Mathematics

Question 1

What is an integer?

Answer 1

A number that has two parts.

Question 2

What is the first part of an integer?

Answer 2

A sign. It shows which side of the zero a whole number is on. + is on the right and - is on the left.

Question 3

What is the second part of an integer?

Answer 3

A whole number, which tells the distance/amount, or how far from the zero the number is.

Question 4

What colour tile do we use to represent positive numbers?

Answer 4

A white tile or yellow chip represents these.

Question 5

What colour tile do we use to represent negative numbers?

Answer 5

A coloured tile or red chip represents these.

Question 6

What does the zero principle state?

Answer 6

When you have equal numbers of positive and negative integers, they sum to be zero.

Question 7

How do you add integers that have the same sign?

Answer 7

Add together the numbers, not paying attention to the sign in front of them. Add the +/- sign from those numbers in front of the sum.

Question 8

How do you add integers that don’t have the same sign?

Answer 8

Use the zero principle to eliminate tiles which will create zero.

Question 9

To add a positive number to a number line we move to the ___.

Answer 9

To add a positive number to a number line we move to the [right].

Question 10

To add a negative number to a number line we move to the ___.

Answer 10

To add a negative number to a number line we move to the [left].

Question 11

What are the parts of the number line checklist? List all four.

Answer 11

• Arrows on both ends
• Tick marks at equal intervals
• Tick marks are labeled correctly with numbers
• Number line is straight

Question 12

When the orientation of a number line is horizontal, how do numbers ascend?

Answer 12

Numbers in ascending order from left to right.

Question 13

When the orientation of a number line is vertical, how do numbers ascend?

Answer 13

Numbers in ascending order from bottom to top.

Question 14

To subtract integers using tiles, you use the zero principle by what is called ____.

Answer 14

“Adding the opposite”.

Question 15

How does adding the opposite work? (Don’t memorize this example, just in case you don’t know!)

Answer 15

Consider the following question: (-3) - (-5)

It’s easy to see that if we have 3 negative tiles, we cannot take away 5 negative tiles. But if you remember that a zero is a combination of a negative and a positive tile, I can add zero to the (-3).

If you add two more negative tiles and two more positives, those four tiles equal zero together and don’t count as you changing the number. Now there are enough negative tiles to remove 5.

If you remove the five negative tiles, you are left with two positive tiles.

So, (-3) - (-5) = (+2).

Question 16

What is the shorter way to subtract integers? (Don’t memorize this example, just in case you want to know how to do it quicker!)

Answer 16

(-3) - (-5)

Change the second integer into its opposite tiles.

(-3) + (+5)

Eliminating the three negatives, and with them, three of the positives, we are left with +2.

Or, instead of eliminating, take the question (-3) + (+5) and flip it: do 5 - 3 = 2.

Question 17

What is special about the way integers are written in equations?

Answer 17

They are always in brackets.

Question 18

How do we “add the opposite” on a number line? (List the four steps.)

Answer 18

1. Rewrite the question adding the opposite.
2. Now on the number line, add the two integers.
3. Starting at zero, move _ units to the positive side (right) to show +_.
4. Now move from that spot _ units to the left in the negative direction.

Where you land is the answer!

Example:

(+4) - (+6)

Rewrite - (+4) + (-6)

Starting at zero, move 4 units to the positive side to show +4.

Now move from that spot 6 units to the left in the negative direction.

You land at (-2). So, (+4) - (+6) = (-2).

Question 19

What is an even number?

Answer 19

A number that ends in a 2, 4, 6, 8, or 0.

Question 20

What is an odd number?

Answer 20

A number that ends in a 1, 3, 5, 7, or 9.

Question 21

Define divisible.

Answer 21

“Divisible” means a number is able to be divided evenly by another number with no remainders.

Question 22

What is the rule for a number to be divisible by two?

Answer 22

The last digit is an even number.

Question 23

What is the rule for a number to be divisible by three?

Answer 23

The sum of the digits is divisible by three.

Question 24

What is the rule for a number to be divisible by four?

Answer 24

The last two digits form a number that is divisible by four.

Question 25

What is the rule for a number to be divisible by five?

Answer 25

The last digit is either a five or a zero.

Question 26

What is the rule for a number to be divisible by six?

Answer 26

The number is divisible by both two and three.

Question 27

What is the rule for a number to be divisible by seven?

Answer 27

You can double the last digit and subtract the sum from the rest of the number, setting an answer that is divisible by seven.

Question 28

What is the rule for a number to be divisible by eight?

Answer 28

The last three digits form a number that is divisible by eight.

Question 29

What is the rule for a number to be divisible by nine?

Answer 29

The sum of all the digits is divisible by nine.

Question 30

What is the rule for a number to be divisible by ten?

Answer 30

The number ends in a zero.

Question 31

Define algebra.

Answer 31

Algebra is the use of variables and numbers to solve problems.

Question 32

Define expression.

Answer 32

An expression is a phrase made of numbers, variables, and operations.

Question 33

Define variable.

Answer 33

A variable is a symbol or letter representing a number.

Question 34

What is the difference between equations and expressions?

Answer 34

Equations have equal signs. Expressions do not have equal signs.

Question 35

What are the parts of equations and expressions?

Label these parts on this expression: 5k + 4

Answer 35

The constant, the variable, and the coefficient.

The constant is 4.
The variable is k.
And the coefficient is 5.

Question 36

Define substitution.

Answer 36

Substitution is plugging a number in for the variable.