497: Factor Grids

Source: #mathsTLP

485: Number Line

On a number line, how many positive integers are closer to 50 than to 100?

source.

483: Time and Time Again

How many times per day do the hands make a straight angle? What are some of these times?


How many times per day do the hands make a right angle? What are some of these times?

482: Angling for More Time

If the MINUTE hand is on 2, and the hour hand and minute hand make an acute angle, what time could it be?

If the MINUTE hand is on 8, and the hour hand and minute hand make an obtuse angle, what time could it be?


source.

471: Digits in Fibonacci

We all recognize the Fibonacci Sequence:  1, 1, 2, 3, 5, 8, 13, 21, ...
What is the units digit of the sixty-first Fibonacci number?

Is there a pattern?

1,1,2,3,5,8,13,21,... What is the final digit of the sixty-first Fibonacci number?

— James Tanton (@jamestanton) May 24, 2015

470: Poor Alex Bellos

Normally, I'm glad when the nedia talks about math, even if it is simply the latest "Super-Hard problem from Asia that All of Us Stupid American Adults and Brits Won't be Able to Solve but Their 8 Year-old Do Routinely."

Throw in "I gave it to a mathematician and he couldn't solve it either" and you've got an instant viral hit, apparently.

All right, rant over.

What's the error?

Oh, and solve it if you want, too. It's not really that hard.

Further questions:

• Which blanks CANNOT have a prime number in them?
• Which blanks COULD have certain prime numbers?
• Which blanks essentially force this problem to be non-unique?

source.
(answer linked from there)

467: Squares

Take a square number and multiply by four. Is it guaranteed to still be a square number?

Can we generalize this rule?
Can your students explain why?

Source:

Subitizing Series #5: These Dots Will Grow on You http://t.co/MWtwbjb9eG Is every sq. # ×4 another square # #mtbos pic.twitter.com/IxwBXCaOGS

— Steve Wyborney (@SteveWyborney) May 18, 2015

457: Codebreaker

What are the values of the letters that will allow you to go as far as possible?

How high can you go?

Is there a better way to solve this than just marching up the line, and guessing at the values for H, R, then for F, U, then for I, V and so on?

The original is below. Is this the best set of values?

source:

Negative numbers code-breaker activity with a twist! #mathschat #MathsTLP pic.twitter.com/bOrXtB7mzS

— MathedUp! (@MathedUp) May 10, 2015

448: Hexagon Puzzle

Why did the puzzle creator only ask for circles A and B?

In the diagram, the 19 circles are to contain the integers 1 to 19 once each.
The sum total along any of the lines is 38.
Determine the integers in circles A and B.

Can you find the rest of the circles, too?


Another puzzle from Five Triangles.

447: Shading a Square

Q1: How many different ways are there to shade this to show ¼?
Q2: How might kids shade this to show ¼?

Source:

Q1: How many different ways are there to shade this to show ¼? Q2: How might kids shade this to show ¼?  pic.twitter.com/vntk6kcYw7
— David Wees (@davidwees) April 25, 2015

443: What are the questions?

source, of course.

439: Fraction / Decimal Tic-Tac-Toe

We all know that playing the middle of a tic-tac-toe game ensures that you can never lose if you play it right, but this one seems to be a bit trickier.

Where is the best place to start?

412: House Numbers

The houses on River Road are numbered consecutively from 10 to 132. Each house number is made with brass digits.

#105 would take 3 digits, for example.


1. How many brass digits are needed to form all the house numbers?

2. The numbers can be purchased for 2.29 each or $20.95 per dozen (of the same digit). What is the cheapest combination of numbers that you can arrange?

375: Pencils and Jars

360: Happy New Year 2015

What do you notice about these three equations?

10 x 9 x 8 x 7 ÷ 6 ÷ 5 * 4 * 3 - 2 +1 = 2015
(4 * 7 * 69 ) + 83 = 2015
(69 - 4) * (38 - 7) = 2015

Which one do you like best?

source: @alexbellos

358: Division and Remainders

Is that diagram correct?

What if the question were 13 ÷ 5 = 2 R3? Could we diagram it in the same way?

340: Giving Raises

A small company wants to give raises to their 5 employees. They have $10,000 available to distribute. Imagine that you are in charge of deciding how the raises should be determined.

1. What are some variables you should consider?
2. Describe mathematically as many different methods you can think of to distribute the raises. (We came up with nine; can you beat that?)
3. What information will you need to compute those raises according to your various methods?
4. Which of your methods do you feel is the most fair?

source: illustrativemathematics.org

Use an atbash cipher decoder: http://rumkin.com/tools/cipher/atbash.php

1. zm vjfzo znlfmg, gdl gslfhzmw vzxs.
2. vjfzo kvixvmgztv yzhvw lm hzozib.
3. mvklgrhn: 1p, 1p, 1p, 1p, Ldmvi'h hlm: 6p.
4. R'n lmv lu gsv vnkolbvvh: 0p, 0p, 0p, 0p, nv: 10p
5. kilwfxgrergb tlzoh: 1p, 1p, 2p, 2p, 4p
6. olggvib, zoo li mlgsrmt.
7. olggvib, 0p, 1p, 2p, 3p, 4p.
8. zokszyvgrxzo liwvi, 0p, 1p, 2p, 3p, 4p.
9. vnkolbvv'h xsrow'h gvhg hxlivh rm gsv olxzo hxsllo ... ru gsviv'h ml rnkilevnvmg, ml ylmfh.

284: Analyzing Digits

When the integers from 1 to 30 are multiplied, determine how many consecutive digits starting from the ones (1s) position are zeros.

Why does this question not require a calculator?

Would this be a fair question for some standardized test?

source.

282: Number puzzle

"The sum of two positive integers is 216. The greatest common factor of the two numbers is 24. What are all the possible pairs of numbers?"

What approach seems the easiest here?
I can see using solution methods such as:

• algebra
• guess and check
• organized list
• visual representation

Which (or which other) method rings true for you?
Which of the two sentences eliminates the most numbers?

The sum of 2 pos int is 216 and their gcf is 24. Find all possibilities.
— David Marain (@dmarain) September 24, 2014

275: Subtracting a series.

If you're a junior or senior, you've seen versions of this problem before, perhaps on the SAT (the source of this problem). As I've said before, the SAT is designed in a way that calculators are not necessary and each question must be solvable in less than a minute. Often, the student is expected to change the form of the question: text to algebra, or algebra to visual (graphical); or rearrange the terms, or work backwards from the known. 

The sum of the positive odd integers less than 200 is subtracted
from the sum of the positive even integers less than or equal to 200.
What is the resulting difference?

As it stands, that question would take you far too long to find an answer for, so it must have a simplification somewhere.

What can we do to make this quicker to answer?
Or simpler to understand?

How can we change it?