Parent Primer: Math

Mathematics is an extremely important subject that provides learners with the tools to: think critically, use inductive and deductive reasoning, problem solve, apply logic, make connections, select the right tools, represent, interpret and analyze information. Children learn math by investigating, solving problems, gathering information to organize, graphing and analyzing, explaining, proving and representing their thinking.

Be positive and encourage risk taking in mathematics. Make mathematics a daily, authentic component in your child’s life. Encourage problem solving and persistence and ask your child to explain their thinking when working through math problems. And most importantly, don't worry! Just by refreshing yourself with one to three of the concepts below, you'll be understanding your child's math's lessons that much more.

K?8 Mathematics is typically structured around the following topics:

• Math Terms
• Geometry
• Number and Operations
• Patterns and Algebra
• Fractions & Decimals

These larger topics are then divided into sub topics such as fractions, place value, properties of two and
three dimensional shapes and figures. The parent primer in mathematics is intended to help parents
understand and support the concepts taught in mathematics. The parent primer is organized around the
key topics and provides information about what children need to know.

Symbols to Know

Symbol	Definition
+	Plus; add; and
-	Minus; less; subtract; take away
*	Times; multiply
/ or ÷	Divided by
=	Equals; is equivalent to;
	Does not equal; not equal to
	Approximately; about equal to; roughly
<	Less than
>	Greater than
	Less than OR equal to
	Greater than OR equal to
%	Percent; per hundred
°	Degree/s
	Square root of
!	Factorial
||	Absolute value
	Pi
	Infinity

Math Terms

Related to Numerals

• Absolute Value - Technically, a number's distance from zero on a number line. An easier way to think of it is the positive value of any number. So the absolute value of -5 is 5. ( |-5|=5.)

• Cardinal Numbers - A fancy name for numbers such as 4, 67, etc.

• Decimal - A fraction whose denominator is a power of ten (10, 100, 1000, etc.) and written by putting the numerator of that fraction to the right of a decimal point. So, 22/100 is 0.22; .056 is equivalent to 56/1000.

• Denominator - The bottom number in a fraction. In 1/2, 2 is the denominator.

• Factor - One number is a factor of another number if it can divide into it exactly, i.e. 3 is a factor of 9, or 5 and 11 are factors of 55.

• Fraction - A number that represents some part of a whole and written a/b. So 1/2 means 1 of 2 parts, or one-half of something.

• Improper fraction - A fraction bigger than 1, such as 3/2 or 9/4.

• Integers - All the whole numbers plus all their negative counterparts (-1,-2,-3). Does not include fractions or mixed numbers.

• Mixed Number - A number that contains both an integer and a fraction, such as 2 1/2 or 3 1/3.

• Multiple - The product of a given whole number and another whole number. On times tables, each number will list its multiples beneath it - i.e. the multiples of 6 are 12, 18, 24, 30, 36, 42, etc.

• Negative Numbers - Any number less than zero.

• Numerals - A fancy word for numbers.

• Numerator - The top number in a fraction. In 1/2, 1 is the numerator.

• Ordinal Numbers - A number that indicates order or position, such as 1st, 3rd, 27th, etc.

• Percent - Means per hundred and shows the ratio of a number to 100.

• Place Value - Where a single number is placed in a larger figure tells you it's value: whether that number stands for the number of tens, hundreds, thousands, etc. 

So, in the number 3,245,093.2...

You can see there are 3 millions, 2 hundred thousands, and so on. The 5 is in the thousands place.

• Prime Number - Any number that can only be divided by 1 and itself.

• Whole Numbers - All the positive numbers and zero - the counting numbers (0,1,2,3...). Does not include fractions or mixed numbers.

Related to Operations

• Dividend - The number to be divided in a division operation. In the problem, 60÷4, 60 is the dividend.

• Divisor - The number that's doing the dividing in a division problem. In the operation, 60÷4, 4 is the divisor.

• Equation - A mathematical statement that says two amounts or expressions have the same value; Any number sentence with an 'equals' sign (2+3=6-1).

• Exponent - In the number 4³, the 3 on top is called an exponent. It indicates that 4 is being raised to the power of 3, or multiplied by itself 3 times.

• Expression - Each part of any number sentence that combines numbers and operation signs (+,-,*, /) is an expression; a number sentence without an equals sign.

• Factorial - Any number factorial (written 3! Or 15!) means that you multiply that number by all the whole numbers less than that number. So 6! means 6*5*4*3*2*1.

• Inequality - a mathematical statement that says that two quantities are not equal. A number sentence with >,<, or .

• Inverse - Related but opposite operations or numbers are inverses of one another. Addition and subtraction are inverse operations. 3 is the inverse of 1/3.

• Operation - Adding, subtracting, multiplying, or dividing two or more numbers.

• Parentheses - Used to show which operation to perform first. For example, in (2+3)*4, you would first add 2+3 and then multiply that sum by 4.

• Power - If you multiply a number by itself, the number of times you multiply it is called a power. For example, 4*4*4 is 4 raised to the third power. It is written 4³.

• Product - The result of multiplying two numbers together. Instead of asking, "What is 3 times 4?" The question might be phrased, "What is the product of 3 and 4?" (The answer is 12 for both.)

• Quotient - The number that results from a division problem, not including the remainder. In the problem, 60÷4, the quotient is 15.

• Remainder - A number 'left over' from a long division problem. In the problem, 61÷4, the answer is 15 with a remainder of 1, or 1r.

Related to Graphs, Charts, & Statistics

• Data - A set of information. For example, all the answers collected for a survey would be the data for that survey.

• Impossible Number - A number that while it's the correct result of an average, it has an impossible real-world value, i.e. the average family has 2.5 children, but you can't have .5 of a person.

• Mean - The average of a group of two or more amounts. To get the mean or average, add the numbers, then divide the result by the number of amounts you summed. Simply, the mean of 3, 15, and 21 is 3+15+21 divided by 3, which is 13.

• Median - The number in the exact middle of a set of numbers. So, in the set: 1,3,4,6,13,15,21 - 6 is the median of the set.
• Pictograph - A graph displaying information through pictures.

• Venn Diagrams - Used to show relationships among two or more groups or sets of things. 

Related to Shapes

• Area - The amount in square units contained in a two-dimensional shape or surface.

• Circumference - The distance around a circle.

• Closed Curve Shapes - A plane shape made with curved lines, like a circle or oval.

• Congruent figures - Figures that are the same shape and the same size. They can be rotated or flipped and still be congruent.

• Diameter - Any line that passes through the center of a circle that joins two points on the circle; Twice the radius.

• Geometry - Math related to shapes and figures such as area, size, volume, and length.
• Line - A straight set of points that extends infinitely in both directions.

• Line Segment - A part of a line with a beginning point and an end point.

• Perimeter - The distance around a polygon; the sum of the lengths of the sides of a two-dimensional figure.

• Plane shape - A two-dimensional or flat shape.

• Polygon - A plane shape with 3 or more straight sides (line segments), like a triangle, hexagon, or rectangle. 

• Radius - The distance from the center of the circle to any point on it; Half the diameter.

• Ray - A part of a line that has one end point and continues infinitely in one direction.

• Solid Shape - A three-dimensional shape, such as a cube, sphere, cone, or pyramid.

• Tessellations - Using a single shape repeatedly to make a larger pattern or mosaic. 

Geometry

Polygons

• understand that polygons are two?dimensional shapes with straight sides that intersect at vertices and the number of vertices is equal to the number of sides
• name the regular polygons (triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, hendecagon, dodecagon)
• use properties (vertices, sides, shapes )to classify polygons. For example, a triangle has 3 vertices and 3 sides
• classify triangle types (scalene, isosceles, equilateral and angle types (right, acute and obtuse)
• understand the properties of and irregular shapes and solids 2 and 3?Dimensional Shapes and Objects
• sort and classify 2?dimensional shapes (triangles, quadrilaterals, pentagons…) and 3?dimensional solids (cubes, cylinders, cones, spheres, pyramids… using attributes like edges, vertices, and sides
• construct nets and determine the 3-dimensional object based on the net
• understand that reflections transform the object by flipping it across a line making it look like a mirror object
• identify reflective or rotational symmetry (reflective symmetry looks the same when reflected on either side of the line and rotational symmetry looks the same when rotated, a heart would have reflective symmetry, a square would have both reflective and rotational symmetry
• 2 shapes are considered to be congruent if one of the shapes can be transformed into the other shape by flipping, sliding or turning it
• understand the concept of slides, flips and turns

Measurement

• tell time with digital and analog clocks and solve problems involving lapses of time, conversions of minutes to hours and days and time as it relates to the future
• measure in both standard (inches, feet, gallons, miles) and non-standard units (paces, finger widths)
• use customary units of measure (feet, inches, gallons, pints, miles, pounds…)to solve a variety of measurement problems and compute measurement conversions
• calculate area, mass, perimeter, volume and capacity
• understand that a line extends forever in both directions, a line segment has two defined endpoints and a ray has one defined endpoint and the other end extends forever
• use the Pythagorean relationship

Angles

An angle is the distance between two rays or two line segments. Three kinds of angles you will encounter are:

Acute Angle	Right Angle	Obtuse Angle
A positive angle measuring less than 90 degrees	An angle of exactly 90 degrees. Indicated in pictures as a square	An angle whose measure is greater than 90 degrees

Triangles

Three general types of triangles:

Scalene Triangle	Isoceles Triangle	Equilateral Triangle
A triangle with no sides of the same length	A triangle with two sides of the same length	A triangle where all the sides (and angles) are the same length

And one special one, a Right Triangle, which is any triangle containing a right angle:

The longest side of a right triangle is called the Hypotenuse. It is always the side opposite the right angle.

Polygons

Parallelogram	Rhombus	Trapezoid
A 4-sided plane shape with 2 pairs of parallel sides of equal length	A parallelogram with 4 sides of the same length	A 4-sided plane shape with 1 pair of parallel sides

Area of a Triangle, Parrallelogram, Square and Rectangle

You can always form a rectangle, square or a parallelogram from two triangles which is why a triangle has an area of half of the rectangle, square or parallelogram. This makes remembering the area of a triangle easy!

The area of a rectangle: A = base x height

The area of a triangle: A = 1/2 (base x height)

Numbers and Operations

Numbers refer to counting, comparing and ordering of whole numbers, decimals, integers and fractions. Operations refer to computations of numbers which include addition, subtraction, multiplication and division.

Counting:

• count forwards and backwards using a variety of starting points
• skip count by 2’s, 3’s, 4’s, 5’s starting at different numbers, sometimes using a hundred’s chart
• answer questions like: what is 2 more than, 3 less than, 10 more than….
• understand that cardinal numbers indicate how many are in a set (9 cats, 12 books) and ordinal numbers refer to position (fifth, seventh, ninth…)

Operations:

• add, subtract, multiply and divide (the four operations) and solve word problems involving the four operations with whole numbers, integers, fractions and decimals
• add, subtract, multiply ad divide when regrouping is involved (carrying, borrowing from the next column)
• use strategies to discover prime (numbers that can only be divided by one and itself: 3, 7, 11…) and composite numbers. (numbers that can be divided by more than one and itself: 2, 4,6, 8, 9…)
• find multiples and lowest common multiples of a pair of numbers
• find factors and greatest common factors

Place Value

• understand the value in placement of numbers (2348.76: 2 is in the thousands place, 2 is in the hundred’s place, 4 in in the ten’s place, 8 is in the one’s place, 7 is in the tenth’s place and 6 in the hundredth’s place

Patterns and Algebra

Students begin working with patterns in kindergarten. As they move into the fifth and sixth grades through to high school, algebra begins to replace patterns. Patterns are the foundation of algebra.

Patterns

• create, extend, describe, and compare growing, shrinking, recursive and repeating patterns using various attributes: shape, color, number, sounds etc.
• determine pattern rules
• use T-charts/function tables to organize information
• predict and prove what comes next in a pattern

For Example: Jen learned that for each year old a person is, a dog is about seven years old. Determine the rule to write the people years for any
number of years for a dog.

A recursive pattern provides the start item or number of a pattern shows how the pattern continues.

For example, a recursive rule for the pattern 5, 8, 11, 14, … is start with 5 and add 3. A shrinking or growing pattern shrinks or grows, the start item(s) or number(s) show how the pattern continues:

(95, 85, 75, 65 ___ ___ ___ or A BB AA BBB AAA BBBB _____ _____ _____ )

A repeating pattern repeats: * * X X X * * X X X ** X X X

Functions and Relationships

A function is a relationship which will often refer to the output when the input is known. For example, if the function is to triple the number, the input would be the number and the output would be what the tripled number would be, the relationship is what you do to the input number to get the output number. Function is finding the rule.

Variables and Equations

?work with variables which can be objects, shapes or letters that represent unknown values or quantities (5 + x = 12)

?solve problems by working backwards, guessing and checking or by maintaining a balance

?solve inequalities by finding the values and whole number solutions of the inequality (15 — X < 8 how many whole number solutions are there?)

Data and Probability

Data and probability concepts begin in kindergarten. Data concepts involve collecting and analyzing data and constructing graphs and charts to display the information. Probability is the likelihood for events to happen, it is determining if an event is impossible or possible and
measures of likelihood are expressed qualitatively or quantitatively.

Data

• use tally marks, line plots, charts and lists to organize information
• read, construct and analyze pictographs and bar graphs
• construct and analyze stem and leaf plots
• work with the mean, median and the mode
• use the algorithm for finding the mean

Probability

• describe the likelihood of events happening using likely, unlikely, certain or possible or impossible
• identify the possible outcomes of probability experiments
• understand the concepts of more likely and less likely with spinners and number cubes
• use a tree diagram to analyze probability experiments

Fractions & Decimals

• Fractions: General

First things first. Fractions are a lot easier to work with if you first reduce them to their simplest form, which means that 1 is the only number that can divide evenly (meaning without a remainder) into the numeration and denominator.

For example: 330/550
We can see right away that both numbers can be divided by 10, reducing the fraction to
     33/55
Both top and bottom can also be divided by 11, giving us the equivalent fraction
     3/5
Neither of these numbers has any common factors, so 3/5 is the simplest form.

Another way to do this would be to find the greatest common multiple of 330 and 550, which is 110. This allows you to reduce the fraction in one step.

• Fractions: Operations

To add or subtract fractions with the same denominator, simply add or subtract the numerators of those fractions.

3/5 + 1/5 = 4/5
4/7 - 2/7 = 2/7

If the fractions have different denominators, you must convert them to fractions with the same denominator. To do this, find the smallest common multiple of both numbers and convert both fractions to ones with that multiple as the denominator:

3/5 + 3/4         The smallest multiple of 5 and 4 is 20

(3/5 * 4/4) + (3/4 * 5/5)

12/20 + 15/20 = 37/20 or 1 17/20

To multiply fractions, simply multiply the numerators and denominators:

1/3 * 4/9 = 1 * 4/3 * 9 = 4/27

To divide by a fraction, such as:

4 ÷ 1/4

Simply flip the fraction (which is the divisor) and multiply by that number like so:

4 * 4/1 (or 3) = 16

Another way to think of it is, "How many ¼'s would fit into 4?" Or how many quarters make up 4 dollars. Any way you look at it, the answer is 16.

• Turning Fractions into Decimals

To convert a fraction into a decimal, simply divide the denominator into the numerator. So ¼ = 1 ÷ 4 = 0.25

• Decimals: Operations

Adding and subtracting decimals is no different than with whole numbers. You just line up the decimal points and perform the operation. It only gets tricky when you multiply or divide.

When you multiply decimals, line up the numbers on the right (not with the decimal points) and multiply as you normally would:

23.21
*   4.2
---------
97482

then place the decimal point in the product by adding up how many numbers in the original are to the right of the decimal point.

23.21 (2 numbers two the right of the decimal or 2 decimal places)
*   4.2 (1 number two the right of the decimal or 1 decimal place)
---------
97.482 (3 numbers to the right of the decimal or 3 decimal places)

So the answer is 97.482

When you divide decimals...
       _____
2.4 /48.96

If the divisor contains a decimal, get rid of it! Move the decimal place over an equal amount in both numbers until the divisor is a whole number (multiply both the divisor and the dividend by whatever power of ten is necessary to get rid of the decimal).
      _____
24 / 489.6

Then perform the division as you normally would. The decimal point moves up into the answer at exactly the same point as it is in the dividend:

       _20.4_
24 /489.6