Measurement and Geometry
Measurement and Geometry are related concepts that fall under what previous curricula called Shape & Space. Throughout K7, 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 2D shapes and 3D 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 K7 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 nonstandard 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 57 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 2
Measurement and Geometry
Students in grade 2 continue to explore measuring and shapes in very concrete ways. They continue to build skills like sorting, increasing the complexity by considering multiple attributes, rather than the single attribute sorting they do in grade 1. The big shift with measurement in grade 2 is incorporating the use of the standard units meters and centimeters for measuring length, width and height of objects. The time spent exploring the relationships between 2D and 3D shapes, measuring objects and and exploring shape attributes provides the foundation for the expansion of measurement from linear to mass and capacity in grade 3.
Key Concepts
Key Measurement and Geometry Concept 1: Direct Linear Measurement
Overview
Grade 2s are introduced to the standard units meters and centimeters for use in linear measurement. A key part of this learning is the introduction of rulers and other linear measurement tools. Questions such as, “Why are standardized units helpful?” are important for students to revisit throughout the learning. Students build their ability to measure accurately and estimate reasonably by being given the opportunity to practice both estimating and measuring in a variety of contexts. To facilitate more experiences, teachers can integrate estimating and measuring across a variety of subjects, such as art, gym and science, whenever opportunities present themselves. Students can also be encouraged to think about and discuss decisions that they make around measurement, such as what unit they will use and when to use estimation versus exact measurements. Presenting students with problems and projects that involve measurement helps encourage connections between mathematical skills and their application in context.
Measurement Foundations:
 Measures using nonuniform unit (ie: hands)
 Measures using uniform units (cubes)
 By lining up multiple units
 By iterating one unit (using one cube to measure the length of a book)
 Compares choices for measuring using nonstandard units
Progression:
 Understands that centimeters and meters are units that have a set length (standardized) used to measure length
 Measures objects using a ruler, tape measure or meter stick
 Explains why standard units are useful
 Identifies items that are “close to a centimeter” and “close to a meter”
 Estimates object lengths in centimeters or meters
 Measures the dimensions of objects for specific purposes (Will it fit?)
Sample Week at a Glance:
Grade 2 is an important year in measurement and geometry for building connections between concrete and symbolic representations. Students will benefit from experiences throughout the year that allow them to measure, draw and sort 2D and 3D objects in context. While the lessons below can be used to plan one week of learning, they are offered as examples of experiences that can be adapted and expanded upon to fit themes and projects throughout the year. Add measuring tools to classroom centres for free play, such as measuring cups, calendars and measuring tapes. Encourage students to measure whenever possible as they engage in daily activities and other subjects. Ask questions like:
 What could we use to measure ____?
 Will it fit?
Focus: Standard measurement and meters
Read Aloud: Measuring Penny by Loreen Leedy
*Explain to students that ‘inches’ are a standard unit of measure that is still used, but most countries now use the metric system, which uses standard measurements that we are going to explore.
Explore (pairs):
 Show students a meter stick and ask them to find an object that is about 1 meter long
 Give each pair a meter stick and ask them to measure their object and label it w a blue sticky for less than a meter, a yellow sticky for exactly one meter and a pink sticky for more than 1 meter.
 Once each group has labeled one item, they will measure items labeled by other students. If they agree with the measurement, they put a checkmark on the sticky, if they disagree, put – for less than a meter or + for more than a meter or = for exactly one meter
 Have students return to their original item, look at the feedback and remeasure/change their sticky if they choose.
 As students work, take note of students who are attending to how to properly use the meter stick and who fix mistakes in progress
Consolidation (gallery walk):
 Gather students together for the gallery walk
 Choose a group/student who demonstrated accurate measurement throughout the activity. Ask them to demonstrate how they measure their object. Highlight important elements like matching up the end with the 0.
 Ask: What is important for us to remember when using measuring tools?
 Choose a group/student who remeasured and changed their sticky. Highlight how their thinking changed and why that helped them.
 Ask: Why is it important to check our measurements or measure more than once?
Focus: Standard measurement and centimeters
Warm Up:
 Give each pair a meter stick and a ruler that have centimeters marked
 Ask: What do you notice about the markings on the tools?
 Students may notice:
 Markings on both are the same distance apart
 Some of the marks are longer than others
 The marks are labeled ‘cm’
 There are numbers above some of the marks
 Explain that meters are made up of centimeters and each numbered line is a centimeter.
 Students may notice:
Scavenger Hunt (pairs):
 Give students the list of measurements above.
 Have them collect objects in the classroom that they estimate match each measurement.
 Once they have found all the items, groups can then measure to see if their estimates were correct.
 Students write the actual measurement of their found items beside the measurement on the list.
 Take note of students who are using strategies for estimating and measuring that will be useful in the consolidation.
*Students who finish early can continue measuring to find objects that are closer to the given measurement on the list.
Consolidation (Whole class):
 Sequence students to share the strategies for estimating and measuring that you noted during the scavenger hunt. You might choose to highlight students who:
 Use a referent when estimating
 Choose a ruler or meter stick to measure depending on the size of the item
Focus: Apply mathematical understanding of measurement through inquiry.
Project: School Garden
Click here to access the School Gardens resources from Farm to School BC.
*Note: The activities listed here could be given as hypothetical contextualized tasks over a period of time or throughout the year in building and managing a real class garden (indoor or outdoor). This lesson can also be used to explore shapes if shape attributes are discussed:
 What shapes are our seeds?
 What shapes are our garden beds/pots?
 What shapes fit best into the space we have?
Part 1: Planning A Garden
 Give students time to explore a collection of gardening books that you bring from the library.
Ask: What will we need to measure to plan our garden?
Students might note: size of the space, size of beds/containers, how many plants, etc.
 Give students a collection of containers or pattern blocks that represent possible shapes of planting spaces. In groups of 3, students can work to find the best arrangement based on the criteria:
 Fits into the template: use graph paper and give them an exact number of squares to cover that relates to your space or give them a shape template if your garden space is not rectangular.
Ask: What shapes of beds/containers fit this space?
Remember: Although we are using grid paper, the focus for grade 2 is on linear measurement, so the focus should be on the squares as arrays of rows rather than areas.
 Fits into the template: use graph paper and give them an exact number of squares to cover that relates to your space or give them a shape template if your garden space is not rectangular.
 Consolidate what students learn about size and number of beds?
 How many beds should we have and how big should they be?
 Encourage students to use their mathematical reasoning to justify their arrangements.
 Extend: Have students use their drawings to mark out the actual beds using string. They can then measure and record the actual measurements on their diagrams.
Part 2: Planting A Garden
 Explore the planting instructions on the seed packets.
Ask: How will we decide how many seeds to plant in each container?  Give students graph paper so that each square represents 1cm. Allow them time to experiment with different models of planting seeds based on the spacing recommendations on the seed packets.
 Consolidate the learning by examining the different plans and discussing strategies for planting. Have students “pitch” their plan using mathematical reasoning.
 Extend: Have students plant their seeds and measure the plants as they grow
Part 3: Harvesting A Garden
There will be lots of opportunities to measure as you harvest. Here are some ideas:
 Which vegetable is the longest?
 What is the difference between the longest/widest and shortest/ narrowest vegetable/plant we grew?
 If we put all the earthworms we found end to end, how long would they be?
Focus: Develop and apply mathematical understanding through play and problem solving.
Math and ADST: The Tallest Tower
*Note: This lesson can also be used to explore shape if questions addressing shape attributes are discussed:
 Which shapes make up your tower?
 What shape is the tower?
 Which shapes are good for building a strong tower? A tall tower?
Part 1 (Hook):
Show students this short marshmallow and spaghetti only video of Mike Holmes and his son doing a similar challenge. This is great to use as a “hook” for students in the opening of the lesson or students can simply do the challenge this way (with spaghetti and marshmallows only).
Part 2 (Build):
There are many adaptations of this challenge that can be found using Youtube or Google. Here are the instructions for one version (see below the picture for video and written instructions).
The spaghetti tower:
 Video instructions (use ‘meter’ instead of ‘yard’)
 Written instructions (Teachers can decide whether to use 30 or 18 minutes and 20 or 30 sticks)
 The challenge can be done without the marshmallow with different materials, such as paper, blocks, styrofoam cups or straws. Ask questions like:
 Which materials make the tallests tower?
 What is the tallest tower we can make?
 Can we build a tower taller than 1 meter?
 How wide a base do we need to support a tower taller/shorter than a meter?
Part 3 (Consolidation):
Discuss the following:
 What strategies helped you build?
 What strategies helped you measure?
 How did we measure whose was “tallest?”
Students should be allowed to measure their own tower and those of others. Discuss how to measure and let the students debate and decide if there are any disagreements. For example, if the top of the tower is leaning over, do we measure straight up from the ground to the marshmallow, or the length of the tower itself? Allowing children to discuss and decide the meaning of “height” will better help them understand measurement than doing this decisionmaking for them.
Continue to look for opportunities for students to engage in linear measurement throughout the year. Ensure that, when you do activities in other subjects that involve measurement, you take time to consolidate that learning each time. Ask students: What strategies did you use to measure accurately? How do you know that your measurement will work? How can we measure this object/distance?
Suggestions for Assessment
Success Criteria (For use by teachers and students)
 Compares standard units to nonstandard units (similarities and differences)
 Measures and estimates in meters and centimeters
 Justifies reasonableness of measurements and estimates
 Uses measurements to solve problems and complete tasks
What to look for:
 Students independently choosing a measurement tool that fits the task
 Strategies for measuring accurately: lining up the zero, keeping the measuring tool still as they find the measurement.
 Use of referents when estimating
 Use of measuring tools, such as their ruler, in play or other activities (unprompted)
Suggested Links and Resources
Key Measurement and Geometry Concept 2: 2D shapes and 3D objects
Overview
Students beginning grade 2 already have two years of exploring shapes to draw upon from kindergarten and grade1. They will use that knowledge and language to explore shapes in increasingly complex ways. They will learn to sort objects using more than one attribute and use multiple attributes to describe, compare and construct 2D shapes. Grade 2 students look at the relationship between 2D and 3D shapes, identifying the 2D shapes that make up 3D objects. Students can be encouraged to explore these shapes in art and the environment, as well as in their pure mathematical forms. Asking questions such as, “Is this a circle/triangle/square?” and asking students to provide evidence of their answer is a great way of getting students to deeply consider the key elements of particular shapes, as well as practice making conjectures supported by mathematical evidence.
Geometry Foundations:
 Attributes of basic 2D shapes
 Sorting shapes using one attribute
 Describing shapes using positional language
 Making shapes out of other shapes (2 triangles to make a rectangle)
 Identifying shapes in the environment
Progression:
 Sort shapes using more than one attribute
 Explain sorting rules using more than one attribute
 Name and describe common 2D shapes (circle, triangle, rectangle)
 Construct 2D shapes
 Identify 2D shapes within 3D objects
Sample Week at a Glance
The activities in this week are meant to demonstrate how teachers can integrate learning about the attributes of 2D & 3D shapes throughout the year. Students in grade 2 have already been introduced to basic 2D and 3D shapes and they are not required to formalize their use of mathematical language (edge, angle, area, etc.) until later grades, so grade 2 is a great year for deep exploration of the attributes of shapes like square, triangle, rectangle and circle, sphere, cone, pyramid, etc.in a broad variety of contexts. Before beginning the following lessons, students need to have a general understanding of how we describe and sort different shapes. They will deepen and broaden that knowledge as they work with the shapes in context. The lessons in this week can follow or be interleaved with the lessons in the Measurement Week at a Glance.
Focus: 2D shape attributes and construction
*Note: This activity can be extended over several days. It can also be set up as a station once students have learned the basic steps.
Activate:
Desmos: Guess My Shape routine (This routine can be adapted to use without technology by using attribute shapes, 3D solids or pictures)
 Project the slides onto a whiteboard or piece of blank chart paper
 Give clues one at a time using shape attributes. For example: The shape has 4 corners.”
 Students eliminate shapes that don’t share the given characteristics until they have determined which shape/solid is the one being described.
 Once students know the routine, it can also be played in small groups or partners.
Explore:
Paper Patchwork activity from NRich
Once students have experimented with this basic fold, there are many resources to be found for extending geometric learning through Origami, some of which can be found in the links below.
Consolidate:
A lot will happen during the exploration. When looking for student examples for the consolidation, focus on the language students use to name and describe shapes, as well as students who create one shape from combining others. You might ask questions like:
 What shapes were you able to create (square, rectangle, triangle)?
 What do the shapes you created have in common?
 What shapes were you unable to create?
 What do the shapes you weren’t able to create have in common?
 Which shapes are helpful for creating other shapes? What properties make a shape useful for construction?
Focus: Develop, demonstrate, and apply mathematical understanding of 2D and 3D shape attributes and relationships through play, inquiry, and problem solving.
Read Aloud: Walter’s Wonderful Web
 Ask: What makes Walter a good mathematician?
He knows lots of shapes. He knows how to put shapes together. He is persistent. He solves his problem using math.
 How could we use our knowledge of shape attributes to make a really strong web?
Use strong shapes (Which shapes are strongest)? Make the shapes/web 3D (What are the names of a 3D square, circle, etc?).
Explore (groups of 3): Explain to students that they are going to help Walter build the strongest web possible using their knowledge of 2D and 3D shapes.
Option 1 (Marshmallows and toothpicks): If students are given these materials to work with, this activity would make a good one to do as the lesson before the Tallest Tower lesson in the measurement week at a glance. Students will build a freestanding “web” using the materials.
Option 2 (string): If this option is chosen, give each group a spool of thread and something to weave around (tree branch or chair legs). Students will create a web that can support a weight balanced in the center.
For both options keep the instructions simple: Construct the strongest web you can that will hold a weight in the center. Encourage students to be creative and experiment with different strategies. Remind them that their web must be constructed of shapes that they can name and describe (both 2D & 3D), but it is also ok if shapes emerge for which they don’t know names.
Once students have worked for about 10 minutes, do a “crosspollination” of ideas by allowing students to circulate and then return to work on their web for another 15 minutes. Give more time if students are actively still constructing.
Test each web to see if it will hold the weight (do a test in advance to make sure your weight works for the materials you’ve chosen).
Consolidate:
 Which shapes are strongest?
 What are the names of a 3D square, circle, etc?
 What attributes of shapes are important when constructing?
 What shapes appeared in your web as you built?
Exit slip: Draw or take a picture of your web. What 2D and 3D shapes did you include? Why did you include those shapes? Note: encourage students to discuss shapes that “appeared” as they built, as well as shapes that they intentionally constructed.
Focus: First People’s world views and mathematics connections to other areas.
Notes: Teaching in Culturally Responsive ways includes integrating activities into the classroom with the appropriate cultural learning and protocols. As BC educators, Northwest and Coast Salish are important groups to learn about, however, if you are from a different area of BC, you may wish to do some learning about the art of those nations as well. You may wish to offer this lesson in conjunction with learning more about Indigenous Peoples in art, social studies or language arts. Robert Davidson (Haida: Northwest Coast), Roy Henry Vickers (Tsimshian, Haida and Heiltsuk: Northwest Coast) and Susan Point (Musqueam: Coast Salish) are just 3 of the Indigenous artists from BC who have made impacts on the international art world while revitalizing and evolving Coast Salish and Northwest Coast traditions through
art and advocacy. All 3 work in both 2D (painting and printing) and 3D (carving), so their work can be used to explore the traditional shapes in both forms.
You can provide this handout so students can cut out the shapes to build their patterns concretely or use the 3D printer code in this folder to create shapes that students can use.
Vocabulary: These words can also be presented in Indigenous languages if you have access to translations for your area.
2D 
3D 
circle 
sphere 
crescent 
lune 
trigon(triangle) 
Triangular prism/pyramid 
oval 
ovoid 
uform 

square 
cube/pyramid 
rectangle 
Rectangular prism 
Activate:
Watch this short video about Northwest Coast and Coast Salish shapes. Jess Kyle is a nonindigenous educator in Surrey School District. This video was created in consultation with Nadine McSpadden and information from other Indigenous sources.
Explore (small group activity):
 Note: Teachers may choose one of the options, expand this lesson into several activity periods or set up the options as stations.
Provide this handout so students can cut out the shapes to build their patterns concretely or use the 3D printer code in this folder to create shapes that students can use.
Option1: Sorting
Compare and contrast geometric shapes (attribute/pattern blocks and 3D solids) with the Indigenous shapes:
 What is the same/different?
 Zoom in: Is a trigon a triangle? Teacher note: Sort of.. However, in math, triangles are generally considered to have straight sides and fall into the category of trigons., which can have curved sides. In artwork shapes are generally stylized, so triangles become trigons. Similarly, straight lines are rarely found in nature, so trigons would be more likely than a mathematical triangle.
Option 2: Scavenger Hunt (shapes in nature)
This activity is best done outside, but can be done inside using books, pictures or natural materials gathered.
Books: Shaping Up Summer, Sorting Through Spring
Have students find multiple representations for the words in the vocabulary table. Have them look outside and inside at both natural and humanmade objects/environments.
Questions for discussion:
 Where do shapes live in nature?
 Compare 2D and 3D shapes listed in the vocabulary table to representations in math and nature.
Option 3: Scavenger Hunt (shapes in art)
Give students art books and pictures by both Indigenous and nonindigenous artists, such as the sample collection below.
Questions for discussion:
 Where do shapes live in art?
 Compare 2D and 3D shapes listed in the vocabulary table to representations in math and art.
 If you have done the nature scavenger hunt beforehand, students can do a 3way comparison with shapes in math, art and nature.
Books: I Spy Shapes in Art, Mathterpieces
Pictures to print:
Consolidation:
 What did we learn about the different ways that shapes are used?
 What is unique about how mathematicians use shapes compared to shapes found in art and nature?
 Why is it important to think about the context/perspective that we are in when we are describing shapes?
Focus: Use technology to explore mathematical concepts and problems using shapes.
Grouping: 1 ipad/laptop per group of 3 students. These activities can also be set up as stations for further practice once students have experienced them.
Low tech adaptations;
 Project the polypad images and have students discuss and draw solutions
 Give students materials such as play dough, paper shapes and scissors, geoboards and pattern blocks or tangrams instead of Mathigon
Mathigon has a few activities and manipulatives that students can engage in to foster spatial reasoning and an understanding of more complex shapes. Introduce them one at a time and then use them as activities for practice or when you are pulling students for support with other concepts throughout the year. This will keep geometry learning fresh and developing for students.
Tangram Builder: Different templates are provided so students can challenge themselves.
With the tools on the polypad, students can add shapes, which can then be scaled, cut, folded, etc. Give students challenges to explore such as;
 Cut the shape into the largest number of triangles possible.
 Make the fewest amount of cuts to transform the shape into a square.
 Can you make a (sun) using only (2 shapes)
 Students will have to discover that they can cut up one shape to make the rays. They may try to claim just a circle is a sun. Ask them to justify their thinking to convince a group or the class and then vote.
 What is the least/most number of sides a shape can have?
 Have students create challenges for each other.
Consolidation:
 What did we learn today about the attributes of 2D shapes?
 What do you still wonder about shapes in math?
 What helps us get better at challenges like these?
Building things, doing puzzles, arts and crafts, patience, persistence, trying ideas, etc.
Focus: Consolidate learning/assessment task
Opening (Whole Class):
Project the menu below or give students a copy. Explain that they need to create enough shapes to satisfy all the attributes on the menu.
Teacher: ”Is there a shape that will satisfy A?”
Student: “Triangle.”
Teacher: (Draws a triangle.) “Now what should we do?”
Student: “Draw a square!”
Teacher:” Why?”
Student: “A square has 4 sides and that’s B.”
Do only enough exchanges at this point that students understand they are to draw shapes to meet the menu criteria. Do not over scaffold at this point. If students ask questions that are ambiguous, ask for justification to the class and discussion, rather than giving an answer.
For example:
Student: “But a square also has 3 sides, plus one, so can’t we just use a square?
Teacher: “Class, S wants to know if we are ok with shapes that have more than the requirement. S will you give your reasons?”
Student: “Well, a square has four sides, but 3 is part of 4, so I think I should be able to use just a square instead of a square and a triangle.”
Teacher: “Would anyone like to offer a counteropinion?”
Student 2: “If we do that then everyone might just pick a giant shape!”
Student 1: “Then it should say ONLY 3 sides.”
Teacher: “Class, should we say ONLY 3 sides or should we allow figures with a greater number of sides?’
These little debates don’t need to take much time and all students will benefit from the thinking involved in making this decision. After all, either answer is mathematically legitimate in the end.
Explore (groups of 3):
 Give students a few minutes to work on the task in their groups. Circulate to gather formative assessment and note students who have helpful strategies to share in the consolidation.
 Offer the next steps as groups are ready for them, rather than to the whole class at once.
 When a group declares they are finished, ask, “What are the fewest number of shapes you can use to satisfy the whole menu?”
 How do you know you have the fewest?
 Is this answer the only answer?
 How many answers are there to the problem?
 Can you create a menu that can be solved with only 3 shapes?
*It is not necessary that all groups complete all steps*
Consolidate:
 What strategies helped you get started?
 What strategies helped you reduce the number of shapes?
 What strategy helped you determine the least number of shapes?
Exit slip:
Students can continue to do activities to help foster spatial awareness, such as lego, playing with tangrams and pattern blocks etc. They should be provided with activities throughout the year that challenge them to think about 2D and 3D shapes and how they can be constructed and manipulated. In grade 3, students focus on the construction of 3D shapes and deepen their understanding of how those shapes work.
Suggestions for Assessment
Success Criteria (For use by both teacher and students):
 Identifies and describes circles, triangles, squares, rectangles, spheres, cubes and other familiar 2D and 3D shapes.
 Constructs and draws 2D shapes
 Identifies 2D shapes that are part of 3D shapes
 Applies their knowledge of shapes to solve problems
What to look for:
 Sorts objects using 2 attributes
 Explains the sorting rule
 Mathematical language used in descriptions and justifications
 Describes relationships between 2D and 3D shapes
Suggested Links and Resources
 Tangrams (digital)
 Paper Folding:
 Purposeful Paper Folding (NRich article)
 Origami in Lessons Collection (Artful Maths)
 NRich Paper Folding activities
 Mathematical Origami (Mathigon)
 Menu Math: