Area
Grades 2/3
Learning Module
- Creator(s):
Abstract
The concept of area is explored in this learning module for an elementary school mathematics classroom.
Keywords
Math, Area, Elementary
The concept of area is explored in this learning module for an elementary school mathematics classroom.
Math, Area, Elementary
Educational Psychology 408 has not only focused on theories of research in the field of child development, it has also incorporated innovative strategies and relevant applications of these ideologies for the classroom. I have included just a few of these ideas and principles into this learning module as described throughout the updates below. This unit serves as a culmination of the most relevant and innovative concepts studied within this course as applicable to my elementary classroom.
The unit begins with a STEM activity in which students must collaborate in small learning communities. Students are immersed in a community of practice centered around an authentic goal. This innovative launch will allow students to access prior experiences, grow in their contextual knowledge, and make meaningful connections to the world around them (Duschl, 2008).
Each subsequent update in the learning module progresses through an appropriate zone of proximal development. Students are led through a deepening complexity of skills based upon what they can do by themselves, what they can do with the help of someone else, and what is still out of their reach. Learning scaffolds ensure realistic, age-appropriate expectations (Durandt & Lauterbach, 2020).
Concepts included within this learning module include productive struggle, scaffolding, zone of proximal development, and many more.
I am a general education teacher in a suburban school district in central Illinois. I teach a self-contained third grade classroom. Our mathematics instruction loosely follows the Everyday Math curriculum. Prior to state testing, our third grade teaching team completes a supplemental geometry unit in which we discuss geometric vocabulary, two-dimensional figures and solid shapes. As a miniature unit, our teaching team has added a few activities to discuss the concepts of area and perimeter.
I have taken this pre-existing list of activities and transformed it into a learning module to better prepare for the possibility of remote learning in addition to further developing the exposure to these skills. This miniature unit is now much more thorough and comprehensive than the existing lessons utilized within our tentative curriculum map. I have minimized the reliance on rote practice with worksheets and incorporated more multi-modal resources. I have included hands on activities in addition to digital practice. Incorporating themes from this course like productive struggle, social mind, and zone of proximal development, this learning module is better suited for students (and teachers) of the 21st century classroom.
Learning objectives are clearly stated in each update of the learning module. They appear as "I can" statements within the student view and appear as Common Core and/or Illinois State Learning Standards within the teacher portal. The standards are comprehensively linked to the context of the curriculum.
Hello third graders!
Over the next two weeks, we will be working with our new geometry skills. I hope you have been practicing your multiplication facts, because you will need those, too!
You will be working online and in-person to better understand certain shapes and how we describe them. By the end of the unit, you will be able to describe a shape by talking about its area. I will teach you some shortcuts that use counting and multiplying. I will also count on you to practice your collaboration skills during STEM.
You will be able to say:
There will be a lot of opportunities to practice and stretch your thinking. Are you up for the challenge?
This learning module is most appropriate for second or third grade students either in preparation for, or in concurrence with, their study of geometric skills. Students should have a familiarity with multiplication fact recall, although mastery (or rote memorization) is not expected at this point. Students should also be quite comfortable with the classroom specific expectations for group learning including, but not limited to, STEM activities, partner work, and digital collaboration.
This learning module correlates with grade three Common Core State Standards (CCSS) in mathematics. These specifically include the following.
This learning module will provide experience with additional Illinois State Learning Standards in social emotional learning. Although these standards are not explicitly assessed they are an ongoing component of a classroom climate. These specifically include the following:
This learning module can be completed over the course of six lessons with additional opportunities for supplementation and differentiation opportunities. Typically, each lesson can be completed in one day. My existing math block is sixty minutes.
Review: It's STEM day! We have been working hard this year to build strong teamwork skills. Before we get started, everyone read our accountability talk anchor chart. In your mind, review some ways that you can help your group succeed.
Learning Target: We will be working in our STEM groups to complete a math learning challenge. I want you to practice your teamwork skills.
You will be able to say: I listened to other people's ideas and experiences that were different than mine!
Today's Learning:
Today's challenge is TOUGH! I want you to work together, make mistakes, and keep trying. #thestruggleisreal
STEM Challenge: When you have read all of the directions carefully, you may find your group and a good place around the room to work.
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When I can tell that your group is ready, I will bring you a farm and your seeds. Good luck!
Check In: Today, you practiced your STEM skills during a math challenge. You worked together through a tough activity to find a solution to a problem. You might have tried a bunch of different times. You might have done something like this before. You might have planted all of your seeds. You might have run out of time. How are you feeling?
Can you say I listened to other people's ideas and experiences that were different than mine?
Homework:
Learning Standards:
Illinois State Social and Emotional Standards
Common Core Learning Standards
Purpose: This update will be the foundation for the mathematical unit on area. This lesson is meant to provide students with an experience of inquiry that will allow them to discover the concept. The instruction that will follow on subsequent days will be more meaningful and connected after this productive struggle. Additionally, students will work in STEM groups. Through this collaboration of the social mind, students will have the opportunity to share previous experiences, innovative ideas, and traits of perseverence.
Teaching Tips: Students should be coached rather than instructed through this activity. The most meaningful learning will occur as groups work through the productive struggle required with this inquiry. Here are some tips for encouraging productive struggle from your students throughout the lesson:
Extension: There are multiple solutions to this challenge. If students finish early, they can be encouraged to try to find another solution.
Enrichment: Additionally, students could be challenged to create their own version of the challenge that correlates with another holiday or curricular unit.
Review: During yesterday's STEM challenge, you practiced finding space for squares and rectangles in pretend Pilgrim farms. You were actually using our next skill that we are going to work with in math. This is called area.
Learning Target: By the end of this lesson, you will know how to find the area of a shape by counting square units.
You will be able to say: I can measure area by counting unit squares!
Important Vocabulary: area, square units
Today's Learning:
When you find the area of a shape, you figure out how many square units it would take to cover the shape. When I think about area, I think about covering the shape with a blanket. You want to be sure that you don't leave any gaps in the shape or that you don't have any overlapping square units.
This anchor chart is just like one in our classroom. It will help us remember all of the important things we need to know about area.
Now that you know that area is the measure of space inside a shape, let's learn how to figure out the area of a shape. The first strategy to find the area of a shape is to count the squares inside the shape. Remember, these squares are called square units.
Watch this video to see a miniature lesson about finding area of shapes.
Lochoff, A. (2020, March 16). Introduction to Area [Video]. Youtube. https://www.youtube.com/watch?v=C4Ah_zzV6WI
Practice: Now it is your turn to practice. Complete iXL skill : DD.6 Find the area of figures made of unit squares.
Check In: Today, you practiced being able to find the area of a shape by counting this square units. You learned two new vocabulary words: area and square units. You watched someone else find the area of shapes and then practiced on your own. How are you feeling? Can you say: I can measure area by counting unit squares?
Homework:
Common Core Learning Standards
Purpose: The purpose of this update introduces the mathematical concept explored during the previous STEM activity. Students will realize that when arranging seeds into squares and rectangles of the Pilgrim Planting STEM activity, they were immersed in an experiential learning process. Additionally, this learning update provides the first instructional experience of the unit.
Teaching Tips: Students may struggle with a one-to-one correlation as they count. Encourage students to follow predictable patterns when counting (ie across rows) or even make a mark in boxes that have already been counted.
Students will also need their iXL usernames and passwords. If you do not have accounts, students may practice without logging in until they meet a daily threshold of practice problems. Practice time will depend upon your alotted math block. For a sixty minute math block, I would anticipate that students will participate in 10-15 minutes.
Extension:
Enrichment: Students can take masking tape or colored washi tape and create shapes on the floor. Students should outline floor tiles to create shapes like the following picture
Extra Practice: Super Teacher Worksheets Area of a Shape
Review: Yesterday, we started learning about area. The area of a shape is the measure of the space inside. We use square units to measure the area of a shape. We worked hard to say: I can measure the area of a shape by counting unit squares!
Learning Target: We will still be practicing finding area by counting square units. Today's lesson is one step harder, because you will have to create your own square units.
You will be able to say: I can partition rectangles into rows and columns!
Important Vocabulary: partition, rows, columns, tiling
Today's Learning:
Sometimes the unit squares are drawn into the shape for you. Other times, you will have to draw your own squares. This is called partitioning. Sometimes, in the older grades we call this tiling. When you partition a shape, you break the shape up into many same sized, square shaped pieces. The pieces of a shape that go side to side are called rows. The pieces of a shape that go side to side are called columns.
This anchor chart is just like one in our classroom. It will help us remember the difference between rows and columns.
Watch this video to see an example of how to partition a rectangle.
eSparkLearningVideos. (2013, July 24). eSpark Learning: Partitioning rectangles using rows and columns (2.G.2) [Video]. Youtube. https://www.youtube.com/watch?v=vb1xchy2vSM
Practice: Now it is your turn to practice. Complete iXL skill : DD.9 Tile a rectangle to find the area.
Check In: Today, you practiced finding the area of a shape by counting the square units. But today, you needed to partition the shape. You learned three new vocabulary words: partition or tiling, rows, and columns. You watched someone else partition a rectangle and then practiced on your own. How are you feeling? Can you say: I can partition a rectangle into rows and columns?
Homework:
Common Core Learning Standards
Purpose: By the end of this update, students will have all of the skills necessary to tile simple square and rectangular shapes. The common core standard 3.MD.C.7a should now be assessable. This update includes an educational psychology concept of behaviorism. Gaming can be interpretted as a modern day Skinner learning machine. Within this update, students will practice tiling on iXL. This digital program provides instant feedback to students. If they get the correct answer, they are rewarded with points and virtual medals of mastery. If students get the incorrect answer, they are walked through the correct problem solving steps.
Teaching Tips: The most challenging part of tiling is creating somewhat equal sized pieces. Give grace when judging section equivalences in hand drawn tiling. Allow students to use rulers or pattern blocks if needed. This tiling concept will appear in our study fractions, as well.
Another difficult concept to grasp is that the number of cuts will not equal the number of rows or columns your students are trying to make. Help students understand this relationship. Some students may need significant reinforcement.
Extension:
Enrichment: Students can partition different pieces of scratch paper, post it notes, construction paper into rows and columns. Here is an example:
Extra Practice: Common Core Sheets: 2g2 Partitioning Rectangles
Review: Yesterday, we practiced partitioning rectangles into rows and columns while we were practicing area. The area of a shape is the measure of the space inside. We use square units to measure the area of a shape. Sometimes the square units were already drawn for us, and sometimes we had to draw our own. We worked hard to say: I can measure the area of a shape by counting unit squares!
Learning Target: Today, we will learn a new strategy to figure out the area of a rectangle.
You will be able to say: I found a pattern between adding and multiplying when I find the area of a shape!
Important Vocabulary: length, width
Today's Learning:
So far, we have been able to find the area of a shape by counting the unit squares that make up the shape. There is another way to find the area of a shape. I call this the shortcut way, because it is a lot faster if you know the secret formula.
Watch this video and see if you can find any shortcuts.
Kahn Academy. (2016, June 13). Transitioning from counting to multiplying to find area | 3rd grade | Khan Academy [Video]. Youtube. https://www.youtube.com/watch?v=mu3HHCdYYtY
Instead of counting every single unit square, we can use our multiplication as a short cut. All we need to know is the length and the width of a rectangle. The length is how long a rectangle is. The width is how tall a rectangle is. By multiplying these two numbers together, we can find out how many square units are on the inside of the rectangle without counting.
Here is another video with more examples.
Let's Do Math. (2016, August 16). Area of a Rectange [Video]. Youtube. https://www.youtube.com/watch?v=CgqgY7a630Q
Practice: Now it is your turn to practice. Complete iXL skill : DD.10 Multiply to find the area of a rectangle made of unit squares.
Check In: Today, you practiced finding the area using a new strategy. You watched a video lesson and found that instead of counting all of the unit squares on the inside of a rectangle, you can use multiplication to find the area of a shape. You practiced several examples on your own. How are you feeling? Can you say: I found a pattern between adding and multiplying when I find the area of a shape?
Homework:
Common Core Learning Standards
Purpose: This update allows for a deeper exploration of area. Students that still rely on counting may continue to do so. This portion of the learning module is relevant as it allows for scaffolding and differentiation based upon student readiness.
Teaching Tips: Now that students have been exposed to the idea that multiplication and addition are related, there are several videos that can be beneficial. Check resources that your district enrolls in like Brain Pop Jr, Discovery Education, etc.
This lesson can be problematic because students may not yet have a quick recall of their multiplication facts. You may allow use of multiplication tables, flashcards, or other reference materials.
Extension:
Enrichment & Extra Practice: Fact recall practice: Xtra Math
Review: Yesterday, we learned a shortcut way to find the area of a shape. We learned that the area of a shape can be found by multiplying the length and the width of a shape. The length is how long the shape is. The width is how tall the shape is. We worked hard to find a pattern between addition and multiplication.
Learning Target: Today, we will practice the multiplication strategy to figure out the area of a rectangle.
You will be able to say: I can use multiplication to find the area of a rectangle!
Important Vocabulary: formula
Today's Learning:
Now that we know how to use multiplication to find the area of a shape, we can develop a formula to help us remember the shortcut. A formula is a math rule that uses letters or symbols to give us clues to help us remember the steps of solving a problem.
Look at this anchor chart. What is the formula for finding the area of a rectangle?
Can you find the secret code? The formula for area is a = l x w. Why do you think we chose those letters to be in our secret code? Can you figure out what the letters stand for?
Practice: Now it is your turn to practice. Around the classroom, I have taped up 14 task cards. You will need to find a task card and complete the mutliplication to figure out the area of the rectangle. When you think you have the correct answer, use the QR scanner on your Chromebook to check the answer. See how many task cards you can find around the room. See how many answers you can get correct! Here is what they will look like.
Check In: Today, you practiced finding the area using the multiplication strategy. We created a secret formula to help us remember the steps for finding the area of a shape. You practiced several examples on your own. How are you feeling? Can you say: I can use multiplication to find the area of a rectangle?
Homework:
Common Core Learning Standards
Purpose: This update will allow for additional practice of the second strategy for finding area within the third grade curriculum. Today's lesson allows students to move around the classroom and complete practice problems in a low risk environment. Students will be able to check their answers without fear of a poor grade. By fostering a safe and engaging learning environment, students are more likely to participate and build their SEL competencies.
Teaching Tips: Be sure to allow plenty of time for this skill. Depending upon the technology available to your students, you may want to put them in small groups. This would be a good time to revisit the accountability talk poster.
Extension:
Enrichment: Using notecards, students can create their own scavenger hunt task cards. Make sure they put their answers on the back. Consider using these student creations to host another area scavenger hunt.
Extra Practice: Math Worksheets 4 Kids Area of a Rectangle
Review: It's STEAM day! We have been working hard to learn how to determine the area of a shape. The area of a shape is the measure of the space inside. We use square units to measure the area of a shape. Sometimes the square units were already drawn for us, and sometimes we had to draw our own. We learned that the area of a shape can be found by multiplying the length and the width of a shape. The length is how long the shape is. The width is how tall the shape is. We worked hard to be able to say that we could find the area of a shape!
Learning Target: We will be working on our math skills during a STEAM project.
You will be able to: I can find the area of some shapes!
STEAM Activity: When you have read all of the directions carefully, you may find your group and a good place around the room to work.
You will get a piece of graph paper from the back table. Using any art supplies from your toolbox, create a robot. Be sure to only use complete square units. When you have finished your artwork, come get a description page from me.
On your description page, name your robot and find the area of the robot's different body parts. What would you need to do to find the total area of the robot? Think about how we have solved similar questions in math to come up with a strategy.
These area robots will be displayed in the hallway. Take your time and do your very nicest, neatest work!
Check In: Today, you finished our unit on area. Throughout the past six lessons, we have worked hard to learn about the counting strategy and the multiplication strategy to find the area. How are you feeling? Can you say: I can find the area of a shape?
Homework:
Common Core Learning Standards
Purpose: The purpose of this update is to allow students a chance to synthesize the information from the past unit in a child-centered, STEAM activity. Students will create an art project for display.
Teaching Tips: Have examples available for ideas. Allow students to create their own variations or deviate from the expectations.
Extension: Students can create more than one robot. Challenge students to create robots with scraps of construction paper. They may either tile each individual unit square of the template, or they may create larger squares or rectangles. This is considered a challenge, because students will need to rely on their multiplication strategy rather than simply tiling.
You will create an anchor chart to include in your interactive notebook. You may use digital resources (like Google Slides or Google Draw), or you may create your work on a separate piece of paper. Be sure to make your anchor chart organized and colorful so that it will be a useful tool for you to reference later on this year.
Remember, this miniature anchor chart should include information from this unit that you think is important to remember about area.
As you create your miniature anchor chart, be sure to look at this rubric. Two of your classmates will review your work. Make sure you impress them!
Purpose: This peer reviewed project will be one of two assessments for this learning module. Students have been tasked with creating an anchor chart that includes some of the concepts from this unit.
Teaching Tips: Allow students to reference existing anchor charts in the classroom. Not only will this help them discern pertinent information, it will help in the organization and creation of the finished product.
Peer Review Rubric: Since the learners in this module are so young, concrete descriptions were used to elicit clear responses.
Hello third graders! We have been working hard over the past two weeks to become the experts in describing a shape's area. Today, you will take a quick survey to show me what you have learned.
Show me that you can say:
I can find the area of some shapes.
I can measure area by counting unit squares.
I can find area by multiplying side lengths.
Assessed Common Core Learning Standards
Purpose: This knowledge survey is a formative assessment to provide the teacher with data needed to assess content standard achievement.
Teaching Tips: This survey is intended to be used as an end of unit assessment. However, it could also be administered as a pre-test.
http://cgscholar.com/survdash/cgsurvey/uauthorsurvey/depid/5f15424fca021229c3af0987
2nd G. Common Core Math. (n.d.) Partition a rectangle: Rows and columns [Photograph]. Pinterest. https://www.pinterest.com/pin/396668679662819963/
Boschen, J. (2017). Partition Rectangles into Rows and Columns [Photograph]. What I have Learned. https://www.whatihavelearnedteaching.com/partition-rectangles-into-rows-columns/
Common Core Sheets. (n.d.) 2g2 Partitioning Rectangles [PDF]. Common Core Sheets. https://www.commoncoresheets.com/downloadWorksheet.php?path=Math/Multiplication/Partitioning%20Rectangles/English&pageNumber=1
Durandt, R., Lauterbach, G. (2020). Strategic Suppot to Students' Competency Development in the Mathematical Modelling Process: A Qualitative Study. Perspectives in Education, 38(1), 211-223. http://eds.b.ebscohost.com.proxy2.library.illinois.edu/eds/pdfviewer/pdfviewer?vid=1&sid=519a4b1b-8bcf-4537-963c-c32c4b7bb152%40sessionmgr103
Duschl, R. (2008). Science Education in Three-Part Harmony: Balancing Conceptual, Epistemic, and Social Learning Goals. Review of Research in Education. 32, 268-291. www.jstor.org/stable/20185118
eSparkLearningVideos. (2013, July 24). eSpark Learning: Partitioning rectangles using rows and columns (2.G.2) [Video]. Youtube. https://www.youtube.com/watch?v=vb1xchy2vSM
Impact [@ImpactWales]. (2018, August 1). 8 habits of Maths teachers who value productive struggle from @MIND_Research Check out these strategies to deepen thinking & learning! [Tweet; Infographic]. Twitter. https://twitter.com/impactwales/status/1024540544884776960
Kahn Academy. (2016, June 13). Transitioning from counting to multiplying to find area | 3rd grade | Khan Academy [Video]. Youtube. https://www.youtube.com/watch?v=mu3HHCdYYtY
Kamrava, N. (n.d.). Area of a Rectangle anchor chart [Photograph]. Pinterest. https://www.pinterest.com/pin/12877548918303382/
Learning with Leah. (n.d.). legoareabylearningwithleahpdf [PDF]. Teachers Pay Teachers. https://www.teacherspayteachers.com/FreeDownload/FREEBIE-Self-Checking-Area-Task-Cards-3MDC7-1436486
Let's Do Math. (2016, August 16). Area of a Rectangle [Video]. Youtube. https://www.youtube.com/watch?v=CgqgY7a630Q
Lochoff, A. (2020, March 16). Introduction to Area [Video]. Youtube. https://www.youtube.com/watch?v=C4Ah_zzV6WI
Math Worksheets 4 Kids. (n.d.) Finding Area: Type1 - Integers [PDF]. Math Worksheets 4 Kids. com. https://www.mathworksheets4kids.com/area/rectangle/customary/integers-t1-l1-1.pdf
Miss Learning Bee. (n.d.). Area Robot Template by Miss Learning Bee [Photograph]. Teachers Pay Teachers. https://www.teacherspayteachers.com/Product/Area-Robot-Template-4221077
Romang, G. (2016, November 30). Pilgrim Crop Planting [Google Draw]. Google Drive. https://docs.google.com/drawings/d/1jUpbp1WnSPSELyiEFILpictqcJdJoxmKVb8SVUhPigk/
Strozyk, P. [@paulastrozyk]. (2015, January 29). LOVE this! RT @KarenMcGaha : “ @perrer1 : Follow up from chat last night on book clubs #tcrwp ”#elafcps #edchat [Tweet; Photograph]. Twitter. https://mobile.twitter.com/paulastrozyk/status/560972824400375809
Super Teacher Worksheets. (n.d.) Area of a Shape [PDF]. www.superteacherworksheets.com. https://www.superteacherworksheets.com/geometry/area-1_TWBDW.pdf?up=1536577811
Taylor, B. (2013). [Area Anchor Chart] [Photograph] Kirby's 3rd Grade Korner. http://kirbys3rdgradekorner.blogspot.com/2013/05/our-math-workshop-anchor-charts-here.html
Teaching Tales Along the Yellow Brick Road. (2012). [Floor Tile Area Models] [Photograph]. teaching-in-oz blogspot.com. http://teaching-in-oz.blogspot.com/2012/09/what-weve-been-up-to-in-5th-grade-lots.html
Teacher's Takeout. (2013). Student Self-Assessment Rubric [Infographic]. Teacher's Takeout. http://www.teacherstakeout.com/2013/07/student-self-assessment-rubric-freebie.html
Teaching Works [@TeachingWorks]. (2017, September 9). Adapted from a "struggle time" anchor chart I saw on-line... It was SO time to have this whole-class discussion! [Photograph]. Instagram. https://www.instagram.com/p/BYzVJMEAy89/