[kevin]

Notice how if you reach the numbers 2 or 3 you always win. If you get 2, you chose 1, and they are forced to chose 1, resulting in a victory. If you get 3, you chose 2, an they are forced to chose 1, resulting in a victory. Therefore, if they reach 4, you win, because they have to chose either 1 or 2 for you to reach 3 or 2. If they reach 7, you win as if they chose 1, you chose 2; and if they chose 2, you chose 1, resulting them reaching 4. Therefore, you will always win if you go second and you play your cards right.

[kevin]

There are 8 ways to arrange a win on a 2-D tic tac board. There are 3 tic-tac boards on a 3-D tic tac board, so 8*3 = 24. We also have to count the ways the marbles intersect all the planes, and find that there are 8 ways to do so.

[kevin]

Since 9 groups of 3 colors results in 27 colors, and that a 3*3*3 cube has 27 cubes, each face has to have every color. Unfortunately, the middle cube counts, so this is never possible (experiment if you wish).

[kevin]

For the problems, calculate the area of each blue figure. It should be in a geometric sequence like

x, xk, xk^2, xk^3, xk^4…

The formula for the sum of n terms in this sequence is [x(1-k^n)]/(1-k). If it is an infinite series, then the formula is x/(1-k).

[Alison Hodges]

Hi Joy
Discovered this site and your work a little too late for the Telegraph interview, but just wanted to say how brilliant my Year 6 students found your Week of Inspirational Maths. This has definitely triggered a Revolution in my maths class. Am now trying to persuade my school to join the GLOW maths hub as that’s our local branch. Really sorry that I missed your talk there – perhaps next time?! Currently doing the Student course with my son aged 10 – great stuff!
Rgds Alison

[Donna Beaton]

I think I have a solution!

[Janet Duncan]

We just started using EngageNY/Eureka Math this year, but it seems very procedural to me. We chose it because it passed all the Gateways in edreports.org reviews (and engageNY is free). There are some powerful math concepts in the curriculum, but I would really like to know what Jo and her team think is the very best.

[David Parascand]

Our School District is going through a 6-12 math adoption and I’ve been asking the same question. What is considered the “best curriculum”for us to purchase?

[jackd1]

Hello Tanya,
Yes, I think there are more than 6 ways.
I like this problem because of the symmetry idea. In a sense, that cuts the work in half!
One way to start counting systematically would be to name the two bead colors, say, B = black and R = red.
Then, start with Black:
How many necklaces can I make with 0 black beads?
How many necklaces can I make with 1 black bead?
How many necklaces can I make with 2 black bead? etc.

One cool thing for students to notice is the relationship between pairs like:
B R R R R R R B (necklace with 1 black bead at each end)
R B B B B B B R (necklace with 1 red bead at each end)

If your list is complete, each necklace with have an “opposite” pair like this.

Please post how your students worked with the task!

[Karen Carter]

Nice problem. It can be done at an elementary / middle school level and at a high school geometry level mathematically proving the ratio.

[Tanya Mochel]

I think I must be doing it wrong. I only got 6 ways to make a necklace. I imagined there would be many more!

[Lyssa Steponaitis]

I, too, have this same question, and would love to gain access to the “number transformer challenge.”

I have used parts of this unit in the past, and believe it would be a great substitution for another unit that I am doing.

I would love an update and a follow-up on where these Number Transformers are. I can build my own, and have in the past, and had students made up their own, but I would like to see how the original supported the other materials in the unit.

[Nicola Turner]

The handout still shows addition. I had to make my own.
Also, can you use a number more than once in a number sentence. I assume also that you have to use all 3 numbers in each sentence.

[Martin Baker]

I wish I had the same response but this was the most difficult lesson for my group. I teach 9th grade pre algebra and this lesson did not resonate with my students at all. They were restless and uninterested. I had to send 2 out to the office in each class and confiscated 4 cell phones. The other lessons were very well received as I had many usually disinterested students actively participating.

[Carolyn Viss]

Here’s how I saw it: (attempting to insert image below 😉 )

[Author]

Posts