p301-307_Gr3BC_Spatial Sense_Consolidating Measurement

Consolidating Measurement Concepts: Guided Math Lesson: Measuring Monday Math Curricular Competencies Learning Standards • R easoning and analyzing: Use reasoning to explore and make connections; estimate reasonably; model mathematics in contextualized experiences • Understanding and solving: Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving; visualize to explore mathematical concepts; develop and use multiple strategies to engage in problem solving • C ommunicating and representing: Communicate mathematical thinking in many ways; use mathematical vocabulary and language to contribute to mathematical discussions; explain and justify mathematical ideas and decisions • Connecting and reflecting: Reflect on mathematical thinking; connect mathematical concepts to each other and to other areas and personal interests Content • M easurement, using standard units: Linear measurements, using standard units; introduce concepts of perimeter, area, and circumference; area measurement, using square units (standard and non-standard); capacity measurements, using standard units; estimation of measurements, using standard referents • Time concepts: Understanding concepts of time; understanding the relationships between units of time; estimating time, using environmental references and natural daily/seasonal cycles, temperatures based on weather systems, traditional calendar Possible Learning Goals • Estimates, measures, represents, and records length, height, and distance using standard and non-standard units • Selects and justifies the choice of standard or non-standard units to measure length • Estimates, measures, and records the distance around objects using standard units • Estimates, measure, and records area using a variety of non-standard units Consolidating Math Concepts 301

Teacher • Describes, through investigation, the relationship between the size of a unit Look-Fors of area and the number of units needed to cover a surface • Describes how changes in temperature affect everyday experiences • What strategies do students use to estimate? Do they use a benchmark (e.g., one fingertip is one centimetre) to estimate the length of an object? • Do they select an appropriate unit based on the attribute of the item being measured and its size? • Can they differentiate between measureable attributes such as perimeter and area? • Can they relate temperature to the type of clothing people wear or the activities they can participate in? • Do they understand how a calendar works and the relationships between various units of time? Math Vocabulary: About the mtkcaemciweelrmaoeinaenlmpateseuie,unmketrr,dcetaeera,adet,tpruhra,,eearoymems,cu,tiperoit,mCeytn,rretaeihlmt,s,eieu, tse,r, Engaging students in an activity that includes all of the measurement 302 Spatial Sense concepts they have learned within one realistic context allows you to assess their ability to distinguish among measureable attributes and apply what they have learned in problem-solving situations. Students need to be able to recognize and distinguish among the attributes of length, capacity, mass, area, perimeter, and time and connect each attribute to its corresponding standard units of measure. Students also need to vary their estimation, measurement, and comparison strategies based on what they are measuring and why. Finally, students must master their measurement skills, which includes knowing how to use and read different measurement tools and how to meaningfully interpret the results within a realistic context. About the Lesson This is an example of a guided math lesson that can be used with the little book Measuring Monday. Modify the lesson as needed to meet the specific needs of students in each group. You can carry out this guided reading lesson with a small group while the rest of the students engage in activities set up at centres. You may have students rotate through the centres over the course of a few days or allow them to freely visit the centres. Do what best suits your class. The purpose of the little book is to provide context for the math and raise curiosity about measurement in daily life. The reading is not supposed to be a barrier to the math nor is the goal to have students independently read the text, although this is a welcome outcome. If students are struggling with the text, read it to them. In this way, they can effectively recognize the mathematical concepts within the context of the story and apply their mathematical thinking.

Materials: Differentiation Measuring Monday little • The sample guided math lesson offers many more prompts and problems than books; chart paper; concrete materials; can feasibly be used in one session. They are intended to give you ideas about measuring tools what you may ask and how you can differentiate from group to group. Adjust (e.g., measuring tapes, your learning goals to meet the individual needs of each group. Create a list of thermometers, metre Look-Fors (see the Teacher Look-Fors above for suggestions), and use them to sticks); masking tape select and formulate prompts to initiate or shape conversations with students. Time: 20–30 As you progress through your guided math lesson, your focus may change, minutes per group depending on students’ responses or any misconceptions that arise. • In your reading with the group, focus on the main text; it will not be possible to discuss all of the questions in the blue boxes in one session. You may have students revisit and independently complete some of the tasks that emerge from these questions after their meeting with you. They could do so at centres while you are meeting with another group. Guided Math Lesson Cover • Read the title and ask students what they think the text might be about. Ask what could be measured on a Monday. Pages 2–3 • Read the main text to students or have them read along. Re-read the second sentence (“Follow me and my friends…”). Ask what Dara and her friends might measure. List students’ suggestions on chart paper. Have students sort the items on the list based on where they could be found (e.g., at school, at home, in the community). • Re-read the sentence “I’ll run and check the temperature on the TV.” Ask how Dara can check the temperature on the TV. Ask where else we can check the temperature. • Re-read the last sentence (“It’s 11°C,…”). Ask what time of year the story may be taking place and why they think so. • Read and discuss the questions in the blue box. Page 4 • Read the main text on page 4. Ask why the story describes the distance to Hayley’s grandma’s house in metres and in kilometres. Ask which unit seems more practical in this situation. • Ask about how long 5 minutes is in relation to other units of time like seconds, hours, and days. • Ask how long it would take Dara and Hayley to get to school if they had to walk there from Hayley’s grandma’s house. • Read and discuss the questions in the blue box. Consolidating Math Concepts 303

Page 5 • Read the main text. Ask what the first Monday of the month is for the month you are in. Ask what numbers the other Mondays in the month would be and how students know. Discuss the pattern in the numbers. • Ask students if they think they are taller or shorter than Kyle. Ask if 114 centimetres is taller or shorter than 1 metre. Ask what other items are about the length of 1 metre. • Read and discuss the questions in the blue box. Page 6 • Read the main text with students. Ask how they could calculate the perimeter of the rug in the text (e.g., measure all sides and add them; measure one length and one width, add them together, and then double the total; measure one length and one width of one of the four smaller rectangles that make up the rug and then repeatedly add the total four times). • Ask what other tools or materials could be used to measure the perimeter of an actual rug. Ask what units would be most suitable. • Ask what part of the rug would represent the area. Discuss how area is different from perimeter. • Discuss the questions in the blue box. If there is no classroom rug, create an area on the floor using tape. Ask students how they could figure out the perimeter of the room by measuring how many students fit only partway around the room. Page 7 • Read the main text. Ask students why it would be tricky to measure the area of the different-shaped tables. Ask which shape of table would be most challenging to measure and have students explain their reasoning. • Ask what other items could be used to measure the area of a desk. • Ask whether the students in the story are measuring accurately with the playing cards. Discuss what is important to remember when measuring area. • Ask what the area of the desk in the picture is. After students work independently to solve the problem, discuss their strategies as a class. Ask why it is not necessary to count every single card. Ask students how they would express their answer. Discuss why both a number and a unit are necessary. • Read the text in the blue box. Students can measure their workspace now or afterwards. Page 8 • Read the text, including the questions in the blue box. Ask what attribute is being measured. Discuss some of the ways that students could measure capacity. • Discuss what students have learned in previous lessons about how the size and shape of a container can affect capacity. 304 Spatial Sense

• Ask what standard units students could use to measure the capacity of the containers if you were to fill them with water. Ask whether each of the containers would hold more than, less than, or the same as 1 litre. Ask about how many millilitres the smallest pot might hold. Page 9 • Read the main text. Ask why it is important to have a clock in the classroom. Ask what standard units of time are evident on a clock. Ask what the difference is between seconds, minutes, and hours. • Ask what other tools students have used to measure the passing of time. • Discuss the environmental clues that can help us know what time it is. Pages 10–11 • Read the main text. Have students study the calendar. Pose some of the following prompts: – O n which date do you think the story takes place and how do you know? How many days are there until Dara’s field trip? – W hat patterns do you see in the calendar? (e.g., Measuring the bean plants happens three weeks in a row on a Tuesday.) What number patterns do you see? – W hy are events and notes in different colours? How are events grouped (categorized)? – H ow many weeks (days) are there from April Fool’s Day to World Art Day and then to Earth Day? – W hat is the next month after this month? What would the calendar for that month look like (e.g., first day, last day)? Page 12 • Read the text. Discuss what Dara could measure at the fun fair (e.g., Ferris wheel). Have students identify measureable attributes (e.g., height, diameter, number of seats) and the units they would use. Discuss why measurement would be important at a fun fair. Consolidating Math Concepts 305

References British Columbia Ministry of Education. (2015). Aboriginal worldviews and perspectives in the classroom. Victoria, BC: Queen’s Printer for British Columbia. British Columbia Ministry of Education. (2016). BC’s New Curriculum: Mathematics. www.curriculum.gov.bc.ca/curriculum/mathematics Burns, M. (1996). 50 Problem-solving lessons: Grades 1–6. Sausalito, CA: Math Solutions. Burns, M. (2000). About teaching mathematics: A K–8 resource, Second Edition. Sausalito, CA: Math Solutions. Chapin, S.H., O’Connor, C., & Canavan Anderson, N. (2009). Class discussions: Using math talk to help students learn, K–6, Second Edition. Sausalito, CA: Math Solutions. Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge. Drake, M. (2014). Learning to measure length: The problem with the school ruler. Australian Primary Mathematics Classroom, 19(3), 27–32. First Nations Education Steering Committee. (2020). Math First Peoples Teacher Resource Guide. www.fnesc.ca/wp/wp-content/uploads/2020/09/ PUBLICATION-Math-FP-TRG-2020-09-04.pdf Moss, J., Bruce, C. D., Caswell, B., Flynn, T., & Hawes, Z. (2016). Taking shape: Activities to develop geometric and spatial thinking grades K–2. Don Mills, ON: Pearson. Newcombe, N. S. (2010). Picture this: Increasing math and science learning by improving spatial thinking. American Educator, Summer 2010, 29–43. Newcombe, N. S., & Frick, A. (2010). Early education for spatial intelligence: Why, what, and how? Mind, Brain, and Education, 4(3), 102–111. Small, M. (2007). PRIME: Geometry: Background and strategies. Toronto, ON: Nelson Education Ltd. Small, M. (2009). Making math meaningful to Canadian students, K–8. Toronto, ON: Nelson Education Ltd. Small, M. (2010). PRIME: Measurement: Background and strategies. Toronto, ON: Nelson Education Ltd. 306 Spatial Sense

Van de Walle, J. A., & Lovin, L. H. (2006a). Teaching student-centered mathematics grades K–3, Volume One. Boston, MA: Pearson. Van de Walle, J. A., & Lovin, L. H. (2006b). Teaching student-centered mathematics grades 3–5, Volume Two. Boston, MA: Pearson. Wai, J., Lubinski, D., & Benbow, C. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101, 817–835. References 307