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- 1. Strategies and Activities to Teach the Math State Standards to Elementary Learners By Michelle Flaming - ESSDACK March 16, 2007
- 2. Agenda <ul><li>Theme Teams: Understanding Data </li></ul><ul><li>Overview of Kansas Mathematics Standards </li></ul><ul><ul><li>Assessed Indicator Sheet </li></ul></ul><ul><ul><li>Assessment Framework </li></ul></ul><ul><li>Math Concepts: </li></ul><ul><ul><li>Numbers and Computation </li></ul></ul><ul><ul><li>Algebra </li></ul></ul><ul><ul><li>Geometry </li></ul></ul><ul><ul><li>Data </li></ul></ul>
- 3. Understanding Data <ul><li>On grid paper, write your first name, one letter per square </li></ul><ul><li>My Family’s First Name - Share </li></ul><ul><li>Sticky note - Write your name and number of letters: Michelle - 8 </li></ul><ul><li>Human Bar Graph </li></ul><ul><li>Post It Note Bar Graph </li></ul><ul><li>Terminology </li></ul>
- 4. Processing Questions: <ul><li>What mathematics were you doing during this exploration? </li></ul><ul><li>What else were you doing while working on this problem? </li></ul>
- 5. Cognitive Categories for Mathematics - Grades 2 – High School <ul><li>Category 1: Memorize Facts/Definitions/Formulas </li></ul><ul><ul><ul><li>a. Recite or recall basic mathematics facts </li></ul></ul></ul><ul><ul><ul><li>b. Recall or recognize mathematical terms, definitions, or concepts </li></ul></ul></ul><ul><ul><ul><li>c. Recall formulas or computational procedures </li></ul></ul></ul><ul><li>Category 2: Perform Procedures </li></ul><ul><ul><ul><li>a. Use numbers to count, order, or denote </li></ul></ul></ul><ul><ul><ul><li>b. Do computational procedures or algorithms </li></ul></ul></ul><ul><ul><ul><li>c. Follow procedures or instructions </li></ul></ul></ul><ul><ul><ul><li>d. Solve equations, formulas, or routine word problems </li></ul></ul></ul><ul><ul><ul><li>e. Organize or display data </li></ul></ul></ul><ul><ul><ul><li>f. Read or produce graphs and tables </li></ul></ul></ul><ul><ul><ul><li>g. Do geometric transformations and/or execute geometric constructions </li></ul></ul></ul><ul><li>Category 3: Demonstrate Understanding of Mathematical Ideas </li></ul><ul><ul><ul><li>a. Communicate mathematical ideas or rules and/or explain the process </li></ul></ul></ul><ul><ul><ul><li>b. Use representations to model mathematical ideas </li></ul></ul></ul><ul><ul><ul><li>c. Explain findings and/or results from data analysis strategies or experiments/simulations </li></ul></ul></ul><ul><ul><ul><li>d. Develop and/or explain relationships between concepts </li></ul></ul></ul><ul><ul><ul><li>e. Show and/or explain relationships between models, diagrams, and/or other representations </li></ul></ul></ul><ul><li>Category 4: Conjecture/Generalize/Prove </li></ul><ul><ul><ul><li>a. Determine the truth of a mathematical pattern, a mathematical statement, and/or proposition or make predictions </li></ul></ul></ul><ul><ul><ul><li>b. Write formal or informal proofs </li></ul></ul></ul><ul><ul><ul><li>c. Recognize, generate, or continue patterns </li></ul></ul></ul><ul><ul><ul><li>d. Find a mathematical rule to generate a pattern or number sequence </li></ul></ul></ul><ul><ul><ul><li>e. Make and investigate mathematical conjectures </li></ul></ul></ul><ul><ul><ul><li>f. Identify faulty arguments or identify misrepresentations of data </li></ul></ul></ul><ul><ul><ul><li>g. Reason inductively or deductively </li></ul></ul></ul><ul><li>Category 5: Solve Non-routine Problems/Make Connections </li></ul><ul><ul><ul><li>a. Apply and adapt a variety of appropriate strategies to solve non-routine problems </li></ul></ul></ul><ul><ul><ul><li>b. Apply mathematics in contexts outside of mathematics (whenever possible, include diagrams/visuals </li></ul></ul></ul><ul><ul><ul><li>c. Analyze data or recognize patterns </li></ul></ul></ul><ul><ul><ul><li>d. Synthesize content and ideas from several sources </li></ul></ul></ul>
- 7. Number Aerobics <ul><li>As the number is stated, if you have any part of that number come to the front and stand in order. </li></ul><ul><ul><li>Example: 567 (500, 60, 7) </li></ul></ul><ul><li>Build the number using base-ten blocks. </li></ul>
- 8. Processing Questions: <ul><li>What mathematics were you doing during this exploration? </li></ul><ul><li>What else were you doing while working on this problem? </li></ul>
- 9. Focus Activity: LCM <ul><li>One volunteer: Skip count by 5’s to 30. </li></ul><ul><li>Another volunteer: Skip count by 3’s to 30. </li></ul><ul><li>Class - Write down what you hear on notebook paper. </li></ul><ul><li>What numbers did you hear from each volunteer that was the same? </li></ul><ul><li>Repeat with 4 and 6 or 8 and 12. </li></ul><ul><li>Through skip counting you are finding the multiples of the number. </li></ul>
- 10. What is the definition of Least Common Multiple? <ul><li>A multiple shared by two or more numbers is a common multiple. </li></ul><ul><li>Think about the individual words, what do they each mean? </li></ul><ul><ul><li>Least - </li></ul></ul><ul><ul><li>Common - </li></ul></ul><ul><ul><li>Multiple - </li></ul></ul><ul><ul><li>Create a visual representation from your definition of the individual words. </li></ul></ul><ul><li>What was the LCM of 3 and 5? </li></ul><ul><li>What is the LCM of 3 and 4? </li></ul>
- 11. Where is LCM Assessed at the State Level? <ul><li>5th Grade - 1.4.K4 </li></ul><ul><ul><li>Identifies, explains, and finds the greatest common factor and least common multiple of two or more whole numbers through the basic multiplication facts from 1x1 through 12 x 12 (2.4.K1d - Factor trees) </li></ul></ul>
- 12. Real World Situation. <ul><li>During the summer months, one ice cream truck visits Lyons every 4 days and another ice cream truck visits every 5 days. If both trucks visited today, when is the next time both trucks will visit on the same day? </li></ul><ul><li>Two frogs are on the edge of the pond. The boy frog jumps on every other lily pad. The girl frog jumps on every 5th lily pad. Which lily pad will they both jump on? </li></ul>
- 13. “The More Ways We Teach, The More Kids We Reach” <ul><li>Venn Diagram </li></ul><ul><li>Table </li></ul><ul><li>Hundreds Chart </li></ul>
- 14. Focus Activity: Greatest Common Factor <ul><li>Select 12 tiles to use. </li></ul><ul><li>Separate the tiles into groups with the same amount in each group and record their results on paper. You may want to draw the groups on paper for better clarity. </li></ul><ul><li>How many, and what kinds of groups did you create? </li></ul><ul><ul><li>1 group of 12 </li></ul></ul><ul><ul><li>2 groups of 6 </li></ul></ul><ul><ul><li>3 groups of 4 </li></ul></ul>
- 15. Focus Activity: GCF <ul><li>Can you make a rectangle out of the different groups? </li></ul><ul><ul><li>12 is an even number, can be arranged into an array or rectangle with no left over pieces. </li></ul></ul><ul><ul><li>Also a composite number (it can be broken into different groups) </li></ul></ul><ul><li>The different groups represent the factors of a number. </li></ul><ul><li>Factors of 12 are: </li></ul><ul><ul><li>1, 2, 3, 4,6, and 12 </li></ul></ul>
- 16. Focus Activity: GCF <ul><li>Select 18 tiles to use. </li></ul><ul><li>Separate the tiles into as many even groups as possible and record their results on paper. You may want to draw the groups on paper for better clarity. </li></ul><ul><li>How many, and what kinds of groups did you create? </li></ul><ul><ul><li>1 group of 18 </li></ul></ul><ul><ul><li>2 groups of 9 </li></ul></ul><ul><ul><li>3 groups of 6 </li></ul></ul>
- 17. What is the definition for Greatest Common Factor? <ul><li>Compare the numbers 12 and 18 to see if they have any factors that are the same. </li></ul><ul><li>A factor shared by two or more numbers is a common factor. </li></ul><ul><li>Think about the individual words, what do they each mean? </li></ul><ul><ul><li>Greatest - </li></ul></ul><ul><ul><li>Common - </li></ul></ul><ul><ul><li>Factor - </li></ul></ul><ul><ul><li>Create a visual representation from your definition of the individual words. </li></ul></ul><ul><li>What was the GCF of 6 and 12? </li></ul><ul><li>What is the GCF of 12 and 27? </li></ul>
- 18. Where is GCF Assessed at the State Level? <ul><li>5th Grade - 1.4.K4 </li></ul><ul><ul><li>Identifies, explains, and finds the greatest common factor and least common multiple of two or more whole numbers through the basic multiplication facts from 1x1 through 12 x 12 (2.4.K1d - Factor trees) </li></ul></ul>
- 19. Real World Situation <ul><li>The 5th (72) grade marching band will be right after the 4th (32) grade band in Saturday’s parade. For aesthetic reasons each row for each band needs to form a complete array. What is the greatest width each band could be? </li></ul>
- 20. Pattern Round Robin <ul><li>Make a repeating pattern using a square, triangle, and a hexagon; </li></ul><ul><ul><li>ABAB; ABC,ABC; AABAAB; etc. </li></ul></ul><ul><li>Put the pattern blocks in the section of the paper labeled “pattern blocks”. </li></ul><ul><li>Rotate one person clockwise. </li></ul><ul><li>Listen for further directions. </li></ul>
- 21. 4 Corners: I prefer to go to the … <ul><li>What mathematics were you doing during this exploration? </li></ul><ul><li>What else were you doing while working on this problem? </li></ul>
- 22. Who’s My Partner <ul><li>Count the money in your baggie. </li></ul><ul><li>Find the person in the room who has the same amount of money. </li></ul><ul><li>Record the amount you have in your baggie at the top of a recording sheet. </li></ul><ul><li>List all the possible combinations to make that amount. </li></ul>
- 23. Pinch Cards <ul><li>Use the Pinch Card to determine how many steps are involved to solve the problem. </li></ul><ul><li>Use the Pinch Card to determine what operation(s) are needed to solve the problem. </li></ul>
- 24. There were 8,357 books in a school library. Then, the library got 1,435 new books. What was the TOTAL number of books in the library after getting the new books? A. 9,782 books B. 9,792 books C. 9,882 books D. 9,892 books
- 25. A camp stove usually costs $225.45. This week it is on sale for $179.99. How much money is saved by buying the stove at the sale price instead of the usual price? A. $45.46 B. $56.56 C. $154.54 D. $405.44
- 26. Daryl bought a shirt for $12.99 and a belt for $3.99. How much money did he spend for the two items? A. $8.00 B. $9.00 C. $15.88 D. $16.98
- 27. Larry bought a baseball for $5.23 and a bat for $19.79. What is the TOTAL cost of the baseball and the bat? A. $14.56 B. $14.92 C. $24.92 D. $25.02
- 28. Carl paid for a toy with a $10.00 bill. He got $3.86 back in change. Exactly how much did the toy cost? A. $7.86 B. $7.24 C. $6.24 D. $6.14
- 29. Lola is saving money to buy a doghouse. The doghouse costs $215. Lola has already saved $148. How much more money does she need to save? A. $67 B. $77 C. $133 D. $177
- 30. During the last year, 375 music books and 3,400 history books were given to a library. How many MORE history books than music books were given to the library? A. 3,025 books B. 3,035 books C. 3,175 books D. 3,775 books
- 31. A baker is making 48 packages of blueberry muffins. He puts 12 muffins in each package. What is the TOTAL number of blueberry muffins in the 48 packages? A. 466 muffins B. 476 muffins C. 566 muffins D. 576 muffins
- 32. A theater has 38 rows of seats. There are 72 seats in each row. What is the total number of seats in the theater? A. 342 seats B. 792 seats C. 2,526 seats D. 2,736 seats
- 33. A school bought 45 new uniforms for the volleyball team. The school paid $21 for each new uniform. What was the total amount of money the school paid for the new uniforms? A. $125 B. $135 C. $645 D. $945
- 34. Each ticket for a football game costs $7. What would be the total cost of buying 28 tickets for the game? A. $4 B. $21 C. $146 D. $196
- 35. Nancy buys 6 posters for $4.63 each. What is the total cost of all 6 posters? A. $10.63 B. $18.78 C. $24.68 D. $27.78
- 36. Cassie buys a salad for $4.95 and a drink for $1.25. She pays for the salad and drink with a $10.00 bill. How much change should Cassie get back? A. $3.80 B. $4.20 C. $4.80 D. $5.10
- 37. Sean buys a puzzle that costs $13.65. He pays for the puzzle with a $20.00 bill. How much change should Sean get back? A. $6.35 B. $6.45 C. $7.35 D. $7.45
- 38. A ship that holds 42,000 gallons of fuel needed 38,426 gallons when it refueled. How many gallons of fuel did the ship have left before it refueled? A. 3,538 gallons B. 3,574 gallons C. 3,684 gallons D. 4,426 gallons
- 39. An office building has 67 offices. Each office has exactly 1,853 square feet (ft 2 ) of carpet. What is the TOTAL number of square feet of carpet in all 67 offices? A. 23,089 ft 2 B. 24,089 ft 2 C. 123,051 ft 2 D. 124,151 ft 2
- 40. Annie needs 8 sheets of plywood to finish her project. The cost of the plywood is $26.42 for one sheet. How much will it cost to finish the project? A. $168.26 B. $231.26 C. $208.36 D. $211.36
- 41. A family meal of fried chicken costs $24.95 and feeds 4 people. A single meal for one person costs $6.98. How much money is SAVED by buying the family meal rather than 4 single meals? A. $2.67 B. $2.97 C. $3.03 D. $3.97
- 42. Steak costs $8 a pound. How many pounds of steak can be bought for $826? A. 103 2/8 pounds B. 103 1/8 pounds C. 13 2/8 pounds D. 13 1/8 pounds
- 43. The distance between two cities using route A is 876.01 miles. Using route B, the distance between the same two cities is 689.7 miles. How many miles shorter is route B than route A? A. 18.631 miles B. 80.704 miles C. 186.31 miles D. 187.71 miles
- 44. It takes 240,000 gallons of water to fill an empty tank. Water is pumped into the tank at a rate of 800 gallons an hour. How many hours will it take to completely fill the empty tank? A. 3 hours B. 30 hours C. 300 hours D. 3,000 hours
- 45. There are about 40 lines of print on each page in a book. The book contains 32,000 lines of print. What is the MINIMUM number of pages in the book? A. 8 pages B. 80 pages C. 800 pages D. 8,000 pages
- 46. 4 Corners: I prefer to play … <ul><li>What mathematics were you doing during this exploration? </li></ul><ul><li>What else were you doing while working on this problem? </li></ul>
- 47. 5 Square Tiles <ul><li>Count out 5 square tiles. </li></ul><ul><li>Investigate to find how many different combinations of polygons can be made using the 5 square tiles. </li></ul><ul><li>If a shape can be flipped/reflected, rotated/turned, or translated/slid and is congruent, it is NOT a different shape. </li></ul>
- 48. 4 Corners: If I worked in the circus … <ul><li>What mathematics were you doing during this exploration? </li></ul><ul><li>What else were you doing while working on this problem? </li></ul>
- 49. Telling Time <ul><li>Linear Clock </li></ul><ul><li>Bobby-Pin Clocks </li></ul>
- 50. McSquares and McTriangles <ul><li>Listen to the story </li></ul>
- 51. Grand Opening! Welcome! We can serve 12 people at a time!
- 52. Welcome! We can serve 40 people at a time!
- 53. McTriangles <ul><li>How many people could Mr. and Mrs. Triangle serve at one time with one table? Two tables? With three, four, and so on up to ten tables? </li></ul><ul><li>How many people could they serve by rearranging the tables into banquet style? </li></ul>
- 54. 4 Corners: My favorite fairy tale is … <ul><li>What mathematics were you doing during this exploration? </li></ul><ul><li>What else were you doing while working on this problem? </li></ul>
- 55. Focus Activity: Making Conversions <ul><li>Use color tiles: 4 blue counters, 40 yellow. </li></ul><ul><li>How many mm are in 1 cm? </li></ul><ul><li>Place 10 yellow counters on the building mat in the right column, whose heading is cm. Count the yellow counters and remove the 10 yellow for 1 blue counter (which represents a cm). </li></ul><ul><li>1 cm = 10 mm </li></ul>
- 56. Focus Activity: Making Conversions <ul><li>Make 30 mm, replace by making cm. </li></ul><ul><ul><li>30 mm = 3 cm </li></ul></ul><ul><li>Make 25mm, make as many cm as possible. How many mm do you have left? </li></ul><ul><ul><li>25 mm = _____ cm + ______ mm </li></ul></ul><ul><li>Make 44mm, make as many cm as possible, how many mm do you have left? </li></ul><ul><ul><li>44 mm = ____ cm + _____ mm </li></ul></ul><ul><li>Make 6 cm and 4 mm, how many total mm are there? </li></ul><ul><ul><li>6 cm + 4 mm = _________ mm </li></ul></ul>
- 57. Focus Activity: Making Conversions <ul><li>Playing the Game. </li></ul><ul><ul><li>Player #1 - Spins the two spinners using a paper clip. </li></ul></ul><ul><ul><li>Player #2 - Place the counters on the building mat according to the amounts shown. </li></ul></ul><ul><ul><li>Player #3 - Make any trades necessary to simplify the number of all counters. </li></ul></ul><ul><ul><li>Player #4 - Records the results as a number sentence </li></ul></ul><ul><ul><ul><li>4 cm + 20 mm = 6 cm </li></ul></ul></ul>
- 58. Where is conversion assessed? <ul><li>6th Grade - 3.2.K3b </li></ul><ul><ul><li>Converts within the metric system using the prefixes kilo, hecto, deka, deci, centi, and milli </li></ul></ul><ul><li>5th Grade - 3.2.K4a </li></ul><ul><ul><li>Converts within the customary system; inches and feets, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallons, pounds and ounces. </li></ul></ul>
- 59. Real World Situation. <ul><li>If each turtle moves 9 cm each day. How many meters will the turtle move in 20 days? </li></ul>
- 60. Focus Activity:Nonstandard to Ruler - Fraction Strip <ul><li>Take one piece of licorice. </li></ul><ul><ul><li>If you were to share this piece of licorice with one person, where would you divide it? Write 1/2 on a sticky note. </li></ul></ul><ul><ul><li>Divide the piece for four people equally. Write 1/4 on a sticky note. </li></ul></ul><ul><ul><li>Using the fraction cards and sticky notes, mark where each would be. </li></ul></ul><ul><ul><li>Use this same process for finding fractions on a number line. </li></ul></ul>
- 61. Where is Measurement Assessed at the State Level? <ul><li>3rd Grade - 3.2.A1a </li></ul><ul><ul><li>Solves real-world problems by applying appropriate measurements: </li></ul></ul><ul><ul><ul><li>A. length to the nearest inch, foot, or yard. </li></ul></ul></ul><ul><li>4th Grade - 3.2.K2a </li></ul><ul><ul><li>Selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy appropriate for a given situation to measure </li></ul></ul><ul><ul><ul><li>A. length, width, and height to the nearest fourth of an inch or to the nearest cm. </li></ul></ul></ul><ul><li>5th Grade 3.2.A1a </li></ul><ul><ul><li>Solves real-world problems by applying appropriate measurements and measurement formulas: </li></ul></ul><ul><ul><ul><li>A. length to the nearest eighth of an inch or to the nearest cm. </li></ul></ul></ul>
- 62. 4 Corners: My favorite holiday is … <ul><li>What mathematics were you doing during this exploration? </li></ul><ul><li>What else were you doing while working on this problem? </li></ul>
- 63. Two-Dice Sums <ul><li>Twelve Skittles </li></ul><ul><li>Arrange your twelve skittles on the numbers 2 through 12. More than one counter can be placed on any number, or possibly no counters on a number. </li></ul><ul><li>Add the numbers on the two dice to find the sum. Remove ONE counter from that number on game board. </li></ul><ul><li>Object of the game - be the first player to remove all of his or her counters. </li></ul><ul><li>Keep track of the number of times the dice are rolled. </li></ul>
- 64. Question to Investigate <ul><li>What arrangement of counters will give you the best chance to clear the game board in the fewest number of rolls? </li></ul>
- 65. Probability Quote <ul><li>Probability theory is the underpinning of the modern world. Current research in both the physical and social sciences cannot be understood without it. Today’s politics, tomorrow’s weather report, and next week’s satellites all depend on probability theory. </li></ul><ul><ul><li>-- Lynn Arthur Steen - St. Olaf’s College, Minnesota </li></ul></ul>
- 66. Processing Questions: <ul><li>What mathematics were you doing while playing the game? </li></ul><ul><li>What else were you doing while working on this problem? </li></ul>
- 67. Key Mathematical Ideas: <ul><li>Some sums (or events) are more likely than others, and there is a mathematical explanation. </li></ul><ul><li>There are organized ways to calculate the probability of each sum. </li></ul><ul><li>It is possible to carry out an experiment to collect data that may give an indication of the likelihood of the sums (events). </li></ul><ul><li>The more times an experiment is performed, the closer the experimental probability should get to the theoretical probability. </li></ul><ul><li>Experimental data usually does not match theoretical probability. </li></ul>
- 68. What’s My Area? <ul><li>Talk through </li></ul>
- 69. Using Activities and Games to Develop Fluency <ul><li>Activities: </li></ul><ul><ul><li>Circles and Stars </li></ul></ul><ul><ul><li>How Many Rows? How Many in Each Row? </li></ul></ul><ul><li>Games: </li></ul><ul><ul><li>Tic-Tac-Toe Products/Sums </li></ul></ul><ul><ul><li>Taxman </li></ul></ul><ul><ul><li>Bowl-a-Fact </li></ul></ul><ul><ul><li>The Game of Skunk </li></ul></ul><ul><ul><li>Pig </li></ul></ul><ul><ul><li>Get to Zero </li></ul></ul><ul><ul><li>Grab Bag </li></ul></ul><ul><ul><li>Fifteen Number Cross Out </li></ul></ul>
- 70. Research Brief <ul><li>With your original theme team: </li></ul><ul><ul><li>Read the Research Brief, Highlighting Important Components. </li></ul></ul><ul><ul><li>Final Word Activity </li></ul></ul>
- 71. Algebra <ul><li>Whole-group Discussions: </li></ul><ul><ul><li>Pattern Round Robin </li></ul></ul><ul><ul><li>Open Number Sentences </li></ul></ul><ul><ul><li>The McSquares and the McTriangles </li></ul></ul><ul><ul><ul><li>T-tables and charts </li></ul></ul></ul><ul><ul><ul><li>Writing Equations </li></ul></ul></ul><ul><ul><ul><li>Coordinate Grids </li></ul></ul></ul>
- 72. Geometry <ul><li>Geometric Shapes </li></ul><ul><ul><li>Pattern Blocks </li></ul></ul><ul><ul><li>Yarn Shapes </li></ul></ul><ul><ul><li>Combining Shapes </li></ul></ul><ul><li>Measurement </li></ul><ul><ul><li>5 Square Lesson </li></ul></ul><ul><ul><li>Linear Clocks/ Bobbypin Clock </li></ul></ul><ul><ul><li>Measuring with nonstandard unit ---- ruler </li></ul></ul><ul><ul><li>Conversion Chart </li></ul></ul><ul><ul><li>What’s My Area? </li></ul></ul>
- 73. Data <ul><li>Probability </li></ul><ul><ul><li>Two Dice Sums </li></ul></ul><ul><li>Data </li></ul><ul><ul><li>Understanding Data </li></ul></ul>

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