## SKILLS THAT MAKE A MATH WHIZ

Whole Numbers & Counting

• Recognize that numerals name numbers

• Associate word names with their corresponding numerals

• Identify equivalent and non-equivalent sets

• Arrange sets in order of size

• Count to 100 and higher (forwards & backwards)

• Count the union of two or more sets

• Skip-count by twos, fives, tens, and other intervals (forwards & backwards)

• Read and write numerals of 1-digit through 6-digits

• Read and write large numbers: millions, billions, and trillions

• Associate numerals with intervals along a number line

• Classify objects into sets

• Associate numerals with sets; write numerals to match sets

• Identify place value for 1-6 digit numerals

• Identify place value for numbers of 1,000,000 or greater

• Express numerals of 1-7 places in expanded notation

• Rename tens as ones, hundreds as tens, and thousands as hundreds

• Rename places of greater value than thousands

• Use whole number concepts in problem-solving situations

• Identify positive and negative integers

• Read and write Roman numerals

• Experiment with a non-decimal based numeration system

• Read exponential numbers

**WORKSHEET & Sample PDF Activity**

**Sample PDF Activity**

## Number Concepts & Relationships

• Identify even and odd numbers

• Identify prime and composite numbers

• Order whole numbers

• Order integers

• Order fractional numbers

• Order decimal numbers

• Recognize ordinal positions (first through tenth)

• Recognize a whole as greater than any of its parts

• Understand the value of 0

• Understand and use the concepts of equality and inequality and the symbols =, < and >

• Compare numbers using words and the symbols < and >

• Complete sequences of whole numbers or integers

• Recognize and extend number patterns

• Describe relationships between numbers

• Round whole numbers to the nearest 10, 100, and 1,000

• Round whole numbers to the nearest 10,000, 100,000 and 1,000,000

• Identify and use number properties

## Addition & Subtraction

• Learn sums through 20 or higher

• Use the terms addend, sum, and difference, and the symbols + and –

• Understand the inverse relationship between addition and subtraction

• Learn fact families through 20 or higher

• Recognize 0 as the identity element for addition

• Use the commutative and associative properties for addition

• Use a number line to find sums and differences

• Add and subtract vertically and horizontally

• Find sums and differences with 1- to 6-digit numerals

• Add and subtract with more than six digits

• Estimate sums and differences

• Check addition problems with subtraction and subtraction problems with addition

• Add and subtract without renaming

• Add and subtract with renaming

• Add long columns of numbers

• Solve word problems using addition and subtraction facts

## Multiplication & Division

• Understand multiplication as the joining of equivalent subsets

• Understand division as the separation of sets into equivalent subsets

• Understand multiplication as repeated addition and division as repeated subtraction

• Recognize the inverse relationship of multiplication and division

• Use the terms factor, product, divisor, quotient, and remainder, and the symbols x and ÷

• Learn and use multiplication facts for factors through 10 or higher

• Learn fact families for products through 100

• Solve multiplication and division problems using a number line

• Recognize 1 as the identity element for multiplication and division

• Use the commutative, associative, and distributive properties of multiplication

• Understand the role of 0 in multiplication and division

• Multiply by a 1- to 4-digit number

• Multiply by large numbers

• Multiply and divide by 10 and multiples of 10

• Identify multiples of numbers 1–15

• Identify factors of a number; distinguish between prime and composite factors

• Complete prime factorization using factor trees

• Find the GCF (Greatest Common Factor) of two or more numbers

• Find the LCM (Least Common Multiple) of two or more numbers

• Divide by 1-digit divisors

• Divide by numbers of 2 or more digits

• Complete division problems that have remainders

• Use division to check multiplication problems and multiplication to check division

• Write and solve word problems using multiplication and division

• Find averages

• Determine if numbers are divisible by the numbers 2, 3, 4, 5, and 10

• Estimate products and quotients

• Select the appropriate operation for a given computation

• Find missing addends and factors in number sentences

• Solve problems with a mixture of operations

## GET YOUR NUMBERS STRAIGHT

Even Numbers — numbers that are divisible by 2

Odd Numbers — numbers that are not even

Prime Number — a number whose only factors are 1 and itself

Composite Numbers — all numbers that are not prime

Whole Number — a member of the set of numbers (0, 1, 2, 3, 4, 5 . . . )

Fractional Number — a number that can be named in the form a—b with a and b being any numbers, with the exception that b cannot be 0

Mixed Fractional Number — a number with a whole number and a fractional number

Decimal Number — a number written with a decimal point to express a fraction whose denominator is 10 or a multiple of 10

Mixed Decimal Number — a number with a whole number and a decimal number part

Integers — the set of natural numbers ( . . . –3, –2, –1, 0, 1, 2, 3 . . . )

Negative Integers — on a number line, all the numbers to the left of 0

Positive Integers — on a number line, all the numbers to the right of 0

Rational Numbers — numbers that can be written as a ratio a—b where both a and bare integers and b is not 0 (all integers and decimals that repeat or terminate)

Irrational Numbers — numbers that cannot be written as a quotient of two integers(decimals that neither repeat nor terminate)

Real Numbers — rational and irrational numbers together are the set of real numbers

Opposite Numbers — two numbers that are the same distance from 0 but are on opposite sides of 0 (3 is the opposite of –3)

Exponential Numbers — a number with an exponent (An exponent is a number written next to a base number to show how many times the base is to be used as a factor.)

Digit — one number in a numeral that holds a particular place

Significant Digits — all non-zero digits and zero when it has a non-zero digit to the left of it (The 0 in 4.03is significant. In 0.66, the 0 is not a significant digit.)

## Math Yellow Pages For Students And Teachers by INCENTIVE PUBLICATIONS IP890 Table of Contents

Skills That Make a Math Whiz (a checklist of math skills covering grades K–8) – 7

Whole Numbers & Counting – 7

Number Concepts & Relationships – 7

Addition & Subtraction – 8

Multiplication & Division – 8

Fractions – 9

Decimals – 9

Ratio, Proportion, & Percent – 10

Problem Solving – 10

Measurement – 11

Coordinate Graphing – 11

Statistics – 11

Geometry – 12

Probability – 12

Pre-Algebra – 13

Get Your Numbers Straight (definitions of various kinds of numbers) – 14

Important Properties (properties of numbers & operations) – 15

Mathematical Symbols (math symbols and meanings) – 16

Can You Speak Metric? (metric prefixes & meanings) – 16

All Kinds of Formulas (geometric formulas) – 17

Math Tools, Treasures, & Tidbits (things to collect for math activities) – 18

Special Math How-To’s (brief explanations of many math processes) – 19

A Handy Guide for Problem Solvers (18 different strategies for attacking & solving problems) – 26

Which Measure? (tables of English & metric measurements) – 29

Converting Measurements (tables of measurement conversions, English to metric & metric to English) – 31

Tricks for Mathematicians (fun tricks with numbers & operations) – 32

Computer Talk (terms to help you find your way around computers) – 35

Web Talk (terms to help you find your way around the Internet) – 37

Math Terms for Every Occasion (an exhaustive glossary of math terms used in grades K–8) – 39

Math Terms: Number Concepts & Relationships – 39

Math Terms: Operations & Computations – 43

Math Terms: Fractions & Decimals – 46

Math Terms: Geometry & Measurement – 48

Math Terms: Statistics, Graphing, & Probability – 58

Math Terms: Pre-Algebra – 60

Fast Facts (ready-to-copy matrices for learning math facts) – 62