EDUC 4334: J/I Mathematics

1. EDUC 4334: J/I Mathematics Week One----Second Class!

2. Week 1: September 12 – 16-- L2 • Math Issue (proportional reasoning): • Mary drew a rectangle 3 cm by 7 cm • She said, “The perimeter is 20 cm and the area is 21 cm2” [Is she correct?] • She then reasoned, “If I make the length and width of the rectangle each 10 times as long, the new perimeter will be 200 cm and the new area will be 210 cm2 .” • Sarah said, “I don’t think that’s right.” • Mary said, “Oh yes it is. Multiply everything by 10.” • Who’s right?

3. Week 1: September 12 – 16-- L2continuing…. • A Note on Class Notes • Name 3 math activities from our first class • A (math) trip back in time—”roped in” • Assignment 1 (if need be) • To be introduced next week • Website: http://www.nipissingu.ca/education/dougf/ • Ontario Mathematics Curriculum • Strands (Important for Assignment 1!) • “Big Ideas” or “Key Ideas” • Next Week.

4. J/I Math Week 1 Class 2 • A Trip Back in Time: “Roped In” • “The rope” • Its characteristics • Volunteers • What triangle types can you make? • A practical history • A website of interest: http://nrich.maths.org/982

5. J/I Math Week 1 Class 2 • The Ontario Curriculum • Its Strands (five) • What might they be? • “Big Ideas” • (Next Slide) • Instruction is built around these “Ideas” • Next week: • Problem Solving—A major focus of contemporary mathematics • Recommended: look at the first sections of the Math Curriculum • Content focus: Geometry & Measurement • We’ll start the first class with a Geometry jigsaw

6. J/I Math Week 1 Class 2 • Key Ideas, continued. For example…. • Small (2009) identifies four Geometry key ideas: • Shapes of different dimensions and their properties can be described mathematically • There are many representations of 2-D and 3-D shapes • Any 2-D or 3-D shape can be created by combining or dissecting other shapes • 2-D and 3-D shapes can be located in space. They can be relocated and reoriented using mathematical procedures • (page 19)

7. Post Week Summary (L1 & L2) • The activities we did this week were intended to illustrate that: • Learning math can be a kinesthetic experience • Connections can be made between math and other subjects (here Language Arts and History, but think of other connections, say to your teachable) • Problem Solving need not be a textbook-based word problem experience • Such activities can be complete in and of themselves, or serve as lead-ins or hooks to a full lesson on the topic

8. Post Week Summary (L1 & L2) continued • A quick activity like the “triangular prism” name plate can serve as a: • Beginning of year review of geometric figures and names • A connection to everyday life (like packaging—Why might Toblerone package their chocolate bars this way? – an investigation) • And other ideas I’m sure you can come up with • The Guess My Number activity can be used as a • Review of elementary properties of number • An opportunity to practice a variety of number-related operations or relationships once they are in a number line • A model—change the nature of the “Guessing”

9. Post Week Summary (L1 & L2) continued • An activity like reading the story can be used to: • Capture students’ attention and interest in math • Same with the “imaging” activity • Highlight particular mathematics concepts • Serve as a lead-in to problem solving • Prepare students to write about their own math experiences, or write short stories that involve mathematics in some way • Engage students in other ways you can think of • There is plenty of children’s literature to draw upon!

10. Post Week Summary (L1 & L2) continued • An activity like the 12-interval (13 knot) rope investigation can be used to: • Invoke practical and/or historical uses of mathematics • Land measurement, carpentry, and so on! • Serve as a short, interesting hook on its own • Serve as a lead in to a full lesson on specific mathematics topics or concepts. For example (with the rope)— • Types of triangles • Right angle triangles (Pythagoras, anyone?) • Properties or relationships between the three sides of a triangle (e.g., Can any 3 lengths be used?) • Get you thinking about other such ideas in mathematics teaching!

11. Post Week Summary (L1 & L2) continued • The Mary and Sarah Problem at the start of L2 was intended to: • Invoke a recollection of some rectangle properties • Invoke a recollection of the concepts of perimeter and area • What do they measure? • What units of measure are used in each case? Why are they different? • Invoke thought as to any relationship between perimeter, area, and their respective units of measure • Although most attention would be on geometry and measurement, “proportional reasoning” was a major underlying theme— • Why, for example, was it right that the new perimeter as just ten times the original perimeter, but the new area was actually 100 times (10 x 10) the original area? • AND—how did people go about solving the problems raised in the various sections? • AND—did you notice this was presented in the form of a dialogue SCENARIO, and not “just” a standard word problem? • This was just an example—be creative but purposeful in developing your own.