Dr. Bob Mann Western Illinois University

On the lined side of your notecard…record  Your name  Your school  Grades and courses you teach

On the back of your notecard, record  The NCTM 5 content standards  The NCTM 5 process standards  Number Sense, Algebra, Geometry, Measurement, Data Analysis and Probability  Problem solving, reasoning and proof, connections, representation, communication

Notecards  Can be used to share information  To ‘index’ information  To record ‘notes’ (or recipes)  To answer problems and checks Area and perimeter  For test prep and ‘low-tech’ clickers  For exit cards….  I have, who has

But they can be used for much more….  Two sizes out there  What are they?  What shape are both?  What is perimeter and area of each?  Are these two rectangles similar?  Why or why not?

Similar?  What does it mean to be similar?  Need for precision  Are they proportional???

Symmetry 1  How many lines of symmetry does your card have?  How do you know?  A rectangle must have _____ lines of symmetry  A rectangle can have ______ lines of symmetry

Area and Perimeter  What is the size of your notecard?  What is its perimeter?  What is its area?  Could show….

Cutting Corners  From the top right corner of your notecard, cut out a smaller rectangle  Leaving an L shape  How does the area of this shape compare to the area of your original notecard?  How does the perimeter of this shape compare to the perimeter of your original notecard?

Area, Perimeter and more 1. Can two shapes have the same perimeter and different areas? 2. Can two shapes have the same area but different perimeters? 3. Cut out a triangle and investigate 4. Build a box…. Build a box….

More measurement…  Everyone needs a 4 by 6 notecard  Then, get out your rulers

We don’t need no stinking rulers…  On your 8.5 by 11 inch sheet of paper draw a diagonal.  Put a point close to the bottom left end of that diagonal  Use your notecard to mark off 6 inches and then 12 inches  What other numbers can you create….. What other numbers can you create…..

NOTECARDS RULE!  What if you could not fold?  If you used a 3 by 5 card? Other cards?  You could do a similar investigation with angles—you begin with a 90 degree angle— what else can you create???  Geometric Thinking….  Tangram 1 Tangram 1  Tangram 2—from Mathforum.org  Tesselations

Homework Check  1. Add ¼ + ¾  2. Add 3/10 + 4/10  2. Add 2/8 + 3/8  POD: Add ¼ + 3/8

Sample Test Question  7. When graphed in the (x, y) coordinate plane, at what point do the lines x + y = 5 and y = 7 intersect?  A. (-2,0)   B. (-2,7)   C. (0,7)   D. (2,5)

True or False  Every Square is a Rectangle.  Every Rectangle is a Square.  Two shapes of equal perimeter can have different areas.  The answer to three of these statements is true.

Short data digression  Dot plot  Bar graph  Line plot  Pie chart

I Have, Who Has  Many possible topics  Pre-make cards  Use over and over

Symmetry  How many lines of symmetry does your notecard have?  Show me.  Test question….

Fractions  Suppose your notecard is a cake and you would like to divide that cake into two equal pieces. Using just one straight cut, how many ways can you do this?  See dynamic notecard See dynamic notecard

More Fractions  Suppose you want to divide your notecard into 4 equal parts.  See how many different ways you can come up with to do this…  Brownie delight and cutting the cake

Midpoint Mania  Find and mark the midpoint of each side.  Connect these points.  What shape do you get? How do you know  Find the midpoints of the sides of these new shapes and connect  What shape do you get? How do you know?

More Midpoint Mania  Is there a pattern in the consecutive areas of the midpoint quadrilaterals?  Is there a pattern in the consecutive perimeters of the midpoint quadrilaterals?midpoint quadrilaterals

Symmetry 2  Fold along one of the lines of symmetry Make one cut across this fold Unfold to get a shape What do you know about this shape?  Fold twice and make a similar cut Unfold to get a new shape What do you know about this shape?

Folding  Fold your notecard in half How many sections?  Fold again so that the second fold is the perpendicular bisector of your first fold How many sections?  Fold again so that the new fold is the perpendicular bisector of your previous fold How many sections?  Patterns? Extensions….how far…..  Fractions? ¼ + 3/8

Foldables  Many possibilities..probably other sessions  Simply fold in half once to create a small book Provide four factoring methods and examples SSS, SAS, ASA, SAA Mean, Median, Mode…Midrange? ??????

Cube nets require 6 adjacent squares in various combinations. Can you use the 24 squares on your notecard to create 4 cube nets? Can you get 3 non-overlapping nets?

AABBB AB AB AAB

Ice, Ice, Baby  Ice Cube’d Ice Cube’d  This version from a Teaching Children Mathematics article

Triangle Tribulations  Let one 6-inch side of your notecard be a base segment and label it BC Determine 6 points A1 to A6 such that triangle ABC is acute Determine 6 points O1 to O6 such that triangle OBC is obtuse Determine 6 points R1 to R6 such that triangle RBC right (no more than 2 of these points can be on a notecard edge!) What can we learn from this??

Triangle Treachery  Use the 6 inch side of your notecard as a base AB.  Place a point anywhere on the opposite side and call it C.  Draw segments to get triangle ABC  What is the area of the triangle?  What is its perimeter? How do you know?perimeter? know  Worksheet Worksheet

Getting the most from your triangle  What is the largest triangle you can make from your notecard?  What is the largest isosceles triangle you can make from your notecard?  What is the largest equilateral triangle you can make from your notecard?  What is the largest square you can make from your notecard?

Making the Most from your tent  Fold your notecard along its longest line of symmetry and consider using this to make a basic pup-tent  How tall should you make this peak (thus bringing in the edges) so that the resulting tent volume is a maximum?  How could we analyze this?analyze this  What can we learn?learn?

A “Plane” Notecard  Put three noncollinear points on your notecard  Draw lines through each pair of points  We now have segments, rays, angles  Triangles  Sum of exterior….  Sum of interior….  More geometric thinking

Build a Bigger Notecard  Begin with 1 notecard  Add to it to get a new notecard that is twice as wide and twice as long  How many notecards do you need?  When we doubled the dimensions, we  _____________________ the area….  How many cards would be needed to triple the dimensions

Fractions and Sums  What is the sum of the infinite series

Fibonacci Fold  Picture Picture  Dynamic Version Dynamic Version

Exit Cards  On your notecard, record 1. One thing you learned today 2. One thing you still have questions about 3. Any comments you have 4. Any contact information you wish Notecards Rule!!