(FAMILIES: if you are supporting your student with a POW, please don't solve it FOR them. Use these hints to keep them thinking and doing their best. Enjoy the math talk and exchange of ideas in your household without the worry of being RIGHT. Celebrate curiosity and perseverance.)
Problem of the Week Helpful Hints
FIRST: UNDERSTAND the problem! Look up words you don’t know, underline important information, draw a picture just to understand the situation. USE your Getting Started Genuine Questions (also on blog). THIS IS THE MOST IMPORTANT PART OF PROBLEM SOLVING!
SECOND: Decide what math makes sense to use and make a PLAN. Keep your focus on what makes sense and why it makes sense; there are many valid ways to solve these problems. Sometimes you have to go down the wrong path in order to find the right one.
ORGANIZE your work so it can be understood...by anyone.
LAST: DOES YOUR ANSWER MAKE SENSE? Why or why not? REVISE your work if you need to. VERIFY that your thinking is correct by solving the problem a different way.
ALWAYS: COMMUNICATE your entire process CLEARLY with pictures, words, and symbols. INCLUDE mistakes and discoveries you made or questions you have. What did you LEARN?
TURN IN a neat copy of your work EACH Tuesday.
POW's should show YOUR BEST WORK.
ASSIGNED 1/9/12, DUE 1/17/12
Pole in the Pond
There is a pole stuck in the mud in the bottom of a pond. One-half of the pole is in the mud, 2/3 of what's remaining is under water, and one foot of the pole is above water. How long is the pole?
ASSIGNED 1/18/12 DUE 1/24/12
Marbles in a Collection
Theo has a marble collection. The marbles are red, blue, and yellow. One-fourth of his collection is red marbles. Two-thirds of the marbles are blue.
a. How many marbles does Theo have? Explain.
b. What fraction of his collection is yellow marbles?
Assigned 1/24 DUE 1/31
Gas in the Tank
POW 3 PDF
Daphne has 1/8 of a tank of gas when she pulls into a gas station. After she puts 15 gallons of gas in her tank, the gas gauge reads 3/4 full. How may gallons of gas does Daphne’s tank hold when it is full?
Assigned 2/7 DUE 2/14
Cars in a Lot
A public parking lot has space for 1000 cars and 2/5 of the spaces are for compact cars only. On Tuesday, the parking lot was 3/4 full and 5/6 of the cars were compact. Assuming each compact space is full, how many compact cars are parked in full-size spaces?
POW 4 PDF
Assigned 2/25 DUE 2/21
Numbers Between Numbers
The improper fraction ￼-11/2 is halfway between the two integers -5 and -6, and -23/4 ￼is halfway between ￼-11/2￼ and -6.
a. What improper fraction is halfway between -23/4 and -6? Show how you found it, and prove you are correct.
b. How many improper fractions exist between -5 and -6? Explain your answer.
POW 5 PDF
What are Genuine Questions?
Here are some REAL questions to ask when working on a mathematical task, in no particular order:
1. What is this task asking me to find?
2. What math ideas or concepts is this task asking me to think about? What do I already know about these concepts?
3. What tools will help me? (manipulatives, sketches, calculator, dictionary, journal, etc.)
4. What information is important and what is not important? How can the information be organized?
5. What math concepts already familiar to me can I use in this situation?
6. Which math ideas explored in class can I use?
7. What else do I need know in order to think about this task?
8. What additional questions do I have? Exactly what part of this task is confusing to me? Where or from whom can I get my questions answered?
9. What strategy or plan do I have? Why have I chosen this strategy? Does it make sense?
AFTER REACHING A SOLUTION:
10. How do I know my solution is accurate? Is there a different way to solve the task?
11. Have I communicated my thinking clearly and precisely? What else should be included?
12. Does my solution make sense? Why or why not?
13. Can I justify my thinking to others? Can I explain HOW and WHY? Do I understand my own reasoning?
14. Did I use math that fits the problem?
15. Have I used ideas explored in class?
16. Is this my best work? How can it be improved?
EXTENDING YOUR THINKING:
17. What conjectures or generalizations can I make? How will I test them?
18. Did I make some excellent mistakes? Did I have any A-HA! moments? Did I include my my mistakes and new insights?
19. What new learning have I gained from working on this task?
20. What kind of connections can I make to other math concepts?
21. How does this task apply to my life and the real world? Where is this kind of thinking useful?
REMEMBER: Record your assignments on your "Journal Self-evaluation" chart (1/2 page, gold). You can have a parental unit sign off that they saw the completed work each day, but do this AT LEAST once every weekend. SHARE your journal and assignments with them and explain what you have been learning BEFORE they sign the chart. DUE EVERY MONDAY.
Journal Entries 1-3
Journal Entries 4-7
Journal Entries 8-11
JE 12 Practice Page- Absolute Value
JE 10, JE11 Integer Practice
JE 13, JE 14
JE16 WITH answer
JE17 Subtraction Practice
Having technical difficulties loading all the assignments. Will post when problem is solved.
JE 20 and 20.5
JE 20.5 is the "plus" activity in the lower right hand corner.
JE 21 Absolute Value with rational numbers
JE 23a/b "word" problems
Here is a fun site to find out how much it would cost to send the gifts from The Twelve Days of Christmas.
Christmas Price Index 2010
Model this situation, determine the requested information, show your work, and clearly communicate your reasoning. (HINT: Use the Genuine Questions to increase your learning and improve the quality of your work!)
"Between midnight and noon and submarine cruised at -200 feet, then dove down 150 feet further, climbed up 115 feet, dove 180 feet, and finally climbed up 100 feet. Determine the difference between the highest and lowest positions of the submarine during this 12-hour period."
Here are links to recent articles about standards or proficiency based assessment.
Article from The New York Times
Article from ASCD
In an effort to clearly communicate expectations, I have provided each student with a Rubric for "letter" Grades. Whenever they (or you) visit Student-Assist, please look beyond the percent that the grading program (eSis) automatically calculates, because this is an average based on a "point" system. Since I am using Proficiency Grading instead, students (or you) will need to focus their attention on the score for each learning target. As explained in the Rubric for Mastery, a score of 4 or 5 indicate that he/she has met or exceeded the minimal expectation. In other words, a 4 does NOT indicate a 4 out of 5! Students will now be able to pin-point specific learning goals (targets) where they need to ask more questions, continue to develop understanding, get extra help, etc., and follow up their additional learning with another assessment.
I'm always looking for ways to help all students succeed. So, beginning in Trimester 2, I will also give each student a "Personal Growth Tracker", which will list the individual Learning Targets for the unit. These Learning Targets are smaller goals within each state Standard.
Each time they are assessed, whether through a traditional test, a work sample, a conference, or a project, students will get feedback in the form of a score from the Mastery Rubric. (They may also receive written comments or questions intended to move their thinking forward.) Now students will be able to record and track their individual progress in each learning target. Both of these tools, used together, will give students a clear picture of their progress towards proficiency.
P.S. I will also use the Grading Rubric at the end of the trimester to provide a letter grade, overriding the percentage grade.
Grading Rubric and Mastery Rubric
Example Personal Growth Tracker
See also: NCTM article, "Rules or Understanding".
For assistance with VISUAL MATH (all that groovy stuff with tiles and manipulatives), go to Math Models I or Math Models II RECTANGULAR PRISMS
Use this link Perfect Packages to explore nets and surface area of rectangular prisms.
(You must have Geometer's Sketchpad to open this file.)
VERY IMPORTANT To open the link below, you MUST press and hold "control" before clicking. Then choose "Save linked file as..." and SAVE AS "TRIANGLE STUDY" into your own student file; next time, you will be able to access this file from your student folder!
Everyone knows a triangle has three sides and three angles. What else can you discover about the this polygon?
Use this link Triangle Study to find out more about triangles!
(This link will only work if your computer has Geometer's Sketchpad.)
Angles and Degrees
VERY IMPORTANT To open the link below, you MUST press and hold "control" before clicking. Then choose "Save linked file as..." and SAVE AS "ANGLE STUDY" into your own student file; next time, you will be able to access this file from your student folder!
How much is 1/3 of a circle? How far do you rotate to turn 25% of a circle? How much of a circle is 45˚?
Use this link Angle Study to explore types of angles and the meaning of angle measurement.
Types of Angles
(This link will only work if your computer has Geometer Sketchpad.)
Welcome to the new school year!
I am so happy to be teaching math to all your wonderful students. We are starting off the year with a Probability module. For a final project, students will be demonstrate their learning and understanding by creating an original board game. The games will be shared with the BPMS community on a school-wide Game Fair in early November. More details will come home.
Feel free to contact me via email at firstname.lastname@example.org I look forward to teaching and learning with all of you!
Penny-toss Experiment: Class Lab
Who Will Win?
Is It Fair? (Spinner Lab will to be completed in class 9/12 and 9/15. DUE 9/15.)
Fair Spinner Lab
NCTM website for on-line spinner lab: Adjustable Spinner
Experiment vs Theory Lab
Here are some REAL questions to ask yourself (or each other) when working on a math problem, in no particular order:
1. What is this problem asking me to find?
2. What information is important in this problem and what is not important?
3. What do I know about this problem?
4. What else do I need know in order to think about this problem?
5. What math ideas I have been learning about are in this problem?
6. What strategies could I use to think about this problem?
7. Why have I chosen this strategy? Does it make sense?
8. Is there another way to look at this problem?
9. How can I organize the information in this problem?
10. Can I explain my ideas and thinking to someone else in a way that they would understand?
11. What kind of questions do I have about this problem?
12. Does my solution make sense? Why or why not?
13. Can I justify my thinking to others? Can I explain HOW and WHY?
14. What kind of connections does this problem have to other math concepts?
15. Can I make a general rule?
16. How can I extend the ideas in this problem?
17. How does this problem apply to my life and the real world? Where is this kind of thinking useful?
18. Is there more than one solution to this problem?
- Math Links
IXL and State Standards
This site contains practice for all the 2007 Oregon State Standards, broken in smaller components. Awesome!
Math and Logic Puzzles
NCTM Illuminations Activities
- Math Minute 2