The Geometry Mobile

Expectations:

E2.1 use appropriate units of length to estimate, measure, and compare the perimeters of polygons and curved shapes, and construct polygons with a given perimeter

E2.2 explain the relationships between millimetres, centimetres, metres, and kilometres as metric units of length, and use benchmarks for these units to estimate lengths

Key Concepts:

• Measurement is the process of assigning a qualitative or quantitative description of size to an object based on a particular attribute. It is always a comparison of the size of one object with another, so the same object can be described using different measurements. Therefore, knowledge of the size of certain benchmarks assists you in meaning.

Materials

• BLM1: Shapes for a Geometry Mobile (1 per pair of students)– diagrams of broken rulers from.BLM2:

• Broken Rulers (1 broken ruler per pair of students)

• scissors (1 per pair of students)

• math journals

• Per3.BLM3: Measuring Perimeter (1 per student)

Link to BLMs:

https://drive.google.com/file/d/1MfqoeZMxeZKz2ftV_XqINlzFXM57cQEq/view?usp=sharing

Have students work with a partner to generate ideas for personal benchmarks for metric length :https://docs.google.com/document/d/1St1Bpz81lpNBMJ8RSkGwN6rb6rDAQCodxC-I83JxxXs/edit?usp=sharing

Create an anchor chart similar to this:

Personal Benchmarks: https://docs.google.com/document/d/1N16uGPrp264X_P331fzpHvVAQLCiUAwxgS5SpEosRMs/edit?usp=sharing

Alternatively, you can provide this document to students for their reference

Benchmark Measurements: https://drive.google.com/file/d/1IPS12OArUB-L7m_LR-eFXsN6gDLwR5RE/view?usp=sharing

Provide each student with a copy of Per3.BLM1: Shapes for a Geometry Mobile. https://drive.google.com/file/d/1MfqoeZMxeZKz2ftV_XqINlzFXM57cQEq/view?usp=sharing

Explain the following situation:

“In math, Frances is learning about two-dimensional shapes. For a project, Frances wishes to create a geometry mobile, using a variety of shapes. She plans to glue a piece of string around the border of each shape in the mobile.”

Explain that the page shows two-dimensional shapes that Frances plans to use in her mobile. Have students identify the shapes (e.g., triangle, quadrilateral or rectangle, pentagon). Discuss their understanding of Polygons at this point, as well

Discuss how Frances will need to measure the perimeter of each shape in order to determine the length of string for the shape. Ask: “How long do you think the string for Shape A will need to be?” Remind students to include a unit (centimeter) in their estimates. Ask a few students to share their estimates with the class, and have them explain their estimation strategies. For example, students might estimate the lengths of the sides by using a personal benchmark (e.g., the width of the tips of the little fingers is approximately one centimeter), or they might refer to previous measurement experiences to judge the lengths of the sides (e.g., “The length of this side looks to be about 10 cm”), and then add the estimated side lengths together. Arrange students in pairs. Provide partners with an opportunity to estimate the perimeters of Shapes B and C. Have students explain how they estimated the perimeters.

Show students a broken ruler cut from Per3.BLM2: Broken Rulers.

Explain the following: “Frances wishes to measure the perimeter of each shape but can find only a centimetre ruler with the ends broken off. How can Frances use a broken ruler to measure the perimeters of the shapes?”

Provide each pair of students with a pair of scissors and a diagram of a broken ruler from Per3.BLM2: Broken Rulers.

Instruct the students to cut out the broken ruler. Challenge the pairs to use the broken ruler to measure the perimeter of each shape on the Per3.BLM1: Shapes for a Geometry Mobile. Observe the strategies used by the students. Some students might place the broken ruler beside each side of a shape, count the number of centimetres along each side, and then add the side length measurements together. Other students might count the number of centimetres along one side, and then continue to count on from this amount as they measure the other sides of the shape. As students work on the activity, ask them the following questions:

•“What strategy are you using to measure the perimeters of the shapes?”

•“How is using a broken ruler like using a regular ruler? How is it different?”

•“How could you measure the perimeters of the shapes in a different way?”

Watch for students who demonstrate misconceptions about measuring length with a broken ruler. For example, students might incorrectly assume that the number indicated by the ruler represents the length of a side, disregarding the fact that the left-most mark on the ruler indicates 6 cm and not 0 cm. Other students might place the ruler against a side and count the marks on the ruler, including the mark at the beginning of the line segment. By counting marks, rather than spaces, students will incorrectly include one unit too many in their measurement. Provide assistance to students who demonstrate misconceptions by showing them that each side length can be found by counting the number of centimetres (i.e., spaces on the ruler).

Provide an opportunity for pairs of students to demonstrate their measurement strategies to the class. Select pairs who used different strategies, so that students can observe various approaches to measuring perimeter with a broken ruler. Review the activity and emphasize concepts about perimeter by asking the following questions:

•“What is the meaning of perimeter?”

•“How could you use a regular ruler to measure the perimeter of a shape?”

•“How could you use a broken ruler to measure the perimeter of a shape?”

•“What advice would you give someone who needs to use a broken ruler to measure the perimeter of a shape?

”Ask students to respond to the following question in their math journals: “How do you measure the perimeter of a shape?”

SEL Self Assessments (English and French)

SEL Teacher Rubric