To Assessment ….. And Beyond!

1. To Assessment ….. And Beyond! By: Amanda Meiners Western Illinois University meinersaj@live.com

2. Illinois Weather • If today is zero degrees outside, and tomorrow is predicted to be twice as cold. How cold is it going to be?

3. A Family Reunion • One grandfather, one grandmother, two fathers, two mothers, fours children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law attended a family reunion. If both halves of a relationship attended (i.e. the father and the son), how many people showed up?

4. Grandmother Mother In Law Grandfather Father In Law Father Son 1 Child 1 Mother Daughter In Law Daughters 1 Sister 1 Child 2 Son 2 Child 3 Daughters 2 Sister 2 Child 4

5. The Brain Games • Based from a book: The Big Book of Brain Games by Ivan Moscivich • My version of the Hunger Games. • Challenges that are more about thinking than math all the time. Let students “play” with math ideas without instructing them how to go about solving the problem. • Opens up the critical thinking and reasoning skills students will need to use in the real world.

6. What is the level of math would you prefer teach? Click all that apply • 6th grade • 7th grade • 8th grade • 9th grade • 10th grade • 11th grade • 12th grade • College and beyond. 1

7. How many homework problems do you plan to assign each day? • I never assign any work outside of class. • 1-5 problems • 5-10 problems • 10-15 problems • 15-20 problems • 20 or more problems a night 1

8. How much time do you expect students to spend on their daily assignment? • 15 minutes • 30 minutes • 45 minutes • 1 hour • 2 hours 1

9. Common Core aligned materials (Option 2) • Manga High http://www.mangahigh.com/en_us/ • Aligned to Common Core • Math based only • 750 Prodigi and Games • Response to Intervention • Pros and Cons

10. Study Aid • Quizlet.com www.quizlet.com • Free online/mobile device • Have 8 free classes • Self made OR use what's out there.

11. MTV (Math Television) • Allow students to make their own (school appropriate) math music video. • Allows students to use the vast amount of math vocabulary they have learned in a particular chapter, unit, or year. • ABC’s of Math

12. Twister Slope • Bring the games students enjoy playing into class. • Buy yourself a twister board and place real number values on the spots. • I had student keep the numbers positive if their right foot/ hand was on the number. If their left foot/hand was on the number it is a negative value. • Composed a worksheet to help students walk through the different ways to convert between the different types of linear equations. (Algebra I) • Could also use this idea when teaching students to compose equations with particular zeros (Algebra II)

13. Where in the World is Variable Equation? • Play on the shows we have/ students like Carmen Santiago • Allows students to learn while they are being assessed under the multiple different equations they will see. • Build confidence in solving lots of equations and having the option to come and ask the “Chief” (teacher) questions as they arise.

14. Jeopardy Conics • This is just one chapter this applies. • Chapters with generalized ideas and/or lots of formulas are great for this kind of review/ assessment. • This can be interactive, you could even allow small groups assess their knowledge.

15. Who Wants to be a Geo-iare? • Millionaire. • Able to work on formulas such as perimeter, area, volume, Etc. building and building • When using the template make sure you place the RIGHT answer in the green box. It will not show up green initially in the presentation, but if students get the answer right it will show green then. • Could also use to test proofs or any other math topics that are more need to know • Test math facts with powers and other items that students need to know in High School

16. Other Game Shows Setups that are out there. • Family Feud • Are You Smarter than a ____ Grader • Deal or No Deal

17. Can I guess your number? • Pick any 3 digit number • Rearrange the digits in reverse order • Subtract from the original. • Want a positive difference, subtract accordingly • Note: if this is equal to a two digit number, think of it as a “three” digit number with a zero in front when reversing the digits. • Take this new number and reverse again • This time add the two numbers

18. You will always get 1089. Classroom use: Also the place value. Intro to Perfect squaresCC: High school-rational and irrational numbers

19. Proof • eg. 534   • Claim: Choose any three digit number with distinct digits represented abc. Reverse • the digits of this number so you have cba. Subtract the smaller of the two numbers from the larger one so you are left with a new number. Take this new number and reverse the digits again to make another new number. Add the two new numbers. Take the square root of that sum, and you will always be left with 33. • Note: if the first difference is equal to a two digit number, think of it as a “three” digit number with a zero in front when reversing the digits. • Proof: Imagine an arbitrary three digit number • Let the number abc be represented as 100a + 10b + c where a,b,c are distinct numbers in the set {0,1,2,3,4,5,6,7,8,9} • Reversing the digits would result in 100c + 10b + a • Subtract the second number from the first • 100a + 10b + c – (100c + 10b + a) = 100a + 10b + c – 100c – 10b – a • = 99a – 99c = 99(a - c) • Our new number is 99(a-c) • Let x represent a-c.

20. Since we know a and c are single digit numbers which do not equal each other, and the difference is at least 1, we know that 1 < x < 8 • We will take this case by case. • 99 * 1 = 099 099+990 = 1089 • 99 * 2 = 198 198+891 = 1089 • 99 * 3 = 297 297+792 = 1089 • 99 * 4 = 396 396+693 = 1089 • 99 * 5 = 495 495+594 = 1089 • 99 * 6 = 594 594+495 = 1089 • 99 * 7 = 693 693+396 = 1089 • 99 * 8 = 792 792+297 = 1089 • We always get 1089 in EVERY case. • The square root of 1089 is 33, hence you always get 33 as an answer.  • q.e.d.

21. Fold’m Eights Fold the values up in a way so that when looked at read 1-8. 8 levels starting off with easy and getting more difficult as they go. Make a check list that students need to mark off a certain number by a certain date or end of a chapter. Great pre-curser to nets or a way to have students fill the last 5 minutes of class. CC: sixth grade Geometry ideas.

22. Magic Tables • Take a look at the 5 cards in front of your group, pick a secret number between 1 and 31. • Put all the cards with that number in the center of the group. • I will guess your number

23. Magic Tables Continued • Reason: Add all the numbers together on the first numbers of the cards given to you: Powers of 2 • Example: If the cards in the center have cards that start with 16 and 4, since when added together this would make their number be 20. • CC: sixth grade- evaluating exponents with whole numbers • Seventh grade- Use properties of operations to generate equivalent expressions • High school: rewrite exponential functions using multiple exponents.

24. CC: 7th grade students solving real life mathematical problems

25. Questions? And Answers! Thank you for coming!