1
Guess my rule! - 1

Students use pattern finding and algebraic skills while learning that there is more than one way to continue any sequence. (Date Revised: Wednesday, June 27, 2001).

 Problem, Hints, Solutions, and Answers. View Web (HTML) Version View Printable (PDF) Version
 Topics. NumberNumerical Patterns and SequencesGeneral Algebra and FunctionsPatterns and SequencesCreating / Representing / Identifying / Extending Patterns and Sequences Algebra and FunctionsPatterns and SequencesArithmetic Sequences and Series Algebra and FunctionsPatterns and SequencesGeometric Sequences and Series Discrete MathematicsPatterns and SequencesArithmetic Sequences and Series Discrete MathematicsPatterns and SequencesGeometric Sequences and Series Technology. Requires No Technology Habits of Mind. Dealing with Non-Unique Solutions Duration of Lesson. Part of a Lesson Mathematics Background. Some Algebra, No Geometry Advanced Algebra, No Geometry
 2
Divisibility 1

First with numbers, students conjecture that (a^n - 1) is divisible by (a-1). Students prove that (a-1) is a factor of (a^n - 1) with elementary algebra, and apply the result to understanding the arithmetic test for divisibility by 9. (Date Revised: Thursday, March 15, 2001).

 Problem, Hints, Solutions, and Answers. View Web (HTML) Version View Printable (PDF) Version
 Topics. NumberFactorization and DivisibilityDivisibility Tests Algebra and FunctionsExpressions and FormulasGeneral Technology. Requires No Technology Habits of Mind. Proving Formulating Conjectures / Generalizing / Abstracting Duration of Lesson. More Than One Day's Work Mathematics Background. Some Algebra, No Geometry
 3
Sally Snail: Travel at constant rate

This set introduces the concept of constant rate. It represents constant rate by increases of both distance and time with equal increments. It connects this representation with the graphical representation of constant rate. It also emphasizes the connection of constant rate with proportional relations. (Date Revised: Thursday, March 15, 2001).

 Problem, Hints, Solutions, and Answers. View Web (HTML) Version View Printable (PDF) Version
 Topics. NumberRatio / Percent / ProportionRates and Unit Rates Algebra and FunctionsLinear FunctionsSlopes and Rates Technology. Calculators and Graphing Calculators Habits of Mind. Working with Graphs Finding and Using Invariants Duration of Lesson. Part of a Lesson Mathematics Background. No Algebra, No Geometry
 4
Triangle with restricted angle sum

In this very short problem, students employ proof by contradiction in a non-formal way, while examining relationships among angles in triangles. (Date Revised: Tuesday, February 27, 2001).

 Problem, Hints, Solutions, and Answers. View Web (HTML) Version View Printable (PDF) Version
 Topics. Geometry and MeasurementTrianglesAngle Sum Technology. Requires No Technology Habits of Mind. Proving Duration of Lesson. Part of a Lesson Mathematics Background. Some Algebra, Some Geometry
 5
Powers of two

Students use a simple context (balance scales) to see that all counting numbers can be expressed as sums of powers of 2. This can be used as an introduction to exponents or the base-2 number system. (Date Revised: Thursday, May 31, 2001).

 Problem, Hints, Solutions, and Answers. View Web (HTML) Version View Printable (PDF) Version
 Topics. NumberArithmetic Expressions / Equations / InequalitiesWriting NumberPlace Value and Different BasesGeneral NumberPowers and RootsPowers Technology. Requires No Technology Habits of Mind. Modeling / Mathematizing Creating / Analyzing an Algorithm Duration of Lesson. Approximately One Day's Work Mathematics Background. No Algebra, No Geometry
 6
Area of regular polygons

Students use congruence tests, area of a triangle, and trigonometry (the tangent ratio) to find formulas for the areas of regular pentagons and hexagons. They generalize the formulas to other regular polygons. (Date Revised: Tuesday, November 06, 2001).

 Problem, Hints, Solutions, and Answers. View Web (HTML) Version View Printable (PDF) Version
 Topics. Geometry and MeasurementTrianglesCongruence Tests Geometry and MeasurementPolygonsAreas of Regular Polygons Geometry and MeasurementCongruenceTriangles Technology. Requires No Technology Habits of Mind. Proving Formulating Conjectures / Generalizing / Abstracting Duration of Lesson. More Than One Day's Work Mathematics Background. No Algebra, Some Geometry
 7
Finding the line of best fit

Students compare two models for a data set (women's tennis earnings) using the absolute value of the residuals (or error). Then they use technology (calculator or software) to find the least squares regression line, and they compare one of the earlier models to that line using squares of the residuals. (Note, the problem set "Tennis, anyone?" makes an excellent precursor to this one.) (Date Revised: Monday, November 19, 2001).

 Problem, Hints, Solutions, and Answers. View Web (HTML) Version View Printable (PDF) Version
 Topics. Algebra and FunctionsLinear FunctionsFit a Linear Function to Data / Linear Growth Algebra and FunctionsRelations / Functions / FamiliesLinear Function Family Statistics and ProbabilityFitting Model to DataLeast-squares Regression Statistics and ProbabilityFitting Model to DataLinear Interpolation and Best-fit Line Statistics and ProbabilityFitting Model to DataLinear Function Family Technology. Calculators and Graphing Calculators Spreadsheets Habits of Mind. Modeling / Mathematizing Duration of Lesson. Approximately One Day's Work Mathematics Background. Some Algebra, No Geometry
 8
Setting up proportions

Students learn how to properly set up proportions by first organizing the three given values and the unknown value. Some solving of set-up proportions is required. (Date Revised: Thursday, February 07, 2002).

 Problem, Hints, Solutions, and Answers. View Web (HTML) Version View Printable (PDF) Version
 Topics. NumberRatio / Percent / ProportionProportions Algebra and FunctionsProportionsGeneral Technology. Requires No Technology Duration of Lesson. Part of a Lesson Mathematics Background. No Algebra, No Geometry

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