Directed Number Tables

 

Dice Game

 

 

Concept Attainment

 

JPN 2-1 GER

 

Desmos link

Vertices Problem

from Rob Southern

 

Tax Collector Game

photo by Kelly Sikkema

Source of this activity:By Gary Antonick, New York Times

Tax Collector is played like this: Start with a collection of paychecks, from $1 to $12. You can choose any paycheck to keep. Once you choose, the tax collector gets all paychecks remaining that are factors of the number you chose. The tax collector must receive payment after every move. If you have no moves that give the tax collector a paycheck, then the game is over and the tax collector gets all the remaining paychecks. 

The goal is to beat the tax collector.

Example:
Turn 1: Take $8. The tax collector gets $1, $2 and $4.
Turn 2: Take $12. The tax collector gets $3 and $6 (the other factors have already been taken).

Turn 3: Take $10. The tax collector gets $5.

You have no more legal moves, so the game is over, and the tax collector gets $7, $9 and $11, the remaining paychecks. 

Total Scores:
You: $8 + $12 + $10 = $30.
Tax Collector: $1 + $2 + $3 + $4 + $5 + $6 + $7 + $9 + $11 = $48. 

Questions:

Is it possible to beat the tax collector in this $12 game? If so, how? What is the maximum score you can get?

Bonus: What if you played the game with paychecks from $1 to $24? How about $1 to $48?

 

Lockers and Bulbs

Task 1 (Source: Illustrative Math)

The 20 students in Mr. Wolf's 4th grade class are playing a game in a hallway that is lined with 20 lockers in a row.

• The first student starts with the first locker and goes down the hallway and opens all the lockers.
• The second student starts with the second locker and goes down the hallway and shuts every other locker.
• The third student stops at every third locker and opens the locker if it is closed or closes the locker if it is open.
• The fourth student stops at every fourth locker and opens the locker if it is closed or closes the locker if it is open.

This process continues until all 20 students in the class have passed through the hallway.

1. Which lockers are still open at the end of the game? Explain your reasoning.
2. Which lockers were touched by only two students? Explain your reasoning.
3. Which lockers were touched by only three students? Explain your reasoning.
4. Which lockers were touched the most? 

Math Taboo Game

 

 

[download the cards from here]

Area Puzzle

 

 

Two Rational Numbers

 

Source:@blatherwick_sam

Three of the many possible solutions:

Estimating and Rounding

 

 

Honeycomb Triangles 2 (Hosoya's Triangle)

 

1. What patterns do you see in the above system?
2. Complete the missing hexagons. (until the row with 144, 89, ...)
3. What other patterns can you identify?

 

 

 

Honeycomb Triangles 1

 

Blaise Pascal was another famous mathematician who in 1653 published his work on a special triangle following a specific pattern.  This became known as Pascal’s triangle, even though many other cultures have studied this pattern thousands of years before.  The observations made from Pascal’s triangle has led to patterns related to probability and statistics, which we will explore later in the semester.

Take a look at Pascal’s triangle.  The first number starts with a 1. Then continue to place the number 1 on the left and right edge of each number 1 from above.  To obtain the missing number below, you add the two adjacent numbers above them. For example, you add the adjacent numbers 1 and 2 to obtain 3 below them.  Fill in the rest of the triangle.

 

1. Write down a few observations and patterns.  Share your observations with your group. Try to get as many observations as you can.
   
2. What happens if you color in all the odd numbers and even numbers.  What do you notice?
3. Describe where you can find these sets of numbers found in Pascal’s triangle.  Some are very easy to pick out, others may be identified by adding some of the cells together in a specific pattern.
   1. Natural numbers
   2. Fibonacci numbers
   3. Multiples of 2
   4. Multiples of 3
   5. Powers of 2: 2, 3, 8, 16
   6. Triangular numbers
   7. Square numbers
   8. Hexagonal numbers
   9. Hockey stick pattern
   10. Other patterns?

 

Resource:Mary Ann Esteban

 

Donkey and the Lake

 

source: @Math26039335

 

 

 

 

 

 

 

 

 

How many triangles?

 I took this lovely activity from Nolan Fossum's tweet. 

Pythagorean Triplets Card Sort 2

 On Jamboard, work with your group friends to organize the following cards into Pythagorean triplets.

 

 

Part 1 (with cards)

Treasure Island

Use the same map for two different tasks given:

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Task 2

 

Expanding Brackets

 

Make your own equation (Jamboard Activity)

 

Truchet Wall

Play with the tiles and create your own art. (Laminated the printouts, then used sticky magnets, students can easily rotate/move the tiles)