U9 Nets and Surface Area
Nets are two-dimensional patterns of three-dimensional figures.
T1
Explore Mar 6
Due 3/6
In a moment, each student will receive one net
Carefully cut out your net. Be sure to keep the gluing tabs. If you have time, you may glue the tabs on your net.
When finished, please leave your 3D shape in the correct bin in the front. If not finished, you may fold and glue your net over the weekend or leave it in the correct bin.
Please clean up your area by putting all scrap papers into the recycling bin.
If you have a calculator, bring it. You are encouraged to use it to find surface area and volume (for practice, test, etc.). You don't need a fancy one, it just needs to add, subtract, multiply and divide.
Let's learn how to sketch a three-dimensional rectangular prism
Surface Area (S.A.) is the total area of all outside faces of a 3D object, measured in square units (ft², in², cm², yd², etc.)
It represents the total space covering an object's exterior, such as the amount of wrapping paper needed to cover a box.
It is calculated by adding the areas of all individual faces.
Play the first minute or so... to tease out some vocabulary
1. What is the surface area of a prism with a height of 13 cm, a length of 7 cm, and width of 7 cm? (square base)
2. What is the surface area of a prism with a height of 13 cm, a length of 6 in, and width of 9 in? (rectangular base)
3. What is the surface area of a cube with a side length of 7 yards?
To find the Surface Area (SA) of a prism:
#1. Sketch the net
#2. Write the dimensions for ALL of the sides
#3. Use the dimensions to find the area of each of the faces
#4 Add the areas to find the total surface area
T2
My Responsibilities Mar 9
Due 3/9
1. Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
p767 1, 2, 3, 4, 5 (Volume 2, Chapter 10, Lesson 3)
2. Write down at least three things to remember about this topic in your math notebook (include examples)
3. Don't give up! If you get stuck, choose to persevere: review your thinking, try another approach, ask for help, search
Thursday is a retake day!
Papers are on the bottom shelf of the bookshelf near Mr. Olsen's desk.
After completing the Check-your-understanding questions, which were important for everyone to do?
Pick one or two problems that you did and show your work to you seat partner.
On the blank side, write: First name, last name, U10T2
Turn-taking ----------------------> Collaboration
When you work with your team (x), you learn and grow (y)
T3
My Responsibilities Mar 10
Due 3/10
1. Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
2. Write down at least three things to remember about this topic in your math notebook (include examples)
3. Don't give up! If you get stuck, choose to persevere: review your thinking, try another approach, ask for help, search
Tomorrow is a retake day!
Papers are on the bottom shelf of the bookshelf near Mr. Olsen's desk.
Where does volume show up in the world around us?
Calculating the volume of water in your pool (cubic gallons, so you can add/buy chemicals)
Comparing backpacks (cubic liters, so you know if you are able to hold all your stuff/gear)
Ordering concrete for a new sidewalk, driveway, or foundation (cubic yards)
The formula for finding the volume of a prism is V = B · h (Volume = Base Area times Height)
To multiply fractions: turn mixed numbers into improper fractions and multiply straight across. Then simplify.
How does area relate to volume? (start 1:00, pause at 2:24)
Show FIAB question involving units
Let's use the rectangular prisms we created in class to explore volume:
1. Calculate the volume of a rectangular prism and use cubes to verify results
2. Use cubes to determine measurements of prism with fractional edge lengths and calculate the volume
To find the volume of a prism:
* If needed, sketch 3d prism (with dimensions)
#1 Write volume formula (V=Bh)
#2 Substitute the formula for finding the area of the base (B)
#3 Substitute dimensions
#4 Multiply and write answer with units³
T4
My Responsibilities Mar 11
Due 3/11
1. Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
p745 14, 15, 16, 17; p743: 1, 2, 3 (Ch10-1, Volume 2)
Answers to odd numbered problems are in the back of the book. Even ones below:
2. Write down at least three things to remember about this topic in your math notebook (include examples)
3. Don't give up! If you get stuck, choose to persevere: review your thinking, try another approach, ask for help, search
Unit 10 Test is next week on Thursday 3/19
No graphic organizer
EVERYONE: If you have a watch, phone, or Chromebook, please turn it off and put it in your backpack. Place your backpack in the front of the room.
Retaking? You need at your desk: the CYUqs you want to trade, pencils and/or pens, and something to do when finished (book to read, paper to draw or write on, NO Chromebooks).
NOT retaking? You need something to quiet to work on (NO Chromebooks or other electronics).
Once everyone is setup, I will call you up row by row to trade me for a retake.
This is a quiet testing environment. No talking or communicating in any way.
Minimum day
¾⋅ ⅔
⅘ ⋅ ⅓ ⋅ ⅗
T4
Extend Mar 13
Due 3/13
1. Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
2. Write down at least three things to remember about this topic in your math notebook (include examples)
3. Don't give up! If you get stuck, choose to persevere: review your thinking, try another approach, ask for help, search
A
Review Mar 16
Due 3/16
Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
For each figure, copy the net and add the dimensions. *I strongly suggest adding the dimensions to all the lines!
1. Unit 10T2:
2. Unit 10T3:
3. Don't give up! If you get stuck, choose to persevere: review the notes, review your thinking, try another approach, ask for help
Math placement test
You need at your desk: Chromebook, pencils and/or pens and something to do when finished (book to read, paper to draw or write on, etc.)
If you have a watch or phone, be sure it is in your backpack. Place your backpack in the front OR back of the room.
SIGN IN TO YOUR CHROMEBOOK. Open Google Chrome. At the top, type in: https://bit.ly/FCUSDmath
Click 'Advanced' and then 'Proceed to unsecure website"
When finished, put your scratch paper in the basket in the front. You may work on something (not electronic) quietly at your desk: read, draw, write, etc. Please do not talk.
You need at your desk: Chromebook, pencils and/or pens and something to do when finished (book to read, paper to draw or write on, etc.)
If you have a watch or phone, be sure it is in your backpack. Place your backpack in the front OR back of the room.
SIGN IN TO YOUR CHROMEBOOK. Open Google Chrome. At the top, type in: https://bit.ly/FCUSDmath
Click 'Advanced' and then 'Proceed to unsecure website"
When finished, put your scratch paper in the basket in the front. You may work on something (not electronic) quietly at your desk: read, draw, write, etc. Please do not talk.
"A calculator is a tool, not a brain. It only works left-to-right, so you must use parentheses to tell it what to do first."
"Calculators don’t know PEMDAS. If you type it in wrong, it will give you a wrong answer confidently."
"Type it in exactly as it should be solved (using parentheses), or the calculator will guess—and it will guess wrong."
A
Review Mar 18
Due 3/18
Today's problems sets are found in Google Classroom. For each question , rewrite the problem and show your work/thinking. After doing a problem, check the answer. If you got it right, move on. If you made a mistake, fix it and/or get help.
U10T2 My Responsibilities Mar 9 - CYUqs and Extend, Do 2 problems from each (you choose)
U10T3 My Responsibilities Mar 10 - CYUqs and Extend, Do 2 problems from each (you choose)
U10T4 My Responsibilities Mar 11 - CYUqs and Extend, Do 2 problems from each (you choose)
Unit 10
You need at your desk: Chromebook, pencils and/or pens, one of the class' calculators, and something to do when finished (book to read, paper to draw or write on, etc.)
If you have a watch or phone, be sure it is in your backpack. Place your backpack in the front OR back of the room.
DO NOT SIGN IN TO YOUR CHROMEBOOK. Click the Apps in the bottom left corner > Pear Assessment > Sign in with Clever > Sign in with Microsoft (sign in with your FCUSD email @student.fcusd.org) and your password > Continue
#5, #6, #7 please cross off the word 'square' and write 'cubic'
When finished, put your test (with your name on it) in the basket in the front. Please return the calculator. You may work on something (not electronic) quietly at your desk: read, draw, write, etc. Please do not talk.
Retake scheduled for next Friday 3/27. Papers are available on the bottom shelf of the bookshelf near Mr. Olsen's desk.
Please raise your hand to let me know!
More time...
I am proud of EVERYONE! I can see you're working hard and doing your best! Keep up the good work!
There is a bit of confusion regarding the exponent and where it goes. Here's the scoop!
On your test, question 4 is T3, questions 6 and 7 are T4. Question 8 is T5. Please cross off and write the correct number.
When you look at PowerSchool, Qs 1-2 are U10T2, Qs 3-4 are U10T3, Qs 5, 6, 7 are U10T4
For T2, there were 2 questions: mild and medium. If you correctly answered 2 questions, score is a 3; if 1 was correct, score is a 2.5; if none were correct, score is a 1
For T3, there were 2 questions: medium and spicy. If you correctly answered 2 questions, score is a 4; if 1 was correct, score is a 3; if none were correct, score is a 1
For T4, there were 3 questions: mild, medium, and spicy. If you correctly answered 3 questions, score is a 4; if 2 were correct, score is a 3; if 1 was correct, score is a 2; if none were correct, score is a 1
Refer to the Proficiency Levels to know what your work says about where you are right now in terms of your understanding on the key learning target(s):
A
Test Corrections Mar 20
Due 3/23
The most important part of the test happens right now: reviewing your work and learning from mistakes.
1. Open Pear Assessment. On your paper test, make a smiley face (or backwards check mark) by the questions you got right. Make a question mark by the ones you missed.
2. Find an expert to help you with the problem you missed. Compare and contrast your work and their work. Ask questions. Think. Don't copy. If needed, review the randomly chosen exemplars to see what your classmates did to answer the question correctly (provided in class).
3. On your corrections worksheet, neatly rewrite the problem, show your thinking, and circle the correct answer.
4. Before moving to the next problem, write down your mistake and what you will do to not make that mistake again.
First, fold the paper in half.
Next, user PowerSchool to write down your current level
Third, organize the ones that are less than 3 by 1st, 2nd, 3rd, etc. (in the order you want to start working on them)
Last, glue one half into your math notebook.
* Tonight, review and practice the first goal you want to work on. If needed ask for help.
In addition to the retake this Friday, we will also have a test over the learning targets we study this week.
I anticipate that you will have time for 1, maybe 2 retakes, so plan accordingly.
Test tomorrow over T1, T2, T3, and T4 -- what we reviewed this week. Please bring your Chromebook (charged)
There will also be time for a couple of retakes.
You need at your desk: pencils and/or pens, the papers you used to practice for a retake, and something to do when finished (book to read, paper to draw or write on, etc.)
If you have a Chromebook, watch or phone, be sure it is in your backpack. Place your backpack in the front OR back of the room.
Please show some thinking (show how you got your answer). If you don't, you will be marked as a Level 2.
When finished, put your test (with your name on it) in the basket in the front. You may:
A. Trade me for a retake, OR
B. Work on something (not electronic) quietly at your desk: read, draw, write, etc. Please do not talk.
Why, How, and What
In order to make sense of the world (DI1); students will reason abstractly and quantitatively (SMP2), model with mathematics (SMP4), and make sense of problems and persevere in solving them (SMP1) while (CCs) taking wholes apart, putting parts together (CC3), and discovering shape and space (CC4)
Grade Six Content Standards
Build and decompose 3-D figures using nets to find surface area. Represent volume and area as expressions involving whole number exponents. (p34)
EE1. Write and evaluate numerical expressions involving whole-number exponents.
EE2. Write, read, and evaluate expressions in which letters stand for numbers.
a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulasV = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2.
G1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
G2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate
unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
G3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
G4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface
area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Nets are two-dimensional patterns of three-dimensional figures.
T1
Explore Mar 6
Due 3/6
In a moment, each student will receive one net
Carefully cut out your net. Be sure to keep the gluing tabs. If you have time, you may glue the tabs on your net.
When finished, please leave your 3D shape in the correct bin in the front. If not finished, you may fold and glue your net over the weekend or leave it in the correct bin.
Please clean up your area by putting all scrap papers into the recycling bin.
If you have a calculator, bring it. You are encouraged to use it to find surface area and volume (for practice, test, etc.). You don't need a fancy one, it just needs to add, subtract, multiply and divide.
Let's learn how to sketch a three-dimensional rectangular prism
Surface Area (S.A.) is the total area of all outside faces of a 3D object, measured in square units (ft², in², cm², yd², etc.)
It represents the total space covering an object's exterior, such as the amount of wrapping paper needed to cover a box.
It is calculated by adding the areas of all individual faces.
Play the first minute or so... to tease out some vocabulary
1. What is the surface area of a prism with a height of 13 cm, a length of 7 cm, and width of 7 cm? (square base)
2. What is the surface area of a prism with a height of 13 cm, a length of 6 in, and width of 9 in? (rectangular base)
3. What is the surface area of a cube with a side length of 7 yards?
To find the Surface Area (SA) of a prism:
#1. Sketch the net
#2. Write the dimensions for ALL of the sides
#3. Use the dimensions to find the area of each of the faces
#4 Add the areas to find the total surface area
T2
My Responsibilities Mar 9
Due 3/9
1. Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
p767 1, 2, 3, 4, 5 (Volume 2, Chapter 10, Lesson 3)
2. Write down at least three things to remember about this topic in your math notebook (include examples)
3. Don't give up! If you get stuck, choose to persevere: review your thinking, try another approach, ask for help, search
Thursday is a retake day!
Papers are on the bottom shelf of the bookshelf near Mr. Olsen's desk.
After completing the Check-your-understanding questions, which were important for everyone to do?
Pick one or two problems that you did and show your work to you seat partner.
On the blank side, write: First name, last name, U10T2
Turn-taking ----------------------> Collaboration
When you work with your team (x), you learn and grow (y)
T3
My Responsibilities Mar 10
Due 3/10
1. Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
2. Write down at least three things to remember about this topic in your math notebook (include examples)
3. Don't give up! If you get stuck, choose to persevere: review your thinking, try another approach, ask for help, search
Tomorrow is a retake day!
Papers are on the bottom shelf of the bookshelf near Mr. Olsen's desk.
Where does volume show up in the world around us?
Calculating the volume of water in your pool (cubic gallons, so you can add/buy chemicals)
Comparing backpacks (cubic liters, so you know if you are able to hold all your stuff/gear)
Ordering concrete for a new sidewalk, driveway, or foundation (cubic yards)
The formula for finding the volume of a prism is V = B · h (Volume = Base Area times Height)
To multiply fractions: turn mixed numbers into improper fractions and multiply straight across. Then simplify.
How does area relate to volume? (start 1:00, pause at 2:24)
Show FIAB question involving units
Let's use the rectangular prisms we created in class to explore volume:
1. Calculate the volume of a rectangular prism and use cubes to verify results
2. Use cubes to determine measurements of prism with fractional edge lengths and calculate the volume
To find the volume of a prism:
* If needed, sketch 3d prism (with dimensions)
#1 Write volume formula (V=Bh)
#2 Substitute the formula for finding the area of the base (B)
#3 Substitute dimensions
#4 Multiply and write answer with units³
T4
My Responsibilities Mar 11
Due 3/11
1. Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
p745 14, 15, 16, 17; p743: 1, 2, 3 (Ch10-1, Volume 2)
Answers to odd numbered problems are in the back of the book. Even ones below:
2. Write down at least three things to remember about this topic in your math notebook (include examples)
3. Don't give up! If you get stuck, choose to persevere: review your thinking, try another approach, ask for help, search
Unit 10 Test is next week on Thursday 3/19
No graphic organizer
EVERYONE: If you have a watch, phone, or Chromebook, please turn it off and put it in your backpack. Place your backpack in the front of the room.
Retaking? You need at your desk: the CYUqs you want to trade, pencils and/or pens, and something to do when finished (book to read, paper to draw or write on, NO Chromebooks).
NOT retaking? You need something to quiet to work on (NO Chromebooks or other electronics).
Once everyone is setup, I will call you up row by row to trade me for a retake.
This is a quiet testing environment. No talking or communicating in any way.
Minimum day
¾⋅ ⅔
⅘ ⋅ ⅓ ⋅ ⅗
T4
Extend Mar 13
Due 3/13
1. Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
2. Write down at least three things to remember about this topic in your math notebook (include examples)
3. Don't give up! If you get stuck, choose to persevere: review your thinking, try another approach, ask for help, search
A
Review Mar 16
Due 3/16
Check-your-understanding questions (CYUQs): Do your own, you choose where to start, check your work with the students around you. If you need help, get help. If someone needs help, give help.
For each figure, copy the net and add the dimensions. *I strongly suggest adding the dimensions to all the lines!
1. Unit 10T2:
2. Unit 10T3:
3. Don't give up! If you get stuck, choose to persevere: review the notes, review your thinking, try another approach, ask for help
Math placement test
You need at your desk: Chromebook, pencils and/or pens and something to do when finished (book to read, paper to draw or write on, etc.)
If you have a watch or phone, be sure it is in your backpack. Place your backpack in the front OR back of the room.
SIGN IN TO YOUR CHROMEBOOK. Open Google Chrome. At the top, type in: https://bit.ly/FCUSDmath
Click 'Advanced' and then 'Proceed to unsecure website"
When finished, put your scratch paper in the basket in the front. You may work on something (not electronic) quietly at your desk: read, draw, write, etc. Please do not talk.
You need at your desk: Chromebook, pencils and/or pens and something to do when finished (book to read, paper to draw or write on, etc.)
If you have a watch or phone, be sure it is in your backpack. Place your backpack in the front OR back of the room.
SIGN IN TO YOUR CHROMEBOOK. Open Google Chrome. At the top, type in: https://bit.ly/FCUSDmath
Click 'Advanced' and then 'Proceed to unsecure website"
When finished, put your scratch paper in the basket in the front. You may work on something (not electronic) quietly at your desk: read, draw, write, etc. Please do not talk.
"A calculator is a tool, not a brain. It only works left-to-right, so you must use parentheses to tell it what to do first."
"Calculators don’t know PEMDAS. If you type it in wrong, it will give you a wrong answer confidently."
"Type it in exactly as it should be solved (using parentheses), or the calculator will guess—and it will guess wrong."
A
Review Mar 18
Due 3/18
Today's problems sets are found in Google Classroom. For each question , rewrite the problem and show your work/thinking. After doing a problem, check the answer. If you got it right, move on. If you made a mistake, fix it and/or get help.
U10T2 My Responsibilities Mar 9 - CYUqs and Extend, Do 2 problems from each (you choose)
U10T3 My Responsibilities Mar 10 - CYUqs and Extend, Do 2 problems from each (you choose)
U10T4 My Responsibilities Mar 11 - CYUqs and Extend, Do 2 problems from each (you choose)
Unit 10
You need at your desk: Chromebook, pencils and/or pens, one of the class' calculators, and something to do when finished (book to read, paper to draw or write on, etc.)
If you have a watch or phone, be sure it is in your backpack. Place your backpack in the front OR back of the room.
DO NOT SIGN IN TO YOUR CHROMEBOOK. Click the Apps in the bottom left corner > Pear Assessment > Sign in with Clever > Sign in with Microsoft (sign in with your FCUSD email @student.fcusd.org) and your password > Continue
#5, #6, #7 please cross off the word 'square' and write 'cubic'
When finished, put your test (with your name on it) in the basket in the front. Please return the calculator. You may work on something (not electronic) quietly at your desk: read, draw, write, etc. Please do not talk.
Retake scheduled for next Friday 3/27. Papers are available on the bottom shelf of the bookshelf near Mr. Olsen's desk.
Please raise your hand to let me know!
More time...
I am proud of EVERYONE! I can see you're working hard and doing your best! Keep up the good work!
There is a bit of confusion regarding the exponent and where it goes. Here's the scoop!
On your test, question 4 is T3, questions 6 and 7 are T4. Question 8 is T5. Please cross off and write the correct number.
When you look at PowerSchool, Qs 1-2 are U10T2, Qs 3-4 are U10T3, Qs 5, 6, 7 are U10T4
For T2, there were 2 questions: mild and medium. If you correctly answered 2 questions, score is a 3; if 1 was correct, score is a 2.5; if none were correct, score is a 1
For T3, there were 2 questions: medium and spicy. If you correctly answered 2 questions, score is a 4; if 1 was correct, score is a 3; if none were correct, score is a 1
For T4, there were 3 questions: mild, medium, and spicy. If you correctly answered 3 questions, score is a 4; if 2 were correct, score is a 3; if 1 was correct, score is a 2; if none were correct, score is a 1
Refer to the Proficiency Levels to know what your work says about where you are right now in terms of your understanding on the key learning target(s):
A
Test Corrections Mar 20
Due 3/23
The most important part of the test happens right now: reviewing your work and learning from mistakes.
1. Open Pear Assessment. On your paper test, make a smiley face (or backwards check mark) by the questions you got right. Make a question mark by the ones you missed.
2. Find an expert to help you with the problem you missed. Compare and contrast your work and their work. Ask questions. Think. Don't copy. If needed, review the randomly chosen exemplars to see what your classmates did to answer the question correctly (provided in class).
3. On your corrections worksheet, neatly rewrite the problem, show your thinking, and circle the correct answer.
4. Before moving to the next problem, write down your mistake and what you will do to not make that mistake again.
First, fold the paper in half.
Next, user PowerSchool to write down your current level
Third, organize the ones that are less than 3 by 1st, 2nd, 3rd, etc. (in the order you want to start working on them)
Last, glue one half into your math notebook.
* Tonight, review and practice the first goal you want to work on. If needed ask for help.
In addition to the retake this Friday, we will also have a test over the learning targets we study this week.
I anticipate that you will have time for 1, maybe 2 retakes, so plan accordingly.
Test tomorrow over T1, T2, T3, and T4 -- what we reviewed this week. Please bring your Chromebook (charged)
There will also be time for a couple of retakes.
You need at your desk: pencils and/or pens, the papers you used to practice for a retake, and something to do when finished (book to read, paper to draw or write on, etc.)
If you have a Chromebook, watch or phone, be sure it is in your backpack. Place your backpack in the front OR back of the room.
Please show some thinking (show how you got your answer). If you don't, you will be marked as a Level 2.
When finished, put your test (with your name on it) in the basket in the front. You may:
A. Trade me for a retake, OR
B. Work on something (not electronic) quietly at your desk: read, draw, write, etc. Please do not talk.