## Thursday, June 5, 2014

### June/July 2014 Newsflash: Math Muscle Challenge

Grades 6 and up: 64 times larger

This month's problems:

Rick goes to the park each day and counts the number of ducks swimming on the pond. On Sunday he counts 1 duck. On Monday he counts 2 ducks. On Tuesday he counts 4 ducks.  On Wednesday he counts 8 ducks. If this pattern continues, how many ducks will Rick count on Friday?

Richard put an important document into a safe with a four digit numerical combination. In order for his partner Kevin to retrieve the document he must enter the correct combination. Richard told Kevin that the first two digits are identical and the last two digits are identical (XXYY). He also said the third digit is the sum of the first two digits and the last digit is the square root of the number formed by the middle two digits. What is the combination? (*Hint – The middle two digits together form a number that is a perfect square.)

### Tips and Techniques: Transposing

Transposing
is an important technique for students to master as they progress from Algebra I to Algebra II and beyond. It’s the process of moving quantities across the equal sign in an equation to make the problem solving process more efficient. Here’s how it works.

Solving an equation means isolating the variable on one side of the equation, either the right side or the left. Generally it is better to isolate the variable on the left side of the equal sign because we read from left to right.

Beginning algebra students are taught the Law of Equations:  whatever you do on one side of an equation, you must do on the other side as well.

Using the Law of Equations, to solve 2x 3 = 13, we can add 3 to both sides, giving us
2x 3 + 3 = 13 + 3 ===> 2x = 16
Then, we divide both sides by 2 to find that x = 8.

To solve 2x 3 = 13 by transposing, we do the following:
moving it from the left side, over the equal sign, to the right side, and changing its sign from “–” to “+.”
Now we have  2x = 13 + 3, which becomes 2x = 16, the same answer we got using the Law of Equations. Again, we find that x = 8.
The beauty of this process is that it is visually easier to see how the parts of the equation change as we solve it. Instead of writing the transposed quantity twice (once on the left and once on the right), we literally pick up the quantity and move it to the other side. The price we have to pay for doing this is changing the sign of the quantity being moved.

Let’s solve 3y + 2x 3 = 7 for y.
Since we want to isolate y, we can transpose 2x and 3.
This gives us y = –2x + 7 + 3. Simplifying, we get y = –2x + 10.
If we used the Law of Equations, we would have to write out
3y + 2x 3 = 7 ===> 3y + 2x 2x 3 + 3 = 7 2x + 3
While simplifying the above does give us y = –2x + 10, it comes with a lot more work.

Note that most classroom teachers will not allow transposing until students learn to use the Law of Equations.

Try these:
1. Solve for x: 4x + 9 = 49
2. Solve for y: 2y + 7 3 = 24
3. Solve for y: 3x + 9y 7 = 49
4. Solve for a: 3b 4a – 6 + 4 = 49
5. Solve for a: 2b + 4a + 5 – 2 = 42 – 2a

### Jump Start Your Summer with Mathnasium and Math Games!

Yay, summer! As you and your kids enjoy a well-deserved break from the pressures of school, we’d like to remind you that summertime also presents many opportunities for kids to keep their math skills fresh and play around with concepts they may encounter next school year. In particular, integrating some time for math games into play dates or family nights encourages kids to flex their math muscles as they spend quality time with their favorite people! Here’s a list of our favorite math games, featuring a few classics as well as some fresh alternatives:

A fun, family-friendly board game in which players move around the board buying and trading properties, building up properties by buying houses and hotels, and charging the other game players rent. Play the game with “dollar” bills only—the debit card version is not as educational.

Math War is a fun variation on the classic card game that challenges players to perform a calculation (in this case, multiplication). The player with the highest product wins the hand!

Set is a fun, portable (deck of cards) game that tests visual perception and pattern recognition by challenging players to choose three cards that all follow the same pattern or a different one.

Battleship is an engaging game for older kids that tests memory and spatial reasoning skills. Based on a numbered and lettered grid, guess where your opponent’s game pieces are positioned. First one to “sink” all of their opponent’s battleships wins.