CCSS.MATH.CONTENT.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
CCSS.MATH.CONTENT.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
⏰LESSON TIME
30 minutes without gameplay, 45 minutes with gameplay
📃 SUMMARY
In this lesson plan, students will learn how to compute perimeter, apply those skills in game-based practice problems and solve perimeter problems using an interactive web-based activity with virtual manipulatives.
📲 TECHNOLOGY REQUIRED
Device with web-browser (Chromebook, laptop or desktop computer); or iOS (iPhone/iPad) with access to Google apps.
📚 Lesson Plan
1. Video: How to Find the Perimeter and Polygons (3:00)
Watch this animated video that explains how to find the perimeter of different polygons, including rectangles, triangles and squares.
Or watch it in Spanish: ¿Cómo encontrar el perímetro de un polígono? (3:12)
2. INSTRUCTIONAL ACTIVITY WITH ASSESSMENT: Interactive perimeter problems activity
CCSS.MATH.CONTENT.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.
D2.His.13.3-5 Use information about a historical source, including the maker, date, place of origin, intended audience, and purpose to judge the extent to which the source is useful for studying a particular topic.
⏰ Time
60 minutes
📲 Technology Required
Students need access to a computer with web browser.
📃 Summary
This lesson begins with a storyboard on the route and major events of the Ojibwe migration. Students then play the Forgotten Trail game, computing the average number of miles a character walked per day, followed by watching a video on map reading. As a group, students reflect on the challenges of the Ojibwe migration, compute the distance for just one segment and convert the distance from miles to kilometers.
📚Lesson
Storyboard on the Ojibwe Migration
Begin with this story board on the route and major events of the Ojibwe migration. We recommend having students read each section of the story as it advances. Alternatively, the teacher may read it to the class or students can read it to themselves either on devices in the classroom or at home.
Watch a video on how to find the mean
Warning: bad singing ahead. This short video tells how to find the mean – in song. You may skip this video if you have already used it in a previous lesson.
Play the Forgotten Trail Game
Map from Forgotten Trail
Students should play the game at least through the first level. The game begins with a middle school class learning about the Ojibwe migration. Students will solve math problems related to the average number of miles walked per day and fraction of distance covered.
Watch a video on using scales in maps
This video is 7 minutes and covers what is a scale, how to use one and that different maps have different scales. If you feel your students are already familiar with this information, you may skip this video. In the days of Google maps and GPS we have found students often are not as familiar with this information as you might assume.
Presentation on Reflections on the Ojibwe Migration
In this Google slides presentation, students are asked to reflect on the Ojibwe migration. What would it have taken to survive such a journey? They use their map skills to estimate the distance of one leg of the journey, in both kilometers and miles.
Now that students have seen synonyms as words for the same thing and miles and kilometers as measures for the same distance, finish up with this short (less than 2 minutes) video on synonyms.
Assessment
Slides 14, 18 and 21 can be printed out for students to answer individually, or can be answered as a group in class. Data are available on activities completed and math problems answered in the Forgotten Trail reports. For more information, check out our reports page.
CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers
📲 Technology Required
Computer with projector, for students learning in class. For students learning at home, materials can be accessed on any device with a browser and application to read PDF files or can be printed out and sent home with students.
⏰ Time Required
2 hours (We recommend doing this over two class periods)
📃 Summary
Teachers begin the lesson with a Google slides presentation explaining the requirements for a statistical question. Students complete an assignment identifying whether or not a question qualifies as a statistical question. After class discussion, students complete a second assignment using a small data set shown on a map. In Part 3, students write and answer their own statistical questions using a data set provided, giving an explanation for their answers. Optionally, students can complete a more challenging assignment drawing conclusions from a graph and/or play a game and identify statistical questions.
Students complete assignment on identifying a statistical question
Have students complete Part 1 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.
Students complete Part 2, assignment on identifying a statistical question using real data
Have students complete Part 2 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.
Then, continue with the Google slides presentation and have students complete Part 2 of the student handout from the U.S. Census Bureau (linked above). Have students discuss their answers with one another.
Either correct the answers as a class or collect these to correct yourself. Remember, the teacher handout, linked above, has the correct answers.
We recommend you end the first day’s lesson here and begin the next lesson after students have had the assignments from Part 1 and Part 2 corrected.
Students complete part 3, creating their own statistical questions from data.
Students complete Part 3 of the handout on “What is a statistical question?”
Discuss students’ answers in class. Provide feedback on whether a question really is a statistical question and whether students’ answers to their questions are correct. Allow students time to explain their conclusions.
Next, have students complete Part 4 from the student handout, “Drawing conclusions from a graph.”
Optional: Play Empiric Empire
After students have completed Parts 1 to 3 of the student handout (and, optionally, Part 4), have them play the game Empiric Empire. As an additional optional assignment, ask students to identify statistical questions asked and answered during the game.
If students do not have phones but have Chromebooks, they can play Disaster Deduction Detectives instead – available June, 2022.
Assessment
For assignments in Parts 1 and 2 the teacher version of the handout has correct answers and explanations. For assignments in Parts 3 and 4 of the student handout, examples of correct responses are given but these will vary as students provide their own statistical questions.
For the Empiric Empire game, the teacher reports show student responses to questions. It should be noted that this game does begin with fractions and decimals, which are a prerequisite to statistics.
NGSS 4-LS1-1: Construct an argument that plants and animals have internal and external structures that function to support survival, growth, behavior, and reproduction.
CCSS.MATH.CONTENT.3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot,
⏰ Time
3-4 hours over 4-5 sessions. The data collection will need to be completed at least two weeks after the seeds are planted.
📲 Technology Required
No technology is required. Students may use Jamboard for line plots and Google docs for word journals, but both of these activities can also be done on paper.
📃 Summary
Teachers read an age appropriate book about plants and record new vocabulary in their personal dictionary. The teacher or student selects an agriculture activity from the booklet More Scrambled States of Agriculture. Garden in a glove is one recommended activity. Students collect and record data on the number of days until germination, showing the results in one more more line plots.
Both the lesson plan for Garden in a Glove and More Scrambled States of Agriculture booklet have several recommendations for age appropriate books on plants in general or specific plants, like wheat. Teachers may wish to read the book aloud to the class, have students take turns reading aloud, either in groups or as a whole class, or assign to students to read on their own. I recommend 2-3 sessions of 15 minutes of read aloud or 20 minutes of independent reading.
Update Word Journals
Students should update their word journals, what some teachers refer to as a “personal dictionary”, with any new words from the book. If this is your students’ first experience using a word journal, you may wish to give them this Google doc to read or read it together as a class, “Creating your personal dictionary.“
Food prep gloves – 1 for each student – that you can probably get from your school cafeteria,
A bag of cotton balls
5 different packs of seeds
A marker
Soak the cotton balls in water, put 3-5 seeds in each one and put five cotton balls, each with different seeds, in the five fingers of the glove. Don’t forget to write on each finger what is in it. Create a chart of the germination time for each type of seed. Read the lesson plan for more detail.
Ask students to generate hypotheses about how long it will take for the seeds to germinate, whether all the seeds will take the same amount of time (assuming you did Garden in a Glove).
Record your measurements
Students create either :
Create 5 line plot showing the number of seeds that germinated for each number of days, one plot for each type of seed, OR
Create one line plot with a different color used for each type of seed.
Ask the students whether their hypotheses were supported.
OPTIONAL: WATCH THIS VIDEO ON CREATING A LINE PLOT
If your students are not familiar with line plots, you may want to have them watch this seven-minute video which explains line plots step by step.
Now that students have watched the video and collected the data, their final task is to create two line plots of their results. Feel free to copy and paste the text below into your Google classroom or other assignment.
LINE PLOT ASSIGNMENT
OPTIONAL: IF STUDENTS ARE LEARNING ONLINE, THEY CAN USE JAMBOARD TO CREATE A LINE PLOT, AS SHOWN IN THE VIDEO BELOW.
Assessment
Three forms of assessment are included in this assignment.
In the personal dictionary or word journal, students are required to include a minimum of five words with definitions for 50 points. Each word, spelled correctly is 2 points and a correct definition is another 8 points. I deduct a point for grammar or spelling errors in the definition, but only one.
For the agriculture activity, this is simply pass/ fail marked as completed or not.
The line plots are scored based on accuracy. I give 10 points for each plot/ type of seed for a total of 50 points possible and another 10 points each for stating a hypothesis and answering whether or not it has been supported.
CCSS.MATH.CONTENT.3.MD.B.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
CCSS.MATH.CONTENT.2.MD.A.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
⏰ TIME
40-50 minutes
📲TECHNOLOGY REQUIRED
The teacher will need a computer with projector or smart board to show the presentation. Students will need a tablet or phone to do the activity and a measurement app installed. They will also need a ruler or tape measure.
This is the second of three lessons that use Augmented Reality apps. If you did the first lesson on perimeter, you already have one of the measurement apps installed.
You’ll need a measurement app installed.
Measure: For iPhones or iPads
Measure app
If using an iPhone, the Measure app should already be installed. On iPads, it may not be. Before starting this lesson, we recommend you check and, if not, parents or teachers can download the app for free here.
For Android Devices
Ruler app
Android devices do not come with a measure app. I tried several free AR measurement apps and all were difficult to use. I can’t honestly recommend any. Not an augmented reality app, but students can use the Ruler app by NixGame. It is simply a ruler on a phone and you can only use it to measure items the length of the phone/ tablet. We tried a lot of ruler and measure apps on Google Play and this is the one we recommend as the easiest for elementary school students to use and with the least annoying ads.
📃 Summary
Students learn that augmented reality is a type of computer application that adds to (augments) the reality we see. They learn that the measure apps on phones and tablets are a type of augmented reality. Students use an app to measure items, then use a ruler or tape measure to measure again. They plot their measurements on line plots and compare the two measures.
This one-minute video is also in the Google slides but it is included here just in case, since we know media doesn’t always play in presentations, even when it should! (You can also check out some AR math apps here.)
Introduce apps your students will be using for measurement
Use this short presentation to explain how to use apps to measure, well, anything. If you already completed the first lesson on measuring perimeter and used this presentation, you may want to show it again to remind them and also to make the point that they were using augmented reality already and didn’t know it!
Optional: Watch this video on creating a line plot
If your students are not familiar with line plots, you may want to have them watch this seven-minute video which explains line plots step by step.
Now that students have watched the video and collected the data, their final task is to create two line plots of their results. Feel free to copy and paste the text below into your Google classroom or other assignment.
Line Plot Assignment
OPTIONAL: If students are learning online, they can use Jamboard to create a line plot, as shown in the video below.
You are going to make TWO line plots.
First, make a line plot of the ten measurements you did with the APP.
Second, make a line plot of the ten measurements you did with the RULER or TAPE MEASURE.
Now that you have your line plots, answer these questions.
Compare the two line plots. Do they look the same?
Compare your line plots with other students in the class.
Assessment
You can assess student’s progress through the assignment completed which shows both their measurement skills and ability to create and interpret line plots.
Individualizing Instruction
For students who are more advanced, you may wish to have them measure items and complete line plots using fractions or mixed numbers rather than just whole numbers.
CCSS.MATH.CONTENT.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
CCSS.MATH.CONTENT.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
⏰LESSON TIME
30 minutes without gameplay, 45 minutes with gameplay
📃 SUMMARY
In this lesson plan, students will learn how to compute perimeter, apply those skills in game-based practice problems and solve perimeter problems using an interactive web-based activity with virtual manipulatives.
📲 TECHNOLOGY REQUIRED
Device with web-browser (Chromebook, laptop or desktop computer); or iOS (iPhone/iPad) with access to Google apps.
📚 Lesson Plan
1. Video: How to Find the Perimeter and Polygons
Watch this animated video that explains how to find the perimeter of different polygons, including rectangles, triangles and squares. (3:00)
2. INSTRUCTIONAL ACTIVITY WITH ASSESSMENT: Interactive perimeter problems activity
CCSS.MATH.CONTENT.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
CCSS.MATH.CONTENT.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
⏰LESSON TIME
45 minutes
📃 SUMMARY
In this lesson, students will learn how to compute perimeter of different polygons using multiplication and apply those skills in game-based practice problems. They will then learn about different Indigenous traditional dwellings. The lesson ends with students contributing to and solving problems that integrate the reading on dwellings and perimeter in an online assessment.
📲 TECHNOLOGY REQUIRED
Device with web-browser (Chromebook, laptop or desktop computer); or iOS (iPhone/iPad) with Google Drive apps.
📚 Lesson
1. Play GAME: Making Camp Premium
For 15 minutes, have students play the game Making Camp Premium.
Instruct them to specifically play the mini-game with this icon
If they need a refresher in how to compute perimeter, they should click this icon to watch a video
ALTERNATIVE: Perimeter is also covered in the second half of Spirit Lake: The Game, which is currently available for Windows and Mac computers.
2.READ: Home, Sweet Home: Tipis, Hogans, Wigwams and More
This activity draws from the “Home, Sweet Home” reading and lessons on perimeter to have students apply their understanding of how to compute the perimeter of rectangles, triangles and hexagons using multiplication. Get the Google slides presentation here. Students contribute numbers to create multiple problem options.
(Estimated time: 10 minutes)
ASSESSMENT
You can view your students’ progress on mastering these standards by viewing your teacher reports. Both Making Camp Premium and Spirit Lake Report links can be found on this reports page. You should have received a password during the Growing Math training. If you need the password, email growingmath@7generationgames.com from your school email account and we’ll get the password to you right away.
State Standards
Minnesota Math Standard 3.3.2.2 – Find the perimeter of a polygon by adding the lengths of the sides.
Minnesota Math Standard 4.3.2.4 – Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements.
45 – 50 minutes depending on the time you allot to students for measuring objects and for playing the game.
📲 Technology Required
Making Camp Premium plays in any browser, so, of course, on Chromebooks. It can also be downloaded on phones or tablets and played offline by students who have limited Internet access. The teacher will need a computer, for showing to students learning from home, and a projector if showing videos in the classroom. If the classroom does not have access to a projector, the videos can be skipped. A phone or tablet with a measuring app is optional. If unavailable, students can use a ruler or tape measure instead. NOTE: The measure app comes on iPhone/ iPad by default but for an Android device you’ll need to install some type of measuring app.
Note: This is the first of three lessons using these apps, so once you have them installed, you will be set for the next two.
Measure: For iPhones or iPads
Measure app
If using an iPhone, the Measure app should already be installed. On iPads, it may not be. Before starting this lesson, we recommend you check and, if not, parents or teachers can download the app for free here.
For Android Devices
Ruler app
Android devices do not come with a measure app. I tried several free AR measurement apps and all were difficult to use. I can’t honestly recommend any. Not an augmented reality app, but students can use the Ruler app by NixGame. It is simply a ruler on a phone and you can only use it to measure items the length of the phone/ tablet. We tried a lot of ruler and measure apps on Google Play and this is the one we recommend as the easiest for elementary school students to use and with the least annoying ads.
📃 Summary
Finding the perimeter activities can be fun in school or out. This is an activity recommended for children learning at home, so the instructions below target what you would send to parents, but this activity can be easily adapted for in-school use as well. Best of all, it combines math with P.E. ! Students watch a video, find the length and width of 10 objects and compute the perimeter. After the hands-on activity, students watch another video to reinforce the concept and then play the Making Camp Premium game to practice their multiplication and division.
Materials needed:
A piece of paper
A pen or pencil
A phone or tablet – if not available, a measuring device like a ruler, measuring tape or yardstick can be used instead.
Making Camp Premium (available online and for download on iOS and Android devices)
📚 Lesson Plan
Step 1: Watch the perimeter video
How to find the perimeter of polygons – 2:21
As you might guess from the title, this video explains how to find the perimeter of an object and how to determine if a shape is a polygon.
Step 2. Make a table like in the example below
OBJECT
Length
Width
Top of a box
Seat of a chair
You can have a Google Doc you share with students with the table in the instructions. However, we recommend that students create their own table with a piece of paper because they are going to be wandering around the house or classroom and it is much easier to carry a piece of paper with you than a laptop.
For this exercise, every object should be a rectangle. Be prepared for the question,
“Is a square a rectangle?”
– every third-grader , ever
Yes. Yes it is. If you want to get technical about it, a rectangle is a quadrilateral with four 90 degree angles. Or you could just say yes, a rectangle is a shape with four sides that are not slanted and a square definitely has four sides and is not slanted.
This is where the physical education comes in. Tell the student he or she has 10 minutes to complete the table with 10 items. An item can be as small as a box of candy or as big as the floor of a room. For each rectangle, write down the name of the object, the length and the width. Just put the whole number. If it says 18 1/4 or 18 1/2 just put 18. You may be tempted to tell the student to just round it but remember, he or she may not have learned fractions yet. That’s a lesson for another day.
If you don’t happen to have a ruler, yardstick or tape measure, your phone may already have a Measure app. This comes by default with an iPhone and if you don’t see it right away look in the Utilities folder. Most kids this age take any opportunity they can get to get hold of a parent’s phone. In school, you can use iPads or go old-timer and use a ruler.
To use it, point at a surface and click to select a point. Then, move the phone until you are at the end of what you want to measure.
Depending on how much exercise you want your child to get, the size of your house and how much peace you need (I won’t judge you), you may want to add a few rules like:
None of the objects can come from the room you are currently in.
They need to find rectangles in at least 3 different rooms
They need to find at least one rectangle in the backyard/ garage/ basement.
Once you have shown your child how to use the measure app and they have the table and a pencil, set the alarm on your phone and tell them to go. The alarm will go off when the 10 minutes are up.
Check their number of rectangles and if they are a few short give an extra 2- 5 minutes to find the rest.
Don’t have an iPhone or iPad?
The Ruler app can be downloaded free from Google Play and used to measure small objects. It only works to the size of your device but it is still easy to use and fun. There are apps in Google Play similar to the iPhone Measure app but these are not available on all Android phones.
Step 4 Watch another video on perimeter
Why? Because experience shows that students often don’t remember something if they only heard it once.
Step 5: Compute the perimeter for each object you have measured
OBJECT
Length
Width
Top of a box
8
4
Seat of a chai r
18
12
Your student does this, not you. You’ve already completed elementary school.
Tell students that these videos came from Making Camp Premium and now that they have finished the rest of the assignment they have 10 minutes to play.
Assessment
This lesson includes three types of assessment, the table of measurement, the perimeter computations from those measures and the automated data collection and scoring from the Making Camp Premium reports.
Minnesota Math Standard 2.3.1.1 – Describe, compare, and classify two- and three-dimensional figures according to number and shape of faces, and the number of sides, edges and vertices (corners).
Minnesota Math Standard 3.3.2.2 – Find the perimeter of a polygon by adding the lengths of the sides.
