Agenda: 1) Warm Up 2) Launch – Strategies for Explore OBJECTIVE: As a result of this lesson you will be able to find the area of right triangles. 1) Warm Up 2) Launch – Strategies for Explore 3) Explore – Problem Set (Partners & Groups) 4) Summary – Share Solutions & Expand 5) Assessment – Find the Area (1 min) 6 In-Class Notes Each bullet point links to its section of the presentation.

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

Right Triangles Classwork Explore Right Triangles Classwork Part 1 – 2 Minutes Work with your PARTNER to find the area of triangle in #2. 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 What strategy did you use to find the area of the right triangle? Show example 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 Jennifer’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 12-14 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 15-17 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 this strategy? Agenda

Explore - More Part 3 - (10 Min) Finish the worksheet in GROUPS Use Jennifer’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 12-14 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 15-17 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

Summary (Part 1) Agenda See All Solutions To Explore 7 min (35-41) 9) 10) 11) 1) 2) 4) 3) 12) 13) 14) 5) 6) 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

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 -Independent Practice (Find a spot on your paper to do this. #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 -Independent Practice (Find a spot on your paper to do this. #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