U3 Graphing Shapes
T1
Launch
Rectangle: (-2, 2) (5, 2) (5, -2) (-2, -2)
When graphing shapes, "Is there something I could do right away without thinking too much?" "Can I do that for all of them?" "What do I do next?" "Could I have done something else next?"
T1
Vertical Collaboration
Draw an x and y-axis. Label both axis. Number by ones between -6 and 6 on both axis.
Acute Triangle: (-4, -2) (-4, 4) (4, 3)
Right Triangle: (4, 4) (4, -4) (-2, 4)
Square: (2, 5) (2, -2) (-5, -2) (-5, 5)
T1
Consolidation
Polygon: a straight-sided plane figure with at least three sides and angles
When graphing on a coordinate plane:
1. If not already labeled, be sure to label the x and y-axis on the coordinate plane
2. Remember that ordered pairs are (x, y)
3. When graphing a point, start with the x-axis (left or right), then go up or down on the y-axis.
T1
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below to open. Do in your work on the 12 Coordinate Planes Handout. You chose where you want to start. If you need help, get help. If someone else needs help, give help.
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T1
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T1
Direct Instruction
Plane Figure: a flat, 2-dimensional shape that has length and width but no thickness or depth
Parallel: two lines that are always the same distance apart and never touch or intersect ||
Congruent: figures have the exact same shape and size ≅
The polygon family of shapes includes QUADRILATERALS. Let's make notes about some of the key vocabulary related to quadrilaterals:
T1
Extend
Click the link below to open. Do in your work on the 12 Coordinate Planes Handout. You chose where you want to start. If you need help, get help. If someone else needs help, give help.
Check answers as you’re working. If you make a mistake, fix it.
T1
Direct Instruction
Angle: the "space" or amount of turn between two lines that start at the same point
Vertex: the common point where the two lines meet
Perpendicular: two lines that cross each other to form a perfect "L" shape (90 degrees)
*** The base is ALWAYS perpendicular to the height.
The polygon family of shapes includes TRIANGLES. Let's make notes about some of the key vocabulary related to triangles:
T1
Entry Ticket (5 min)
Above the coordinate plane, write: First name, last name, U3T1
Graph the ordered pairs.
Write the ordered pairs next to each point.
Connect the dots.
(-5, 2) (3, -4) (5, 2) (-3, -4)
T2
Direct Instruction
Perimeter (P) is the total distance around the outside edge of a two-dimensional shape.
T2
Launch
Find the perimeter of the quadrilateral
Model writing P = a + b + c + d, substituting the length of the side, and working down
Vocabulary: formula, substitution, simplify by working down, circle answer (P= )
T2
Consolidation
Formula: a special recipe for solving a math or science problem. Instead of words, it uses letters and symbols to show what to do.
One way to write a formula for perimeter is P = a + b + c + d
Substitution: replacing a variable (a letter that stands for an unknown number) with its actual number value
T2
Guided Practice
Let's find the perimeter of the polygons we drew in Target 1:
T2
Explore
If you want to see the formula for finding the distance between points, search "what is the distance between (1,2) and (4, -3) to the tenths place"
T2
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below to open. Do your work in your notebook. Write a perimeter formula and substitute. Do all 12. If you need help, get help. If someone else needs help, give help.
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
A
Thursday is a Retake Day
To retake a summative assessment score in PowerSchool that is less than 3:
1. Go to Google Classroom > Classwork. Scroll down to
find the student responsibilities for the unit and target
you are looking for (e.g. U1T1 Student Responsibilities)
2. Click View Instructions. Review the notes. Do the
CYUQs (to a level 3 or better) and check answers as
you’re working. If you get stuck, review your thinking, try different
approaches, ask for help, and/or search.
3. Bring your Level 3 CYUQs to the retake day and trade
me for a retake
T2
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
Review your work and discuss: what does it mean to find the perimeter?
T2
Entry Ticket (5 min)
On the blank side, at the top of your paper, write: First name, last name, U3T2
Show how you would use a formula and substitute to find the perimeter of this rectangle:
T3
Direct Instruction
Area (A) is the amount of space inside a flat, two-dimensional shape
T3
Explore
Work with your seat partner to find the area of each shape. Prove your thinking in your notebooks.
T3
Direct Instruction
Most shapes that we want to find the area of aren't drawn on a coordinate grid. For that reason, we use formulas!
Neatly write each of the five area formulas in your notebook:
T3
Guided Practice
Let's use our formulas to find the area of a few shapes:
T3
Summarize
To find the area of each of the 12 shapes we drew on the coordinate plane:
1. Identify the shape and write the correct area formula.
2. To get the numbers you need for the formula, calculate the distances between points.
T3
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below to open. Do your work in your notebook. Write the correct area formula and substitute. Do all 12. If you need help, get help. If someone else needs help, give help.
#5 and #6 are LEVEL 4 questions. Do your best, but feel free to work on these after you find the area of the other shapes...
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T1
Glue & Review
T2
Glue & Review
T3
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
Review your work and discuss: what does it mean to find the area?
T3
Memorize
When you take the test for this unit, you will have two tests: computer-based and paper. For the computer based-test, you will be able to use your graphic organizer. For the paper test, you must have the five formulas memorized.
T3
Direct Instruction
When using a formula to find the area:
1. Identify the shape and write the correct area formula.
2. Below the formula, replace the letters with the correct numbers
3. Simplify (work your way down NOT SIDEWAYS)
T3
CYUqs
Do your work in your notebook. Write the correct area formula and substitute. If you need help, get help. If someone else needs help, give help.
* If needed, use a calculator for the multiplication and division
p667: 14, 15; p665: 2, 3; p664: 2, 3 (Volume 2 Ch9-1)
p679: 14, 15; p677: 6, p676: 2, 5 (Volume 2 Ch9-2)
p689: 1, 2; p691: 15, 17; p688: 1, 2 (Volume 2 Ch9-3)
A
Retake Day
A
Retake or Prepare (35min)
Trade your CYUqs for a retake.
If unprepared, open PowerSchool and review your progress. If you have a summative assessment goal that is less than 3, do the CYUqs (at a level 3) and prepare for retaking. When ready, trade me. Repeat this process until your goals are all 3's or better.
If your goals are all 3's or better OR you are done retaking, practice and review the math we are currently working on by signing into Delta Math > click Login > Sign in with Google > with your school Google Account > Base, Height, and Area Practice (You are welcome to use a calculator.)
T3
Entry Ticket (5 min)
On the top of the blank side, write: First name, last name, U3T3
What is the area of a triangle with a base of 11 units and a height of 7 units?
Be sure to write the formula, show your work and circle your answer.
T3
Direct Instruction
In a trapezoid, the bases are always parallel
T4
Knowledge Application
Today you are inventing a brand new polygon. Here are the project requirements:
1. Made up of at least one (rectangle OR parallelogram OR trapezoid) and ONE triangle -- ONLY TWO SHAPES
2. Drawn on the coordinate plane
3. All vertices clearly visible and labeled with the correct ordered pair
4. Find the perimeter (Neatly write a formula, show steps, and circle answer)
5. Calculate the area: (Neatly write two or more formulas, show steps, and circle answer)
6. Name your shape
If you need to find the distance between points on a slanted line, use this search: "What is the distance between the points (a,b) and (c,d) rounded to the tenths place"
T3
Glue & Review
T4
Discuss (2 min)
How did your shape turn out? Share your invention with your neighbor. Share what was easy and what was difficult about the project.
If you did not trace your shape (perimeter) with color, use some of my colored pencils to make sure your invention stands out. USE A RULER OR STRAIGHTEDGE to make the lines straight.
T5
Direct Instruction
A composite figure is a two-dimensional figure made up of basic two-dimensional shapes such as one triangle and one rectangle.
T5
Consolidation
When you break up a composite shape, think about it two ways:
1. Was the shape made by adding one or more simple shapes?
2. Or, could the shape be made by subtracting a smaller shape from a bigger shape?
Either way, try to imagine the fewest number of shapes.
T5
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below to open
Do your work in your notebook. Draw the composite figure. Draw the smaller, simple shapes. Include dimensions.
Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T5
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Think, Pair, Share
Start by working in your notebook to figure out the length of the missing sides. After one minute, discuss your work with your seat partner. Take turns. If needed, modify or make changes to your original thinking.
1. Identify missing dimensions
1A
2. Identify missing dimension
T5
Summarize
To find a missing dimension after breaking up a composite figure:
First, break it into simpler shapes and include the numbers that make sense.
Second, use addition or subtraction to determine the missing sides
Example A: To find the height of the triangle:
Example B: To find the base of the triangle:
Third, verify that you have all the dimensions
T6
Vertical Collaboration
What is the area of the composite figure?
1
1A
2
2A
3
3A
4
4A
T6
Summarize
To calculate the area of a composite figure:
1. Decompose the figure (i.e. break it into simple shapes)
2. Write the dimensions
3. Calculate the areas of each simple shape, and add or subtract them.
T6
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → p721: 1, 2; p723: 11 (Volume 2 Ch9-6)
Do your work in your notebook. Draw the composite figure. Draw the smaller, simple shapes. Include dimensions. Write the formulas and find their areas.
Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T6
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T6
Vertical Collaboration
Shape 1
Area is 81 units squared. Click to see Shape 1 partial solution with shapes decomposed and dimensions:
Shape 2
Area is 229.5 units squared. Click to see Shape 2 partial solution with shapes decomposed and dimensions:
* Next move: "How could you do this a different way and get the same answer?"
T6
Group Notes
Prompt:
Worksheet with questions:
Sample student work and things to remember:
T6
Extend
U3T6 Extend. Pick any ONE of the polygons and find the area. Medium level: 4 and 5. Spicy: 2, 3, and 6. You CHOOSE.
First, neatly sketch the composite figure and its dimensions.
Next, mentally break the shape into simpler 2D figures. Next to the original figure, sketch the simple figures and their dimensions.
Finally, find the area of each simple shape and add or subtract the areas to find the area of the original composite figure.
Check your answer!
If needed, use a calculator to help you crunch the numbers.
T6
Review Examples
Yesterday's group consolidation went really well! Let's take a look at some of the work and comments that were shared:
T6
Critique the reasoning of others
YOU ARE THE TEACHER! Can you find the mistake?
Start by looking for one thing that the group did well.
Then, see if you can find the error or mistake that led them to come up with the wrong solution.
A
Class Info
Unit 3 Test is Tuesday 10/21.
The test will cover everything we studied in the unit and focus mainly on T3 and T6 (the essential standards).
It will be on the computer and on paper
A
Review
For each of the following, click the link to open the worksheet. Do only the assigned problems. Check answers as you work.
In your notebook, sketch each image and write the dimensions. Write the formula, and substitute to find the area. Be neat.
Parallelograms: Do 1-7 (If you're interested, try the spicy ones: 13-15)
Parallelograms Answers
Triangles: Do 1-10 (If you're interested, try the spicy ones: 13-15)
Triangles Answers
Trapezoids: Do 1-7
Trapezoids Answers
* If you need a calculator:
A
Summarize
Click the link below to open the unit's graphic organizer:
Complete each box by adding notes, examples, and annotations (notes that explain what is happening in your examples). Refer to your notes, CYUqs, entry tickets, vertical collaboration, Google Search, etc. Work together. Help each other.
You may use the notes you make on this graphic organizer during the test (nothing else).
A
Review
Click the link to open the worksheet. (There are two pages.) Do all six on the worksheet or in your notebook. For each problem: sketch the image, decompose it, write the dimensions, write the formulas, and substitute.
If you choose to work with a partner, be sure the two of you focus and work together. DON'T divide and conquer. Work on each problem together!
A
Test
Unit 3
A
Test Directions
Take out your Chromebook, something to write with, and your graphic organizer. No phones, smart watches, or other electronic devices.
DO NOT SIGN IN TO YOUR CHROMEBOOK. If you are signed in, sign out. Click the Apps in the bottom left corner > Pear Assessment > Login with Google (sign in with your FCUSD email @student.fcusd.org). Sign in again with @student.fcusd.org and your password > Continue
Click Start Assessment to open the Unit 3 Answer Sheet. Do your work on your test. Type the answers into the Pear Assessment
When finished, put your paper test, graphic organizer, and calculator in the basket in the BACK. You may read (Sora), draw, write, work on an assignment, or rest. Do not talk.
A
Were you absent yesterday?
Please raise your hand to let me know!
A
Goal Setting
Start by opening PowerSchool. On your Goal Sheet, check off each goal that you have a 3 or better in. If you have a score of less than 3, leave the "Got It" blank.
Where it says "Date", that is the date you plan to retake and show me you understand!
At that the bottom of your goal sheet you see the NEXT STEPS for goals that are less than 3. Please follow those steps BEFORE the retake date. Don't show up on the retake date and do your CYUQS in class. Have them ready before class!
A
Watch & Discuss
A
Pass Back Papers
A
Review
After reviewing your tests, I see that EVERYONE has been working hard and doing their best. The time you are spending thinking and working together is paying off. I am proud of YOU.
Please open Pear Assessment. On your paper test, if you got the question correct, make a smiley face. If you got it wrong, put a checkmark.
A
Test Corrections
The most important part of the test happens right now: reviewing your work and learning from mistakes.
1. Find an expert. Compare and contrast your work and their work. Discuss what you notice. Ask questions. Think. Don't copy.
2. On your corrections worksheet, neatly rewrite the problem, show your thinking, and circle the correct answer.
3. Before moving to the next problem, write down your mistake and what you will do to not make that mistake again.
Why, How, and What
In order to predict what could happen (DI2), students will look for and make use of structure (SMP7) and look for and express regularity in repeated reasoning (SMP8) while discovering shape and space (CC4)
Description
Use coordinates to represent the vertices of polygons, graph the shapes on the coordinate plane, and determine side lengths, perimeter, and area. (p34)
Standards
- 6.G.3 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.
- 6.G.1 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.
- 6.G.4 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.
- 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
- 6.EE.2 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 formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.
- Source:
- 2013 CACC Math Content Standards
T1
Launch
Rectangle: (-2, 2) (5, 2) (5, -2) (-2, -2)
When graphing shapes, "Is there something I could do right away without thinking too much?" "Can I do that for all of them?" "What do I do next?" "Could I have done something else next?"
T1
Vertical Collaboration
Draw an x and y-axis. Label both axis. Number by ones between -6 and 6 on both axis.
Acute Triangle: (-4, -2) (-4, 4) (4, 3)
Right Triangle: (4, 4) (4, -4) (-2, 4)
Square: (2, 5) (2, -2) (-5, -2) (-5, 5)
T1
Consolidation
Polygon: a straight-sided plane figure with at least three sides and angles
When graphing on a coordinate plane:
1. If not already labeled, be sure to label the x and y-axis on the coordinate plane
2. Remember that ordered pairs are (x, y)
3. When graphing a point, start with the x-axis (left or right), then go up or down on the y-axis.
T1
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below to open. Do in your work on the 12 Coordinate Planes Handout. You chose where you want to start. If you need help, get help. If someone else needs help, give help.
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T1
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T1
Direct Instruction
Plane Figure: a flat, 2-dimensional shape that has length and width but no thickness or depth
Parallel: two lines that are always the same distance apart and never touch or intersect ||
Congruent: figures have the exact same shape and size ≅
The polygon family of shapes includes QUADRILATERALS. Let's make notes about some of the key vocabulary related to quadrilaterals:
T1
Extend
Click the link below to open. Do in your work on the 12 Coordinate Planes Handout. You chose where you want to start. If you need help, get help. If someone else needs help, give help.
Check answers as you’re working. If you make a mistake, fix it.
T1
Direct Instruction
Angle: the "space" or amount of turn between two lines that start at the same point
Vertex: the common point where the two lines meet
Perpendicular: two lines that cross each other to form a perfect "L" shape (90 degrees)
*** The base is ALWAYS perpendicular to the height.
The polygon family of shapes includes TRIANGLES. Let's make notes about some of the key vocabulary related to triangles:
T1
Entry Ticket (5 min)
Above the coordinate plane, write: First name, last name, U3T1
Graph the ordered pairs.
Write the ordered pairs next to each point.
Connect the dots.
(-5, 2) (3, -4) (5, 2) (-3, -4)
T2
Direct Instruction
Perimeter (P) is the total distance around the outside edge of a two-dimensional shape.
T2
Launch
Find the perimeter of the quadrilateral
Model writing P = a + b + c + d, substituting the length of the side, and working down
Vocabulary: formula, substitution, simplify by working down, circle answer (P= )
T2
Consolidation
Formula: a special recipe for solving a math or science problem. Instead of words, it uses letters and symbols to show what to do.
One way to write a formula for perimeter is P = a + b + c + d
Substitution: replacing a variable (a letter that stands for an unknown number) with its actual number value
T2
Guided Practice
Let's find the perimeter of the polygons we drew in Target 1:
T2
Explore
If you want to see the formula for finding the distance between points, search "what is the distance between (1,2) and (4, -3) to the tenths place"
T2
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below to open. Do your work in your notebook. Write a perimeter formula and substitute. Do all 12. If you need help, get help. If someone else needs help, give help.
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
A
Thursday is a Retake Day
To retake a summative assessment score in PowerSchool that is less than 3:
1. Go to Google Classroom > Classwork. Scroll down to
find the student responsibilities for the unit and target
you are looking for (e.g. U1T1 Student Responsibilities)
2. Click View Instructions. Review the notes. Do the
CYUQs (to a level 3 or better) and check answers as
you’re working. If you get stuck, review your thinking, try different
approaches, ask for help, and/or search.
3. Bring your Level 3 CYUQs to the retake day and trade
me for a retake
T2
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
Review your work and discuss: what does it mean to find the perimeter?
T2
Entry Ticket (5 min)
On the blank side, at the top of your paper, write: First name, last name, U3T2
Show how you would use a formula and substitute to find the perimeter of this rectangle:
T3
Direct Instruction
Area (A) is the amount of space inside a flat, two-dimensional shape
T3
Explore
Work with your seat partner to find the area of each shape. Prove your thinking in your notebooks.
T3
Direct Instruction
Most shapes that we want to find the area of aren't drawn on a coordinate grid. For that reason, we use formulas!
Neatly write each of the five area formulas in your notebook:
T3
Guided Practice
Let's use our formulas to find the area of a few shapes:
T3
Summarize
To find the area of each of the 12 shapes we drew on the coordinate plane:
1. Identify the shape and write the correct area formula.
2. To get the numbers you need for the formula, calculate the distances between points.
T3
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below to open. Do your work in your notebook. Write the correct area formula and substitute. Do all 12. If you need help, get help. If someone else needs help, give help.
#5 and #6 are LEVEL 4 questions. Do your best, but feel free to work on these after you find the area of the other shapes...
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T1
Glue & Review
T2
Glue & Review
T3
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
Review your work and discuss: what does it mean to find the area?
T3
Memorize
When you take the test for this unit, you will have two tests: computer-based and paper. For the computer based-test, you will be able to use your graphic organizer. For the paper test, you must have the five formulas memorized.
T3
Direct Instruction
When using a formula to find the area:
1. Identify the shape and write the correct area formula.
2. Below the formula, replace the letters with the correct numbers
3. Simplify (work your way down NOT SIDEWAYS)
T3
CYUqs
Do your work in your notebook. Write the correct area formula and substitute. If you need help, get help. If someone else needs help, give help.
* If needed, use a calculator for the multiplication and division
p667: 14, 15; p665: 2, 3; p664: 2, 3 (Volume 2 Ch9-1)
p679: 14, 15; p677: 6, p676: 2, 5 (Volume 2 Ch9-2)
p689: 1, 2; p691: 15, 17; p688: 1, 2 (Volume 2 Ch9-3)
A
Retake Day
A
Retake or Prepare (35min)
Trade your CYUqs for a retake.
If unprepared, open PowerSchool and review your progress. If you have a summative assessment goal that is less than 3, do the CYUqs (at a level 3) and prepare for retaking. When ready, trade me. Repeat this process until your goals are all 3's or better.
If your goals are all 3's or better OR you are done retaking, practice and review the math we are currently working on by signing into Delta Math > click Login > Sign in with Google > with your school Google Account > Base, Height, and Area Practice (You are welcome to use a calculator.)
T3
Entry Ticket (5 min)
On the top of the blank side, write: First name, last name, U3T3
What is the area of a triangle with a base of 11 units and a height of 7 units?
Be sure to write the formula, show your work and circle your answer.
T3
Direct Instruction
In a trapezoid, the bases are always parallel
T4
Knowledge Application
Today you are inventing a brand new polygon. Here are the project requirements:
1. Made up of at least one (rectangle OR parallelogram OR trapezoid) and ONE triangle -- ONLY TWO SHAPES
2. Drawn on the coordinate plane
3. All vertices clearly visible and labeled with the correct ordered pair
4. Find the perimeter (Neatly write a formula, show steps, and circle answer)
5. Calculate the area: (Neatly write two or more formulas, show steps, and circle answer)
6. Name your shape
If you need to find the distance between points on a slanted line, use this search: "What is the distance between the points (a,b) and (c,d) rounded to the tenths place"
T3
Glue & Review
T4
Discuss (2 min)
How did your shape turn out? Share your invention with your neighbor. Share what was easy and what was difficult about the project.
If you did not trace your shape (perimeter) with color, use some of my colored pencils to make sure your invention stands out. USE A RULER OR STRAIGHTEDGE to make the lines straight.
T5
Direct Instruction
A composite figure is a two-dimensional figure made up of basic two-dimensional shapes such as one triangle and one rectangle.
T5
Consolidation
When you break up a composite shape, think about it two ways:
1. Was the shape made by adding one or more simple shapes?
2. Or, could the shape be made by subtracting a smaller shape from a bigger shape?
Either way, try to imagine the fewest number of shapes.
T5
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below to open
Do your work in your notebook. Draw the composite figure. Draw the smaller, simple shapes. Include dimensions.
Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T5
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Think, Pair, Share
Start by working in your notebook to figure out the length of the missing sides. After one minute, discuss your work with your seat partner. Take turns. If needed, modify or make changes to your original thinking.
1. Identify missing dimensions
1A
2. Identify missing dimension
T5
Summarize
To find a missing dimension after breaking up a composite figure:
First, break it into simpler shapes and include the numbers that make sense.
Second, use addition or subtraction to determine the missing sides
Example A: To find the height of the triangle:
Example B: To find the base of the triangle:
Third, verify that you have all the dimensions
T6
Vertical Collaboration
What is the area of the composite figure?
1
1A
2
2A
3
3A
4
4A
T6
Summarize
To calculate the area of a composite figure:
1. Decompose the figure (i.e. break it into simple shapes)
2. Write the dimensions
3. Calculate the areas of each simple shape, and add or subtract them.
T6
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → p721: 1, 2; p723: 11 (Volume 2 Ch9-6)
Do your work in your notebook. Draw the composite figure. Draw the smaller, simple shapes. Include dimensions. Write the formulas and find their areas.
Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T6
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T6
Vertical Collaboration
Shape 1
Area is 81 units squared. Click to see Shape 1 partial solution with shapes decomposed and dimensions:
Shape 2
Area is 229.5 units squared. Click to see Shape 2 partial solution with shapes decomposed and dimensions:
* Next move: "How could you do this a different way and get the same answer?"
T6
Group Notes
Prompt:
Worksheet with questions:
Sample student work and things to remember:
T6
Extend
U3T6 Extend. Pick any ONE of the polygons and find the area. Medium level: 4 and 5. Spicy: 2, 3, and 6. You CHOOSE.
First, neatly sketch the composite figure and its dimensions.
Next, mentally break the shape into simpler 2D figures. Next to the original figure, sketch the simple figures and their dimensions.
Finally, find the area of each simple shape and add or subtract the areas to find the area of the original composite figure.
Check your answer!
If needed, use a calculator to help you crunch the numbers.
T6
Review Examples
Yesterday's group consolidation went really well! Let's take a look at some of the work and comments that were shared:
T6
Critique the reasoning of others
YOU ARE THE TEACHER! Can you find the mistake?
Start by looking for one thing that the group did well.
Then, see if you can find the error or mistake that led them to come up with the wrong solution.
A
Class Info
Unit 3 Test is Tuesday 10/21.
The test will cover everything we studied in the unit and focus mainly on T3 and T6 (the essential standards).
It will be on the computer and on paper
A
Review
For each of the following, click the link to open the worksheet. Do only the assigned problems. Check answers as you work.
In your notebook, sketch each image and write the dimensions. Write the formula, and substitute to find the area. Be neat.
Parallelograms: Do 1-7 (If you're interested, try the spicy ones: 13-15)
Parallelograms Answers
Triangles: Do 1-10 (If you're interested, try the spicy ones: 13-15)
Triangles Answers
Trapezoids: Do 1-7
Trapezoids Answers
* If you need a calculator:
A
Summarize
Click the link below to open the unit's graphic organizer:
Complete each box by adding notes, examples, and annotations (notes that explain what is happening in your examples). Refer to your notes, CYUqs, entry tickets, vertical collaboration, Google Search, etc. Work together. Help each other.
You may use the notes you make on this graphic organizer during the test (nothing else).
A
Review
Click the link to open the worksheet. (There are two pages.) Do all six on the worksheet or in your notebook. For each problem: sketch the image, decompose it, write the dimensions, write the formulas, and substitute.
If you choose to work with a partner, be sure the two of you focus and work together. DON'T divide and conquer. Work on each problem together!
A
Test
Unit 3
A
Test Directions
Take out your Chromebook, something to write with, and your graphic organizer. No phones, smart watches, or other electronic devices.
DO NOT SIGN IN TO YOUR CHROMEBOOK. If you are signed in, sign out. Click the Apps in the bottom left corner > Pear Assessment > Login with Google (sign in with your FCUSD email @student.fcusd.org). Sign in again with @student.fcusd.org and your password > Continue
Click Start Assessment to open the Unit 3 Answer Sheet. Do your work on your test. Type the answers into the Pear Assessment
When finished, put your paper test, graphic organizer, and calculator in the basket in the BACK. You may read (Sora), draw, write, work on an assignment, or rest. Do not talk.
A
Were you absent yesterday?
Please raise your hand to let me know!
A
Goal Setting
Start by opening PowerSchool. On your Goal Sheet, check off each goal that you have a 3 or better in. If you have a score of less than 3, leave the "Got It" blank.
Where it says "Date", that is the date you plan to retake and show me you understand!
At that the bottom of your goal sheet you see the NEXT STEPS for goals that are less than 3. Please follow those steps BEFORE the retake date. Don't show up on the retake date and do your CYUQS in class. Have them ready before class!
A
Watch & Discuss
A
Pass Back Papers
A
Review
After reviewing your tests, I see that EVERYONE has been working hard and doing their best. The time you are spending thinking and working together is paying off. I am proud of YOU.
Please open Pear Assessment. On your paper test, if you got the question correct, make a smiley face. If you got it wrong, put a checkmark.
A
Test Corrections
The most important part of the test happens right now: reviewing your work and learning from mistakes.
1. Find an expert. Compare and contrast your work and their work. Discuss what you notice. Ask questions. Think. Don't copy.
2. On your corrections worksheet, neatly rewrite the problem, show your thinking, and circle the correct answer.
3. Before moving to the next problem, write down your mistake and what you will do to not make that mistake again.