High Measurement and Geometry MASSI
MASSI: Math Activities with Scripted Systematic Instruction
Activity: Preparing a Picture to Give as a Gift
Grade Band: High School Concept: Measurement/Geometry |
Common Core State Standard | Core Content Connectors | MASSI OBJECTIVES |
HSA-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | HS H.ME.1b2 Solve a linear equation to find a missing attribute given the area, surface area, or volume and the other attribute | * Calculate to find a missing attribute when given area
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Be sure to provide specific practice to students on the skills that correspond to their grade level.
Combined materials provided: finished examples of pictures in frames, picture frames of multiple sizes, boxes of multiple sizes
Teacher materials: pictures, ruler, calculator, laminated equation for area and volume
Student materials (need one set for each student): Calculators, pictures (pre-labeled with length and width), pictures (pre-labeled with length and area, but NOT width), box (pre-labeled with length, width, and height), box (pre-labeled with length, height, and volume, but NOT width) 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, height, and volume. Then, the calculating area and volume is introduced as a prerequisite to the grade aligned component. If your students can already calculate area and volume, it is ok to move to the next section of the MASSI. The HS grade aligned component is then introduced, calculating to find a missing attribute given area and volume.
SCRIPT FOR LESSON |
BUILD ESSENTIAL UNDERSTANDING: CONCEPT AND SYMBOLS: Perimeter, Area, Length, Width, Height, and Volume (Skip this section for students who understand these relationships and can identify these concepts). |
INTRODUCE ACTIVITY: Today we are going to learn about packing up a picture as a present for (insert friend/family name here). Look, here's a picture that I want to send as a present to (insert name of friend/relative/etc.). Show students a picture in a picture frame. First, let's all get our pictures that we want to send as a gift. Parents can send in pictures/digital pictures, students can use their school photos, or if those are unavailable, students can print a favorite picture from the internet or clip from a magazine. Make sure each student has a picture. Pictures should be sized in appropriate sizes to fit in common picture frames (4x6) (5x7) (8.5x11). We also need a box to send our pictures. Give each student a box that could be used to ship the picture. ______________________________________________________________________________________________________________________ INTRODUCE THE PROBLEM: Before we get started finding out what size picture frame we need, we need to review some vocabulary. MODEL THE PROCESS: Hold up your photo and use your finger to trace the outside edge. The perimeter is the edge that goes along the outside of the photo. Show me the perimeter of this photo. Wait for students to point or eye gaze towards the perimeter of your photo. Correct? Praise: Good. No response? Guide student to make the response. \[\[File:Insert Picture here.jpg\]\]STUDENT PRACTICE: Give each student their own photo. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. CHECK AND SCORE Step Teacher Says/Does Student Response Now let's practice with your photo. Show me the perimeter of your photo. Student uses finger to trace the outside edges of the photo.
Now let's practice with your photo. Show me the area of your photo. Student uses hand to indicate the area of the photo.
Now let's practice with your photo. Show me the length of your photo. Student uses finger to point to the length of their photo.
Now let's practice with your photo. Show me the width of your photo. Student uses finger to point to the width of their photo.
Now let's practice with the boxes you have. Show me the volume of the box. Student uses hand to indicate the volume of the box.
Step Teacher Says/Does Student Response Now let's practice with the boxes you have. Show me the length of the box. Student uses finger to point to the length of the box.
Now let's practice with the boxes you have. Show me the width of the box. Student uses finger to point to the width of the box.
Now let's practice with the boxes you have. Show me the height of the box. Student uses finger to point to the height of the box.
CHECK AND SCORE Step Teacher Says/Does Student Response Show me the perimeter of the _____. Student uses finger to trace the outside edges of the item. Show me the area of the _____. Student uses hand to indicate the area of the item. Show me the length of the _____. Student uses finger to point to the length of their item. Show me the width of the _____. Student uses finger to point to the width of their item. Show me the length of the __(3D object). Student uses finger to point to the length of their item. Show me the width of the __(3D object). Student uses finger to point to the width of their item. Show me the height of the __(3D object). Student uses finger to point to the height of their item. Show me the volume of the __(3D object). Student uses hand to indicate the volume of the item.
\[\[File:Insert Picture here.jpg\]\] This may be a good stopping point. Let students use art supplies to decorate frames/pictures with stickers, ribbon, paint, etc. There is a generalization worksheet with this level. You can use this for additional guided practice or to send home as homework. Measurement/ Geometry Skill Test Teacher Says/Does Student Response Error Correction Give each student the Measurement/ Geometry Skills Test 1: Concepts and Symbols. Read directions for each problem and have student select response. Record whether response is correct or incorrect. Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing. Once the student has completed the test, review missed problems with the student. NOW
INTRODUCE THE PROBLEM (AREA): Now, you will show students how to calculate the area using a formula. Give each student a photo to determine the area. The poster should have the length and width written on it (see materials for an example). We are going to learn how to find the area of a rectangle, like our photo. The formula for area 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. MODEL THE PROCESS: We need to calculate the area of this photo. I am going to use a ruler to measure the length of my photo. Use a ruler/measuring tape and show how to measure the length of your photo. The length is ____, so I'll write it in my equation. Now I will use the ruler to measure the width of my photo. Use a ruler/measuring tape and show how to measure the width of the photo. 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. The area of my photo is _____square inches. \[\[File:Insert Picture here.jpg\]\]STUDENT PRACTICE: Give each student Worksheet 2. Look at your photo, the length and width are already written on it. All you need to do is calculate the area using the formula and a calculator. Use a talking calculator for students with visual impairments. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. \*\*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 Look at your worksheet. This says length (pointing to the length space in the equation). What is the length of your photo? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the length. Now we need to find the width. What is the width of your photo? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the width. Now enter the formula into your calculator to find the area of your photo. Wait for students to independently enter the length into the calculator or say "What's next?" Student enters the length into the calculator. Wait for students to independently enter the times button or say "What's next?" Student enters the multiplication sign into the calculator. Wait for students to independently enter the width or say "What's next?" Student enters the width into the calculator. Wait for students to independently enter the equals button or say "What's next?" Student enters the equals button into the calculator. What is the area of the photo? Student says or writes/stamps/Velcro's the area of the photo onto the worksheet. Student must say/indicate unit of measurement squared (e.g., "inches squared").
MODEL THE PROCESS: We need to calculate the volume of this box. I am going to use a ruler to measure the length of this box. Use a ruler/measuring tape and show how to measure the length of the box. The length is ____, so I'll write it in my equation. Now I will use the ruler to measure the width of the box. Use a ruler/measuring tape and show how to measure the width of the box. The width is ____, so I'll write that in my equation. Now I will use the ruler to measure the height of the box. Use a ruler/measuring tape and show how to measure the height of the box. The height is ____, so I'll write that in my equation. Now I will use a calculator to calculate the volume. Remember, volume equals length times width times height. First I type in the length, (say number), then push the times button, then I type in the width (say number), then push the times button, then I type in the height (say number), and push the equals button. Look, the volume of the box is _____inches cubed (or other unit of measure). \[\[File:Insert Picture here.jpg\]\]STUDENT PRACTICE: Look at the box I gave you, the length, width, and height are already written on it. All you need to do is calculate the volume using a calculator. Use a talking calculator for students with visual impairments. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. \*\*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 Look at your worksheet. This says length (pointing to the length space in the equation). What is the length of the box? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the length. Now we need to find the width. What is the width of the box? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the width. Now we need to find the height. What is the height of the box? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the height. Now enter the formula into your calculator to solve for volume of the box. Wait for students to independently enter the length into the calculator or say "What's next?" Student enters the length into the calculator. Wait for students to independently enter the times button or say "What's next?" Student enters the multiplication sign into the calculator. Wait for students to independently enter the width or say "What's next?" Student enters the width into the calculator. Wait for students to independently enter the times button or say "What's next?" Student enters the multiplication sign into the calculator. Wait for students to independently enter the height or say "What's next?" Student enters the height into the calculator. Wait for students to independently enter the equals button or say "What's next?" Student enters the equals button into the calculator. What is the volume of the box? Student says or writes/stamps/Velcro's the volume of the box onto the worksheet. Student must say/indicate unit of measurement cubed (e.g., "inches cubed").
\*As students repeat the lesson, try to fade the equation prompt for area and volume and see if students can memorize the formulas and calculate area and volume independently without the support of the equation prompt.
Give each student the Measurement/ Geometry Skills Test 2: Calculating Area and Volume. Read directions for each problem and have student select response. Record whether response is correct or incorrect. Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing. Once the student has completed the test, review missed problems with the student. NOW
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HS BUILD A GRADE ALIGNED COMPONENT: Calculating a Missing Attribute Given Area and Volume INTRODUCE PROBLEM: Give each student Worksheet 3 and a new picture and a new box. Each picture should be labeled with the length and area, but NOT the width. Students are now working on solving for width (see example in materials section). Each student should also get a new box. The boxes should also be labeled with length, height, and volume, but NOT width (teachers will calculate these ahead of time to properly label the box). Students will also be solving for the width of the box. Look at these pictures. First, we need to select a picture frame for our photo. Look at the photo, it is labeled with the length and the area, but not the width. We need to know the width of the photo so that we get the correct size of picture frame. Look, picture frames come labeled by length and width. This picture frame is labeled 5 x 7 (or 8 x 10, etc.). Show students picture frames. So we need to find the width of our photo to make sure we get the right size frame. MODEL THE PROBLEM: Watch me solve for the width of my picture. Use the provided visual on the next page to teach this to students. The teacher will write the equations on the board and say the words in the bubbles as he/she goes. \[\[File:Insert Picture here.jpg\]\] \[\[File:Insert Picture here.jpg\]\]STUDENT PRACTICE: Now it's your turn. Look at your worksheet. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. \*\*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 Look at your worksheet. This says area (pointing to the area space in the equation). What is the area of your photo? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the area (pink box). This says length (pointing to the length space in the equation). What is the length of your photo? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the length (yellow box). We don't know the width of the photo. We need to write "width" (or "w") here. Have students copy the equation into the spaces below before moving to step 37. Student writes/stamps/uses Velcro "width" or "w"/points to/eye gazes to the width (blue box). Now solve for the width of your photo. Wait for students to independently write the number for the length under both sides of the equation or say "What's next?" Student writes/stamps/uses Velcro \# /points to/eye gazes to place the number for the length under both sides of the equation (yellow boxes). Wait for students to independently cancel out the \#'s for length on the right side of the equation or say "What's next?" Student writes an "X"/stamps/Velcro's/or eye gazes to cancel out the length on the top and bottom of the right side of the equation. Wait for students to independently rewrite the equation reflecting the cancelled numbers or say "What's next?" Student writes/stamps/uses Velcro \# /points to/eye gazes to place the number for the area on the top of the left side of the equation (pink box) and the number for length on the bottom side of the left side of the equation (yellow box) leaving the word width alone on the right (blue box). Now use your calculator to solve for the width. Student enters the number for the area into the calculator. Wait for students to independently enter the divide button or say "What's next?" Student enters the division sign into the calculator. Wait for students to independently enter the length or say "What's next?" Student enters the length into the calculator. Wait for students to independently enter the equals button or say "What's next?" Student enters the equals button into the calculator. What is the width of the photo? Student says/writes/stamps/selects the width of the photo onto the worksheet. Student must say/indicate unit of measurement (e.g., inches).
MODEL THE PROBLEM: Watch me solve for the width this box. Use the provided visual below to teach this to students. The teacher will write the equations on the board and say the words in the bubbles as he/she goes. \[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]STUDENT PRACTICE: Now it's your turn. Look at your worksheet. Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. \*\*Note: Have the students write the number 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 Look at your worksheet. This says volume (pointing to the volume space in the equation). What is the volume of the box on your desk? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the volume (pink box). This says length (pointing to the length space in the equation). What is the length of the box? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the length (yellow box). This says height (pointing to the height space in the equation). What is the height of the box? Student writes/stamps/uses Velcro numbers/points to/eye gazes to the height (brown box). We don't know the width of the box. We need to write "width" (or "w") here. Have students copy the equation into the spaces below before moving to step 49. Student writes/stamps/uses Velcro "width" or "w"/points to/eye gazes to the width (blue box). Now solve for the width of the box. Wait for students to independently write the number for the length under both sides of the equation or say "What's next?" Student writes/stamps/uses Velcro \# /points to/eye gazes to place the number for the length under both sides of the equation (yellow boxes). Wait for students to independently cancel out the \#'s for length on the right side of the equation or say "What's next?" Student writes an "X"/stamps/Velcro's/or eye gazes to cancel out the length on the top and bottom of the right side of the equation. Wait for students to independently rewrite the equation reflecting the cancelled numbers or say "What's next?" Student writes/stamps/uses Velcro \# /points to/eye gazes to place the number for the area on the top of the left side of the equation (pink box) and the number for length on the bottom side of the left side of the equation (yellow box) leaving width variable (blue box) and height (brown box) alone on the right. Now use your calculator to divide the left side of the equation. Student enters the number for the volume into the calculator. Wait for students to independently enter the divide button or say "What's next?" Student enters the division sign into the calculator. Wait for students to independently enter the length or say "What's next?" Student enters the length into the calculator. Wait for students to independently enter the equals button or say "What's next?" Student enters the equals button into the calculator. Student writes/stamps/uses Velcro \# /points to/eye gazes to the quotient (green box) and copies right side of the equation (width variable in blue box and height in brown box). Have students copy the equation into the spaces below. Now you need to finish isolating the width. That means we need to move the height to the other side of the equation. Do it just like you did for the length. Wait for students to independently write the number for the height under both sides of the equation. Student writes/stamps/uses Velcro \# /points to/eye gazes to place the number for the height under both sides of the equation (brown boxes). Wait for students to independently cancel out the \#'s for height on the right side of the equation or say "What's next?" Student writes an "X"/stamps/Velcro's/or eye gazes to cancel out the height on the top and bottom of the right side of the equation. Wait for students to independently rewrite the equation reflecting the cancelled numbers or say "What's next?" Student writes/stamps/uses Velcro \# /points to/eye gazes to place the number for the area on the top of the left side of the equation (green box) and the number for height on the bottom side of the left side of the equation (brown box) leaving the variable for width alone on the right. Now use your calculator to solve for the width. Student divides using the calculator. What is the width of the photo? Student says/writes/stamps/selects the width of the photo onto the worksheet. Student must say/indicate unit of measurement (e.g., inches).
Measurement/ Geometry Skill Test Teacher Says/Does Student Response Error Correction Give each student the Measurement/ Geometry Skills Test 3. Read directions for each problem and have student select response. Record whether response is correct or incorrect. Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing. Once the student has completed the test, review missed problems with the student.
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MASSI CULMINATING ACTIVITY: Have students find photos to wrap. Give them each a picture frame. Have students measure and calculate to see if the photos will fit in the picture frames. Then do the same for picture frames and boxes.
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 | Sample Activity | What Student Does | Generalization/ Fluency |
Solve a linear equation to find a missing attribute given area | Have students calculate the length when given width and area | Uses a calculator to complete the steps to solve the equation. | Calculate width when given length and area. Use a variety of problems. |
Solve a linear equation to find a missing attribute given surface area | Have students calculate the length when given the formula, surface area, width, and height | Uses a calculator to complete the steps to solve the equation. | Calculate surface area when either width or height is missing. Use a variety of problems. |
Solve a linear equation to find a missing attribute given volume | Have students calculate the length when given the formula, volume, width, and height | Uses a calculator to complete the steps to solve the equation. | Calculate volume when either width or height is missing. Use a variety of problems. |
Coefficients | Solve linear equations and inequalities with one variable and coefficients greater than 1 (multi-step problem). For example, 3x+8=17. | Uses a calculator to complete the steps to solve the equation. | Use a variety of problems with varying coefficients. |
Worksheet 1: Build Essential Understanding
Use a marker to draw a line on the perimeter of this shape. If student is unable to use a marker, they can put stickers on the perimeter or use their finger to trace it.
Use a marker to color the area of the shape. If student is unable to use a marker, they can put stickers in the area or use their finger to show it.
\[\[File:Insert Picture here.jpg\]\]
The length is the longest side of a rectangle. Use your marker to draw a line along the length.
The width is the shortest side of a rectangle. Use your marker to draw a line along the width. If student is unable to use a marker, they can put stickers along or use their finger to trace it.
The height is the side that goes up and down on a three dimensional cube/box. Use your marker to draw a line along the height. If student is unable to use a marker, they can put stickers along height or use their finger to trace. \[\[File:Insert Picture here.jpg\]\] The volume is the space inside a three dimensional cube/box. Use a marker to color the volume of the shape. If student is unable to use a marker, they can put stickers in the volume or use their finger to show. \[\[File:Insert Picture here.jpg\]\] Worksheet 2: Symbol Use- Calculating Area and Volume Area:
length x width = area
_______________________ X ____________________________ = __________________________
Length Width Area
Volume:
length x width x height = volume
_____________________ X _________________________ X _________________________ = ________________________
Length Width Height Volume
Worksheet 2: Generalization
Betty has a garden where she plants tomatoes, lettuce, cauliflower, and broccoli. Her garden is 8 feet by 4 feet. What is the area of her garden?
\[\[File:Insert Picture here.jpg\]\] |
________________ x _________________ = __________________ Length Width Area |
Jerry is making a quilt. He has cut a piece of fabric that is 3 feet by 5 feet that he will cover in quilt squares. What is the area of his quilt?
\[\[File:Insert Picture here.jpg\]\] |
Area = length x width Area = __________________________________ |
What is the volume of the box shown below?
\[\[File:Insert Picture here.jpg\]\]
length x width x height = volume
_________ x __________ x _________ = __________ length width height volume
Josie got a new aquarium. She needs to know the volume of the aquarium to know how much water to put in and how many fish to buy. What is the volume of the aquarium shown below?
\[\[File:Insert Picture here.jpg\]\] | length x width x height = volume |
Volume = _____________
Worksheet 3: Building a Grade Level Concept- Calculating finding a missing attribute given area and volume
Calculating width when give area and length:
\[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]
Calculating width when give volume, height, and length: \[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]
\[\[File:Insert Picture here.jpg\]\]
Worksheet 3: Generalization What is the width of the rug shown below?
\[\[File:Insert Picture here.jpg\]\] | Area = length x width
Width = _______________ |
What is the height of the box shown below?
\[\[File:Insert Picture here.jpg\]\] | Volume = length x width x height
Height = _______________ |
Materials:
area = length x width
volume = length x width x height
Example of poster board labeled with length and width: \[\[File:Insert Picture here.jpg\]\]
Example of box labeled with length, height, volume, but NOT width: \[\[File:Insert Picture here.jpg\]\]
'Student Vocabulary Card:' \[\[File:Insert Picture here.jpg\]\]\[\[File:Insert Picture here.jpg\]\]