a quote “teachers spend much more time worrying about what they are going to tell students than...
Post on 21-Dec-2015
218 Views
Preview:
TRANSCRIPT
A Quote
“Teachers spend much more time worrying about what they are going to tell students than thinking about what experiences they are going to providefor students. To ensure that students learn in class requires carefully designed experiences that keep them engaged and make them think” Weisman
© Project Maths Development Team 2014 www.projectmaths.ie
Chief Inspector’s Report
Teach for Understanding
Mathematical Rigour
Students Collaborating
Making Connections
Challenge Able Students
Justify Reasoning
© Project Maths Development Team 2014 www.projectmaths.ie
A Different Type of Lesson 1
Watch the videoand try to guessthe question I’m going to ask!!
© Project Maths Development Team 2014 www.projectmaths.ie
Guesstimation!
Without any calculations, guesstimate how many Post-its are needed to cover all sides of the file cabinet apart from the base?
(P.S. you are allowed to get it wrong!!!)
© Project Maths Development Team 2014 www.projectmaths.ie
A Different Type of Lesson
7.618cm
© Project Maths Development Team 2014 www.projectmaths.ie
Actual Dimensions
Height183cm
Width91 cmWidth91 cm
Depth46 cm
© Project Maths Development Team 2014 www.projectmaths.ie
Do the Math!!!
© Project Maths Development Team 2014 www.projectmaths.ie
Can you come up with further questions?
If the WIDTH of the cabinet was doubled, how many more post-its would be needed?
If the HEIGHT of the cabinet was doubled, how many more post-its would be needed?
If the DEPTH of the cabinet was doubled, how many more post-its would be needed?
How long would it take to cover if it took 40 seconds for every 5 Post-its?
If you had 1,000,000 Post-its, what kind of file cabinet could you cover?
© Project Maths Development Team 2014 www.projectmaths.ie
Teaching this Way
Engaging for students
Covers the Learning Outcome(s). (3.4 Applied Measure)
Accessible to most abilities
“Realistic”
Differentiation: Challenging extension questions
© Project Maths Development Team 2014 www.projectmaths.ie
Challenge 1
2
Draw a square on the dotted grid paper
encompassing exactly 25 units .
: All vertices must be on grid points.Note
© Project Maths Development Team 2014 www.projectmaths.ie
Challenge 2
2
Now, draw a square on the same dotted grid
paper encompassing exactly 29 units .
: All vertices must be on grid points.Note
2Verify that the area is 29 units in different ways.three© Project Maths Development Team 2014 www.projectmaths.ie
Class Investigation
2
Investigate how many separate squares (regular or tilted)
with areas between 1 and 16 units inclusive can possibly be
drawn on dotted grid paper. Again, all vertices must be
on grid points.
© Project Maths Development Team 2014 www.projectmaths.ie
Searching for Patterns: Regular Squares
1 4 9 16
Square 1 2 3 4 ……………. n
Area 1 4 9 16 ……………. 2n
© Project Maths Development Team 2014 www.projectmaths.ie
Searching for Patterns: “1-up” Tilted Squares
2 5 10 17
Square 1 2 3 4 ……………. n
Area 2 5 10 17 ……………. 2 1n © Project Maths Development Team 2014 www.projectmaths.ie
Your Turn: “2-up” Tilted Squares
Square 1 2 3 4 ……………. n
Area …………….
Square 1 2 3 4 ……………. n
Area 5 8 13 20 ……………. 2 4n
5 8 13 20
© Project Maths Development Team 2014 www.projectmaths.ie
Searching for Patterns
Square 1 2 3 4 ……………. n
Regular
1 4 9 16 …………….
1-Up 2 5 10 17 …………….
2-Up 5 8 13 20 …………….
3-Up 10
13 18 25 …………….
4-Up 17
20 25 32 …………….
2n
2 1n 2 4n 2 9n 2 16n
What does the formula for the area of tilted squares look like? © Project Maths Development Team 2014 www.projectmaths.ie
Proof: Area of a Tilted Square
a
b2 2 a b
2 2a b
© Project Maths Development Team 2014 www.projectmaths.ie
Extension Question2Draw a square of area 25 units tilted
What are the areas of
the next squares which
can be represented as both
regular and tilted squares
on the grid paper? Explain
how you got your answer.
three
© Project Maths Development Team 2014 www.projectmaths.ie
Further Investigation 1
How many tilted squares will fit inside a square with area 25?
How can I count the number of tilted squares
which will fit inside regular square ? any
1713
© Project Maths Development Team 2014 www.projectmaths.ie
Further Investigation 2
Tilted Equilateral Triangles
© Project Maths Development Team 2014 www.projectmaths.ie
Extension 1: Pushing Brighter Students
The opposite vertices of a
tilted square have coordinates
(a,b) and (c,d). What are the
coordinates of the other two
vertices?
© Project Maths Development Team 2014 www.projectmaths.ie
Extension 2: Pushing Brighter Students
1. Can you prove that numbers of the form 4n+3 are not possible areas of tilted squares?
2. When is a number expressible as the sum of two squares?
© Project Maths Development Team 2014 www.projectmaths.ie
Content Slopes of Perpendicular and Parallel lines
Pythagoras’s Theorem
Area of Squares and Right Angled Triangles
Finding areas by “dissection” methods
Surds/ Number Theory
Investigating and Collecting Data
Searching for Patterns
Generalising to a method
Proof
Reasoning, Problem Solving, Persevering.© Project Maths Development Team 2014 www.projectmaths.ie
Teaching this Way
Connects to other areas of the syllabus
Similar to doing “real” mathematics
Can be adapted to all levels
Level Playing Pitch (entry point is accessible for all)
Enjoyable for Students/Teacher as “guide on the side”
Preparation for exams e.g. Jigsaw question
© Project Maths Development Team 2014 www.projectmaths.ie
top related