Measurement and Geometry
Measurement and Geometry are related concepts that fall under what previous curricula called Shape & Space. Throughout K-7, the big ideas all share the foundational concept of the ability to describe, measure, and compare spatial relationships. This key concept is a critical part of numeracy as our learners develop spatial sense.
In Primary grades students identify, describe, build, and sort 2-D shapes and 3-D objects by exploring attributes and recognizing similarities and differences. As they go through the Intermediate grades students learn to classify shapes by their attributes, including learning vocabulary relevant to each type of shape or object. Our visible world is full of shapes and objects that our learners experience every day.
Many of these geometrical concepts then connect to number concepts through exploring measurement. Over K-7 students measure and compare length, area, volume, capacity, mass, time, and angles. Students begin developing the concepts by measuring common attributes through comparison. They then learn to appreciate the value of direct measurement, at first using non-standard units and then standard metric units. Indirect measurements are figured out by using direct measurements, for example, using dimensions to determine an area.
Beginning in Grade 4 with symmetry, students also develop spatial sense with transformations. In Grades 5-7 students identify and construct transformations using slides (translations), flips (reflections), and turns (rotations).
As students explore measurement and geometry, there are many opportunities to connect to students’ lives, community, culture, and place. With these experiences we are honouring the following First Peoples Principle of Learning: Learning is holistic, reflexive, reflective, experiential, and relational (focused on connectedness, on reciprocal relationships, and a sense of place).
As we learn about key concepts in measurement and geometry, we will also be developing many curricular competencies. Three that we have chosen to focus on in our designing of lesson ideas are:
- Estimate reasonably
- Visualize to explore mathematical concepts
- Use mathematical vocabulary and language to contribute to mathematical discussions
Although these three curricular competencies have been highlighted, there will be many opportunities to develop many curricular competencies during the investigation of measurement and geometry.
Learning Story for Grade 4
Measurement and Geometry
In grade 4 the new concept of line symmetry is introduced, providing students a new way of visualizing and describing shapes and patterns. Upon adding the understanding and language for line symmetry to their toolkit, Grade 4 students will continue to build on previously developed concepts of identifying, sorting, and comparing shapes according to their multiple attributes and are introduced to formalized language for describing both regular and irregular polygons. Using the formalized categories of triangle, quadrilateral, pentagon, etc, students will sort and describe multiple shared attributes within each type of polygon. Students will also discern between irregular and regular polygons. Here, we can reconnect with the newly introduced concept of line of symmetry and have students integrate it as another attribute that can be used to classify polygons.
Building upon the grade 1 concept of measurement with non-standard units and grade 2’s introduction to measurement with standardized units, and perimeter, grade 4 students will consolidate this knowledge to create, represent, measure, and calculate perimeter. When taking measurements, Grade 4 students may use measuring devices such as rulers and measuring tapes to measure the perimeter of spaces such as the classroom and consider the appropriate units that may be used to represent and communicate their findings. When calculating the perimeter, students will work towards seeing patterns and developing formulas for the perimeter of the rectangle and regular polygons.
Key Concepts
Regular and Irregular Polygons
Students continue exploring 2D shapes and are introduced to the concept of regular and irregular polygons. Students use a variety of attributes to describe polygons, comparing the difference between regular and irregular polygons.
Perimeter of regular and irregular shapes
Determining the perimeter of regular and irregular shapes using standard and non-standard units.
Key Measurement and Geometry Concept 1: Line Symmetry
Overview
Grade 4 is when students are formally introduced to line symmetry. This line can also be called an axis of symmetry or a mirror line. Before this point, it is expected that students would have an understanding of equal parts (grade 3 fraction concepts). This key concept on its own may not require an entire week, however, this is a great opportunity to spiral back to fraction concepts, attributes of 2D shapes, and connections to First Peoples architecture and art found in the local community.
Measurement and Geometry Foundations:
Foundational, supporting concepts and related competencies that are needed to develop this grade level concept:
- Identifying attributes of 2D shapes and images (length of sides, color, area)
- Equal parts (fractions concept)
Progression:
- Understanding the meaning of line symmetry
- Recognizing line of symmetry in shapes and then images
- Exploring and investigating the relationship between number of sides and vertices in a regular polygon and the number of lines of symmetry
- Creating images that have 1 or more lines of symmetry
- Finding line symmetry in the environment
Sample Week at a Glance:
Before this week of lessons students would benefit from understanding vocabulary words such as reflection, mirrored, folding, matching, and half. If they are unfamiliar to students, building a math word wall as the class is introduced to these terms would be beneficial.
Focus: Introducing the word line symmetry and exploring symmetry all around us.
Before: Read Seeing Symmetry by Loreen Leedy
Access the video read aloud if you do not have access to the hardcopy book.
https://www.youtube.com/watch?v=GL0Cvu_7pKY
During:
Problem-based Concept Launch by Jenna Laib
- Whole class discussion: Show students image “a.” with the writing covered and ask them “What do you notice? and What do you wonder?” Help guide the discussion toward symmetry. Reveal the writing at the end of the discussion.
- Show students the three different problems they will be tackling today. Give each student a copy of the three diagrams below. Have students work independently for the first 2-5 minutes (this allows for students to develop their own unbiased ideas). Once independent work time is over students may work in small groups.
Techniques that students may use:
- Folding
- Creating physical replicas
- Imaginary mirror and drawing what should be on the other side
- While students are working, the teacher can select a few students to share their strategies and solutions at the end of the class.
Share: Strategies to highlight
Have students come back together to listen to the selected students present their strategies. While students are presenting, create a Line of Symmetry Anchor Chart that has four sections (1) Definition, 2) Strategies, 3) examples, 4) non examples) and start adding their strategies and examples to the chart.
Focus: Exploring lines of symmetry in a variety of objects and images.
Before: Which one does not belong? Shapes
Consider prompting students to consider line symmetry in their thinking.
During: Math Workshop
Station 1)
- Reflector Mirror drawing with printouts from Loreen Leedy’s Free PDF. Using a reflector mirror, have students complete the drawings on page 8/9 of the Loreen Leedy PDF resource.
Station 2) (Teacher-guided station)
- Shapes and images symmetry investigation. Provide students with a collection of images/shapes and have them investigate lines of symmetry as they did in yesterday’s activity. Include regular and irregular polygons, logos from popular brands that they may know, sports team logos, etc. They may fold, measure, and use the reflector mirror to determine if and where the lines of symmetry may be. They can then glue the symbols they choose in their math notebooks and draw in the lines of symmetry along with the sentence, “I determined that this image has ____ lines of symmetry by ___________.”
Station 3) Copy Cat Pattern block symmetry
- Have students work in pairs. Provide them with a sheet of paper with a symmetry line down the middle. Students will take turns being the leader and the copycat. Each person works on one side of the line of symmetry.
- Leader: Place blocks on the sheet on their side of the symmetry line.
- Copycat: copies the leader on their side of the line of symmetry
- When the whole page is filled up the students switch.
Example:
Station 4) Snowflake Symmetry
- Tech Station: https://snowflake.nature.ca/drawing
- Have tablets or computers set up so students can explore creating their snowflakes that have 3 lines of symmetry. Use these worksheets to supplement or if technology is not available.
Station 5)
- For large classes, teachers may consider adding a 5th station with a math game that spirals back and reinforces a previous topic. Ideally, this game has been played before so that students already know what they need to do.
After: Four Corners Reflection
In the four corners of your room have a sun, cloudy sun, cloud, and thunderstorm cloud posted. Have students go to the corner that reflects how they felt about their learning today.
- Sun: I feel great! I totally get it!
- Sunny Cloud: I mostly got it, I still need some more practice.
- Cloud: I understand some parts of what we worked on but some parts are confusing.
- Thunderstorm: I felt confused and frustrated most of the time today.
Once they are in their corners they have to chat with a friend about why they picked that corner.
Focus: Exploring lines of symmetry in various objects and images.
Before: Show students a small collection of flags that have different numbers of lines of symmetry. Consider using flags that the class is connected to. Ask the students to explore them for lines of symmetry and put them in order.
Example:
(a) 
(b) 
(c) 
(d) 
During: Math Workshop (Continuation of the stations from Tuesday)
After: Exit Ticket with 2-3 shapes/images of different numbers of line symmetry. Have students draw the lines of symmetry on the object (see example below).
Focus: Connection between line symmetry and Indigenous perspectives.
Before: Symmetry in Squamish Art
Activate student thinking and highlight how line symmetry is used in Squamish
By Sinàmkin (Jody Broomfield)
By Mintle-e-da-us (Wade Stephen Baker)
During: Birch Bark Biting
Birch Bark Biting is art created by using teeth to create an indentation in folded birch bark to create a symmetrical design. This art form was traditionally practiced by Cree, Ojibwe, and Algonquin people.
Play these 3 videos of Half Moon Woman (Pat Bruder) and Rosella Carney introducing Birch Bark Biting for students. Throughout the Pat Bruder videos pause the video and ask students if they see lines of symmetry in the artwork. Also highlight the representation of nature in her art.
- Halfmoon Woman Short Intro
- Halfmoon Woman demonstrating Birch Bark Biting
- Rosella Carney Talking about her design process.
Provide Students with examples of Birch Bark Biting and have them examine them for lines of symmetry.
Have students try out birch bark biting. Birch bark is the best material to use but if you do not have access to it, patty paper, carbon paper, or wax paper can be used as well.
After: Partner share
Have students find a partner to share their birch bark creations.
Focus: Symmetry in our environment
Before: Complete the Drawing
Provide students with a copy of this image and have them complete the drawing so that it has two lines of symmetry.
During: Symmetry Scavenger Hunt
Give students a scavenger hunt sheet labeled with 0-5. Have them go around the outside and inside of the school to look for both natural and unnatural objects that have 0 to 5 lines of symmetry. Have students draw and annotate their findings.
Help support students who may have shown emergent or developing understanding of the topic on their Wednesday exit tickets.
After: Show me what you know assessment (Frayer Model)
Line Symmetry is… (explain using word | These are the techniques I use to find line symmetry… |
Provide 3 examples of line symmetry | Provide 3 examples where there is no line symmetry |
In the following weeks students can apply their understanding of line symmetry to solving perimeter problems by finding the perimeter of half the polygon and doubling the number. This knowledge will also go towards deriving the formula for the perimeter of a rectangle. Further exploration of line symmetry may connect with planes of symmetry in 3D objects.
Suggestions for Assessment
By the end of grade 4, students will be able to identify lines of symmetry in shapes and images. They will also be able to use lines of symmetry as an attribute when describing and classifying shapes and images. Students may also be considering the use of line symmetry in art and exploring the role of line symmetry in their artistic creations. Students will be able to describe the symmetry found in a variety of Indigenous art.
Suggested Links and Resources
Key Measurement and Geometry Concept 2: Regular and Irregular Polygons
Overview
Prior to grade 4, students have had practice naming polygons and classifying them according to the number of sides, vertices, size, etc. During grade 4, we will take a closer look at polygons that share the same number of sides and vertices and how they can be further sorted. At this point, students are formally introduced to the concept of categorizing polygons as regular and irregular polygons. Regular polygons are closed shapes where all the sides and interior angles are equal. Irregular polygons are closed shapes where not all sides and interior angles are equal.
Measurement and Geometry Foundations:
Foundational, supporting concepts, and related competencies that are needed to develop this grade level concept:
- Identifying, describing, and classifying 2D shapes according to multiple attributes (number of sides, number of vertices, size, color etc)
- Names of 2D shapes
- Comparing 2D shapes with some shared attributes
Progression:
- Sorting polygons according to the number of sides and vertices
- Naming polygons according to the number of sides
- Understanding that vertices have exterior and interior angles
- Understanding that BOTH side length and interior angles need to be considered when classifying a polygon as regular versus irregular
- Sorting and classifying polygons with the same number of sides and all equal interior angles as regular polygons and polygons with different length sides and/or a variety of interior angles as irregular (ex. Rhombus has 4 equal sides but not all interior angles are equal so it is considered a irregular polygon)
- Connecting prior learning of line symmetry to irregular and regular polygons
- Identifying regular and irregular polygons in the environment
Sample Week at a Glance
Prior to this week students will have explored 2D shapes in K to grade 3. They would have experience communicating and categorizing shapes according to a variety of attributes such as size, color, number of sides,, etc. This week we will connect concepts such as line symmetry, measurement using standardized units, and interior/exterior angles with the concept that polygons can be categorized as regular and irregular.
Focus: Review of the multiple attributes that can be used to categorize 2D shapes. Review 2D shapes and their names. Connecting Line Symmetry with regular polygons.
Before: Which one doesn’t belong?
During: Task and Share
Polygon sorting investigation:
Put students in groups of 3 with a variety of polygons (irregular and regular) and have them sort the polygons into categories that they can all agree on. .
Materials:
- Print out of image below (black& white is ideal) on 8×11 paper
- Rulers
- Scissors & glue
- Colored writing utensils
- 11×17 piece of paper
Once students are done, have them walk around and look at how other groups have sorted their polygons.
After:
Bring the class together and name the polygons. Create an anchor chart with 3 to 10 sided polygons.
Focus: Definition of regular and irregular polygons.
Before: Music Activation
Have students listen to this song to review their learning from yesterday.
During:
Focused Lesson:
Image one:
Some shapes have sides that are all the same/equal and some shapes have sides that are different lengths. Both these shapes are called Pentagons. The one with equal sides is a regular pentagon and the one with different length sides is an irregular polygon.
In addition to side lengths, we also have to consider interior angles when deciding if a polygon is regular or irregular.
Task:
Provide Students with a collection of regular and irregular polygons they used on Monday and the Carroll Diagram below. Have them sort the polygons according to the chart.
Ask them to draw a polygon of their own in each of the 4 categories.
After:
Bring the class together with their charts and ask them to highlight the box that is Regular Polygons with one color and the three boxes that house the irregular polygons with another color.
If time permits, start the construction of the below anchor chart.
Class construction of Polygon Anchor Chart
Draw the Frayer model graphic organizer below on a big piece of chart paper and start constructing it with your class.
Prompting questions may be:
All the shapes we worked with today are polygons. What do they all have in common?
- Straight lines
- Closed shapes
What are the differences between regular and irregular polygons?
If a polygon has straight lines and is a closed shape. Can you come up with examples of shapes that are not polygons? (heart, circle etc.)
Frayer Model:
Definition of a polygon: | Definition/Examples of irregular Polygons |
Definition/Examples of irregular Polygons | Non-examples of Polygons |
Focus: Investigating different regular and irregular polygons.
Before: 2D shapes Carroll Diagram Activation Game
Click on the image of the game. Select Level 3.
Project the game for the class to see. Label the 4 quadrants
During: Math Workshop
Station 1) Symmetry in regular and irregular polygons
Provide the same collection of polygons that was used on Monday and Tuesday and have students explore the polygons for lines of symmetry.
Station 2) Polygon Art
Provide students with centimeter dot paper and have them create a design or drawing using both irregular and regular polygons. Have them label their drawing or provide a legend with the names and types of polygons.
Station 3) Tangram Builder
Have students work in pairs. One student is the robot and is in charge of the computer, the other student is the “coder” and gives the robot instructions to move the tangrams around to form the image. Tell the students that the robot is color blind so they have to use their polygon language to describe the shapes.
Station 4) Classroom Polygon Hunt
Have students find and draw the dfiferent polygons they find in the classroom in their math journal. Provide students with measuring tapes and rulers to measure the side lengths of the polygons in the class. Students should label their polygon with the side lengths measurements.
After:
Exit Ticket: Draw a regular and irregular Quadrilateral.
Focus: Continued from Wednesday
Before: Visualizing Patterns
Select one that connects geometry with patterns.
Example by Simon Gregg
What kind of polygons do they see in this pattern?
How many triangles and how many square will be in the 4th step? How many in the 8th?
During: (see workshops from Wednesday)
After: Four Corners Reflection
In the four corners of your room have a sun, cloudy sun, cloud, and thunderstorm cloud posted. Have students go to the corner that reflects how they felt about their learning today.
- Sun: I feel great! I totally get it!
- Sunny Cloud: I mostly got it, I still need some more practice.
- Cloud: I understand some parts of what we worked on but some parts are confusing.
- Thunderstorm: I felt confused and frustrated most of the time today.
Once they are in their corners they have to chat with a friend about why they picked that corner.
Focus: Inquiry in Mathematizing Art: Tessellations
Before: Show students some pieces of tessellation art. Have them discuss the notice.
Examples:
https://www.deviantart.com/quipitory/art/Tessellating-Arrows-195935915
https://frugalfun4boys.com/fall-stem-leaf-tessellation/
https://zippyquilts.blog/tag/tessellation/
During:
Tessellations with Pattern Blocks
Have students create their own tessellations using their choice of 2 to 3 types of patterning blocks to form a core pattern. Have them repeat that core pattern to see if it can cover a whole index card with no spaces showing. Not all pattern blocks will work together to form tessellations so have students test out their choices. Once they have found a core pattern that can tessellate, have them trace out their tessellation using the blocks on a piece of paper. Once they have completely covered the paper, they can use color to develop designs or create patterns and dimension.
Materials:
- Pattern Blocks
- Paper
- Pencil
- Coloring supplies
Example: The core pattern is circled in blue.
After:
Have students complete a gallery label for their art, example below.
Gallery walk of everyone’s tessellation art.
After learning about regular and irregular polygons, students can be challenged to create art such as cityscapes, polygon monsters, and super heroes using all the different regular and irregular polygons they can create. Students can explore further classifying irregular polygons.
Suggestions for Assessment
At the end of grade 4 students will be able to communicate their understanding and classification of polygons using terminology such as irregular, regular, interior angle, and their appropriate names such as quadrilateral, pentagon, hexagon, etc. Provided with a shape students should be able to explain and justify why it is a regular or irregular polygon.
Suggested Links and Resources
Key Measurement and Geometry Concept 3: Perimeter of Regular and Irregular Shapes
Overview
Grade 4 is when students are formally introduced to the term perimeter. Students will develop the ability to use a variety of strategies such as measuring with rulers, repeated addition, doubling (for symmetrical shapes), and multiplication to determine the perimeter of irregular and regular polygons. Students will communicate their thinking using appropriate standard units of measurements. Students will also explore the concept that different polygons may have the same perimeter. In grade 5, once area has been introduced, students will explore the relationship between perimeter and area.
Measurement and Geometry Foundations:
Foundational, supporting concepts, and related competencies that are needed to develop this grade level concept:
- Identifying and understanding that polygons are 2D-shapes bounded by straight lines
- measurement using standard linear units
Progression:
- Understanding that the sides of a shape form the perimeter of a 2D space.
- Compare, estimate, measure perimeter using non-standard units
- Compare, estimate, measure perimeter using standard units
- Using repeated addition to determine the perimeter of polygons
- Finding patterns in determining the the perimeter of regular polygons (measuring one side of regular polygons since all sides are equal, measuring one side of the perimeter of a symmetrical figure since the other side has the same perimeter)
- Using multiplication to determine the perimeter of polygons
- Develop and use perimeter formulas
- Understanding that different shapes can have the same perimeter
Sample Week at a Glance
Prior to this week students will have developed an understanding of the difference between regular and irregular polygons. Students will also be able to multiply a multi-digit number with single digit numbers. If multiplication has not been covered yet this year, use single digit measurements for side lengths. When developing perimeter formulas, students will need to have a firm understanding of the relationship between addition and multiplication.
Focus: Review estimation and comparison of perimeter.
Before:
How big is our classroom? Have them estimate first. Hold up a meter stick as a possible guide.
Provide students with a bin of tools (meter stick, measuring tape, string etc) and have them measure the perimeter of the classroom.
Bring students together for a class discussion of how they determined the size of the classroom. Highlight that this week we will focus on using perimeter to describe shapes and spaces.
Play this catchy song to focus students into perimeter:
https://www.youtube.com/watch?v=ZeNBKdAslwk
During:
Have the students pick 3 to 5 objects from a pile of flat loose parts or loose parts that have a flat face. Provide students with a piece of blank paper or have them use their math journals to follow these prompts, demo each step as you go along with your own set of objects:
Pick one face for each object that you are going to focus your perimeter investigation on. (Provide students with dot stickers if necessary so they can keep track).
Order your objects from the smallest perimeter to largest perimeter according to the face you picked for each one.
* maybe where we discuss what is perimeter? How do we estimate? Etc.
Trace the chosen face of each object onto your notebook.
(Provide students with rulers, and string/tape measures if round objects were provided)
Find the perimeter of each face, label your drawing with your findings.
Was your initial estimation/comparison correct?
After:
Have students share their findings in groups of three. Taking turns to present their work.
Focus: Exploration of measuring and calculating perimeter
Before:
During: Math Workshop
Station 1) Practice: Worksheets for perimeter of a rectangle,. The focus for students should be calculating the perimeter of the shape when they are provided with the measurement of the lengths.
Station 2) Cuisenaire Creations: Have students create images with cuisenaire rods. Provide students with centimeter grid paper that students can draw and annotate their creations on. Since each cuisenaire rod is a set number of centimeters students will not need a ruler to measure the creations.
Station 3) Floor Polygons: Using painters tape, tape out a variety of polygons on the floor. Provide students with grid paper and a variety of measuring tools (tape measures, meter sticks, rulers etc.). Students should draw, measure, and record the side lengths of each shape and then use the data they have collected to determine the perimeter of each shape.
Examples:
Station 4) Geoboard Shapes
Provide students with geoboards/elastics and have them create shapes with a variety of different perimeter measurements. Provide whiteboards at this station so students can calculate the perimeter of their shape creations and communicate that information with a partner.
Station 5) Robotics
If your school has robotics/coding equipment this would be a great place to use it! Spheros, coding&go mice, botley, dash/dot etc would all work. Have students code the robots using block code to walk/draw a series of polygons. Students will have to draw upon prior knowledge of regular v. irregular polygons and knowledge of perimeter to complete these tasks.
Tasks cards examples:
Draw a square with a perimeter of 40cm.
Draw a rectangle with a perimeter of 60cm.
After: Four Corners Reflection
In the four corners of your room have a sun, cloudy sun, cloud, and thunderstorm cloud posted. Have students go to the corner that reflects how they felt about their learning today.
- Sun: I feel great! I totally get it!
- Sunny Cloud: I mostly got it, I still need some more practice?
- Cloud: I understand some parts of what we worked on but some parts are confusing.
- Thunderstorm: I felt confused and frustrated most of the time today.
Once they are in their corners they have to chat with a friend about why they picked that corner.
Focus: Exploration of measuring and calculating perimeter
Before: Which one doesn’t belong?
During: Math Workshop (Continue stations from Tuesday)
After:
Exit Ticket
Draw and calculate the perimeter of a square that has side lengths of 3 cm.
Draw a polygon that has a perimeter of 18 cm. Label its side lengths.
Focus: Different shapes can have the same perimeter.
Before:
Non Geometry related number sense routine that spirals back to a concept taught in a previous term. A variety of instructional routines can be found here.
During: Task and Share
Question/Task:
Draw as many different rectangles as you can with a perimeter of 30 cm. Label each rectangle’s width and length measurement and write an expression using the width and length to represent the perimeter.
Material: Centimeter grid paper(s), pencils, eraser, colors
Have students work with a partner on the task.
After: Bring the class together and project the centimeter grid paper. Have students share their examples. Ask students to consider one unit of the projected grid paper as one centimeter.
Ask students to consider what patterns they see in the expressions written for each rectangle. Possible student’ answers maybe: there are always 2 lengths, there are always 2 widths, there are always two measurements that are the same”. If students aren’t able to pick up on this we might prompt with the question, “How many widths, and how many lengths?”
From this we may ask students if they can come up with a rule for finding the perimeter of a rectangle using l to represent length, w to represent width, and P to represent perimeter.
Students may start with P=l+l+w+w
Prompt students with is there another way to write:
l+l → 2l
w+w->2w
P=2l+2w
Focus: Develop formulas for other regular polygons.
Before: Other than rectangles, what other shapes can you draw with a perimeter of 30 cm.
During: (this lesson may take two days to complete)
Guided Math & Learning Stations
Stations:
Put out 3-4 of the activities that students have completed during measurement and geometry as learning stations. Have students choose which activities they want to continue exploring.
Guided math:
Bring small groups of students to you and guide them through developing perimeter formulas for regular polygons (squares, pentagons, hexagons, septagon etc.) Challenge students to create a rule that works for all regular polygons.
Provide students with a variety of regular polygon shapes, scissors, rulers etc. Have them measure and record their results on the table. The table can be done as a group.
Name of Polygon | Draw a Picture | Number of sides | Side Length | Calculate Perimeter |
Prompting Questions:
- Are there any patterns that you see in your data?
- Is there a relationship between the number of sides, length of the sides and a shape’s perimeter?
- Can we write a rule using words that describes how we can find the perimeter of a regular polygon?
- Perimeter equals the (number of sides) multiplied by the (length of side)
- Does this rule work for all regular polygons?
- Can we replace some of the words with symbols?
- Goal: P = (number of sides) x (number of lengths) or P= n x l
After:
Bring the class together to discuss the question:
Why do we use formulas to calculate perimeter instead of simply measuring and adding each side?
Based on the formative assessment information from this week, next week’s planning would include measuring and calculating the perimeter of larger shapes and spaces using perimeter formulas. When determining the perimeter of larger spaces, students will need to consider what unit of measurement is appropriate for communicating their findings as well as converting between different units of measurement. If decimals have been taught, this would be a good time to spiral back and have students perform measurements or perimeter calculations where there is a decimal in the side length.
Suggestions for Assessment
By the end of grade 4, students will understand the definition of perimeter and be able to determine the perimeter of both regular and irregular polygons. Students will have developed that ability to determine perimeter by using tools such as rulers and tape measures with standard units. Students will also be able to calculate the perimeter of regular and irregular polygons using a variety of methods (repeated addition, multiplication etc.). When working with standard units, students will develop the ability to select the appropriate measurement units to communicate their mathematical thinking.
Suggested Links and Resources
Literature to support conceptual understanding:
Chickens on the Move: https://www.youtube.com/watch?v=pvj4N6Go9ks
Minecraft perimeter lesson: https://education.minecraft.net/en-us/lessons/perimeter-2