Question
Write 10 things that you know to be true. Try to solve and graph the solution.
Function of the Day: How much is one candy bar worth?
What do you know?
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Vocabulary Terms - Define/Illustrate
Expression
Equation
Order of Operations
5 Problems - SHOW ALL WORK!
GEOLOGY ROCKS: A geologist and has a laboratory full of rocks. He knows that each rock weighs exactly one pound (+1), and he would like to figure out how many rocks are in each crate. He places crates and rocks on a scale until they are balanced. Using his math skills, he is able to reason how many rocks are in each crate without having to look inside. Write an equation. Can you use mental math to see how many rocks are in each crate for each scenario?
Think of 4x - 1 = 15. What value of x would make 4x - 1 equal to 15?
What do I need help with?
Answers
Answered by
GPT-4o mini
### 10 Things I Know to Be True:
1. The Earth revolves around the Sun.
2. Water freezes at 0 degrees Celsius.
3. The sum of angles in a triangle is always 180 degrees.
4. The speed of light in a vacuum is approximately 299,792 kilometers per second.
5. A full-grown adult human has 206 bones.
6. The capital of France is Paris.
7. In a right triangle, the Pythagorean theorem applies (a² + b² = c²).
8. Gravity pulls objects toward the center of the Earth.
9. The chemical formula for water is H₂O.
10. Photosynthesis is the process by which plants convert sunlight into energy.
---
### Vocabulary Terms
1. **Expression**: A combination of numbers, variables, and operators (like +, −, ×, ÷) that represents a value. For example, 3x + 5 is an expression.
**Illustration**:
2. **Equation**: A mathematical statement that two expressions are equal, indicated by the equals sign (=). For example, 3x + 5 = 11 is an equation.
**Illustration**:
3. **Order of Operations**: A set of rules used to determine the order in which operations are performed in a mathematical expression. The common acronym is PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
**Illustration**:
---
### 5 Problems – GEOLOGY ROCKS
#### Problem Set-Up:
Let's denote the number of rocks in each crate as \( r \). If there are \( c \) crates, then the total number of rocks will be \( c \cdot r \).
When the geologist balances the weighing scale, we can set up an equation to find \( r \).
#### Problem 1:
- **Scenario**: 3 crates balance with 9 rocks.
- **Equation**: \( 3r = 9 \)
**Solving**:
\[
r = \frac{9}{3} = 3 \text{ rocks per crate}
\]
#### Problem 2:
- **Scenario**: 4 crates balance with 16 rocks.
- **Equation**: \( 4r = 16 \)
**Solving**:
\[
r = \frac{16}{4} = 4 \text{ rocks per crate}
\]
#### Problem 3:
- **Scenario**: 5 crates balance with 20 rocks.
- **Equation**: \( 5r = 20 \)
**Solving**:
\[
r = \frac{20}{5} = 4 \text{ rocks per crate}
\]
#### Problem 4:
- **Scenario**: 2 crates balance with 10 rocks.
- **Equation**: \( 2r = 10 \)
**Solving**:
\[
r = \frac{10}{2} = 5 \text{ rocks per crate}
\]
#### Problem 5:
- **Scenario**: 6 crates balance with 12 rocks.
- **Equation**: \( 6r = 12 \)
**Solving**:
\[
r = \frac{12}{6} = 2 \text{ rocks per crate}
\]
---
### Solving \( 4x - 1 = 15 \)
To find the value of \( x \):
\[
4x - 1 = 15
\]
Add 1 to both sides:
\[
4x = 16
\]
Now, divide by 4:
\[
x = \frac{16}{4} = 4
\]
### What Do I Need Help With?
Please specify any areas or concepts regarding math, equations, or any specific problem-solving strategies that you would like additional assistance with!
1. The Earth revolves around the Sun.
2. Water freezes at 0 degrees Celsius.
3. The sum of angles in a triangle is always 180 degrees.
4. The speed of light in a vacuum is approximately 299,792 kilometers per second.
5. A full-grown adult human has 206 bones.
6. The capital of France is Paris.
7. In a right triangle, the Pythagorean theorem applies (a² + b² = c²).
8. Gravity pulls objects toward the center of the Earth.
9. The chemical formula for water is H₂O.
10. Photosynthesis is the process by which plants convert sunlight into energy.
---
### Vocabulary Terms
1. **Expression**: A combination of numbers, variables, and operators (like +, −, ×, ÷) that represents a value. For example, 3x + 5 is an expression.
**Illustration**:
2. **Equation**: A mathematical statement that two expressions are equal, indicated by the equals sign (=). For example, 3x + 5 = 11 is an equation.
**Illustration**:
3. **Order of Operations**: A set of rules used to determine the order in which operations are performed in a mathematical expression. The common acronym is PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
**Illustration**:
---
### 5 Problems – GEOLOGY ROCKS
#### Problem Set-Up:
Let's denote the number of rocks in each crate as \( r \). If there are \( c \) crates, then the total number of rocks will be \( c \cdot r \).
When the geologist balances the weighing scale, we can set up an equation to find \( r \).
#### Problem 1:
- **Scenario**: 3 crates balance with 9 rocks.
- **Equation**: \( 3r = 9 \)
**Solving**:
\[
r = \frac{9}{3} = 3 \text{ rocks per crate}
\]
#### Problem 2:
- **Scenario**: 4 crates balance with 16 rocks.
- **Equation**: \( 4r = 16 \)
**Solving**:
\[
r = \frac{16}{4} = 4 \text{ rocks per crate}
\]
#### Problem 3:
- **Scenario**: 5 crates balance with 20 rocks.
- **Equation**: \( 5r = 20 \)
**Solving**:
\[
r = \frac{20}{5} = 4 \text{ rocks per crate}
\]
#### Problem 4:
- **Scenario**: 2 crates balance with 10 rocks.
- **Equation**: \( 2r = 10 \)
**Solving**:
\[
r = \frac{10}{2} = 5 \text{ rocks per crate}
\]
#### Problem 5:
- **Scenario**: 6 crates balance with 12 rocks.
- **Equation**: \( 6r = 12 \)
**Solving**:
\[
r = \frac{12}{6} = 2 \text{ rocks per crate}
\]
---
### Solving \( 4x - 1 = 15 \)
To find the value of \( x \):
\[
4x - 1 = 15
\]
Add 1 to both sides:
\[
4x = 16
\]
Now, divide by 4:
\[
x = \frac{16}{4} = 4
\]
### What Do I Need Help With?
Please specify any areas or concepts regarding math, equations, or any specific problem-solving strategies that you would like additional assistance with!