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Math Practice 5/6/14 Southwest Washington Common Core Mathematics 3
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TEACHER NOTESSummary• Students build a model of a
suspension bridge using corkboard, a chain and weights. Then find the key features and write equations in standard form.
Supplies for each team:• Large sheet of corkboard with
grid• 16-24 inches of chain• weights – paper clips with
washers
Language:• parabola• vertex• maximum or minimum• line of symmetry• orientation• roots• intercepts• quadratic function• quadratic function in
standard form • vertex form
5/6/14 Southwest Washington Common Core Mathematics 1
Build a Bridge
PA.2 Graphing Parabolas
25/6/14 Southwest Washington Common Core Mathematics
Math Practice
5/6/14 Southwest Washington Common Core Mathematics 3
Math Practice
5/6/14 Southwest Washington Common Core Mathematics 4
Learning TargetsA-REIc I can represent and
solve equations and inequalities graphically.
Understand and verify that every point (x, y) on the line is a solution to the quadratic equation.
FIFc I can analyze functions using different representations
Find vertex, maximum, minimum, orientation, roots, and intercepts of a parabola.
F-IFb I can interpret functions that arise in applications in terms of the context.
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; relative maximums and minimums; symmetries (origin, x-axis, y-axis); end behavior.
5/6/14 Southwest Washington Common Core Mathematics 5
LAUNCH• Watch this video
https://www.youtube.com/watch?v=xox9BVSu7Ok
Creative Commons License The St. Johns Bridge in Portland Oregon by Cacophony is licensed under a Creative Commons Attribution 4.0 International License.
St. John’s Bridge
Why would I show you this picture?
75/6/14 Southwest Washington Common Core Mathematics
Suspension Bridge• The suspension bridge has a parabolic shape. • The parabolic shape allows for the forces of
compression to be transferred to the towers, which upholds the weight of the traffic.
• In a suspension bridge, the roadway is actually hanging from large cables. The cables run over the top of two large towers (which are rooted deep into the earth) and connect to anchorages at each end of the bridge.
85/6/14 Southwest Washington Common Core Mathematics
Build your BridgeYou will make a model of the center part of the
bridge with• cork board with a grid on it• 1 chain hung from the origin and x-axis• 5 – 11 evenly spaced
weights
95/6/14 Southwest Washington Common Core Mathematics
Creative Commons License - Suspension Bridge by Matthias079 is licensed under a Creative Commons Attribution 4.0 International License
Build your Bridge
Find1. The roots: (0, 0) & (d, 0)2. The line of symmetry.3. The vertex: (x, y)4. The orientation.
5. The equation modeled by your chain.
Use quadratic regression OrUse ax(x – d) = y with
the vertex and roots to find a.
Write your equation in standard form.
5/6/14 Southwest Washington Common Core Mathematics 10
A Challenge – Write your Equation in Vertex Form
5/6/14 Southwest Washington Common Core Mathematics 11
Build your BridgeUse the weights on your chain to find points that
lie on your parabola.Verify these points with the equation(s) you
found.
5/6/14 Southwest Washington Common Core Mathematics 12
©Evergreen Public Schools 2010 13
Debrief• How is this parabola similar to
the ones you saw in the previous section?
• How is it different?