Perfect Practice Makes Perfect # Puzzle #4 – Number Sense Puzzles What people don’t realize is that professionals are sensational because of fundamentals” – Barry Larkin

Number sense if a fundamental skill.  I like to refer to it as “Number Familiarity“. How familiar are are you with numbers.  For example, take the number 64.  How familiar are you with the number 64?

• – Do you know it’s a perfect square?
Do you know it’s a power of 2?
Do you know it’s a perfect cube?
Do you know it’s the product of two perfect squares?

64 equals all of these – it’s 82,   26,   43  and   (22)(42).

I think that simply stated number puzzles are a great way to increase number sense.  It doesn’t matter if you’re seven or eighty-seven, concise number puzzles can be beneficial.  Here’s a few concise number puzzles to try:

1. Can you think of two numbers that when multiplied make 8 and when added make 6?
2. Can you think of two numbers that when multiplied make 32 and when added make 18?
3. Can you think of two numbers that when multiplied make 48 and when added make 14?

These puzzles should not be solved algebraically (e.g. via a system of equations).  Instead, these puzzles should stimulate thinking and making number connections.  They should also generate confidence.  There are very few things that generate confidence better than success.  Once these puzzles are mastered, change it up a bit.  Keep the puzzles generally the same, but ask for something different.  Instead of asking for the numbers, ask for the difference of the numbers, or ask for the smaller or larger number.  This adds another level of challenge to the problem.  Here are a few additional number puzzles to try:

1. What is the difference of two numbers that when multiplied make 18 and when added make 9?
2. What is the larger number of two numbers that when multiplied make 30 and when added make 13?
3. What is the smaller number of two numbers that when multiplied make 48 and when added make 19?

These puzzles are similar to the first set of puzzles, but differ as they are more challenging because the two numbers must be further manipulated to obtain the correct answer.  Continuing this theme of making the puzzles more challenging, here are a few more number puzzles to try:

1. Can you think of two numbers that when multiplied make 16 and adding one number to twice the other makes 8?
2. Can you think of two numbers that when multiplied make 24 and adding one number to twice the other makes 14?
3. Can you think of two numbers that when multiplied make 36 and adding one number to three times the other makes 21?

These puzzles will help build fundamental number sense.  They can be easily stated, understood and quickly solved.  They serve as great 1-minute problems and can assist in building confidence which will lead to even better problem solving skills.  Give them a try and share them if you like them.  Have fun and good luck!