Unit 2 Project

Unit 2 Project

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summary

During this project, you will be using different symbols and images to represent numbers... but still find their values!

Variables

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Rules

Practice

variables

• 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.

Reasoning Using the Basic Rules of Math

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

Variables Are Unknown Values

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.

Changing What Variables Look Like

rules

Integers Only between 0 and 9

Unique Values

Mathematical Operations

• 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.

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.

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

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Practice

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.

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.

There are two possibilities that make the equation true.

• The panda bear equals 0 because any number times 0 equals 0.

OR

• The clock equals 1 because any number times 1 equals itself.

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!

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More practice

• The first equation showed the panda bear could be 0 or the clock 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 clock is 1, the panda bear cannot be 0, and the phone cannot be 0.

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

• Because the clock is 1, using 1 for the clock 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.

Make your best attempt at quantifying each symbol.

Answer Key