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### Unit 2 Project

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Variables

Rules

Practice

### summary

Reasoning Using the Basic Rules of Math

• Because any number minus itself is always zero, you know the bumblebee must represent the number zero, 0.
• Even though you know the bumblebee is 0, there is not enough information to determine what value the elephant is representing.

Variables Are Unknown Values

The variable represents an unknown value. You can find the value of the variable using mathematically correct steps and logic.

variables

Changing What Variables Look Like

For example, if an unknown value is being represented by a butterfly, and "2 times a butterfly equals 6," the butterfly must represent 3 just like x.

Notice Addition, Subtraction, Multiplication, Division, Exponents, and Inequalities

rules

Integers Only between 0 and 9

• Only integers between 0 and 9 will be represented by new symbols.
• No symbol can represent a number greater than or equal to 10.
• No symbol can represent a negative number.
• No symbol will represent a fraction or decimal.

Unique Values

All symbols will have unique values. For example, if you find that a turtle represents the number 4, then no other image in the problem will also represent the number 4.

Mathematical Operations

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Adding or subtracting 0 to (or from) any number does not change the number. For example, 6 plus 0 is 6 and 6 minus 0 is 6.

Applying this to new symbols, the examples to the right show that adding or subtracting 0 to the snake will not change the snake to a new symbol!

Examine the example to the right. You can see adding or subtracting the balloon does not change the other number. Therefore, you know the balloon must be 0.

##### There are two possibilities that make the equation true.
• The panda bear equals 0 because any number times 0 equals 0.
OR
• The watch equals 1 because any number times 1 equals itself.

Practice

Now examine the third equation.This equation lets you determine the other values.

• Because the watch is 1, using 1 for the watch in the third equation, 1 + 1 = 2 you know the panda bear is 2!
• Using the known value for the panda bear in the second equation, you know 2+2=4; therefore the phone is now known to be 4.

• The first equation showed the panda bear could be 0 or the watch could be 1.
• The second equation proves the panda bear is not 0 because the panda bear added to itself changes its value!
• This equation also tells you the phone is not 0 because any number plus itself, other than 0, is greater than 0.
• Therefore, the watch is 1, the panda bear cannot be 0, and the phone cannot be 0.

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