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Math is figure-out-
able!
Cathy Fosnot - Young
Mathematicians at Work• Big, rich problems
•Class congress: specific groups share toward targeted goal•More directed, focused mini-lessons
Landscape of Learning
The New TEKS
A.b.3Students will study linear, quadratic, and exponential functions and their related transformations, equations, and associated solutions.
The New TEKS
A.b.3Students will use technology to collect and explore data and analyze statistical relationships.
The New TEKS
A.b.3Students will study polynomials of degree one and two, radical expressions, sequences, and laws of exponents. Students will generate and solve linear systems with two equations and two variables and will create new functions through transformations.
The New TEKS
A.c.3Linear Functions, Equations, InequalitiesThe student will determine the effects on the graph of the parent function f(x) = x when f(x) is replaced byaf(x), f(x) + d , f(x - c), f(bx) for specific values of a, b, c, and d
Motion Sensor
TI CBR2
What Other Scenarios?
How Can I Walk?
•a line that goes up?
•a line that is steep?
•a curve that opens up?
•a curve that opens down?
•a graph that starts at 6?
•a horizontal line?
Watch the Bird Fly
What Did We Learn?
Birds Fly
What Did We Learn?
Compare Birds’ Flights
What Did We Learn?
Problem
Strings
2 x 274 x 278 x 2710 x 279 x 275 x 27100 x
2799 x 27
Problem
Strings
49 + 287 x 7 + 4 x 777 + 6311 x 7 + 9 x
756 + 247 x 8 + 3 x 8
88 + 7211a + 9a
Counting
Additive
Multiplicative
Proportional Reasoning
Algebraic Reasoning
Problem
Strings
Start at 2, walk away 1 ft/s
Start at 10, walk toward 2 ft/s
Start at 5 and stand stillSaw at 2 ft at 1 s, 3 ft at
2 sSaw at 16 ft at 3s, 15 ft
at 2 sSaw at 4 ft at 3 s, 8 ft at
6 s
Wait Time ...
Piaget
•Social Knowledge
•Logico-Mathematical Knowledge
Do you go up first or over? (2, -3)
Which axis is called x? y?Who is the 8th president of the
US?Whose variable notation do
we use?
Math is Figure-out-able
•Give kids a chance to build intuition
•It’s about relationships:
- Between what you know and the new, build to the new
- Between teachers and students to build young mathematicians
