Middle Measurement and Geometry MASSI
MASSI: Math Activities with Scripted Systematic Instruction
Activity: Preparing Posters for Spirit Club
==Grade Band: Grades 6-8==
==Concept: Measurement/Geometry==
Common Core State Standard | Core Content Connectors | MASSI OBJECTIVES |
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. | 6th 6.GM.1d1 Find area of quadrilaterals | Using formula to calculate area of rectangles |
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. | 7th 7.GM.1h2: Find the surface area of three-dimensional figures using nets of rectangles or triangles | Using nets and formula to calculate surface area of rectangles |
8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | 8th 8.ME.1e1 Describe the changes in surface area, area, and volume when the figure is changed in some way (e.g., scale drawings) | Using formula to calculate changes in area |
Be sure to provide specific practice to students on the skills that correspond to their grade level.
Combined materials provided: finished examples of posters decorated for local team, paint (may want to sabotage by labeling something like "recommended for an area of _____"), stickers, markers, glue, pictures of school/local team's mascot and players, tiling squares
Teacher materials: Multiple sizes of poster board, calculator, measuring tape/yardstick, box, printed nets (see materials), laminated equation for area and surface area. Note: Although this lesson has a lot of steps, a large majority of the steps break down the calculations into discrete steps.
Student materials (need one set for each student): Scientific or graphing calculators; multiple sizes of poster board (pre-labeled with length and width); worksheets 2, 3, 4; smaller pictures of favorite team's players/mascots (e.g., 3"x 5", 4"x 6"); boxes (pre-labeled with height, width, and length); printed nets Worksheets: There are student worksheets to review each component of the lesson. Assessments: Progress Monitoring for taking data during the lesson; Skills Test 'TEACHING OVERVIEW:' The first section of the MASSI provides remedial practice on the concepts of perimeter, area, length, width, surface area, height, and tiling to find area. Then, the 6th grade aligned component, calculating area, is introduced. This is a good review for your 7th and 8th graders. Next, the 7th grade aligned component, calculating surface area, is introduced. This is useful for your 6th and 8th graders to gain fluency with equations. Lastly, the 8th grade aligned component is calculating changes in area. While the 8th graders work on calculating changes, 6th and 7th graders can also work on this skill or you can let the 6th and 7th graders practice calculating area and surface area.
SCRIPT FOR LESSON |
BUILD THE ESSENTIAL UNDERSTANDING: CONCEPT AND SYMBOLS: Perimeter, Area, Length, Width, Surface Area, Height, and Tiling to Find Area (Skip this section for students who understand these relationships and can identify these concepts). |
INTRODUCE ACTIVITY: Today we are going to learn about how to be good spirit club members. We are going to be in a spirit club to cheer for and support the (insert school team name or local sports team). We are going to make posters to hold up to support our team. In order to make the posters correctly, we must first learn about area and surface area. Show students an already completed/decorated poster. This is my spirit poster. See how I painted it, and then I decorated it with buttons, pictures, and markers. Before we get started decorating our posters, we need to review some vocabulary. _____________________________________________________________________________________________________________________ INTRODUCE THE PROBLEM: We need to know what the words "perimeter," "area," "length," "width," "height," and "surface area" mean. MODEL THE PROCESS: Hold up your poster. Use your finger to trace the outside edge of the poster. The perimeter is the edge that goes along the outside of the poster. Show me the perimeter of this poster. Wait for students to point or eye gaze towards the perimeter of your poster. Correct? Praise: Good. No response? Guide student to make the response. File:Insert Picture here.jpgSTUDENT PRACTICE: Give each student a blank poster board. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. CHECK AND SCORE Step Teacher Says/Does Student Response
INTRODUCE THE PROBLEM: We need to know the size of the poster so that we can get enough paint to cover it in paint. One way that we can find out the area of a small surface is to use one-inch tiling squares to cover the area of it. It would take too many tiling squares to cover our poster, so let's practice with some sports pictures first. We can add these to our poster to decorate it. MODEL THE PROCESS: Look at this picture of the (sports team). This is a tiling square. Hold up the tiling square for the students to see. Now, I will line up the tiling squares to cover the area of the picture, watch me. Teacher covers the top of his/her picture with the tiling squares while the students watch. Then, we just count how many tiles we used. Let's count together, 1, 2, 3… Teacher should point to each of the tiles as the students count aloud. File:Insert Picture here.jpgSTUDENT PRACTICE. Each student should have a photo and more than enough tiling squares to cover the picture (don't give the exact amount; give more than needed so students have to stop at the appropriate number). Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed. \*\*Note: When students are counting: If the student is nonverbal, counting may be done using an assistive technology device or with a response board (containing the numbers 1-10 or higher when appropriate). The student should "count" by pointing to the tile, then pointing to the corresponding number. For example, the student points to the first tile and points to the number one, then points to the second tile and points to the number two, etc. Student may also tap as teacher counts or move hands/AT scanner from number to number as teacher counts. Look for an action that the student can perform independently and encourage this action as the tiles are counted. Some examples are: a tap, a head nod, blink, leg movement, finger movement. CHECK AND SCORE Step Teacher Says/Does Student Response
Measurement/ Geometry Skill Test Teacher Says/Does Student Response Error Correction
NOW
6th BUILD A GRADE ALIGNED COMPONENT: Calculating area, 7th & 8th SYMBOL USE: Calculating area INTRODUCE THE PROBLEM: Now, you will show students how to calculate the area using a formula. Give the students a piece of poster board that they will decorate. The poster should have the length and width written on it (see materials for an example). There is an easier way to calculate the area of a rectangle than using tiling squares. This is especially helpful when we need to know the area of a large space, like a poster. Instead of counting all these tiles, we can use a formula. The formula is area equals length times width. Show them the equation for area or write it on the board and point to each part as you read it. MODEL THE PROCESS: We need to calculate the area of this poster board to get enough paint to cover it. I am going to use a yardstick (or measuring tape) to measure the length of my poster. Use a yardstick/measuring tape and show how to measure the length of your poster board. The length is ____, so I'll write it in my equation. Now I will use the yardstick (or measuring tape) to measure the width of my poster board. Use a yardstick/measuring tape and show how to measure the width of the poster board. The width is ____, so I'll write that in my equation. Now I will use a calculator to calculate the area. Remember, area equals length times width. First I type in the length, (say number), then push the times button, then I type in the width, (say number), and push the equals button. Look, the area of my poster is _____ square inches. Note: Always say unit of measurement with numerical value. File:Insert Picture here.jpgSTUDENT PRACTICE: Give each student Worksheet 2 and have them use the front page with formula template. Look at your poster board. The length and width are already written on it. All you need to do is calculate the area using a calculator and the formula for area. Use a talking calculator for students with visual impairments. Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed. \*\*Note: Have the students write the numbers into the formula on the worksheet, but do not score writing ability. If students are unable to write the number, they can use number stamps or direct the teacher to write it for them. CHECK AND SCORE Step Teacher Says/Does Student Response
CHECK AND SCORE Step Teacher Says/Does Student Response
INDEPENDENT PRACTICE: Measurement/ Geometry Skill Test Teacher Says/Does Student Response Error Correction
NOW
|
7th BUILD A GRADE ALIGNED COMPONENT: Calculating surface area
INTRODUCE PROBLEM: Now that we've made some posters, we need to put them in a box to take them to the pep rally. We need to decorate our box to match our posters. First, we need to find the surface area of the box so that we know how much paint we need to cover our box. Remember that surface area is the space inside the net, or what the box looks like if you flatten it (show the model of the net). Just like we learned for area, we can find the surface area by using tiling squares or by using a formula. MODEL THE PROBLEM: Use the nets on pg. 34-36. I will show you how to find the surface area of this net using tiling squares. I will line up the tiling squares to cover the area of the net. Watch me. Teacher covers the top of his/her net with the tiling squares while the students watch. Then, we just count how many tiles we used. Let's count together, 1, 2, 3… Teacher should point to each of the tiles as the students count aloud. The surface area of my net is ___ square units or units squared. File:Insert Picture here.jpgSTUDENT PRACTICE: It would take too many tiling squares to cover our boxes, so let's practice with some nets. Give each student a net and more than enough tiling squares to cover the net (don't give the exact amount; give more than enough so students have to stop at the appropriate number). Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed. \*\*Note: When students are counting: If the student is nonverbal, counting may be done using an assistive technology device or with a response board (containing the numbers 1-10 or higher when appropriate). The student should "count" by pointing to the tile, then pointing to the corresponding number. For example, the student points to the first tile and points to the number one, then points to the second tile and points to the number two, etc. Student may also tap as teacher counts or move hands/AT scanner from number to number as teacher counts. Look for an action that the student can perform independently and encourage this action as the tiles are counted. Some examples are: a tap, a head nod, blink, leg movement, finger movement. CHECK AND SCORE STEP Teacher Says/Does Student Response
CHECK AND SCORE Steps Teacher Says/Does Student Response
File:Insert Picture here.jpg This may be a good stopping point. Let students use the art supplies to make spirit posters and boxes for their team. There is a generalization worksheet with this level. You can use this for additional guided practice or to send home as homework. INDEPENDENT PRACTICE: Measurement/ Geometry Skill Test Teacher Says/Does Student Response Error Correction
NOW
8th BUILD A GRADE ALIGNED COMPONENT: Calculating changes in area File:Insert Picture here.jpgSTUDENT PRACTICE: Give each student worksheet 4. This particular step (calculating area) was taught in the 6th grade level portion of the MASSI. If students are unable to complete this step, go back and re-teach the 6th grade portion. Ok, we've made a few posters for our pep rally, but let's make one more poster. Let's calculate the area of this poster board so we can make sure we get enough paint. Give students each a piece of poster board that is intentionally very small. Make sure the length and width are labeled on the poster board. Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed. \*\*Note: Have the students write the numbers into the formula on the worksheet, but do not score writing ability. If students are unable to write the number, they can use number stamps, Velcro numbers, or direct the teacher to write it for them. CHECK AND SCORE Steps Teacher Says/Does Student Response
CHECK AND SCORE Steps Teacher Says/Does Student Response
MODEL THE PROBLEM: We need to calculate difference in area of the smaller piece from the larger piece. Watch me calculate the difference in area. This poster board is larger (point to bigger poster board). The area of the larger poster board is ____, so I will write it on the "larger area" line. This poster board is smaller (point to smaller poster board). The area of the smaller poster board is ____, so I'll write it on the "smaller area" line. Now I will use a calculator to find the difference in area. Say each button aloud as you push it and point/have students follow along in the equation. Look, the difference in the area of the poster boards is _____ square inches. File:Insert Picture here.jpgSTUDENT PRACTICE: Now it's your turn. You need to calculate the difference in the areas so that we know how much more paint we'll need. Use LEAST INTRUSIVE PROMPTS script to help student with each step as needed. CHECK AND SCORE Steps Teacher Says/Does Student Response
|
MASSI CULMINATING ACTIVITY: Have a pep rally day. Have students wear the school/team colors. Let students find pictures of their favorite teams and players to use. Practice having them find the area of their posters and decorate. If possible, incorporate general education peers who play on sports teams.
BUILD TOWARDS FULL GRADE LEVEL COMPETENCE Here are ideas to build competence towards the full grade level competence using this same activity. See the unit plan and talk with the general education teacher for more ideas.
Component | Activity | What Student Does | 'Generalization/ Fluency' |
Measuring in feet and inches | Practice using yardstick or measuring tape to measure distances, and converting to feet and inches (e.g., 28 inches = 2 feet, 4 inches). | Uses yardstick or measuring tape to measure objects or distances. Makes conversion. | Vary the objects/distances you have students measure. Try different yardsticks or measuring tapes. |
Calculating area of irregular shapes (e.g., trapezoid) on grid paper by dividing them into regular shapes and adding areas together. | Give students graphing paper with irregular shapes drawn on them and have them divide shape into regular shapes, find areas, and add together (e.g., rhombus = rectangle and triangle). | Student divides irregular shape into two or more regular shapes, then calculates area for each shape using formulas, and then adds together to find area of irregular shape. | Use a variety of irregular shapes. |
Calculate area when given dimensions, but not told the formula. | Give students the dimensions to a rectangle and ask them to calculate the area. Incorporate word problems to provide context. | Student multiplies length times width to find area without visual prompts or formula provided. | Use a variety of different size rectangles and word problems. |
Find area of triangles and circles | Give students formula for area of a triangle (area = ½ length x width) or a circle (area = πr2; π=3.14) and ask them to calculate area. | Student uses formula to calculate area of triangle or circle. | Use a variety of different size triangles. |
Volume | Give students the dimensions to a rectangular prism or cube and ask them to calculate the volume. Incorporate word problems to provide context. | Student uses formula to calculate volume of a box/cube. | Use a variety of different size boxes and cubes. |
Changes in Surface Area and Volume | Teach students to calculate changes in surface area and volume. | Student uses formula to calculate changes in surface area and volume. | Use a variety of different sizes of rectangular prisms and cubes. |