbers, using exponents.
In geometry, what does (x, y, z) mean?
X = horizontal point Y = vertical point Z = Depth
Distributive Property
You can add and then multiply or multiply then add [a(b+c) = (a x b) + (a x c)].
How many grams are in 1 kilogram?
1,000 grams
How many meters make up 1 kilometer?
1,000 meters
How many milliliters (ml) are in 1 liter?
1,000 mililiters
How many milligrams are in 1 gram?
1,000 milligrams
Number concepts taught in First Grade
1. Ability to create sets of tens and ones using concrete objects to describe, compare, and order whole numbers, reads, and writes numbers to 99 to describe sets of concrete objects, compares and orders whole numbers to 99 (less than, greater than, equal) using sets of concrete objects and pictorial models. 2. Separates a whole into 2, 3, or 4 equal parts and use appropriate language to describe parts such as 3 out of 4 equal parts. 3. Models and creates addition and subtraction problem situations with concrete objects and writes corresponding number sentences. 4. Identifies individual coins by name and value and describes relationships among them.
How do you convert a common fraction to a percent?
1. Carry out the division of the numerator by the denominator of the fraction. 2. Round the result to the hundredths decimal place. Move the decimal point over two places to the right (adding 0's as placeholers, if needed) and round as necessary.
Number concepts taught in the Sixth Grade
1. Compares and orders non-negative rational numbers, generates equivalent forms of rational numbers including whole numbers, fractions, and decimals, uses integers to represent real-life situations. 2. Able to write prime factorizations using exponents, identifies factors of a positive integer, common factors, and the greatest common factor of a set of positive integers.
Four stages of learning concepts in mathematics
1. Comparing objects by matching- ordering items based on size. 2. Comparing a variety of objects for measuring- using body parts, blocks, cubes, etc. 3. Comparing objects using standard units- standart and metric. 4. Comparing objects using suitable units for specific measurments- choosing standard units.
Number concepts taught in Pre-K
1. Exploration of concrete models and materials, arrange sets of concrete objects, count by ones to 10 or higher, by fives or higher, and combine, separate, and name "how many concrete objects. 2. Begin to recognize and describe the concept of 0 (meaning there are none), to identify first and last in a series, to compare the numbers of concrete objects using language ("same", "equal").
Composite Number
A number greater than 0 which is divisible by at least 1 other number besides one (1) and itself resulting in an integer (it has at least 3 factors. For example, 9 because it has three factors: 1, 3, 9.
Fraction
A number that represents part of a whole, part of a set, or a quotient in the form A/B which can be read as A divided by B.
Simplify the fraction 2/4 and explain how you got to your conclusion.
1. Find a number that can be divided evently into the numerator and the demoninator [in 2/4, 2 fits evenly into 2 and 4]. 2. Divide the numerator and denominator by 2 and get the results 2/4 = ½.
Irrational Numbers
A number that cannot be represented as an exact ratio of two integers. The decimal form of the number never terminates and never repeats [the square root of 2 (√2) or Pi (π)].
Vertex
The union of two segments or points of intersection of two sides of a polygon.
Write 25 as a percentage, fraction, and decimal.
25%; 25/100 [¼]; 0.25.
Number concepts taught in Second Grade
1. Uses concrete models of 100s, 10s, and 1s to represent a given whole number in various ways. Begins to use place value to read, write, and describe the value of whole numbers to 999, uses models to compare and order whole numbers to 999, and records the comparisons using numbers and symbols. 2. Uses concrete models to represent and name fractional parts of a whole object. 3. Models addition and subtraction of two-digit numbers with objects, pictures, words, and numbers, solve problems with and without regrouping, and is able to recall and apply basic addition and subtractions facts (to 18). 4. Determine the value of a collection of coins up to one dollar and describes how the cent symbol, dollar symbol, and the decimal point are used to name the value of a collection of coins.
Number concepts taught in Third Grade
1. Uses place value to read, write, and describes the value of whole numbers and compares and orders whole numbers through 9,999. 2. Uses fraction names and symbols to describe fractional parts of whole objects or sets of objects and compares fractional parts of whole objects in a problem situation using concrete models. 3. Selects addition and subtraction and uses the operation to solve problems involving whole numbers through 999. Uses problem-solving strategies, able to use rounding and compatible numbers to estimate solutions to addition and subtraction problems. 4. Applies multiplication facts through 12 by using concrete models and objects, uses models to solve division problems, and uses number sentences to record the solutions. Identifies patterns in related multiplication and division sentences.
Number concepts taught in the Fifth Grade
1. Uses place value to read, write, compare, and order whole numbers through 1 million and decimals through the thousandths place. 2. Identifies common factors of a set of whole numbers, uses multiplication to solve problems involving whole numbers and uses division to solve problems involving whole numbers, including solutions with a remainder.
Number concepts taught in Fourth Grade
1. Uses place value to read, write, compare, and order: whole numbers through 1 million and decimals involving tenths and hundredths, including money, using concrete objects and pictorial models. 2. Uses concrete objects and pictorial models to generate equivalent fractions. 3. Uses multiplication to solve problems (no more than 2 digits, times 2 digits) and uses division to solve problems. 4. Uses strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems.
Number concepts taught in Kindergarten
1. Uses whole number concepts to describe how many objects are in a set (through 20) using verbal and symbolic descriptions, uses sets of concrete objects to represent quantities given in verbal or writing form (through 20), uses one-to-one correspondence and language such as more than, same number as, and names the ordinal positions in a sequence such as first, second, third. 2. Begins to demonstrate part of and whole with real objects. 3. Sorts to explore numbers, uses patterns, and able to model and create addition and subtraction problems in real situations with concrete objects.
How many quarts are in 1 liter?
1.0556 quarts
1.25 X 0.6 = ??
1.25 X 0.6 = .750 1.25 X0.6
1.44 ÷ 0.3 = ??
1.44 ÷ 0.3 → 14.4 ÷ 3.0 = 4.8
1/2 + 1/3 = ??
1/2 + 1/3 = 5/6 To rename the fractions ½ and 1/3, you must find the lowest common denominator, which is 6. 1/2 needs to multiplied by 3 to get 3/6 and 1/3 needs to be muliplied by 2 to get 2/6. These numbers can then be added 3/6 + 2/6 = 5/6.
1/5 ÷ 3/8 = ??
1/5 ÷ 3/8 = 8/15. 1/5 x 8/3 = 1x8=8, 5x3=15.
How many millimeters (mm) make up 1 centimeter?
10 millimeters
How many centimeters make up 1 meter?
100 centimeters
Write 100 as a percentage, fraction, and decimal.
100%; 100/100 [1]; 1.0.
List some common multiples of 2, 3, and 4.
12, 24, 36, 48, 60...
How many fluid ounces are in 1 gallon?
128 fluid ounces
How many fluid ounces (oz.) are in 1 pint?
16 fluid ounces (oz.)
How many ounces are in a pound?
16 ounces
How many yards make up 1 mile?
1760 yards
The sum of the measures of the angles of a triangle
180°
If a circle is divided into 360 even slices, how do the angles measure?
1° each
2 5/10 + 1 4/10 = ??
2 5/10 + 1 4/10 = 3 9/10. 5+4=9; homogenious denominator; 2+3=5.
How many cups are in 1 pint?
2 cups (C.)
How many lines of symmetry do rectangles have?
2 lines
How many pints are in 1 quart?
2 pints (pt.)
How many pounds make up 1 ton?
2,000 pounds
How many centimeters are in 1 inch?
2.5 cm
2/3 X 3/4 = ??
2/3 X 3/4 = 6/12 = ½ 2x3=6; 3x4=12; 6/12÷6/6=½.
2/5 + 1/5 = ?
2/5 + 1/5 = 3/5
Write 2/7 as a percentage.
2/7 = 2 ÷ 7 = 0.286 = 29%.
Temperature water boils at (both in °F and °C)
212°f or 100°c
23.5 + 20.4 = ??
23.5 + 20.4 = 43.9.
Natural Numbers
A positive integer or a non-negative integer. They are all whole numbers. Do not include negative numbers, fractions, or decimals [1, 2, 3, 4, ... ∞].
Algebraic Pattern
A set of numbers and/or variables in a specific order that form a pattern.
Algebraic Inequality
A statement that is written using one or more variables and constants that shows a greater than or less than relationship [2x + 8 > 24].
Table
A systematic or orderly list of values, usually in rows and columns. They are often organized from a function or relationship.
Probability
A way of describing how likely it is a particular outcome will occur.
Integer
A whole number that includes all positive and negative numbers, including zero [-5, -3, -1, 0, 1, 3, 5].
Common Multiple
A whole number that is a multiple of 2 or more given numbers.
Find the area of the rectangle with l=10m and w=5m.
A=lxw → A= 10m x 5m → A = 50 meters².
Find the area of the rectangle where s=5 feet.
A=s² → A=5ft² → A = 25 feet².
How do you add and subtract mixed numers?
Add or subtract the fractions,then add or subtract the whole numbers. "Borrow" from the whole numbers if necessary to complete teh operation as needed.
How to add whole numbers
Align the numbers based on place value [ones, tens, hundreds, etc.]. Add beginning with the ones- in a right to left progression.
Permutations
All possible arrangements of a given number of items in which the order of the items makes a difference. For example, the different ways that a set of four books can be placed on a shelf.
Monomial
An algebraic expression with one term. With two terms it is called a binomial.
Algorithm
An established and well-defined step-by-step problem solving method used to achieve a desired mathematical result.
Graphs
An image or a chart representation used to show a numerical relationship. Four kinds used in EC-6 are pictorial, bar, pie, and line.
How many lines of symmetry do circles have?
An infinite number of lines
Multiplication
An operation of combining groups of equal amounts. It may be described as prepeated addition and/or the inverse of division.
Two types of clocks
Analog and digital
≅
Angles are congruent.
Obtuse angle
Angles greater than 90 degrees but less than 180 degrees
Acute angle
Angles of less than 90 degrees
Supplementary Angles
Angles that add up to 180°
Complementary Angles
Angles that add up to 90°
Segment
Any portion of a line between two points on that line. It has a definite start and a definite end. The notion for a segment extending from point A to point be is AB − [on top]
Chord
Any segment that goes from one spot on a circle to any other spot.
When does the formal operational stage of cognitive development begin?
Around 11 years of age (puberty) and continues until adult hood.
How do you add or subtract decimal numbers?
Arrange them vertically, aligning decimal points then add or subtract as for whole numbers.
Equation to find the circumference of a circle
C=2 π r C=π d
Children in the preoperational stage experience problems with at least which 2 perceptual concepts?
Centration and conservation
How do you find the percentage of a known quantity?
Change the percent to a common fraction of a decimal fraction. Multiply the fraction times the quantity. The percentage is expressed in the same units as the known quantity.
Centration
Characterized by a child focusing only on one aspect of a situation or problem (heighth of a tube vs. how much is in the tube)
Why are manipulatives so important in math?
Children are able to use sight, touch, and hearing and are encouraged to talk their way through each problem. Children learn best when they can manipulative materials to check their understanding and link what they are learning to real-life situations.
Describe congnitive development and math
Children need to create and recreate relationships in math in their own mind. They need direct and concrete interactions.
Describe developmentally appropriate instruction for math.
Children need to understand the concept of numbers and quantity- not just assigning a name to an object (one block, two block). This can be done by asking them to hand you 5 blocks. Give concrete objects to manipulate.
Addition
Combining two or more numbers into a sum.
Children in the concrete operational stage exhibit the developmental processes of what?
Decentering, reversibility, conservation, serialization, classificiation, elimination of egocentrism
Real Numbers
Describes any number that is positive, negative, or zero and is used to measure continuous quantities. Includes numbers, which have decimal representations, even those with infinite decimal sequences [Pi (π)].
How do you change an improper fraction to a mixed number?
Divide the numerator by the denominator and represent the remainder as a fraction. [5/2 would then be changed to 2½].
How do you multiply decimals?
Does not require aligning decimal points. The numbers can be arrange vertically, with right justification. The numbers can then be multiplied as if they were whole numbers. The numbers of digits to the right of the decimal point in teh product should be equal to the sum of the number of digits to the right of the decimal point in the two factors.
Faces
Each of the plain regions of a geometric body.
6 principles that should guide mathematics instruction
Equity, curruiculum, teaching, learning, assessment, technology
Equation to find the number of faces, edges, and faces
F + V = E + 2
How many faces, edges, and vertices does a cube have?
Faces = 6 Edges = 12 Vertices = 8
X on a graph
First number listed in an ordered pair (x, y); represents the horizontal point.
Angles
Formed when two rays (or lines) share an endpoint
Perimeter of a Triangle
Found by adding the measures of the three sides [P = s₁ + s₂ + s₃].
Perimeter of a Rectangle
Found by adding twice the length of the rectangle to twice the width of the rectangle [P = 2l + 2w; P = 2(l + w].
Area of a rectangle
Found by multiplying the measure of the length by the measure of the width [A = l x w].
Area of a square
Found by squaring the measure of the side [A = s² → s is the measure of the side].
Decimal numbers
Fractional numbers taht are written using base ten.
Waht is the greatest common divisor (GCD) (42, 56)?
GCD = 14. 42/56 = 3 X14/4X14 = 3/4.
Estimating
Generally done by rounding the numbers to the nearest decimal place required for accuracy [the sum of 23+35. Round 23 down to 20 and 35 up to 40. 20+40=60].
Radius
Half the diameter of a circle from the center to an edge.
6 sided polygons
Hexagons
Right angle
If an angle has exactly 90 degrees
SSS (Side-Side-Side)
If three pairs of sides of two triangles are equal in length, then the triangles are congruent.
AAS (Angle-Angle-Side)
If two pairs of angles of two triangles are equal in measurement and a pair of corresponding sides equal in length, then the triangles are congruent.
ASA (Angle-Side-Angle)
If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.
SAS (Side-Angle-Side)
If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
Expanded Form
In algebra, it is the equivalent expression withouth parentheses [263= 200 + 60 + 3; (a+b)² = a² + 2ab + b²].
Translation (or Slide)
In geometry, means moving. Every one has a direction and distance (transformation). Each of the points in the geometric figure moves the same distance in the same direction.
Rotation (or Turn)
In geometry, this is known as a transformation that means to turn the shape around. Each rotation has a center and an angle for movement around a given number of degrees.
Reflection (or Flip)
In geometry, this is known as transformation that means to reflect an object or make the figure/object appear to be backwards or flipped. It produces the mirror image of a geometric figure.
How do you divide fractions?
Invert (flip) the second fraction (the one doing the dividing) and multiply the numbers as described earlier.
Inductive Reasoning
Involves examining particular instances to ome to some general assumptions. It is informal and intuitive. Students make hypotheses, extend thought patterns, use analogies, and make reasonable conclusions from examining what appears to be a large enough body of evidence. Conclusionis arrived are not always necessarily true.
How do you multiply fractions?
Involves multiplying the numerator together and teh denominators together (horizontally), then simplifying the product.
How do you add fractions with different denominators?
It is necessary to rename fractions using a common denominator.
Variables
Letters used in many mathematical expressions. They are classified as either free or bound.
Ray
Line a line segment, except it extends forever in one direction. The notion for a ray originating at point X (an endpoint) through point Y is XY→ [on top].
Customary Units
Linear Measurement: length [inches, feet, yards, and miles]. Measurement of Mass: weight [ounces, pounds, tons]. Volume Measurement: capacity [teaspoons, tablespoons, cups, pints, quarts, and gallons].
Metric Units
Linear Measurement: length [millimeters, centimeters (basic unit), meters, and kilometers]. Measurement of Mass: weight [grams (basic unit) and kilograms]. Volume Measurment: capacity [milliliters and liters (basic unit)].
Linear or non-linear: y=4x
Linear, can be written as y=mx+b.
Linear Functional Relationship
Many functions can be represented by pairs of numbers. When the graph of those pairs results in points lying on a straight line, it is said to be linear.
How do you change mixed numbers into fractions?
Multiply the denominator by the whole number then add the results to the numerator to obtain the new numerator.
Rational Numbers
NUmbers that can be expressed as a ratio or quotient of two non-zero integers. Can be expressed as common fractions or decimals, such as ½ or 0.6. Also include finite decimals, repeating decimals, mixed numbers, and whole numbers.
Positve x Negative = ?
Negative
Linear or non-linear: y=7/x
Non-linear, it cannot be written as y=mx+b
Linear or non-linear: y=x²+x-2
Non-linear, it cannot be written as y=mx+b
5 content standards of mathematics
Numbers and operations, algebra, geometry, measurement, data analysis and probability
8 sided polygons
Octogons
The greatest common divisor (GCD)
Of two or more non-zero integers, is the largest positive integer that divides into the numbers without producing a remainder. This is useful for simplifying fractions into their lowerst terms.
Linear Function
One whose graph is a straight line.
Linear Function
One whose graph is a straight line. Always satisfies: f(x+y) = f(x) + f(y) and f(αx)=αf(x) [x and y are input variables and α is a constant].
Non-linear equations
Ones that cannot be written as y=mx+b.
Division
Operation involving two numbers that tells how many groups there are or how many are in each group.
Variable
Or an unknown. Is a letter taht stands for a numer in algebraic expression.
Find the perimeter of a square with S=5 feet
P = 4s → P=4(5 feet) → P=20 feet.
Equation to find the perimeter of a rectangle
P=2l + 2w or P= 2(l + w)
Find the perimeter of a rectangle with l = 10 meters and w = 5 meters
P=2l+2w → P=2(10 meters)+2(5 meters) → P=20+10 → P=30 meters
Equation to find the perimeter of a square
P=4s
Find the perimeter of a triangle with the sides measuring at 3 inches, 4 inches, and 5 inches
P=s₁+s₂+s₃ → P= 3in + 4in + 5in → P = 12 inches
What is the order of operations?
Parentheses, Exponentiation, Multiplication, Divison, Addition, and Subtraction (PEMDAS).
Examples of Tessellations
Paving stones or bricks, cross sections of behives.
5 sided polygons
Pentagons
Four kinds of graphs used in grades Pre-K through 6th grade
Pictorial, Bar, Pie, and Line
Isosceles Triangles
Polygon with 2 equal sides and two equal angles.
Scalene Triangle
Polygon with 3 unequal sides
Negative x Negative = ?
Positive
Positive x Positive = ?
Positive
Line Graphs
Present information in a similar fashion as bar graphs but it uses points and lines. Tracks one or more subject. One element is usually a time period over which the other element increases, decreases, or remains static.
Equation for finding the probability of something
Probablity = number of favorable outcomes / total number of possible outcomes
Gabrielle is randomy choosing a marble from a bag containing three marbles- 1 red, 1 blue, 1 green. What is the probablity that she will choose a green marble on a single pull?
Probablity of choosing a green marble = 1/3 Probablity = number of favorable outcomes / total number of possible outcomes There is 1 green marble in the bag. There is 1 favorable outcome. There are 3 marbles in the bag. There are 3 possible outcomes.
5 process standards of mathematics (highlight ways of acquiring and applying content knowledge)
Problem solving, reasoning and proof, communication, connections, representations
4 sided polygons
Quadrilaterals
Volume
Refers to how much space is inside of three-dimentsional, closed containers [V= l x w x h].
Linear Function
Refers to the first-degree polynomial function of one variable. Sometime used to mean a first-degree polynomial function of variable.
Pictorial Graphs
Represent a transition from the real object graphs to symbolic graphs. Used in pre-k to 1st grade to teach graphs. [ex: using pictures of hotdogs and pizza to represent the number of children who prefer one food over the other].
Line Plot
Represents a set of data by showing how often a piece of data appears in that set.
Digital clocks
Represents the time using Arabic numbers seperating the hours from the miuntes with a colon [12:45], which makes it realatively easy to read.
Deductive Reasoning
Requires moving from the assumption to conclusion. It is the reasoning from general to the specific. Conclusions reached are only sound if the original assumptions are actually true.
Y on a graph
Second number listed in an ordered pair (x, y); represents the vertical point.
4 Developemental stages as stated by Piaget
Sensoimotor (birth-2 years) Preoperational (2 years-7 years) Concrete operational (7 years-11 years) Formal operational (11 years- adult)
Expanded Notation
Showing place value by multiplying each digit in a number by the approapriate power of 10. [523 = 5X100 + 2X10 + 3X1 OR 5X10² + 2X10¹ + 3X10⁰].
If 2 polygons are the same shape but different sizes, they are said to be what?
Similar
Diameter
Straight line segment that goes from one edge of a circle to the other side, passing through the center.
Preoperational stage of development include what processses
Symbolic functioning, centration, intuitive thought, egocentrism, inability to conserve.
Exponential Notation
Symbolic way of showing how many times a number or variable is used as a factor. In the notation 5³, the exponent 3 shows that 5 is a favor used three times (5X5X5).
4 standards for teaching mathematics
Tasks (projects, problems, questions) Discourse (Representing, thinking, talking, agreeing in those tasks) Environment (Setting for learning) Analysis (Systematic reflection in which teachers engage)
Celcius Scale
Temperature scale used for science experiments.
Describe children in the preoperational stage (2 yrs- 7 yrs) while learning math
Tend to fix their attention on a single aspect of a relationship. If they have two rows with equal amounts of quarters but they are spaced differently, they may think one holds more value. Their response is based on their own perception- not reasoning.
Characteristics of the formal operational stage focuses on what?
The ability to use symbols and to think abstractly.
Tessellations
The arrangement of polygons that form a grid. Patterns form by a repetition of a single unit or shape that, when repeated, fills the plane with no gaps and no overlaps.
Mean of a set of data
The average of the data values. To find it, add all the data values and then divide this sum by the number of values in the set.
Place Value
The basic foundation for understanding mathematic computation [Thousand, hundred, ten, one; 1984- 1000, 900, 80, 4].
Classification
The child can name and identify sets of objects according to appearance, size, or other charactheristics. Can arrange objects based on characteristics.
Seriation
The child is able to arrange objects in order according to size, shape, or any other attribute. Can arrange geometric forms by shape, size, color, and thikness of the form.
Conservation
The child understands that quantity, length, or number or items is unrelated to the arrangement or appearance of the object. Can discern that if water is transferred to a pitcher it will conserve the quantity and be equal to the other filled cup.
Symmetry
The correspondence in size, form, and arrangment of parts on opposite sides of a plane, line, or point.
Range of a set of data
The difference between the greateset and the least numbers in the data set. Subtract to find the difference.
Perimeter of a two-dimensional shape or object
The distance around the object. Measured in linear units (feet, inches, meters).
Equilateral Triangle
The meausres of all sides of the triangle are equal (all angles will be equal as well).
Median of a set of data
The middle value of all the numbers. To find the middle value, list the numbers in order from the least to greatest or from greatest to least. If there are two values in the middle, find the number halfway between the two values by adding them together and dividing their sum by 2.
How do you divide decimals?
The number of digits to the right of the decimal point in the divisor is how far the decimal point in the answer (quotient) should be moved to the right.
Absolute Value
The number's distance from zero on the number line. This action ignores the + or - sign of a number. |x| is the graphic used to describe this action [|-5| = 5].
Coefficient
The numbers that precede the variable to give the quantity of the variable in teh expression.
Commutative Property
The order of addends or factors do not change the result [a+b=b+a; a x b = b x a].
Associative Property of Multiplication and Addition
The order of the addends or product will not change the sum or the product [(a+b)+c=a+(b+c); (a x b) x c=a x (b x c)].
Algebraic Solution
The process of solving a mathematical problem using the principle of algebra
Subtraction
The process/operation of removing objects from a larger group, or finding parts of a whole.
Statistics
The science or study of data. Methods are used to describe, analyze, evaluate, and interpret information. The information is used for predicting, drawing inferences, and making decisions.
Sample Space
The set of all possible outcomes of an experiment.
Property of Zero
The sum of a number and zero is the number itself, and the product of a number and zero is zero [8+0=8; 8x0=0].
Slope-Intercept equation
f(x) = mx + b M and B are real constants and X is a real variable.
Perimeter of a Square
found by multiplying four times the measure of a side of the square [P = 4s → s is the measure of the side].
What do the letters represent in a linear function equation (y=mx+b).
m = slope b = y-intercept
Solve: 3 + 2 x 6 = n
n=15 2x6=12+3=15
Linear function equation
y= mx + b. Or f(x) = mx + b (function form).
