december and january training

MATHCOUNTS Coaching Kit 23

DECEMBERSession 10

If you do have an invited guest speaker (see suggestions at the end of Session 9), adjustthe schedule as you see fit depending on what he or she wants to do. Otherwise proceed asfollows:

Materials Needed:Paper / Pencils / Calculators / Toolboxes / Score SheetMATHCOUNTS School Handbook problems for Competition PracticeAwards / Proportional Reasoning Stretch #1-5 (on page 24 of this booklet)

Minutes 1 - 5Meet the kids at the door, take attendance, chat.Direct them to the Proportional Reasoning Stretch.

Minutes 6 - 15Discuss the problems and their solutions using Problem Solving Strategies.

Minutes 16 - 24Drill: Squaring a number with a units digit of 5

(Toolbox, Section X on page 47)Study the examples; then try some more.

Minutes 25 - 55Competition Practice Rounds: (MATHCOUNTS School Handbook)

Sprint WarmUp 13 # 1-10Target Warm-Up 14 # 1-10Team Workout 7 # 6-10

Discuss students answers on appropriate problems.Record individual scores.

Minutes 56 - 60Award prizes for todays winners. Confirm next meeting time.Thank your guest speaker.Clean up and escort students out of the building. Wait for parents.

Its already December! Make plans to deal with snow days if appropriate.


PROPORTIONAL REASONING STRETCH

1. On Monday Eulers Bakery discounted the price of pies20%. On Tuesday it discounted the pies an additional 70%.What is the combined percent discount?

2. A 12-foot board is cut into three pieces whose lengths arein the ratio of 3:1:2. How many inches are in the length ofthe shortest piece?

3. If 3 tics balance 9 tacs, and 3 tacs balance 6 toes, howmany tics are needed to balance 36 tacs plus 36 toes?

4. Jessica completed 7/8 of a training run in 2 hours and55 minutes. If Jessica runs at a constant pace, what isthe number of minutes left in her run?

5. Mecklenburg, in Culver County, has population 2570. Thepopulation of Culver County is 64,250. What percent ofthe Culver County population lives in Mecklenburg?

ANSWER KEY:1. 76 (C)2. 24 (C,M)3. 18 (F)4. 25 (C,M)5. 4 (C,M)

DecemberSession 10

1. _________

2. ________

3. ________

4. ________

5. ________

* Letters correspond to Problem SolvingStrategies found in the MATHCOUNTS

School Handbook *


DECEMBERSession 11

Materials Needed:Paper / Pencils / Calculators / Toolboxes / Score SheetMATHCOUNTS School Handbook problems for Competition PracticeAwards / Proportional Reasoning Stretch #6-10 (on page 26 of this booklet)

Minutes 1 - 5Meet the kids at the door, take attendance and chat with students.Direct them to the Proportional Reasoning Stretch.


Minutes 16 - 24Drill: Factorization (Toolbox, Section XII on page 48)

Study the examples, then try other numbers.


Sprint Warm-Up 15 # 1-10Target Warm-Up 16 # 1-10Team Workout 8 # 6-10


Minutes 56 - 60Award prizes for todays winners.Confirm next meeting time.Clean up and escort students out of the building. Wait for parents.

How about adding a holiday activity next week? Check the sources on the resource page forideas or ask a teacher in your building for a suggestion.

Have you noticed the kids are becoming YOUR kids?Congratulations! Youre connected.


PROPORTIONAL REASONING STRETCH

6. Diameter AB is equal to the sum of the six smaller diameters. What is the number of units in the difference between the circumference of the largest circle and the combined circumferences of the six smaller circles?

7. The rectangular courthouse in Pleasantville measures 1980 ftby 440 ft. One square mile equals 640 acres. How many acresdoes the courthouse cover?

8. Xa worked 2 hours and 15 minutes, Yo worked 1 hour and40 minutes, and Zu worked 2 hours and 30 minutes. Combined,they were paid $77. If each of them is paid the same hourlywage, how many dollars should Xa receive?

9. Homer paid $3 for 6 donuts. At this rate, how many dollarswould Homer pay for 3 dozen donuts?

10. A page of 12-point type contains 500 words; a page of 10-pointtype contains 660 words. A student printed a report using10-point type, and the result was 25 full pages. If she printsit in 12-point type, how many pages will the report contain?

ANSWER KEY:6. 0 (F,M)7. 20 (F,C, calculator)8. 27 (C,F)9. 18 (C)10. 33 (C,M,G)

DecemberSession 11

6. _________

7. ________

8. ________

9. ________

10. ________


School Handbook *


DECEMBERSession 12

If you found a holiday activity you would like to do this week, adjust the schedule as you seefit. A holiday snack also adds fun to this time of year. Otherwise proceed as follows:

Materials Needed:Paper / Pencils / Calculators / Toolboxes / Score SheetMATHCOUNTS School Handbook problems for Competition PracticeAwards / Factoring Stretch #1-5 (on page 28 of this booklet)

Minutes 1 - 5Meet the kids at the door, take attendance and chat with students.Direct them to the Factoring Stretch.


Minutes 16 - 24Drill: Pascals Triangle (Toolbox, Section IX on pages 46 - 47)Study patterns used to interpret probability and to simplify (a+b)n and 2n.


Sprint Warm-Up 17 # 1-10Target Warm-Up 18 # 1-10Team Workout 9 # 6-10


Minutes 56 - 60Award prizes for todays winners.Discuss holiday break and set time and place to meet in January.Clean up, escort students out of the building and wait for their parents.

Enjoy the holiday break. Youve earned it!

Call the coach of a school near you with a MATHCOUNTS team and invite the team andcoach over for a scrimmage after the holidays. Check the list of schools in your area on theWeb site www.mathcounts.org.


DecemberSession 12

1. _________

2. ________

3. ________

4. ________

5. ________


School Handbook *

FACTORING STRETCH

1. What is the sum of all of the distinct, positive primefactors of 1260?

2. What is the product of all of the values of n that make546,324,16n divisible by 6?

3. Billy tosses one fair 6-sided die with faces labeled1 through 6. He records the outcome. Billy does thisthree more times and the product of his four outcomes is120. How many possible combinations of 4 rolls could hehave rolled? (Rolling a 1, 1, 2, 2 is considered the samecombination as rolling a 1, 2, 2, 1.)

4. The numbers 1 400, inclusive, are put into a hat. What isthe probability that the first number chosen at random isa multiple of 4 or 17? Express your answer as a commonfraction.

5. If a and b are distinct, odd primes, then how many distinctpositive factors does 4a2b3 have?

ANSWER KEY:1. 17 (C)2. 16 (F,E,G)3. 3 (P,G,E)4. 59/200 (P,E)5. 36 (F,P)


JANUARYSession 13

If you arranged a scrimmage with another school, work with the other coach to adjust theschedule as you see fit. Otherwise proceed as follows:

Materials Needed: (There is something new on the list this time.)Paper / Pencils / Calculators / Score Sheet / AwardsCompetition from a previous year for Competition Practice(The Chapter and State Competition written rounds from the previous year can bedownloaded from the MATHCOUNTS Web site www.mathcounts.org. CountdownRounds must be purchased through Sports Awards.)

Minutes 1 - 5Meet the kids at the door, take attendance and chat with students.

Minutes 6 - 15Review the format and rules of a MATHCOUNTS competition.Set up teams of four if possible.

Minutes 16 55Competition Practice Rounds:

Time to use previous competitions and PLAY FOR KEEPS!Sprint # 1 - 15Target # 1 - 4Team # 1 - 5Countdown Round - # 1 - 36

Discuss students answers on all problems.Record individual scores.

Minutes 56 - 60Award prizes for todays winners.Confirm meeting time for next practice session.Clean up, escort students out of the building and wait for their parents.

It might be a good time to invite another guest to your next practice session.Contact the local coordinator (check the list on www.mathcounts.org) to see if he or she cancome out and talk to your team about the local competition.

ARE YOU READY FOR SOME MATHCOUNTS ? ! ? ! ? !


JANUARYSession 14

BRING ON THE COMPETTION PRACTICE!

Materials Needed:Paper / Pencils / Calculators / Score Sheet /AwardsCompetition from previous year for Competition Practice

Minutes 1 - 5Meet the kids at the door, take attendance and fire up your students!

Minutes 6 15Review competition rules and procedures.Set up teams of four if possible.

Minutes 16 - 55Competition Practice Rounds:Time to use previous competitions and PLAY FOR KEEPS!

Sprint # 16 30 (allow approx. 20 minutes)Target # 5 8 (allow approx. 6 minutes for each pair of questions)Team # 6 10 (allow approx. 10 minutes)Countdown Round - # 37 69 (allow a max. of 45 seconds each)

Discuss students answers on all problems.Record individual scores.

Minutes 56 - 60Award prizes for todays winners.

Make sure students know the School Competition will be NEXT week and it will lastabout 2 hours. Make arrangements with the school for extra time.

Clean up. Escort students out of the building. Wait for parents.

You are in the home stretch. Arrange with the PTO/PTA to have some type of awards foryour school winners, as well as a token for everyone who participated in the competition.These awards can be presented at a school assembly or PTO/PTA meeting.

december and january training

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