Linear Measurement Week Three

Here's some background info on this Math main lesson block:

Linear Measurement & Coordinate Graphing - Intro

Linear Measurement Week Two

Here is what we did this week:

Day Six

• read Whose Garden Is It? by Mary Ann Hoberman



• students were asked a variation of the "Puddle Problem" from Puddle Questions Grade 4: Assessing Mathematical Thinking by Joan Westley

  "Pose this question to the students:

  "'Suppose you wanted to tell someone how large [your garden] is. What are some different ways you could do it?'

  "Tell the students to write a report on all the different ways they thought of to measure [their garden].

  "Your report should show the measuring tools you would use and tell how you would go about taking the measurements. You may need to explain how you would calculate the measurements. Be sure to use sketches wherever you think they would help."

  

  Mathematical Ideas: exploring length, width, depth, perimeter, area, capacity; using measurement tools

• after our Zoom session, students were asked to measure their gardening projects in the ways they described in their reports

Day Seven

• have students share their experiences with measuring their gardens
• review the process of finding a common denominator in order to add and subtract fractions
• look at the Puddle Problem/Garden Problem rubric and sample scored responses from Puddle Questions book
• after our Zoom session, students were asked to revise and improve their written reports based on their own self-scoring, re-measure their gardens if needed, and create a sketch of the geometric shape of their garden labeled neatly with the measurements they took

Day Eight

• show my example scale drawing of my garden on graph paper (1 cm) complete with title, scale, compass rose; recall the Continent Maps
• tell students that they will draw their garden on graph paper; explain how to count the squares available on your piece of paper (which will vary based on size) and determine what scale should be used for the garden plan so that your garden fits on your paper in a logical way

some graph paper options that are free on Teachers Pay Teachers:

Graph Paper - 1 inch

Graph Paper - 1/2 inch

Graph Paper - 1 cm

• have students share their ideas for measuring (measurement tools, aspects of garden that could be measured) as well as their figures
• explain how to calculate Circumference when you know the diameter of a circular garden pot (circumference = diameter x pi)
• explain Perimeter; have each child calculate the perimeter of their own garden
  square garden - 6 feet long, 6 feet wide
  perimeter is 24 feet

  square garden - 4 ft 3.25 inches long, 4 feet 0.25 inches wide
  perimeter is 16 ft 7 inches

  triangle garden - 79 inches, 59 inches, 97 inches
  perimeter is 235 inches

  circular garden pots
  3.5 inch diameter is approximately 11 inch circumference
  4 inch diameter is approximately 12.5 inch circumference

• do Perimeter Differentiated Task Cards #1-8
• after our Zoom session, students were asked to use graph paper in whatever size they chose to create a scale drawing of their garden

Day Nine

• error analysis of an incorrectly solved perimeter problem
• explain how to calculate Circumference with the formula C=2πr and that you need to know the radius of your circle to calculate Volume; explain how to calculate Volume of a right cylinder with the formula V=πr²h (of course, most garden pots narrow at the base, so this formula would be rarely used... but it's an interesting exploration and got us into a useful discussion of 3-D and measuring in cubic units)
• do Perimeter Differentiated Task Cards #9-24
• do Mr. Honey's Pig Pen (part 1 for everyone; part 2 for early finishers)

I deliberately skipped over Area in going from Perimeter to a short chat about Volume; I am interested in whether considering Volume and thinking about 3-D first will alleviate the difficulties children frequently encounter in moving directly from Perimeter to Area (2-D).

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