Building Pre-Algebra SkillsThrough Project-Based Learning

Pier Sun HoArlene LaPlante

March 1, 2010

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Agenda

• The role of ConnectEd

• Why create project-based pre-algebra curriculum?

• What does the curriculum look and feel like?

• Implementation considerations

• Questions and comments

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Organizing Principles forLinked Learning

• Pathways prepare students for postsecondary educationand career—both objectives, not just one or the other.

• Pathways connect academics to real-world applicationsby integrating challenging academics with a demandingtechnical curriculum.

• Pathways lead to a full range of postsecondary and careeropportunities by eliminating tracking and keeping alloptions open after high school.

• Improve student achievement

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Core Components of a Pathway

A multi-grade program consisting of:

• A challenging academic core meeting postsecondary admissionsrequirements of UC, CSU, and community colleges

• A demanding technical core meeting industry standards

• Work-based learning experiences that complement classroominstruction

• Support services including supplementary instruction, counseling,and transportation

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Why Project-Based Pre-algebra?

• Many avoid post-secondaryscience and engineeringprograms because of their mathrequirements.

• A survey of math and CTEteachers showed that studentslack pre-algebra skills. Thisleads to difficulty in allsubsequent math, science, andtechnical courses.

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Why Project-Based Pre-Algebra?

• MMath concepts and skills students struggle with:• NNumber sense and fundamental arithmetic (fractions, percents, decimals,

estimation of reasonable answers)

• BBasic problem solving skills

• UUsing geometry tools: ruler, protractor, compass

• BBasic math vocabulary

• PProportional reasoning, Slope, and Scale

• CConcept of Area

• SSolving simple equations

• UUsing formulas correctly in context

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Why Project-Based Pre-Algebra?

• Projects create a need toknow and motivation to learnmath. They add relevance,authentic problem solving,and 21st century skills to mathcontent.

•Hands-on, contextualizedactivities show students thatmath can be enjoyable, useful,and important. This increasesachievement and retention.

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Access Ramp Activity

• Find a partner.

• You need a ruler, pencil, and thehandouts.

• Complete the assignment withyour partner. As you work, listthe math concepts you neededto be successful.

What Does Project-Based MathLook Like?

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Access Ramp: Math Concepts

• Measurement

• Fractions

• Proportional Reasoning: scaledrawings

• Proportional Reasoning:slope, linear growth

• Problem solving strategies

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Unit 1: Wind Power

What are efficient wind turbine designs?

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Unit 1: Wind Power

Skills and Concepts:

• Measurement – Length, Area,and Angles

• Equivalent Fractions

• +/-/×/÷ Fractions

• Calculate percentages

• Express constraints and range ofresults as inequalities andcompound inequalities

•Graph and interpretexperimental results

•Build a working wind turbineto meet certain constraints thatoptimizes results

•Present wind turbine design toclass and justify design choices

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Unit 1: Wind Power

Practice addition and subtraction of fractions bybuilding a tower for the wind turbine.

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Unit 1: Wind Power

Practice fraction multiplication by building rotor blades of agiven area.

Calculate percentages when analyzing quantity of scrap materials.

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Unit 1: Wind Power

Test designs and record results as inequalities.

Interpret graphs of results and present findings.

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Unit 2: Blueprints and Models

How do you design a construction project?

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Unit 2: Blueprints and Models

Skills and Concepts:• Measurement – Length and Area

• Mapping space to scale

• Solving problems involvingproportions and ratios

• Understanding slope as it relatesto linear growth

• Calculating and convertingfractions, percents, and decimals

• Performing unit conversions

• Creating pie charts

• Calculating percent ofincrease or decrease

• Designing and constructing amodel of a building to fulfillspecific constraints andpreferences

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Unit 2: Blueprints and Models

Review proportions, scale, and slope by building a modelwheelchair ramp that meets ADA guidelines.

Practice unit conversions by creating a materials list and costchart.

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Unit 2: Blueprints and Models

• Calculate and interpret the spaceallocation of buildings.

• Create pie charts to presentfindings.

• Practice solving construction-related problems involving ratiosand proportional reasoning.

• Design a remodeling plan underspace and structural constraints,including a cost estimate.

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Unit 3: People Movers

How do you engineer an

effective funicular

system?

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Unit 3: People Movers

Skills and Concepts:

• Solving problems involvingproportions and ratios,including gear ratios

• Interpreting the meaning oflinear and non-linear graphs

• Understanding the slope ofdistance vs. time and velocityvs. time graphs

• Arithmetic with negativenumbers

• Understanding and solvingproblems using thePythagorean Theorem

• Simplifying square roots

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Unit 3: People Movers

Use the Pythagorean theorem to construct a ramp for the funicular.

Apply the concept of similarity and parallel line relationships tobuild a platform for the funicular car to ride on.

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Unit 3: People Movers

Use integer operations to calculate and describe position and velocity.

Determine the travel time by applying knowledge of gear ratios.

Graph and interpret linear and non-linear results.

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Unit 4: Safe Combinations

How safe is a

combination lock?

Cardboard fence

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Unit 4: Safe Combinations

Skills and Concepts:

• Tree diagrams andpermutations

• Definition of exponents,graphing exponential growth

• Rules of exponents

• Order of operations

• Inverse operations

• Equivalent equations andsolving 1–5 step equations

• Translating sentences intoalgebraic equations

• Building and analyzing aworking safe with acombination lock tospecifications

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Unit 4: Safe Combinations

• Calculate the total possiblenumber of combinations for alock.

• Use the rules of exponents toanalyze changes to thenumber of lockcombinations.

• Practice solving equations by“coding” and “decoding” lockcombinations.

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Practical Considerations

• Initial Cost: $200 - $500

• Consumable Materials: $10-$25 per unit

• Many materials can be borrowed from the school sciencedepartment.

• None of the units require power tools, lab space, or specialengineering knowledge.

• Approximately 70 hours of instruction• Example: 6 week summer school, ~2.5 hours/day

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Other ConnectEd Curriculum

Algebra I Project-Based Units

• Can be used as either supplemental or replacement materialduring the year

• Expands and reinforces the engineering theme and practice ofproblem solving skills in math class

• Covers major Algebra I standards (linear and quadraticequations, rational expressions, exponents, polynomials)

Engineering Integrated Units

Biomedical and Health Sciences Integrated Units

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Thank You For Participating!

Please contact us for more information about curriculummaterials and professional development:

ConnectEd: The California Center for College and Career

http://www.ConnectEdCalifornia.org

Pier Sun Ho: psunho@ConnectEdCalifornia.orgRob Atterbury: ratterbury@ConnectEdCalifornia.org