Question
Math Practice U7 L1
Unit 7 Math Practice Links - Click here
Live Lesson Recording
*Passcode can be found on the Connexus Pushpin under your Math Class! Use the one for Mrs. Garcia!
Function of the Day:
You want to find out how many servings of popcorn this popcorn popper makes.
What do you know?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Vocabulary Terms - Define/Illustrate
Cylinder
Cone
Sphere
5 Problems - SHOW ALL WORK!
What is the radius if the Diameter is 20cm?
What is the Diameter if the Radius is 6in?
Find the Area of the circle if the given radius is 3 cm in terms of pi and with an estimated area.
Find the Circumference of the circle if the diameter is 20” in terms of pi and with an estimated answer.
Unwrap the figure and tell what 2D shapes make up the 3D figure. Include dimensions of the shapes.
What do I need help with?
Unit 7 Math Practice Links - Click here
Live Lesson Recording
*Passcode can be found on the Connexus Pushpin under your Math Class! Use the one for Mrs. Garcia!
Function of the Day:
You want to find out how many servings of popcorn this popcorn popper makes.
What do you know?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Vocabulary Terms - Define/Illustrate
Cylinder
Cone
Sphere
5 Problems - SHOW ALL WORK!
What is the radius if the Diameter is 20cm?
What is the Diameter if the Radius is 6in?
Find the Area of the circle if the given radius is 3 cm in terms of pi and with an estimated area.
Find the Circumference of the circle if the diameter is 20” in terms of pi and with an estimated answer.
Unwrap the figure and tell what 2D shapes make up the 3D figure. Include dimensions of the shapes.
What do I need help with?
Answers
GPT-4o mini
Let's break down your math practice session.
---
### Function of the Day:
To find out how many servings of popcorn the popcorn popper makes, we need to know more details like the volume or amount of popcorn per serving, but in this context, it seems we are working on geometry related to shapes.
### What do you know?
1. The shape of the popcorn popper could be a cylinder.
2. We need to understand geometric formulas for circles.
3. We can connect measurements of diameter and radius.
4. We can calculate area and circumference.
5. Unwrapping 3D figures into 2D shapes is essential in geometry.
6. Popcorn poppers usually have specific dimensions that affect how much popcorn they can hold.
7. Area is measured in square units, while volume is in cubic units.
8. The circumference of a circle relates to the diameter and radius.
9. Geometry plays a critical role in understanding real-world applications like cooking appliances.
10. This exercise strengthens problem-solving skills.
### Vocabulary Terms - Define/Illustrate
1. **Cylinder**: A three-dimensional shape with two parallel circular bases connected by a curved surface. (Illustration needed)
2. **Cone**: A three-dimensional shape with a circular base and a single vertex. (Illustration needed)
3. **Sphere**: A perfectly round three-dimensional shape, every point on its surface is equidistant from the center. (Illustration needed)
### 5 Problems - SHOW ALL WORK!
1. **What is the radius if the Diameter is 20 cm?**
\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm}
\]
2. **What is the Diameter if the Radius is 6 in?**
\[
\text{Diameter} = 2 \times \text{Radius} = 2 \times 6 \text{ in} = 12 \text{ in}
\]
3. **Find the Area of the circle if the given radius is 3 cm in terms of pi and with an estimated area.**
\[
\text{Area} = \pi r^2 = \pi (3 \text{ cm})^2 = 9\pi \text{ cm}^2 \quad (\text{Estimated area} \approx 9 \times 3.14 = 28.26 \text{ cm}^2)
\]
4. **Find the Circumference of the circle if the diameter is 20” in terms of pi and with an estimated answer.**
\[
\text{Circumference} = \pi d = \pi (20 \text{ in}) = 20\pi \text{ in} \quad (\text{Estimated circumference} \approx 20 \times 3.14 = 62.8 \text{ in})
\]
5. **Unwrap the figure and tell what 2D shapes make up the 3D figure. Include dimensions of the shapes.**
Let's take a cylinder as an example. When unwrapped, a cylinder consists of:
- 1 rectangle (the lateral surface): height = \(h\) cm, width = circumference = \(2\pi r\)
- 2 circles (the bases): radius = \(r\) cm
If the radius is 5 cm and height is 10 cm:
- Rectangle: height = 10 cm, width = \(2\pi(5)\approx 31.4\) cm (~31.4 cm)
- Circles: Diameter = 10 cm
### What do I need help with?
- If you have specific topics or problems you find difficult or need more clarification on, please specify!
---
Feel free to elaborate on any part of this or provide any additional questions!
---
### Function of the Day:
To find out how many servings of popcorn the popcorn popper makes, we need to know more details like the volume or amount of popcorn per serving, but in this context, it seems we are working on geometry related to shapes.
### What do you know?
1. The shape of the popcorn popper could be a cylinder.
2. We need to understand geometric formulas for circles.
3. We can connect measurements of diameter and radius.
4. We can calculate area and circumference.
5. Unwrapping 3D figures into 2D shapes is essential in geometry.
6. Popcorn poppers usually have specific dimensions that affect how much popcorn they can hold.
7. Area is measured in square units, while volume is in cubic units.
8. The circumference of a circle relates to the diameter and radius.
9. Geometry plays a critical role in understanding real-world applications like cooking appliances.
10. This exercise strengthens problem-solving skills.
### Vocabulary Terms - Define/Illustrate
1. **Cylinder**: A three-dimensional shape with two parallel circular bases connected by a curved surface. (Illustration needed)
2. **Cone**: A three-dimensional shape with a circular base and a single vertex. (Illustration needed)
3. **Sphere**: A perfectly round three-dimensional shape, every point on its surface is equidistant from the center. (Illustration needed)
### 5 Problems - SHOW ALL WORK!
1. **What is the radius if the Diameter is 20 cm?**
\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm}
\]
2. **What is the Diameter if the Radius is 6 in?**
\[
\text{Diameter} = 2 \times \text{Radius} = 2 \times 6 \text{ in} = 12 \text{ in}
\]
3. **Find the Area of the circle if the given radius is 3 cm in terms of pi and with an estimated area.**
\[
\text{Area} = \pi r^2 = \pi (3 \text{ cm})^2 = 9\pi \text{ cm}^2 \quad (\text{Estimated area} \approx 9 \times 3.14 = 28.26 \text{ cm}^2)
\]
4. **Find the Circumference of the circle if the diameter is 20” in terms of pi and with an estimated answer.**
\[
\text{Circumference} = \pi d = \pi (20 \text{ in}) = 20\pi \text{ in} \quad (\text{Estimated circumference} \approx 20 \times 3.14 = 62.8 \text{ in})
\]
5. **Unwrap the figure and tell what 2D shapes make up the 3D figure. Include dimensions of the shapes.**
Let's take a cylinder as an example. When unwrapped, a cylinder consists of:
- 1 rectangle (the lateral surface): height = \(h\) cm, width = circumference = \(2\pi r\)
- 2 circles (the bases): radius = \(r\) cm
If the radius is 5 cm and height is 10 cm:
- Rectangle: height = 10 cm, width = \(2\pi(5)\approx 31.4\) cm (~31.4 cm)
- Circles: Diameter = 10 cm
### What do I need help with?
- If you have specific topics or problems you find difficult or need more clarification on, please specify!
---
Feel free to elaborate on any part of this or provide any additional questions!