Grade 5 – Measurement Unit Lesson #1: Converting Units Big Idea(s)
The unit chosen for a measurement affects the numerical value of the measurement; if you use a bigger unit, fewer units are required. (BIM6)
Curriculum Expectations Expectations Overall Expectations • determine the relationships among units and measurable attributes, including the area of a rectangle and the volume of a rectangular prism. (M) • solve problems involving the multiplication m ultiplication and division of multi-digit whole numbers, and involving the addition and subtraction of decimal numbers to hundredths, using a variety of strategies; (NS)
Specific Expectations Expectations • select and justify the most appropriate standard unit to measure length, height, width, and distance, and to measure the perimeter of various polygons (M) • solve problems requiring conversion from metres to centimetres and from kilometers to meters (M) • multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies (NS)
Getting Started (or Minds On)
Introduction to Learning Activity
Because this is the first lesson in the unit, I would definitely take the t ime at the beginning to gauge the students’ understanding of the mathematical concepts that will be explored throughout the unit. To do this, I would use an anticipation guide in order to assess where students are in terms of their current levels of understanding. As suggested in Marian Small’s text Making Math Meaning to Canadian Students, K-8, K-8, at the end of the unit, I would revisit the stateme nts to allow students an opportunity to reflect on their learning. Outlined below is a detailed account of how the learning activity will be introduced as well as the various cooperative learning strategies and groupings that will be used to get students talking about their thinking. Assessment for Learning Throughout the ‘Getting Started’ stage I would use ongoing observation to help assess the st udents’
current levels of understanding. Groupings The Report of the Expert Panel on Early Math in Ontario reiterates the importance of a variety of different groupings. “Students need time to communicate with their peers about mathematics and time to work independently.” (Early Math, 32) For this r eason I chose to include a variety of different groupings within the lesson, to allow students an opportunity to wor k with others. I also chose to give students a choice in their grouping for the ‘Working on It” depending on their comfort level with t he task/concept. Materials Students will be made aware that they may use any of the classroom c lassroom materials to help them answer the question however they will be required to write out their t hinking/answers on a piece of chart paper so they can display their thinking in the Gallery Walk. Markers and the chart paper will be made available at their desks. If they need any additional markers/paper they may take some from the supply table. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Introduction to the Unit (to gather data about the students’ current level of understanding about the content that will be addressed throughout the unit) : Four Corners (strongly agree, agree, disagree, strongly disagree) Ask students to agree or disagree with statements about measurement o Use the PowerPoint presentation with statements projected so all students can see Think-Pair-Share: Students discuss with peers who are at the same corner why they o made that choice Ask some students to share their reasoning
Minds On Write the following units of measurement on the board: mm, cm, dm, m, km Ask: “What do these symbols represent?” Show students a number of objects Ask: “What units would you use to measure these objects? Why?” Think-Pair-Share: Give an example of when you would use each of these units and explain why you chose this particular unit Ask: “Could you use a bigger or smaller unit? How could you do this?” Think-Pair-Square: “Why might we want to change from one unit to another? Give some real life examples.”
Present students with the parallel questions Explain to students that they will have a choice betwee n what question they can answer and they may use any of the classroom c lassroom materials to help them answer the question Tell students that they may work by themselves or with a partner
Review what to do if you have difficulties answering the question Remind students of the teachers role (that you will be circulating the classroom as they work and may stop and ask questions/take notes) Tell students that they will be required to record their solutions/thinking on a piece of chart paper so we can engage in a Math Congress
Working On It (or Action)
Task Students will be provided with a choice o f two open-parallel questions. Students may choose one of the questions to answer depending on their level of comfort with decimal numbers. Students will have the opportunity to either work individually or in pairs to solve the problem. (see problem below) Students would be asked to write the ir solutions/thinking on a piece of chart paper t o prepare for our Math Congress. Parallel Questions: Nicole drew a line longer than 0.08m but shorter than 99mm. How long might the line be? How do you know? Nicole drew a line longer than 8cm but shorter than 99mm. How long might t he line be? How do you know? Possible Errors and Misconceptions not distinguishing between units not recognizing the need for common units of measurement difficulties converting from one unit to another belief that all smaller units relate to large r ones in the same way difficulties multiplying decimal numbers not justifying their answer moving the decimal in the wrong direction
Demonstrating Understanding In order for students to be successful at demonstrating their understanding of converting units of measurement students should meet the following success criteria: Learning Goal: I am learning to change from one unit of measurement to another. Success Criteria: I can multiply and divide numbers by multiple of 10s I can recognize how many m any places I need to move the dec imal point I can move the decimal point in the appropriate direction I can organize my work clearly
I can show my thinking/work Assessment In order to gather g ather assessment data I would use a c hecklist similar to the one on page 609 in Marian Small’s text Making Math Meaningful to Canadian Students, K -8. The chart would include some of the behaviours/performances (the success criteria) I would look for as w ell as a section for anecdotal anecdo tal notes. I would circulate the classroom c lassroom as students were working on the problem and chec k off instances that I observed the desired behaviour. I would also include some of lists of probing questions that we have seen throughout the past two modules to help elicit some o f the behaviours and guide student thinking/communication (i.e. Questions and Prompts from A Guide to Effective Mathematics Instruction, K-6 – Volume Two: Problem Solving and Communication pp.81-84.) Sample: Student
Multiplies/divides
Recognizes how
Moves the
Organizes work
Shows
#s by multiples of
many places I
decimal point in
clearly
thinking/work
10
need to move
the appropriate
the decimal
direction
Notes
point Tracy Savage Ashley Mitchell
Extension Activity I my math classroom I would wo uld have an area set up with a box full of laminated task cards that students can take and work on. I would ensure that the task cards relate to the current topic that we are learning (in this case, because it would be at the beginning of the unit, I would have the task cards centered around converting units – as the unit went on there would be more task cards car ds including perimeter and area, etc.) et c.) Students could also write a journal entry about their new learning in their math journal (journal prompts provided at the beginning of the year). Examples of Task Cards for this Area are below (taken from Sharon Drummond, Elementary Enrichment Resource Teacher, Lambton Kent District School Board, Alternate Activity Menus for Math, 2009) Task #1 Do some research about world record(s) (using the Guinness Book of World Records or Websites). Create a PowerPoint presentation or a poster about some/an interesting world record(s) for length or distance. For each record, state the measurement as it is recorded in the record. Then, convert it to another unit of measurement. Find a picture of a different object that is approximately the same length as the world record object, and include it for comparison. Task #2
Create a scrapbook about units of measurement for length and distance. The first page should show how to choose an appropriate unit for measurement and how to convert measurements from mm to cm to m to km. km . The following pages will be about mm, cm, m, and km. Include pictures of objects you would measure with each unit. Task #3 Choose 10 lengths or distances to measure. Be sure to choose at least one object to measure in cm, mm, m and km. Explain which tool you would use to measure each one. For one of the objects that is measured in meters, express the measurement in mm, cm and km.
Reflecting and Connecting (or Consolidation) Consolidation)
Selecting Student Work Prior to debriefing with the students, I would have students post their solutions up around the classroom so that their classmates can walk aro und and see different ways of solving the problem/representing the solution (similar to the Gallery Walk described in our reading but at this time I wouldn’t have them give feedback to each and every student) I would then choose 3-4 samples to bring to Math Congress (depending on student solutions). I believe that the selection of student work really depends on what the students come up with. As I circulated the classroom, if there were any particular students who used a different/unique strategy or representation I would definitely highlight this. I would use the success criteria to help me decide which student samples to select. I would choose samples that may need to work on a particular aspect of the success criteria cr iteria (ex. student samples where students struggled a bit and highlight where they had success as well as students who maybe came up with the right solution, however, didn’t necessarily communicate their thinking or organize their work c learly, etc.). Key Questions Throughout the class sharing I would ask questions” to guide the discussion, to emphasize the mathematics, and to build connections between solutions and concepts in order to deepen understanding for all students.” (Guide to Effective Instruction in Mathem atics, K-6: Vol. 2, 66) Two key questions that I would definitely ask during debriefing would be:
Ask: “What did you notice about the numbers when you c hanged the unit of measurement?” (Relate back to the Big Idea) Ask: “When would knowing how to convert unit of measurements be useful?”
Bibliography
Drummond, Sharon. Alternate Activity Menus for Math. Ontario: Lambton Kent District Sc hool Board, 2009. Ontario. Early Math Strategy: The Report of the Expert Panel on Early Math in Ontario. The Ministry of Education. Ontario, 2003. Ontario. Guide to Effective Instruction in Mathematics, K-6. Volume 2: Problem Solving and Communication. Ministry of Education. Ontario. Guide to Effective Instruction in Mathematics, K-6. Volume 3: Classroom Resources and Management. Ministry of Education. Small, Marian. Making Math Meaningful to Canadian Students, K-8. United States: Nelson Education. 2009.
