## Tuesday, April 16, 2013

### This Week's Work : Week 8 -- for Inquisitive Young Mathletes

Assignment 1:
Using Algebra and Number Sense as Shortcuts from Mathcounts Mini

Watch the video and work on the activity sheet below the video on the same link for more practices.

Also, review the following:
$$x^{2}-y^{2}=\left( x+y\right) \left( x-y\right)$$ $$\left( x+y\right) ^{2}=x^{2}+2xy+y^{2}$$ $$\left( x-y\right) ^{2}=x^{2}-2xy+y^{2}$$ $$\left( x+y\right) ^{2}-2xy =x^{2}+ y^{2}$$
$$\left( x-y\right) ^{2}+ 2xy =x^{2}+y^{2}$$
$$\left( x+y\right) ^{2}-4xy =\left( x-y\right) ^{2}$$

Assignment 2:

Pascal's Triangle  from Math is Fun

Pascal's Triangle and Its Patterns

Assignment 3:
It'll be sent through e-mail.
Happy problem solving !!

### This Week's Work : Week 6 and 7 Review -- for Inquisitive Young Mathletes

Watch Joint Proportion from Art of Problem Solving

Spend some time pondering on "Work" word problems from Purple Math.
These are some very standard word problems you'll encounter in competition math.

Review --
dimensional change and probability links from previous weeks.

More practices on inverse and direct relation

From Regents Exam Prep

New concepts:

Height to the hypotenuse
How many ways to arrange the word "banana"? (with elements repeating)
Probability that two of the 3 friends were born on the same week day.

Question : If you can earn 0, 1, 3, 7 or 10 points with each shot and each person has three chances, how many scores can't be made?

Note:
Percentage increase (don't forget to minus the original 100% or 1) is very different from at what percent will it return to the original size or what is the size compared to the original.

### This Week's Work : Week 5 -- for Inquisitive Young Mathletes

Evan (a 5th grader in PA) 's Problem of the Week:
A man notices a sign in Shop-a-Lot that says: "All prices are marked 25% off today only!" He decides to buy a shirt that costs $65.12 before the discount. He then uses a$16 gift certificate and the clerk applies 12% sales tax. What is the final cost of the shirt after all the steps are applied? Express your answer to the nearest hundredth.

Solution:
When there is a discount that is 25% off, the original price is going to be 75% times the original price. Therefore, 75% of $65.12 is$48.84. Next, subtracting $16, we obtain$32.84. Finally, applying 12% sales tax, we get $32.84 x 112% (since original price is added to the sales tax "price") which is$36.7808. This rounded to the nearest hundredth is $36.78. Assignment 1: Painted Cube Problems Visualization of the Painted Cube Problems It's more fun if you dig out Legos or Unit Cubes and just build some cubes (and later rectangular prism) and spend some time observing how it works. Assignment 2: Review special right triangle, Pythagorean triples, theorem : 30-60-90 , 45-45-90 special right triangle angle ratios Dimensional Change ### This Week's Work : Week 4 -- for Inquisitive Young Mathleges First of all, problem of the week from Evan, a 5th grader: A man notices a sign in Shop-a-Lot that says: "All prices are marked 25% off today only!" He decides to buy a shirt that costs$65.12 before the discount. He then uses a \$16 gift certificate and the clerk applies 12% sales tax. What is the final cost of the shirt after all the steps are applied? Express your answer to the nearest hundredth.

This week, we'll learn two very common sequences : arithmetic and geometric sequences.
There are quite a few similarities between these two types and they are closely linked to ratio, proportion
so just watch the videos and play around/generate a few/ponder on those sequences. I don't expect you to learn them in just one week.

Notes from Regents Exam Prep: Arithmetic and Geometric Sequences and Series

From Mthcounts Mini:

Easier concepts:

Sequences

Arithmetic sequence/determine the nth term

Arithmetic and geometric sequences

Harder concepts:

Relationship between arithmetic sequences, mean and median

Sequences, series and patterns

From my blog :
Some special arithmetic sequences and the easier way to find their sum

Write some notes of the most important features of the arithmetic sequence.
The best note will be posted here to share with other students.
Be creative !!

### This Week's Work : week 3 -- for Inquisitive Young Mathletes

Assignment 1:
Watch and learn Simon's Favorite Factoring Trick.

Work on some of the problems as well to check your understanding.

Assignment 2:
Just learn as much as you can.
We'll keep practicing counting and probability.

Counting Permutations : from Art of Problem Solving

With or Without Replacement : from Art of Problem Solving

Notes on Permutations from the Math Page

Permutations with Some Identical Elements

### This Week's Work : Week 2 -- for Inquisitve Young Mathletes

Assignment 1:
Mathcounts Mini related to the "Set" concept
Download the word problems below the video and work on them for this week.

Pascal's Triangle from Math is Fun.

Below is problem of the week, which continues with Evan's problem from last week so read it carefully.
Two players play a game starting with a pile of 26 sticks. The players alternate turns, each taking 1, 2, or 3 sticks on his or her turn.The player who takes the last stick wins.Who has the winning strategy in this game, the first player or the second player? How many sticks he/she needs to take? Why?

Assignment 2:
Review special right triangles: Notes from my blog

30-60-90 Triangles from Art of Problem Solving

Powers of Pythagorean Triples from Art of Problem Solving

Working together rate  problems from Art of Problem Solving.