# Mathematical problems:

Assorted and by content categories

Problems are organized by content ares.

- Number value & operations
- Algebra & patterns
- Geometry & spatial reasoning
- Data analysis, probability, ratio, & proportion,
- Measurement

All problems require different amounts of reasoning, logic, representation, problem solving, communication.

- Assorted problems not categorized yet.
- Questions from standardized achievment tests, SAT, FAA, MCAT, ...

## Number value and operations

- Doorbell problem for Pat Hutchins book:
*The Doorbell Rang* - Magic triangle add numers 1 - 6 to add to 9 in all directions
- Magic square perimeter add numbers 1-8 to 12 in all directions
- Representing addition and subtraction of fractions with unlike deominators
- Activities for primary students to use as problems
- How many dots?
- Bus & train passengers getting on & off, work backwards, undo, and algebra. Includes floor plan for representation diagrams.
- Bucket problems
- Muliplication on a grid
- Division with 12 & 4, & the importance of problem diversity
- Bean toss and Fold Book activities
- Ten & more (Teen numbers) Fold Book
- Ten & more (Teen numbers) worksheet

## Algebra & patterns

- Acrobats Logic Problem, draw a diagram, proportion
- Calendar problems, patterns, facrtors, pi, primes, palidromes, & more
- 13 Plus Calendar problems: Discover patterns with dates (multiples, factors, powers, primes, ...)
- Mowing
- Wages for Pet Care
- How Big is Two Million $
- Fractional Parts Puzzle
- Bottle and cork
- Four Consecutive Numbers
- Problem in an email - Magic with your phone number
- Pizzas
- Cartography - map making, angle measurement, compass, clinometer, measure height, measure distance, locating objects with distance and angle combinations, contour maps
- Eight by Eight Square with 16 colored squares: How many patterns?
- Bodies and proportions
- Card tricks
- Bridge building problem --->>> same problem more directed worksheet
- Fibonaccii sequence deomonstration
- Odd plus odd makes? deomonstration three concrete, semi concrete, and symbolic
- How many grains of sand in the Universe? Archimedes' proof in The Sand Reckoner. (Problem solving, algebra, geometry)

## Geometry and spatial reasoning

- How many Squares? - four sizes
- How Many Squares? - five sizes -[teaching suggestions & discussion of how math process dimensions are related]
- Eight by Eight Square with 16 colored squares: How many patterns?
- Pentomino puzzles
- Tooth pick problems Flash | page |
- Surveilance camera puzzle
- What are the angles and sides of a pattern block star?
- Measuring the circumference of the Earth
- Trapezoid area thirty-six
- Pizzas
- Cartography - map making, angle measurement, compass, clinometer, measure height, measure distance, locating objects with distance and angle combinations, contour maps
- Five piece square puzzle
- Names - it's a matter of lines
- Area and perimeter worksheet
- Tangrams puzzle and table

## Data analysis, probability, ratio, & proportion

### Data analysis

- Categorical sorting
- One variable data analysis and graphs --- > M & M's, ping-pong ball race --- > [ M &M's Activity by Lanette VonSeggerrn ] -- > > Color Percentages of M & Ms in the United States and Throughout the World Collected and created by: April Thede 2005
- Stem and leaf plots
- Find your classes hang time and vertical jump statistics

*Probability*

- Three coins
- Aces for Dinner
- Win a Car Contest
- The Case of the Carnival Probability Game with Reader's Theatre
- Envelopes with Cash Contest
- Sack lunches
- Capture recapture problem simulation
- Capture recapture problem simulation -2
- Bingo addition a possibility of different digits for sums
- Bingo subtraction and possibility of different digits for differences
- Six card draw two game - who has the better probability?Flipping one coin, two, three, ... what are the possibilities?

- Spinners and probability

### Ratio & proportion

- Ratio and proportion problems
- Bodies and proportions
- Acrobats Logic Problem, draw a diagram, proportion

## Measurement

- Cartography - map making, angle measurement, compass, clinometer, measure height, measure distance, locating objects with distance and angle combinations, contour maps
- Rubber band simulation

*Challenges*:

- Math and science challenges
- Five piece square puzzle Make one for yourself and a friend. Why is it so challenging?
- Tangram pieces
- Petals on a rose - A dice puzzle.
- SUDOKU logical strategies for solving them and a puzzle.
- Triangles in ten shapes puzzle

- There are
*10*kinds of people in the world. Those who understand binary and those who don't.

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Jeffery Weld asks:

*Why is it whenever* students don't do well on a national test the news agencies report one or a few particular items that were on the test by stating the test questions, then they believe it is necessary to provide the answers. *If their listeners need the answers, why should we expect students to be able to answer it correctly? *

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*U.S. Students*

Score in the top tier on

the PISA 2012 Math Creative Problem SolvingAssessment

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