Algebra in Action by: The Whiz Kids

Algebra in Action by: The Whiz KidsJoel BradshawTracey GuidaNina MunNancy ScottSteve WeitlichHow we see math word problems:

If you have 4 pencils and I have 7 apples, how many pancakes will fit on the roof?

Purple, because aliens dont wear hats.Why Algebra in Action?

Bridge Design ProBlem1. Design a truss bridge (Warren, Howe, or Pratt) with the following specifications:Span = 102 cmWidth = 11.5 cm (# 3)Vertical and Horizontal Beams = 17 cm (# 4)Diagonal Beams = 24 cm (#5)2. How many joints, vertical and horizontal beams, and diagonal beams will be used in your design?3. Sketch your design. 4. Build your bridge.

Bridge Design: PrattABCDEFGHIJKLExternally Applied Force, FUsing PASCO Bridge Set: L = 17 cm = 0.17 mh = 17 cm = 0.17 ma = 24 cm = 0.24 mahLFree-Body Diagram (FBD)ABCDEFGHIJKLExternally Applied Force, FRARLFind the reaction forces at A and L, RA and RL, respectively by applying the equilibrium equations: F = 0 and M = 0 Method of JointsUse the Method of Joints to analyze each beam in terms of: The magnitude of internal forceWhether the force is in compression or tensionUse symmetry and analyze only of the truss. Analysis of Joint AARAFBD of Joint AFABFACahLxy Fy = 0RA FAC = 0FAC = RAahhaFACahL(FAC)x(FAC)y Fx = 0- FAB + FAC = 0LaFAB = RA For the internal force in member AC resolved into rectangular component forces: Method of Joints: Analysis ResultsABCDEFGHIJKLExternally Applied Force, FRARLCCCCCCCCCCTTTTTTTension: TCompression: C Buckling Force, FbucklingFEF = RAah=ahF4ahFbuckling4=Fbuckling 4h FEFa 4h (2EI)a (a2) 4h 2EIa3===Fbuckling = 769 N0.01016 m0.01016 m0.00254 mE = 2.29 x 109 N/m2I = 6.92 x 10-10 m4Taking a safety factor of 2, the resulting maximum load is 384.5 N or a load mass of 39 kg. 0.006756 mTesting the bridge5. Place your load in the middle of the bridge. Analyze the joint at the support.Why should you begin your analysis with this joint?Analyze the load distribution throughout the truss including the magnitude of an internal force and whether it is in tension or compression. 6. Now, change the location of your load. What happens to the load distribution? Does it change?

How can we use this in our classrooms?Discussion Questions on BridgesIntro: The following diagram is a picture of a Warren Truss Bridge. The bridge is comprised of horizontal, vertical, and diagonal beams. Each of the beams are connected using a joint. Note: the horizontal and vertical beams are the same length.

Classroom use continued.1. Use the picture above: A. How many horizontal deck beams on the bottom chord are there?

2. Determine how many horizontal beams will be required to construct the bottom chord of the bridge in the following situations.A. Span of the bridge is 170 cm. The length of the beam is 17 cm.B. Span of the bridge is 24 m. The length of the beam is 4 m.C. Span of the bridge is 4km. The length of the beam is 5m.D. How are your answers in problems 1a and 2a related?E. Span of the bridge is S. The length of the horizontal beam is L.

Research based approach

Based on the idea of Pattern Tasks by Margaret SmithDevelops students algebraic reasoningBegins with observing a pattern from a pictureThe pattern is used for concrete problemsStudents connect patterns to algebraic equationsAllows multiple representationsMaze Design ProblemTotal Area for the Shipping Terminal: 20,000 ft2Container Storage Area: 75% of the total terminal area.Loading and Unloading Area: 10% of the total terminal area.Administration Area: equivalent to 50% of the loading and unloading area.Rail and Trucking Space: 7% of the terminal area.Repair and Maintenance Area: (to be determined by you!)

Design a shipping terminal with the following specifications. Your goal is to maximize the number of storage containers in the container storage area.Specifications for the Container Storage Area:The container storage area is comprised of containers and pathways around the container.The dimensions of a standard storage container are 8 ft x 20 ft.Each container must have a pathway on at least 2 sides.Pathways must be 8 ft wide.

The MathTotal Area for the Shipping Terminal: 20,000 ft2Container Storage Area: 15,000 ft2Loading and Unloading Area: 2,000 ft2Administration Area: 1,000 ft2Rail and Trucking Space: 1,400 ft2Repair and Maintenance Area: 600 ft2

Maximum Capacity: 33.48 storage units.Interpret this and incorporate it into design.

Pertinent Variables: Amount of pathway around container, design, and layout

How can we use this in our classrooms?Apply system analysis method of problem solvingIntroduce in early educationGeneric approach to setting up problems byDefine systemDraw a pictureIdentify variablesIdentify independent equationsIdentify given informationSolve literal equationsPlug in numbersHow can we use this in our classrooms?You are going to design a rectangular garden. The area of the garden is 100 ft2. The perimeter of the garden is 80ft. The length of the garden 2 times more than the width. Find the dimensions of the garden.

System: Rectangular GardenVariables: Area (A), Perimeter (P), Length (l), Width (w)Independent Equations: A = l*w P = 2l + 2wGiven Information: A = 100 ft2, P = 80 ft. l = 2wSolve Literal Equations: l2 (lp)/2 + A = 0Plug in your numbers!

ConclusionProblems are easily adaptable for any age

More scaffolding for lower levels

More variables and difficult math for higher levels

If we introduce system analysis at a young age, they will be better prepared for their STEM careers in the future