Problem 49: Mr. Oswald's phone

Mr. Oswald forgot the pass lock pattern on his mobile phone. He remembers that the pattern starts from the dot labeled A, and ends on the dot that is labeled B. The pattern is made by 4 strikes.

He decides to unlock his phone by trying some patterns. However after 5 wrong patterns the phone will be disabled for 5 minutes.

i.          How many different pattern can be drawn from A to B with 4 strikes?

ii.          What is the probability that he can unlock his phone without disabling it?

A pattern example is drawn on the phone image above.

Problem 48: 6-Digit Divisibility Challenge

Math Poster: Linear Equations

This week, I created 3 posters to use in my classroom.

1. Parallel lines have the same gradient. Collinear points are on the same line.

2. Equation of a Line

3. Gradient Types of Lines

PDF Versions for downloading:
Parallel Lines-Collinear Points
Equation of a Line [y-intercept form]
Gradient Types of Lines

Problem 47: Greatest Number

Problem 46: Feet and Tails

Mrs. Eleanor Abernathy has 7 female cats. This May all her cats gave birth to new kittens. Some of the cats had 3 babies, some had 4 and the remaining ones had 5 baby cats. 

The number of cats that gave birth to 5 babies is 1 less than the number of cats that have quadruplets or triplets.

Mrs. Abernathy is interested in counting and she counts 150 legs in her house. 

Can you find the number of cats who has quints(5 babies)?

Rich Tasks 11: Making Sequence Competition

Rules and Explanations
-Students can change the order of the numbers to make sequences,
-When there is a team challenge, I give the points to the first two teams who produce a sequence with a reasonable description.
-Using two dice may be better in order to emphasize term to term rule or the nth rule.

Here is another version as a worksheet.

Problem 45: Escalator Ride

 

Source 

Rich Tasks 10: Finding the Number between the Fractions

Problem 44: Hexagonal Coins

This puzzle is from one of my favorite authors, Alex Bellos. The aim is to get all 6 coins to the hexagonal order given above starting with the given order below in three moves:

You can slide any coin as long as it touches to other coins in the new position.
See the Numberphile video for details and solutions.

Problem 43: Alien Encounter

I saw this problem on another blog page. It is from Steven Strogatz's famous book Professor Stewart's Cabinet of Mathematical Curiosities. I like such Knights and Knaves type of logical reasoning questions. I use them a lot while teaching "Logic" in IB DP Math Studies course.

Here is the question:

 

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Solutions to such questions need seeing the big picture of the case, and often students struggle doing this. That's why I prefer them drawing diagrams or truth table-like charts. 

Sometimes a tree diagram from probability unit is helpful.
So let's try a solution using tree diagrams.

Assume that Alfy tells the truth. Therefore he must be a Veracitor. What he tells about Betty is also true. So Betty is Gibberish. Betty says Alfy and Gemma are same species but she is lying. Therefore Gemma must be Gibberish. This coincides with Gemma saying Betty is Veracitor, which she is not. So Gemma is a liar and it matches with what we found from Alfy and Betty's answers. So our answer is Alfy: Veracitor; Betty and Gemma: Gibberish.

It is better to see the other option where Alfy is dishonest. This time we see that, if he is a liar, then Betty must be a Veracitor. If Betty is Veracitor, then Gemma must be Gibberish since Betty is honest in this option. However being a Gibberish, Gemma must be a liar. However, Gemma says Betty to be a Veracitor which is true. This truth creates a contradiction. Therefore this option is not reasonable at all and Alfy must be telling the truth. So the answer is the previous one.

Problem 42: Pink Triangle

Although an easy one, @solvemymaths's following similarity question on Twitter went viral on the Internet, so I have decided to keep it here:

What fraction is shaded?

Problem 41: Estimation

Math Pics 4: Pentagonal Totals

I saw this on Twitter. It is an amazing work. The total of numbers on each side of the pentagon is equal to each other.

Problem 40: Patterns with Watermelons

How many watermelons will there be in the 73rd step?

Source: Visual Patterns

Problem 39: Big Numbers

Which of these do you think is the biggest number?

-Number of cells in the human body

-Number of different orders you could shuffle a deck of cards
-Number of stars in the universe
-Number of seconds since the beginning of the time

Source:@ToddMalarczuk

http://www.planetsmarty.com/2016/07/b-is-for-big-numbers.html

Rich Tasks 9: Sequence Making using the die

Problem 38: Analogy between two problems

I have been reading 'Why Don't Students Like School?' by Daniel Willingham, and I came across with these problems:

Problem 1:
Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. It is impossible to operate on the patient, but unless the tumor is destroyed, the patient will die.There is a kind of ray that can be used to destroy the tumor. If the rays reach the tumor all at once at a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity, the healthy tissue the rays pass through on the way to the tumor will also be destroyed. At lower intensities, the rays are harmless to healthy tissue, but they will not affect the tumor either. What type of procedure might be used to destroy the tumor with the rays and at the same time avoid destroying the healthy tissue?*

Problem 2:
A dictator ruled a small country from a fortress.The fortress was situated in the middle of the country, and many roads radiated outward from it, like spokes on a wheel. A great general vowed to capture the fortress and free the country of the dictator.The general knew that if his entire army could attack the fortress at once, it could be captured. But a spy reported that the dictator had planted mines on each of the roads.The mines were set so that small bodies of men could pass over them safely because the dictator needed to be able to move troops and workers about; however, any large force would detonate the mines. Not only would this activity blow up the road, but the dictator would destroy many villages in retaliation. How could the general attack the fortress?**


The two questions describe similar phenomena, but the people who solved the first one or given the solution to the first one, mostly cannot answer the second one. Or they do not see the same relationship between the two triangles. Can you see?

*Willingham, Daniel T. Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom (p. 98). Wiley. Kindle Edition. 

**Willingham, Daniel T. Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom (pp. 98-99). Wiley. Kindle Edition.