Grade 7 Advance Math

This course is designed for above average grade 7 students who are planning to compete in the University of Waterloo Gauss 7 math contest.

Understand the concept of absolute values
Be able to perform operations involving negative integers
Be able to use negative numbers in real life applications
Work with BEDMAS

Absolute value: absolute value of a number is the magnitute of that number. Two vertical bar symbol (| _ |) is used to represent the absolute value.
Integers are the set of positive and negative whole numbers, including zero.
Negative/Positive Integers: to be defined by student

Topics covered in this unit:

Add, subatract, multiply, divide integers
- Let N and K be ingeters and N > K, then there exists a positive integer D such that N = K + D
  Exampe: take N = 25 and K = 10, then D = 15 because 25 = 10 + 15
Exponents
| n | = n if n >= 0, and | n | = -n if n 0

Calculate: 8 + (-5)
Calculate: -8 + (-5)
Calculate: -8x3 + (-5)
Calculate: -8x3 + 3(-5)
Calculate: -8x3 + (-3)(-5)
Calculate: -8x(-3) + (-3)(-5)
15 - 21
15(4) - 21(4)
15(-4) - 21(-4)
15(-4) - 21(4)
15(4) - 21(-4)
Determine | 5 |, | -5 |
Evaluate | 5 | + | -5 |
Evaluate | 5 | - | -5 |
Evaluate 3 x | 5 | - | -5 x 4 |
Evaluate 3 x | 5 | x | -5 x 4 |

The temperature rises 7 degrees C, then drops to -2 degrees C. What is the overall change in temperature?
The temperature in Calgary, Alberta, was 12 degrees C. A Chinook came through and the temperature rose 15 degrees C. At nightfall, it fell 7 degrees C. What was the final temperature? Support your answer with a drawing.
A submarine was situated 800 meters below sea level. If it ascends 250 m, what is its new position?

Understand the concepts of divisibility, divisors, muiltiples and remainders
Know the divisibility rules
Be able to find remainders in a division algorithm
Finding GCF and LCM of pairs of numbers

Factor: if a number N is divisible by another number K then K is said to be a factor of N
Multiple if a number N is divisible by another number K then N is said to be a multiple of K
Prime number: positive integers greater than 1 that are not divisible by any number other than 1 and itself.
Remainder: remainder is the left over part when one number is divided by another number

Know the following divisibility rules

Divisibility Rule of 2
Divisibility Rule of 3
Divisibility Rule of 4
Divisibility Rule of 5
Divisibility Rule of 6
Divisibility Rule of 8
Divisibility Rule of 9
Divisibility Rule of 10
Divisibility Rule of 11 (grades 8+)
If k is a factor of n then when n is divisible by k
If k is a factor of n then when n is divided by k, the remainder is zero
Remainder Theorem - grade 7 version: Let q be the quotient and r be the remainder when a number n is divided by a number k. Then we can write n as
n = qk + r .
When the above remainder is zero ( r = 0) then we k is a factor of n, and the above equation can be written as
n = qk
Divisibility Theorem - grade 7 version: If a number k is a factor of some number n, the there exists a number d such that
n = k x d

What is the remainder with 3628 is divided by 2?
What is the remainder with 3628 is divided by 3?
What is the remainder with 3628 is divided by 4?
What is the remainder with 3628 is divided by 5?
What is the remainder with 3628 is divided by 6?
What is the remainder with 3628 is divided by 8?
What is the remainder with 3628 is divided by 9?
What is the remainder with 3628 is divided by 10?
What is the remainder with 3628 is divided by 11? (Grades 8+)

Grandma has $76.75. If she were to gave her money to 3 grand children (each receiving an equal amount), and keeps the left over. How much was the left over amount?
Larry makes a list of all numbers less than 100 that is divisible by 3. Carl make a list of all numbers less than 100 that is divisible by 7. How many numbers are in both Larry's and Carl's lists?

Be able to reduce fractions using different methods
Know how to convert between fractions, percents and decimals
Perform operations involving fractions, percents and decimals
Work with BEDMAS involving fractions
Solve word problems involving fractions and percents

Denominator: denominator is the lower or bottom part that represents the total parts in which the fraction is divided.
Equivalent fractions
Fraction: a fraction is a numerical value, which defines the parts of a whole.
Improper fractions
Inverse : an inverser of a fraction is is a fraction form by swapping the numerrator and denuminiator of the orginal fraction
Mixed fractions
Numerator: numerator is the upper part of the fraction, that represents the sections of the fraction
Proper fractions
Simplified/Reduced fractions
Reduced fractions

Expressions - grouping like terms in expressions
Convert phrases to expressions
Solving single step equations
Solve multi-step equations

Constant: a constant has a fixed value. Any number without a variable is a constant.
Expression: An Algebraic Expression is the combination of constant and variables.
Variable: represented by a letter, a variable does not have a fixed value

Expressions can add, substract, multiply, and divide with other expresions

Understand the concept of parallel and perpendicular line
Know the rules for identifying angles when two lines intercept
Solve problems involving interior angles
Work with perimeter and area of common shapes
Solving real world problems involing geometry

Properties of a circle
Measurements of a circle
Finding perimeter and area of circles

Understanding the coordinate system
Plotting points on a coordinate system
Reflection and translation of objects

Know the definition of additive patterns
Be able to identify additive patterns
Solve problems involving additive patterns
Deriving the sum of an additive pattern

Introduction to sets and subsets
Finding subsets of a set
Introduction to probability
Solving probability problems

This chapter covers

Introduction to exponents
Perfect squares
Scientific notation
Operations involving exponents

Make Makes Sense 7
Make Links 7 (by Nelson)
McGraw-Hill California Mathematics 7
University of Waterloo Gauss 7 contests
Kangaroo 7-8 math contests