Unit 1 Problem Solving Challenges

If you feel like you have mastered all of the content covered in Unit 1, give these problem solving challenges a try!  Please email me your response along with a complete mathematical explanation.

“Gran, How Old Are You?”

Mom and her four children live with Grandma at 13 Drywater Street.

One day, Charlie, who is the third child, asked, “Gran, how old are you?”

Grandma answered, “My grandmother would have said ‘As old as my tongue and a little older than my teeth!’ but I will tell you how to work out my age.

“If you multiply your mom’s age with your age and with the ages of your brothers and sisters you will get the answer 111111. If you add your Mom’s age along with the ages of all of you four children the total will be my age.”

Charlie worked this out very quickly, because he knew his Mom’s age, his age and the ages of his brothers and sisters.

“Gran!” he called as he ran off to play outside, “You are old!”  How old was Grandma?

The Moons of Vuvv

The planet of Vuvv has seven moons, which lie spread out on one plane in a great disc round it. These Vuvvian moons all have long and confusing names so scientists usually call them by their initials: A, B, C, D, E, F and G, starting from the nearest one to the planet.

When two of these moons line up with the planet it is called a 'lunar eclipse'. When three line up with the planet it is called a 'double eclipse', when four do it is a 'triple eclipse' and so on. Once in a while all seven moons line up with the planet and this is called a 'super-eclipse'.

Moon A completes a cycle around the planet in one Vuvvian year, Moon B takes 2 years, Moon C takes 3 years, Moon D takes 4 years, and so on.

How long is it between each 'super-eclipse' on the planet of Vuvv?

Order of Operations Uber Challenge

Can you solve this Order of Operations uber challenge?  If you are able to solve it correctly and show me all your steps you will get a special prize!

Good luck!

(This problem is taken from this teacher's website!)

Base 12 System

There is a group of mathematicians who have been trying to change the way you count!

We currently operate using the base 10, or decimal system.

It looks like this: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20...

The group of mathematicians want people to start using the base 12, or duodecimal system!  They believe that the duodecimal system would make basic math way easier than the current decimal system.

The duodecimal system looks like this: 1 2 3 4 5 6 7 8 9 X E 10 11 12 13 14 15 16 17 18 19 1X 1E

It looks confusing, right??

Watch the video below which explains more how the base 12 system works.

Which do you think is better - the decimal or duodecimal system?  Why?

Convert the following base 10 numbers to base 12...

1. 36
2. 48
3. 54
4. 100
5. 120
6. 75
7. 2000
8. 395
9. 482

Apples & Remainders

We did this problem in my Math 6+ class, but I don't want my Math 6 students to feel left out!

If you are up for a challenge complete this problem and email me your response.

Best of luck!

Out of the 6000 apples harvested this year, every third apple was too small, every fourth apple was spotted, and every tenth apple was bruised. The remaining apples were good. How many good apples were there?

Clearly SHOW and EXPLAIN your thinking.

Awe

I saw this video at the EdTech Singapore Summit this weekend and was absolutely awed by it!  Check it out:

I'm happy to saw that I was awed quite recently.  I am taking a dive certification course and just last week I had my first pool dive.  My first breath underwater was AMAZING and I had to constantly remind myself that I was able to breathe at the bottom of a swimming pool!  It made me even more excited to go diving in the ocean next weekend.

When was the last time you were awed by something?

Share as a comment below!

Perfect Numbers

I was just doing some work and listening to one of my favorite songs, "Tonight You're Perfect" by the band New Politics.  As I was listening to the song, I was reminded of something we learned in class last week - perfect numbers!

Recall that perfect numbers are numbers whose sum of their proper factors is equal to the number itself.

For example, 6 is a perfect number because its proper factors are 1, 2, and 3.  The sum of 1+2+3 is 6.

By 1999, only 38 perfect numbers have been found!

Can you determine the next three perfect numbers after 6?

Is it possible for a perfect number to be a prime number?

Are all perfect numbers even?

Is it possible to have a perfect number that is prime?

Share your answers as a comment!

Multiples & Days of the Month!

Suppose the 1st day of a month is a Thursday.

On which days of the month will Saturdays fall, assuming it is a 31-day month?

How does this connect to your knowledge of multiples?

(Don't use a calendar or a table to help you; try to work this one out mentally!)

Post your answer and reasoning as a comment!

Finish early with the MAP test?

Pick any of these games to play if you finish early with your MAP test!

Thanks Mrs. McComb for the links!

Coordinate Plane: Cops and Robbers

Logic and reasoning: Tower of Hanoi

Angles: Estimating Angles

Factors and Multiples: Missing Multipliers

Divisibility: Dozens

Factors and Multiples: Factors and Multiples Game (interactive activity at bottom; for single players try to see how high a score you can get)

Division: The Remainders Game

Logic and Reasoning: Got It

Logic and Reasoning: NIM

Basic Facts and Reasoning: Shifting Times Table

Measurement: All in a Jumble

Chess: Use application on your MacBook