Perfect Practice Makes Perfect

# Number Sense

## Tuesday’s Twister #18 – Number Sense (Order of Operations)

October 25th, 2015 by John Lehet

Here’s another Number Sense Puzzle. Today’s puzzle centers around another fundamental skill that gives many students a really difficult time – Order of Operations. This is geared to younger puzzlers to help them improve their Order of Operations skills. As always, let me first give a general introduction. There will be 8 statements each corresponding to a number. You have to use the numbers 0 through 9 once and only once to fill in the correct number for each statement. You will need to use and develop your deductive problem solving skills in order to correctly place the numbers. Since there are only 8 answers and 10 numbers (0 through 9), some of the answers will require two digits. In this puzzle, some of the answers will be negative, that’s no problem, just make sure the digits use 0 through 9 once and only once.

I created an interactive puzzle that will automatically check your answer and provide feedback. I also created a pdf file that can be used in classrooms or with pencils for those so inclined. The goal is to have fun and challenge yourself.

select Check when complete to check your answers

I hope you enjoy these puzzles. If you find these interesting, Click Here for a selection of more Number Sense puzzles that I’ve created. I will be adding to the selection over time. Good Luck and pass the puzzles onto others who may enjoy them!

## Tuesday’s Twister #17 – Number Sense (Negatives)

October 22nd, 2015 by John Lehet

Here’s a puzzle that I introduced back in December called Number Sense Puzzles.  They are geared for younger puzzlers to help them improve their number sense.  Let me first give a general introduction. There will be 8 statements each corresponding to a number.  You have to use the numbers 0 through 9 once and only once to fill in the correct number for each statement.  You will need to use and develop your deductive problem solving skills in order to correctly place the numbers.  Since there are only 8 answers and 10 numbers (0 through 9), some of the answers will require two digits.  In this puzzle, some of the answers will be negative, that’s no problem, just make sure the digits use 0 through 9 once and only once.

I created an interactive puzzle that will automatically check your answer and provide feedback. I also created a pdf file that can be used in classrooms or with pencils for those so inclined. The goal is to have fun and challenge yourself.

Today’s puzzle is all about adding and subtracting negatives. I’ve found that this is an area that gives many students a really difficult time. It looks easy, but remember to take your time so you use each number once and only once!

select Check when complete to check your answers

I hope you enjoy these puzzles.  If you find these interesting, Click Here for a selection of more Number Sense puzzles that I’ve created.  I will be adding to the selection over time. Good Luck and pass the puzzles onto others who may enjoy them!

## SAT Math Blast – #4

September 3rd, 2015 by John Lehet

Here’s the fourth SAT Math Blast for those preparing for the SAT this Fall. The questions are in the Easy/Moderate level and all pertain to Numbers and Operations:

 Topic – Numbers Level – Easy/Moderate Questions – 10

Remember, just select “START” to give it a try. Use the “NEXT” and “PREV” buttons to navigate and when you’ve answered all of the questions, select “COMPLETE”. You’re results will be posted. Also, you will be able to return to any of the questions to review (just select the question number in the results window).

As always, I hope you enjoyed this post. Please pass it onto others who may enjoy and please click LIKE below if you like it! (you need Adobe Flash in order to interactively run the above exam)

## SAT Math Blast – #2

August 26th, 2015 by John Lehet

Here’s the second SAT Math Blast for those preparing for the SAT this Fall (or the ACT too).  Here’s today’s information about the practice exam:

 Topic – Numbers and Operations Level – Easy Questions – 10

Remember, just select “START” to give it a try. Use the “NEXT” and “PREV” buttons to navigate and when you’ve answered all of the questions, select “COMPLETE”. You’re results will be posted. Also, you will be able to return to any of the questions to review (just select the question number in the results window).

As always, I hope you enjoyed this post. Please pass it onto others who may enjoy and please click LIKE below if you like it! (you need Adobe Flash in order to interactively run the above exam)

## SAT Math Blast – #1

August 24th, 2015 by John Lehet

In preparation for the SAT exam scheduled for October 3rd, I’ve decided to periodically post review math exams on the MathMaverick Blog. This goes right along with my “Perfect Practice Makes Perfect” theme. Each exam will contain between 10 to 20 questions of varying levels of difficulty. Areas covered will be as follows:

 Numbers and Operations Algebra and Functions Geometry Data Analysis

For each SAT post, I will update the following table to reflect the contents of the days questions:

 Topic – Numbers and Operations Level – Easy Questions – 10

Just select “START” to give it a try. Use the “NEXT” and “PREV” buttons to navigate between the questions. When you have answered all of the questions, select “COMPLETE”. You’re results will be posted. Additionally, you will be able to return to any of the questions to review (just select the question number in the results window).

As always, I hope you enjoyed this post. Please pass it onto others who may enjoy and please click LIKE below if you like them!  (you need Adobe Flash in order to interactively run the above exam)

## Tuesday’s Twister #13 – Prime Numbers

May 19th, 2015 by John Lehet

“There are three kinds of people: Those that make things happen, those that watch things happen and those that wonder what happened. ” – Agent Garbo (Juan Pujol Garcia)

Prime numbers are everywhere and they are really easy to understand.  There are just two simple rules to follow:

• – a prime number is a positive integer greater than 1
• – a prime number is evenly divisible by only 1 and itself

That’s pretty straight forward.  Many people assume 1 is a prime number, but by definition, it’s not.  It’s important to realize and remember this when dealing with primes.  Also, 2 is the only even prime number, as all other even numbers are divisible by 1, 2 and itself.

Here’s a couple of prime number puzzles to start you off.

puzzle 1: What is the smallest 2-digit prime number in which both digits are prime and their sum is prime?

puzzle 2: What is the largest 2-digit number in which both digits are prime and their sum is prime?

Let’s look at an example number, say 73.  73 is a prime number and it’s digits, 7 and 3 are both  prime.  However, the sum of the digits 7+3 equals 10, which is not prime.  So, 73 will not work for either puzzle 1 or puzzle 2.

Once you solve the first two puzzles, you should have a good handle on prime numbers.  I recommend listing all of the prime numbers less than 100.  To make it a bit more challenging, let’s look at 3-digit numbers.

puzzle 3: List all 3-digit numbers that have prime numbers for all three digits.

puzzle 4: Of the numbers listed in puzzle 3, list the numbers in which the digits sum to a prime number.

puzzle 5: Of the numbers listed in puzzle 4, which of the numbers are themsleves prime?

Let’s look at an example 3-digit number, say 235.  the digits, 2, 3 and 5, are all prime numbers.  However their sum, 2+3+5, equals 10, which is not a prime number (so it doesn’t work for puzzle 4).

Good luck with the puzzles and have fun.

## Tuesday’s Twister #12 – Sequences

May 13th, 2015 by John Lehet

“Lost time is never found again.” – Ben Franklin

When working with students in elementary school, I like to talk about sequences or number patterns.  I often present them with the start of a sequence, say the first three numbers.   I then ask the class to give me the next term (or number) in the sequence.  Letting everyone in the class mull it over for a bit, I ask for the pattern (the code essentially) and the next few numbers.  When I first did this, I was amazed!  I had a sequence in mind, but the students kept giving different, yet very viable sequences.  Not only that, they could justify their answers by supplying the “code” for the sequence.  I quickly realized that with just three numbers at the start of a sequence, the possibilities were plentiful.  It was quite the challenge for the students also.

So, I started doing this as a “break the ice” activity with classrooms.  We would use the same three numbers again and again, and see how many different (yet viable) sequences could be made.  When they give me a sequence and its corresponding justification, I would say “great, let’s find another” and erase it leaving only the first three “seed numbers” that I had originally written.  I  would then ask them to give me another different sequence and the whole thing would start over again.  Each time I do this, I am still amazed at how many different sequences they come up with and how challenging they find it.  Here’s the start of a sequence for you to try …

## Here’s three numbers that start a sequence:    2, 3, 5, . . .

What do you think the next number can be?  How about the number after that?  Remember, it has to follow a pattern, so you can easily find each successive number by applying the pattern.

I’ve given this pattern to numerous classrooms.  Each time,  they came up with a variety of different answers, all of which make a valid sequence.  For the next number, classes have given 7,  some have given 8 while others have given 14.  In all, from all of the classes, I have received 9 different sequences that these three numbers can generate (and there’s even more!).

My challenge to you is to find as many different sequences that can be generated using the first three numbers  2, 3, 5.  Remember don’t just come up with the sequence, but identify the pattern that it follows.  Challenge yourself to see if you can find nine different sequences.  Good luck, have fun and challenge others, the more the merrier!

## Tuesday’s Twister #11 – Number Circuits

May 5th, 2015 by John Lehet

“Go fast slowly” – Clarence Stephens

Number Circuits are an original puzzle that I came up with a few years ago.  They are number sense puzzles that require you to arrange a set of numbers in a designated pattern.  I used magic squares as a theme using shapes other than squares. In all, I was able to develop over 200 puzzles all with this same theme.  Fortunately, Mindware liked the puzzles and published two books.  I was pretty excited (and still am).  The books differ in difficulty, although neither set of puzzles are too difficult (although all puzzle are challenging when you can’t solve them!).  Below are four puzzles, two from each book.  I believe they’re representatve of each collection and Number Circuit puzzles in general.  Click each picture to open a full sized pdf image of each puzzle in a new window.

 from Number Circuits A from Number Circuits B

As always, I hope you enjoyed these puzzles. Please pass them onto others who may enjoy them and please click LIKE below if you like them!

MIndware currently has the books for sale for only \$3.95 (that a 69% savings!).  If interested in purchasing either book just click below:

Number Circuits A (Beginner Puzzles)

Number Circuits B (Advanced Puzzles)

## NBA Expands Uniform Numbers

April 1st, 2015 by John Lehet

In breaking news today, the National Basketball Association (NBA) commissioner Adam Silver announced major reform to player’s uniform numbers.  Starting today, April 1st, 2015, player’s uniform numbers can be any real number. This breaks with the NBA tradition of allowing only whole numbers (that’s the natural or counting numbers including 0) on player’s uniforms. The commissioner announced that “The NBA today breaks all uniform numbering traditions in an attempt to broaden our limited view of number. Although some may see this as a radical move, today we rejoice in including negative integers, rational numbers, in both fractional and decimal form, radicals and yes even π as accepted uniform numbers. This has been long overdue.”

The National Association of Numbers (NAN) was quick to comment, “This is indeed a major gain for number equality. We know that all numbers are not equal, but with this major step forward, each and every number will have the equal opportunity to emboss an NBA uniform.”

NAN spokeswoman Ellen E. Todax (a.k.a. “X”) agreed that this was a step in the right direction. However, she continued, “complete number equality is far from a reality. Imaginary numbers and their natural extension complex numbers were not included by the NBA.   The same can be said for e and φ. Even decimals numbers are cut short to two decimal places for positive numbers and only one decimal place for negative numbers. These are mere approximates of the actual value. You call that fair?  I don’t think the NBA went far enough.” When asked to expound on this view, Commissioner Silver replied “It’s not about fair, it’s about space.  There’s only so much room on a jersey.”

The Cantor Institute was also quick to respond. Representative Ann B. Yond issued a formal statement “We at the Cantor Institute regret that the NBA has not included Transfinite numbers. We believe that this is a harsh and infinitely hurtful. We are prepared to take this issue to court if necessary and willing to fight for their rights without bound!”.

Number critic I.M.Thicke thought the additional numbers were excessive.   He wrote, “There are too many numbers already, 24 second shot clock, 3 second lane, 5 seconds to in-bounds, 10 seconds to cross midcourt, 60 second timeouts, 30 second timeouts! And now all of these crazy uniform numbers! Where will it end? From a peach basket to this – It’s all too much!”

The last big step forward in uniform numbers was the inclusion of the number “00” as a valid uniform number. In the 1977-78 season, Robert Parish, then with the Golden State Warriors, was the first player to were the number “00” (like that’s a number). At the time this was thought to be outlandish, but this did not deter Parish. He wore the number for the next 21 seasons. Others followed, including Slick Watts the next year and Orlando Woolridge three years later.

Merchandizing, the backbone of the NBA, is off to a slow start. New, real numbered jersey orders have trickled in.   Shirtmakers complain that specialty jerseys may require new embossing and embroidery equipment. The added expense may cause jersey prices to skyrocket.

The NBA first player to select a new number was little used Syrian center Ihäté Al Jabbar, who chose the number 3.42 in honor of the number of minutes he’s played this season.

So at  your next NBA game, don’t be surprized to hear ” … that’s four fouls on number √2 Johnny Jones.  Looks like he is going to be replaced by number -1.3 Sammy Slick …”.  We’ll just have to wait and see!

## Tuesday’s Twister #6 – Number Riddles

February 3rd, 2015 by John Lehet

Attitude is a little thing that makes a big difference.” – Winston Churchill

Riddles have always been one of my favorite types of puzzles.  Riddles are easily said and understood, but solving them is another issue.  Riddles come in all shapes and sizes.  There are true riddles, rhyming riddles, associative riddles, metaphoric riddles and joke riddles just to name a few.

Today’s twister is a series of riddles, all with a number theme.  Three of the following riddles are original and one is borrowed.  In either case I think that the following selection of four riddles will challenge everyone that gives them a try.  Remember, stick with it – the fun of riddles is figuring them out, not having them answered for you!

1.
What occurs twice in a week but never in a day?

2.
I’m closest number to the number 9
But not when looking at a number line
As a smile it to a frown
You need only turn me upside down

What number am I?

3.

Either Add 1 to me
or Subtract 1 from me
and a palindrome you’ll see

What number am I?

4.

What number is twice the number of letters in it?

Good Luck and pass these riddles onto others who may enjoy them! And remember to LIKE US below!