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 free-standing “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 “cross-pollination” 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.

Activate:

Watch this short video about Northwest Coast and Coast Salish shapes. Jess Kyle is a non-indigenous 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 human-made 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 non-indigenous 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 3-way comparison with shapes in math, art and nature.

Books: I Spy Shapes in Art, Math-terpieces

Pictures to print:

Susan Point

Roy Henry Vickers

Robert Davidson 

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.

Polypad(Geometry): 

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 counter-opinion?”

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: