Area of Right Triangles

Area of Right Triangles
21st Century Lessons Area of Right Triangles Mrs. Thompson Level 1

Lesson Overview (1 of 3) Lesson Objective Lesson Description
Lesson Objective: SWBAT determine the area of a right triangle by enclosing the triangle in a rectangle and taking half of the area of that rectangle. Student-Friendly Objective: SWBAT determine the area of any right triangle and defend their method. Lesson Description Overview: This is a constructivist lesson that will help students connect their previous knowledge about the Area of Rectangles with the Area of Right Triangles. This lesson assumes that students are comfortable with the idea of Area and can efficiently find the Area of Rectangles. Getting Ready: This activity is meant to stimulate student interest, as well as help students visualize shapes as being able to break down into other shapes. Launch: The launch is a brief introduction to the activity and is meant to give the students a common language to work with during the explore section, and clarify directions. Explore: Broken up into 3 sections, the explore is “chunked” to allow students time to make some connections independently, then communicate with partners, groups, and then the whole class and share their findings. Summary: This is time for students to check their work, share their strategies, and communicate about what they’ve done. In part 2, they will be asked to extend what they did to a less concrete format and do some calculations. Assessment: Students will answer 2 multiple-choice questions using a “body-language” protocol which will give the instructor feedback about individual students’ learning.

Lesson Overview (2 of 3) Lesson Vocabulary Materials Scaffolding
Base – A side of a figure that a height can be drawn from. Height – The distance of a line, perpendicular to the base, measured from the base to the opposite side or vertex. Area – The number of Square Units that cover a closed figure Square Unit – Units used to measure area (in2, cm2, ft2, etc.) “Surrounding Rectangle” – (Informal) A rectangle that can be drawn around a shape as a reference for finding its area. Compose – Combining shapes to construct new ones. Decompose – Breaking shapes apart into familiar pieces. Materials -Projector on Whiteboard -Photocopies of classwork and homework Scaffolding Alternate Worksheet: An additional worksheet has been created with matching problems at the end to replace the drawing problems. This will be helpful for students with motor skill problems as well as struggling learners Enrichment Advanced Objective: SWBAT determine the shaded area of a shape with a “subtracted” section (see problems 12-14). Meeting the Advanced Objective: Have students turn in a written description of their strategies for problems or have them teach their strategy to another group. Online Resources for Absent Students

Lesson Overview (3 of 3) Common Core State Standard Before and After
Geometry 6.G Solve real-world and mathematical problems involving area, surface area, and volume. 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. Before and After Before: Introduction to Concept of Area – PK.MD.MA1 (pre-kindergarten) Composing Shapes – 1.G.2 (first grade) Square units – 3.MD.5 (third grade) Perpendicular and Parallel Lines – 4.G.1 (fourth grade) After: Solving real-life math problems with area, surface area, and volume – 7.G.4 Shape orientation (transformations) – 8.G.4 Solving equations with one variable – 8.EE.7 Topic Background Ancient Egyptian mathematicians have had a significant influence on the development of geometric concepts. Sources such as the Rhind Papyrus and the Moscow Papyrus demonstrate that the Ancient Egyptians knew how to compute areas of several geometric shapes (triangles, rectangles, circles, etc.) and the volumes of cylinders and pyramids – the pyramids being one of the world’s wonders for which they are famous. Greek mathematicians were also fundamental contributors to the development of geometric concepts. Euclid, often referred to as the “Father of Geometry,” produced “Elements,” a series of books that covered various geometry concepts (including area) as well as much of what is now known as algebra, trigonometry, and advanced arithmetic. “The Pythagorean Theorem,” one of the most famous geometric concepts, has been attributed to the Greek philosopher and mathematician Pythagoras. While the Theorem is not directly related to this lesson or unit, a strong understanding of triangles and special quadrilaterals will lay the foundation for later learning.

Warm Up A = b x h A = 25 x 8 height A = 200 ft2 base
OBJECTIVE: SWBAT determine the area of any right triangle and defend their method. 1) What is the Area of the Parallelogram below? A = b x h A = 25 x 8 A = 200 ft2 10 ft 8 ft height base 25 ft Calculate (5 min) 0 – 5 In-Class Notes Purpose/Desired Results: Review previous day & activate some fraction knowledge Make sure students have a working method for these types of fraction problems (Students will need to work with fractions for some of the practice set) *Preparation Notes For the sake of practice, the Parallelogram question picks right up where the students left off the day before; identify the base and height, substitute into the formula, then evaluate. The students can use their notes and classwork from the previous day to complete this section and it should be familiar. The Fraction Problems (I know, I know….the kids are going to complain…), are included because the classwork has a few problems that will require that these skills are readily available for kids to apply. It is also going to be important for them to be comfortable with the idea that multiplying by ½ is essentially the same as dividing by 2 when they need to make the connection from the formula/strategy they derive themselves and the one that inevitably will show up in textbooks and on formula sheets for standardized tests. That will happen explicitly in the next lesson, but the students should see it a few times so they’re comfortable when it comes time to make the connection. (Click for Detailed Solutions) Agenda

Warm Up (Click to Return)
OBJECTIVE: SWBAT determine the area of any right triangle and defend their method. (5 min) 0 – 5 In-Class Notes Purpose/Desired Results: Review previous day & activate some fraction knowledge Make sure students have a working method for these types of fraction problems (Students will need to work with fractions for some of the practice set) *Preparation Notes For the sake of practice, the Parallelogram question picks right up where the students left off the day before; identify the base and height, substitute into the formula, then evaluate. The students can use their notes and classwork from the previous day to complete this section and it should be familiar. The Fraction Problems (I know, I know….the kids are going to complain…), are included because the classwork has a few problems that will require that these skills are readily available for kids to apply. It is also going to be important for them to be comfortable with the idea that multiplying by ½ is essentially the same as dividing by 2 when they need to make the connection from the formula/strategy they derive themselves and the one that inevitably will show up in textbooks and on formula sheets for standardized tests. That will happen explicitly in the next lesson, but the students should see it a few times so they’re comfortable when it comes time to make the connection. (Click to Return) Agenda

Agenda: 1) Warm Up 2) Getting Ready – Geometry Puzzles
OBJECTIVE: SWBAT determine the area of any right triangle and defend their method. 1) Warm Up 2) Getting Ready – Geometry Puzzles 3) Launch – Strategies for Explore 4) Explore – Problem Set (Partners & Groups) 5) Summary – Share Solutions & Expand (1 min) 6 In-Class Notes Each bullet point links to its section of the presentation. 6) Assessment – Find the Area

Getting Ready– Puzzle! 1) How many rectangles can you find? What are their areas? (2 objects = 5 min total!) 7-11 In-Class Notes Logistics: Project images onto a whiteboard, or prepare a copy to project via transparency/document reader Purpose: Activate Interest & Identify composite shapes and shapes within larger ones Solution: There are 36 in total! Preparation Notes (for Getting Ready Section) Have fun with this section! You have an opportunity here to get the students very engaged and excited about the lesson while having some excellent conversations about the fact that shapes can be made from combining other shapes. Make sure you really push that point home, but let the kids see if they can find all of the different rectangles in the first shape and all of the interesting combinations of shapes that can come out of the second one. If needed, there are “Hints” buttons that will direct you to some animations that might help those who are struggling. Also, keep an eye on time and don’t get too carried away. If the kids are still interested by the end, offer the problem(s) as a challenge for homework. Hints Agenda

Getting Ready – Puzzle! Here are a few solutions. Can you find ALL of the rectangles? (2 objects = 5 min total!) 7-11 In-Class Notes Shapes will animate automatically. Help students describe the shapes in terms of dimensions (1x2, 3x3, etc) When you finish: Click “Problem” to return to the blank image or click forward to move to the next slide. Preparation Notes See Slide 5 Problem Agenda

Getting Ready – Puzzle! 2) How many shapes can you find? Name them if you can. (2 objects = 5 min total!) 7-11 In-Class Notes Logistics: Project images onto a whiteboard, or prepare a copy for projecting on an overhead or document reader. Purpose: Activate Interest & Identify composite shapes and shapes within larger ones Solution: If you find all of them, let me know ;-) Preparation Notes The purpose of this is to preview the concept that shapes can be made from other shapes. Hints Agenda

Getting Ready – Puzzle! Click Shape Name for Examples: Triangles
Squares Rectangles Parallelograms Trapezoids (2 objects = 5 min total!) 7-11 In-Class Notes Click the name of each shape to animate some examples. Help students describe the shapes by name (parallelogram link shows a rectangle and a square…good for conversation) When you finish: Click “Problem” to return to the blank image or click forward to move to the launch. Preparation Notes The purpose of this is to preview the concept that shapes can be made from other shapes. Octagon Problem Agenda

Launch This is a right triangle. What is a right triangle?
A right triangle is a triangle that has one 90⁰ angle. What is the area of this right triangle? How do you know? 2 Triangles -5 min!!! (12-16) In-Class Notes *Don’t give out the handout until after this slide (problem 2)!!! First: Have the students name the shape and describe the dimensions (1x1 right triangle) Desired results: Get the kids to see that this triangle is ½ of the square and that the area can be ½ of a square unit. Preparation Notes This section, remember, is to help the students get started on their Exploration. Be careful not to give too much away, but make sure that they all have an access point and can get started on their work. Start by asking questions, rather than telling the students what they need to know. “What type of triangle is it? How do you know?” “What shape is this surrounding the triangle?” “If the area of the Square is 1 cm2 (grid paper), what is the area of the triangle?” etc. It will be helpful if you can project this slide onto a whiteboard and highlight the Square with a marker, but if that isn’t possible, use a document reader or an overhead projector with a pre-prepared transparency. On the next slide, the same process should happen, but make sure you are explicit about how students should be showing their work. Model drawing a rectangle to surround the triangle (call it the “Surrounding Rectangle”), show the area of the surrounding rectangle, and the area of the triangle labeled with the correct unit (cm2). It is not necessary to show calculations for those areas at this point, as you want to allow for some students to simply count rather than relying on a formula, though it is likely that you will want to later in the lesson. How can you show your work/prove your answer? = 1 square unit Agenda

Launch What is the area of the shaded region? How do you know?
How can you show your work/prove your answer? 2 Triangles -5 min!!! (12-16) In-Class Notes *Give out the handout before talking about this slide. First: Have the students name the shape and describe the dimensions (right triangle, base 2 & height 1) Desired results: Get the kids set up with at least 1 strategy they can work with for the explore (likely triangle as ½ of a rectangle) and a way to show their work visually on the worksheet you’ve provided. Preparation Notes Slide 9 Agenda

Explore Part 1 - (5 Min) 1-Partners
Work with your PARTNER to find the area of triangles. Make sure you can show or explain your strategy! 1-Partners 2-Strategy Check 3-Groups Online timer link on slide - 5 min (17-21) In-Class Notes Focus on strategies and help struggling pairs find one that works (Strategies Below) Look for groups/pairs that are decomposing (breaking shapes into pieces and rearranging) too! Preparation Notes During the first part of the explore, your main focus should simply be to make sure that all students a) interpreted the directions accurately b) are engaged in their task and c) have some sort of working strategy that they can use to complete the assignment. Be supportive and ask guiding questions when students get stuck (i.e. “How is this problem different than the last one you did?”, “Can you explain to me your process so far?...what’s your strategy?”) If students seem to have the hang of the “surrounding rectangle” strategy and are working quickly, you might consider asking them to try and see if they can come up with another method (though the rectangle method is likely to be the dominant one), and possibly guide them to the idea of breaking the triangles into pieces that can be “reassembled” into more easily counted square units. Agenda

Explore – Check In Part 2 - (5 Min)
What strategies are you using to find the areas of the right triangles? Show examples and explain your reasoning! 1-Partners 2-Strategy Check 3-Groups Online timer link on slide - 3 min (22-24) In-Class Notes Use calling sticks or strategically choose pairs. Make sure ALL students have an effective strategy at this time Navigation: There is a link at the bottom; “To Summary”. This will skip you ahead a few slides to give you access to pictures of each problem, should you want to project them and have students share their thinking publicly. Preparation Notes At this point, hopefully all students have a working strategy to complete the assignment. The purpose of the check-in, then, is to catch up any stragglers, but also to get the students to begin articulating their thinking. Remember, the end-goal of the lesson is to have student decide on a method for finding the area of a right triangle and defend their method. This is really where they begin the “defense of method” piece. Most students will do much better at the end of class, having had a few chances to explain their thinking as they work through the details. To Summary Agenda

Explore – Understanding the Strategy
Angela’s Strategy Draw a “surrounding rectangle” Determine the area of the rectangle The area of the triangle is half the area of the rectangle! Online timer link on slide -10 min (25-34) In-Class Notes Look for students that use interesting/unique strategies and ask them to present for the summary. To meet the objective, students should complete (at least) page 1 of the classwork accurately and be able to defend their strategy. Meeting the Advanced Objective: Have students turn in a written description of their strategies for problems or have them teach their strategy to another group. Preparation Notes This last part of the explore lasts a little longer than the previous ones so the students really have a chance to play around with the shapes. Some of the triangles and composite shapes on page 2 of the worksheet may be tricky for them, so this part of the explore should be done in GROUPS rather than partners, though if you find that students are working well in pairs you may not need to allow them the extra interaction if you prefer. As a support, there is a Strategy button on the bottom that will display a list of the 3 steps for the “surrounding rectangle” strategy. Again, this may not be necessary but it is available if you need. Also, there is a modified worksheet where problems are matching rather than draw-your-own for students that have motor skill issues or are simply struggling with the more challenging problems. This allows them a different perspective on the problem in order to expand the students’ thinking, but is not as challenging and will allow more students access. Do you understand Angela’s strategy? Agenda

Explore - More Part 3 - (10 Min) Finish the worksheet in GROUPS
Use Angela’s Strategy to find the area of the remaining triangles on the worksheet. 1-Partners 2-Strategy Check 3-Groups Online timer link on slide -10 min (25-34) In-Class Notes Look for students that use interesting/unique strategies and ask them to present for the summary. To meet the objective, students should complete (at least) page 1 of the classwork accurately and be able to defend their strategy. Meeting the Advanced Objective: Have students turn in a written description of their strategies for problems or have them teach their strategy to another group. Preparation Notes This last part of the explore lasts a little longer than the previous ones so the students really have a chance to play around with the shapes. Some of the triangles and composite shapes on page 2 of the worksheet may be tricky for them, so this part of the explore should be done in GROUPS rather than partners, though if you find that students are working well in pairs you may not need to allow them the extra interaction if you prefer. As a support, there is a Strategy button on the bottom that will display a list of the 3 steps for the “surrounding rectangle” strategy. Again, this may not be necessary but it is available if you need. Also, there is a modified worksheet where problems are matching rather than draw-your-own for students that have motor skill issues or are simply struggling with the more challenging problems. This allows them a different perspective on the problem in order to expand the students’ thinking, but is not as challenging and will allow more students access. Agenda

Create your own: Click here
Summary (Part 1) 9) 10) 11) 1) 2) 4) 3) 12) 13) 14) 5) 6) Create your own: Click here 7) 7 min (35-41) In-Class Notes See All Solutions FIRST – Displays all answers with no images Then, Have students show their solutions and ask questions - Click each shape to zoom in and see individual answers To Explore – Links back to Part 2 of the Explore section (for use during check-in) Preparation Notes The most important thing to keep in mind when you get to this section is that, in order to meet the objective, the students need to be able to describe and defend their strategies. As you discuss their work, make sure you are demanding that students articulate their strategies clearly and thoroughly. It is difficult to anticipate which students will choose to work with the “standard” strategy and which ones will come up with a more unique one, but as long as their ideas have mathematical integrity be sure to acknowledge their strength. DO NOT try to go through every problem. That would take up far too much time and would likely not be productive. We would recommend you, first, click “See All Solutions” and display all of the answers for students to check their work. Afterwards, allow students to ask questions about the problems they struggled with. Plan on doing 3 or 4 of them at the most. If students don’t seem to be struggling and have gotten most of the answers correct, this would be a good opportunity to have some of them showcase interesting strategies to facilitate a deeper discussion than just “right or wrong?”. 8) See All Solutions To Explore Agenda

½ cm2 The area is: Classwork Solution #1 Summary
Summary Part 1: 7 min (35-41) In-Class Notes Use this page to display problems for discussions Click “Summary” to return to the Main Summary Page Summary

1 cm2 The area is: Classwork Solution #2 Summary

1 ½ cm2 The area is: Classwork Solution #5 Summary

7 ½ cm2 The area is: Classwork Solution #7 Summary

2 cm2 The area is: Classwork Solution #9 Solution Summary
Summary Part 1: 7 min (35-41) In-Class Notes Use this page to display problems for discussions Click “Summary” to return to the Main Summary Page Solution Summary

Summary Part 1: 7 min (35-41) In-Class Notes Use this page to display problems for discussions Click “Summary” to return to the Main Summary Page Solution Summary

Summary Part 1: 7 min (35-41) In-Class Notes Use this page to display problems for discussions Click “Summary” to return to the Main Summary Page *Subtracted Section Problem: Students can find the area of the “larger triangle” and subtract the area of the triangles in the middle. Solution Summary

Summary Part 1: 7 min (35-41) In-Class Notes Use this page to display problems for discussions Click “Summary” to return to the Main Summary Page *The students might point out that this is a parallelogram and use A=bh…this is a good thing! They remember the lesson from yesterday! Solution Summary

Summary Part 1: 7 min (35-41) In-Class Notes Use this page to display problems for discussions Click “Summary” to return to the Main Summary Page *Subtracted Section Problem: Students can find the area of the “larger triangle” and subtract the area of the triangles in the middle. Solution Summary

6 ½ cm2 The area is: Classwork Solution #13 Solution Summary
Summary Part 1: 7 min (35-41) In-Class Notes Use this page to display problems for discussions Click “Summary” to return to the Main Summary Page *Subtracted Section Problem: Students can find the area of the “larger triangle” and subtract the area of the triangles in the middle. Also note, the base of the triangle is 1 ½ cm. This is the reason for including problem #4 in the warm-up! Solution Summary

Classwork Solutions- Create Your Own
Summary Part 1: 7 min (35-41) In-Class Notes Use this page for students to display triangles that they create (Problems 15-17). Click “Summary” to return to the Main Summary Page Summary

½ cm2 1 cm2 2 cm2 1 ½ cm2 6 cm2 7 ½ cm2 5 cm2 2 cm2 4 cm2 3 cm2 3 cm2
Classwork Solutions ½ cm2 1 cm2 2 cm2 1 ½ cm2 6 cm2 7 ½ cm2 5 cm2 2 cm2 4 cm2 3 cm2 Summary Part 1: 7 min (35-41) In-Class Notes Click “Summary” to return to the Main Summary Page Click forward to move on to the next part of the summary 3 cm2 6 ½ cm2 5 cm2 Summary

Summary (Part 2) Explain the Strategy Turn and Talk: Common Language:
Lefty, tell Righty the strategy for finding the area of ANY right triangle. Righty, tell Lefty the strategy. Common Language: Can you explain the strategy we learned that will work for finding the area of ANY right triangle? Why does this strategy work? 3 min (42-44) In-Class Notes Make sure each student can verbalize their strategy. Do This: Write strategy on chart paper for display, and/or add to students’ notes *Lead students to a shared class strategy of “Compose a Surrounding Rectangle, Find its area, cut in half/divide by 2 (to make sense of the formula!) Preparation Notes Again, the objective of the lesson includes a requirement that students are able to defend their method for finding the area of a triangle, so it is important that students are able to articulate their strategies as a first step. By now, the students have had enough experience with the shapes and they should feel confident that the “compose a surrounding rectangle” strategy works for all of the right triangles. The essential piece of the lesson that happens here is the construction of common language that the students can use to connect their experience to the more abstract work they will do later. Agenda

Summary (Part 2) Expand your Thinking
Does this strategy work when there are no grid lines? 1 min (45) In-Class Notes Do This: Have students share their thoughts aloud. Have them try it on the next slide. Preparation Notes Up to this point, the students have only worked with right triangles on gridlines, but they will eventually be asked to work with triangles in less sterile configurations and possibly draw their own. The next few slides, to be presented with respect to the Interleaving method, simply ask students to draw triangles, given certain dimensions, and construct the “surrounding rectangle” in order to connect this new step to the strategy they have been employing already. Getting to this slide and the next part of the summary is key for the exit ticket. If students are not struggling with this part, it would be worth spending some focus on the last step (area of the rectangle divided by 2 and connect that idea to multiplying by ½ as the formulas they are likely to see in the future will probably be written in the A=½bh format. There is an adorable eraser with eyeballs on the next few slides that will offer a thought that will segue nicely into that conversation, should the students in front of you be ready to make the leap. Agenda

Area of “Rectangle”: 5 ft x 10 ft = 50 ft2 Area of Triangle
Summary (Part 2) Try It (As a Class): Draw and label a triangle with a base of 5 ft and a height of 10 ft. Then find the area. Area of “Rectangle”: 5 ft x 10 ft = 50 ft2 Area of Triangle 50 ft2 ÷ 2 = 25 ft2 10 ft (2 min) (46-47) In-Class Notes Interleaving: Do this problem AS A CLASS & have students copy examples on lined paper. The strategy being illustrated is “Compose a Surrounding Rectangle….” Extension: If your students are confident, connect the idea of multiplying by ½ instead of dividing by 2 (for the formula) Preparation Notes Slide 32 Oh yeah… Half of 50 is 25! 5 ft Hmmm… Agenda

Summary (Part 2) Independent Practice
#1) Draw and label a triangle with a base of 8 in and a height of 3 in. Then find the area. Area of “Rectangle”: 8 in x 3 in = 24 in2 Area of Triangle 24 in2 ÷ 2 = 12 in2 3 in 4 min (48-51) In-Class Notes Interleaving: Have students do this problem INDEPENDENTLY on lined paper (below previous example) The strategy being illustrated is “Compose a Surrounding Rectangle….” Extension: If your students are confident, connect the idea of multiplying by ½ instead of dividing by 2 (for the formula) Preparation Notes Slide 32 8 in Oh yeah… Half of 24 is 12! Hmmm… Agenda

Summary (Part 2) Independent Practice
#2) 8 ft 5 ft Rectangle area = ______ Triangle area = ______ #3) 12 m 4 m Triangle area = _______ Rectangle area = ______ 40 ft2 48 m2 (2 min) 52 – 54 In-Class Notes Interleaving: Students do these problems independently, mentally, and rather quickly. The purpose is to help students become more confident on using the strategy without formally using a formula. Extension: If your students are confident, connect the idea of multiplying by ½ instead of dividing by 2 (for the formula) 20 ft2 24 m2 Agenda

Exit Ticket 4 cm What is the area of the “Surrounding Rectangle” for this Right Triangle? 9 cm 13 cm2 18 cm2 36 cm2 d) 25 cm2 2 min (54-56) In-Class Notes Students can do this in their notes and give you hand signals OR you can print out the Exit Ticket Have students do calculations on lined paper (below previous example) Hand signal assessment: Make a note of the students and misconceptions. Preparation Notes Have students use the body language shown to express their answers. Make a note of how many students choose each answer and which students have misconceptions. For example, if they choose letter a), they likely just added the numbers and don’t recognize that they should multiply 9 and 4 to find the area. If they choose letter (b), the correct answer, they multiplied the base times the height and didn’t divide by two. At the same time students could be giving answer (c), jumping ahead anticipating the question on the area of the triangle, or they could be giving that answer incorrectly for another reason. Agenda

Exit Ticket 4 cm What is the area of the Triangle? 9 cm 4 ½ cm2 18 cm2
d) 11 cm2 2 min (56-58) In-Class Notes Students can do this in their notes and give you hand signals OR you can print out the Exit Ticket Have students do calculations on lined paper (below previous example) Hand signal assessment: Make a note of the students and misconceptions. Preparation Notes Slide 37 Agenda

1st Time Users of 21st Century Lessons
Description of 21st Century Lessons: Welcome to 21st Century Lessons! We are a non-profit organization that is funded through an AFT (American Federation of Teachers) Innovation Grant. Our mission is to increase student achievement by providing teachers with free world-class lessons that can be taught via an LCD projector and a computer. 21st Century Lessons are extremely comprehensive; we include everything from warm–ups and assessments, to scaffolding for English language learners and special education students. The lessons are designed into coherent units that are completely aligned with the Common Core State Standards, and utilize research-based best practices to help you improve your students’ math abilities. Additionally, all of our lessons are completely modifiable so you can adapt them if you like. Next Slide Back to Overview

Standards for This Unit The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: *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. Note: The state of Massachusetts amended 6.G.1 to include the area and circumference of circles, since we are a Massachusetts based organization we included these topics in our unit. Next Slide Back to Overview

Requirements to teach 21st Century Lessons: In order to properly use 21st Century Lessons you will need to possess or arrange the following things: Required: PowerPoint for P.C. (any version should work) Note: Certain capabilities in the PowerPoint Lessons are not compatible with PowerPoint for Mac, leading to some loss of functionality for Mac PowerPoint users. An LCD projector Pre-arranged student groups of 2 – (Many lessons utilize student pairings. Pairs should be seated close by and be ready to work together at a moment’s notice. Also, depending on which side of the class they are sitting on, one partner should be identified as “Lefty” and one as “Righty.”) Scissors – at least 1 for every pair Next Slide Back to Overview

Strongly Suggested to teach 21st Century Lessons: Computer speakers that can amplify sound throughout the entire class “Calling Sticks” – a class set of popsicle sticks with each student’s name on one A remote control or wireless presenter tool– to be able to advance the PowerPoint slides from anywhere in your classroom Personalize PowerPoints by substituting any names and pictures of children we included in the PowerPoint with names and pictures of your own students. Since many lessons utilize short, partner-processing activities, you will want a pre- established technique for efficiently getting your students attention. (“hands- up”, Count from “5” to “0” etc.) Have students reinforce the key questions of the unit by creating, studying, and quizzing each other using flashcards. This practice is further outlined below. (Research is clear that the active recall of concepts, definitions, etc. helps students improve their memory. See “Recommendation 5” in ies.ed.gov/ncee/wwc/pdf/practiceguides/ pdf ) Project onto a whiteboard so you or your students can solve problems by hand. (Lessons often have a digital option for showing how to solve a problem, but you may feel it is more effective to show the work by hand on a whiteboard.) Internet connectivity – without the internet you may not have full functionality for some lessons. Next Slide Back to Overview

Lesson Preparation (Slide 1 of 2) We suggest spending minutes reviewing a lesson before teaching it. In order to review the lesson run the PowerPoint in “Slideshow “- Presenters View and advance to the “Lesson Overview” slide. By clicking on the various tabs this slide will provide you with a lot of valuable information. (The table below gives a brief explanation of each tab.) It is not necessary to read through each tab in order to teach the lesson, but we encourage you to figure out which tabs are most useful for you. Note: All of our lessons are designed to be taught during a 60-minute class, we allow for 5 minutes of transitions/non-productive time so the lesson notes consider that you have only 55 minutes. If your class is shorter than 60 minutes you will have to decide which sections to condense or remove. If your class is longer we suggest incorporating some of the “challenge” questions into your lesson as well as allowing time for your students to quiz each other using flashcards. Next Slide Back to Overview

Lesson Preparation (Slide 2 of 2) After reviewing the overview slide, click your way through the PowerPoint. As you go, make sure to read the presenter note section beneath each slide. The note section is divided into two sections: “In-Class Notes” and “Preparation Notes.” The In-Class Notes are designed to be concise, bulleted information that you can use “on the fly” as you teach the lesson. Included in In-Class Notes are: a) a suggested time frame for a 55 minute lesson, so you can determine whether you want to speed up, slow down, or skip an activity, b) key questions and points that you may want to bring up with your students to get at the heart of the math, and c) answers to any questions being presented on the slide. The Preparation Notes use a narrative form to explain how we envision the activity shown on the slide to be delivered as well as the rationale for the activity and any insight that we may have. Next Slide Back to Overview

Features built into each PowerPoint lesson There are several features which have been incorporated into our PowerPoint lessons to help make lessons run more smoothly as well as to give you access to additional resources during the lesson should you want them. These features include: Wait Signal/Stars – These symbols at the bottom right of each slide indicate when the teacher should wait for an animation (“wait”), click for the next animation (“yellow star”), or click to advance to the next slide (“green star”). Agenda Shortcuts – On the agenda slide, click on any section title and you will advance to that section. Action Buttons – On certain slides words will appear on the chalk or erasers at the bottom of the chalkboard. These action buttons give you access to optional resources while you teach. The most common action buttons are: Scaffolding – gives on-screen hints or help for that slide Answers – reveals answers to questions on that slide Challenge – brings up a challenge questions for students Agenda – will return you to the agenda at the beginning of the lesson Next Slide Back to Overview

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