Our family received the 9 Apples card game from Discovery Express Kids to try out. There are a lot of cards and the goal is to reach a target number each round. The cards are positive or negative, and there are also cards that allow you to switch the sign of a card. The rules reward you for using more cards to reach the target number. On the first round, you try to use cards to reach the number 9. Each round you work your way down until you have a target number of zero. The game ends when someone reaches zero.
First I tried out 9 Apples with my nearly seven year old daughter. She is my math lover! She enjoyed the game, but it was really the two of us working together to get the answers. She wasn’t able to do the multi-step addition and subtraction in order to reach the target number. She also struggled to switch the signs. But we enjoyed working together to make the longest row of cards possible. Next time, we’ll put a number line out and actually jump around with our finger using the cards to see how close we can get to our target number. I think this will help her practice the math and visually see what she is doing with each card. It would be even nicer if the card deck had a sturdy fold up number line in the box already. Using a number line would help kids of all ages see relationships and patterns in math more easily.
A few weeks after working with my daughter, I tried it out with my sons and some neighbors. I was a little nervous that my home-schooled boys wouldn’t be able to do the multi-step math as fast as their public-schooled friends. I needn’t have worried. All the boys did fine. The older boys were able to use more cards than the youngest (8 years old), but they all understood the game really quickly. They weren’t feeling competitive so I heard them giving each other ideas and suggestions about how to make the number they needed for the round. Things like, “Can I give him my change sign card? Then he can just add the six and four together and subtract the three so he gets seven.” It is nice to hear the thought processes going on in your kids’ minds! I was gratified to see my own sons’ math thinking ability, and their intuitive understanding of math.
I asked the kids for their likes and dislikes (in exchange for the cookies you see in the picture). They said it was “funner” than they thought, and that it was harder than they thought. The public-schooled kids said it was a lot more fun than worksheets!
I liked that it was a lot of math in a simple and fun way. I liked that the change sign cards gave it a lot of variety and dynamics. One drawback is the sheer number of cards. It’s a pretty fat deck of cards! I told the boys today that we’ll play it again with the booster pack of division and multiplication cards. Should have seen their faces!
This is a guest blog post by Danny Phelan, who is a student at Wake Technical Community College in Raleigh, NC, studying for an Associates Degree in Arts. Danny’s eventual goal is becoming a novelist and screenwriter, as well as editor for fantasy, science fiction, and horror novels.
When I was in high school, I noticed a curious pattern: one plus three equals four, plus five equals nine, plus seven equals sixteen, and so on. Each whole square was a certain number greater than the next, and the difference between the squares would increase by two every time. When I mentioned this to a math teacher, she either did not see it that way or misunderstood my phrasing, for she dismissed it as simple coincidence, not a natural law. After class, however, I was not convinced. Stubbornness is both a vice and a virtue of mine, and I continued to puzzle over how a series of odd numbers, increasing by two each time, connected to the succession of perfect squares.
Eventually, I drew the pattern out on scrap paper and saw something interesting: each square on a grid increases by the addition of new units to a side; being two-dimensional, they increase by two new units each time–one for each dimension.
We came up with an equation that represented the pattern. Since we want to look at the difference between squares (how much you add to get the next whole square), we added 1 to r, which stands for the square root. There’s the 2 pattern!
(r+1)2 = r2+2r+1
But I was still not fully satisfied. Something felt missing. I reasoned that if one could calculate differences between squares, surely a similar pattern might hold true in three dimensions–that is, whole cubes. The formula would be more difficult to visualize, but fortunately, my friend Ray owned a bowl of small cubes which we used to crack this puzzle. Three new squares would need to be added with each successive layer, and by holding cubes together, we discovered that the edges between sides would also need to be accounted for.
We determined that the formula is:
(r+1)3 = r3+3r2+3r+1
Applied fascination, when shared with other curious thinkers, spurs the creation of wonders.