2016-02-09: Multiplication to Powers

Tonight's midnight math discussion of multiple-digit multiplication took a turn and ended up as a discussion of powers.

2015-08-30: Multiple Borrowing Midnight Math

Dad tried to stump Nigel on multiple borrowing problems during Midnight Math tonight. Multiple borrowing didn't throw him, in fact he seemed excited to show Dad how he could do it. They talked it through, and Dad was able to show him a shortcut to multiple borrowing. (What is one less than the whole number you are borrowing from, so do all the borrowing in one stroke, rather than each place value one at a time.)

As an aside, doing math before bedtime stories has proven to be a useful tool. Nigel is a bit fresher that way, and stories are more relaxing for him than math.

2015-07-25: Odd and Even Numbers

Nigel and Dad talked through what constitutes an odd or an even number today, for Midnight Math. Dad wrote the set of even numbers vertically down a whiteboard, and Nigel noticed that the evens all end with 0, 2, 4, 6 or 8.

2015-06-06 Cap'n Crunch Gift Card Math

A question arose this morning while Nigel was looking at the back of a box of Cap'n Crunch: Which is more in total, 1,000 $50 gift cards or 500 $20 gift cards. Some discussion produced a specific answer for each, though it would also have been a good opportunity to discuss estimation techniques (e.g. multiplying a smaller number by another smaller number will never be larger than multiplying a larger number by another larger number).

2015-05-15: Cereal Nutrition Battles

Nigel has independently invented a game played by countless children (Dad included) growing up: breakfast cereal nutrition battles. Dad really believes he did not plant the idea for this, aside from answering Nigel's questions about what the numbers on the side of cereal boxes represent. Nigel has been playing this game off and on for a few months now, comparing various types of cereal, and been getting more strategic about his choice of cereal: he usually picks whatever Dad is eating, and gives Dad the box he is eating.

Nigel has recently introduced a variation to this game, in which the nutrient's score comes not just from its value with or without milk, but with those values added together. Dad is thrilled with this rule, as though it doesn't change any of the outcomes*, it includes addition practice atop the numerical comparisons, and makes for an even better math game.


*The exception to this statement is Cheerios, which has an additional column of nutritional ratings for children under 4, making it nearly undefeatable. Dad is plotting to bring out the Special K to combat Nigel's Cheerios soon.

2015-03-14: Powers of 10 for Pi Day

Nigel and Dad worked on powers of 10 for Pi day this evening. They talked about the decimal point and about how to move numbers back and forth.

2014-12-07: Go Fish War

Nigel invented a new game for Midnight Math tonight: Go Fish War. He really likes playing War, and he and Dad have now come up with a few variations of it to keep things interesting. Sometimes they play two-card war in which the cards are added together for comparison, with the largest value winning, and other times they do two-card subtraction, in which the smallest value wins. (In subtraction-style, if Nigel is feeling disadvantaged, he will sometimes subtract the larger number from the smallest and use the negative result to ensure a victory.)

In Go Fish War, the cards are divided between the players, who then take turns asking if their opponent has any of a given number. With only two players, and all cards having been dealt, that is easy to anticipate. Upon taking the cards from the other player and making a complete set of that number, the player then lays that set down and adds up the total from the four cards. The opponent then lays down one of their card sets and adds up their total, with the larger amount taking both sets. Nigel and Dad played with sets of 2s through 9s.

Tonight, this ended up being a complete rout of Dad, taking Nigel only two rounds through Dad's hand to empty it. Then, the real math work began. Nigel wanted to add up all the points he had collected. Dad had been wanting to do some work with an abacus and figured this was his excuse to do so.

He asked Nigel if he wanted to use the abacus to count up the points. Nigel said yes, and as he seemed to have an idea in his head about how to do that, Dad just let him proceed on his own. After a minute or so of flipping beads around and starting to seem frustrated, Dad asked if Nigel wanted a suggestion. Given that approval, Dad rotated the abacus around so that counting a bead involved sliding it from the bottom to the top, rather than from side to side. Next, Dad reminded Nigel to use each bead column as a 10s place value, and they reiterated what values each place would be. Then he demonstrated abacus addition starting with the 9s (adding a 10s bead and taking away a 1s bead). After demonstrating that technique, Nigel added the four 9s, and they counted up how many points he had so far. They repeated this with 8s and 7s, and encountered the situation in which there are not enough 1s beads to continue taking away. At this point, Dad demonstrated that there would be enough 1s beads to add the number of 1s beads back in, then let Nigel continue.

At 6s, Dad let Nigel figure out how to add 6 by himself, and Nigel performed the remaining tasks by himself, with the exception of Dad clarifying what to do when Nigel reached ten 10s. 176 was his final answer.

2014-12-02: Color Wheel and Abacus

Dad got a color wheel recently, and he and Nigel have been learning about colors the past two nights. They have discussed primary, secondary and tertiary colors, and how to mix colors to create the secondary and tertiary colors.

Tonight, for Midnight Math, Nigel picked to do a Bedtime Math problem, and when he was stymied by adding larger quantities together, he had the idea to get out the abacus to help. Nigel spent a few minutes fiddling around with the abacus, having had little or no instruction on how to use it, mainly trying to use all the rows of beads as having a place value of one and just continuing to count them. A good idea, but he got tripped up performing all the manipulations and started over a couple of times. Seeming to be a bit frustrated, he then decided he would just do the addition in his head instead, one column at a time, and came to the correct answer that way.

Afterward, Dad asked if he wanted to see how to sue an abacus to solve a problem like this. Nigel did, and they turned the abacus sideways and Dad demonstrated how each column of beads could be used to represent a base-10 place value. They counted out what place value each column would represent, discovering that this abacus had a billions column! Then Dad walked through two addition problems using the abacus, one with and the other without carrying. Nigel caught on quickly.

2014-10-25: Learning to Tell Time

Nigel and Dad have spent three out of the last four nights learning about telling time for Midnight Math. Nigel is now able to read an analog clock as long as the minute hand is pointing at one of the 5-minute marks. Soon to reinforce the idea of narrowing in on the exact minute.

2014-10-12: Cuisinaire Rods Problems for Dad

This evening, while Dad was cooking dinner, Nigel saw the Cuisinaire rods and started giving math problems to Dad. Dad then asked one of Nigel: What is the smallest rod that three of will make more than 10?

Nigel's initial guess was the 5-unit rod, saying, "Two fives make ten, so three fives must be more than ten." Well reasoned, but then Dad reiterated the question and asked if any smaller rod would work. It didn't take Nigel long to try the 4-unit rod, which he then thought was the answer. Dad asked him to check the 3-unit rod, and Nigel quickly established that the answer was definitely the 4-unit rod.

2014-09-28: Matching Socks

Dad proposed a problem for Midnight Math tonight that went something like this: I have two colors of socks in my drawers and I want to wear matching socks, but I don't want to take extra time trying to find matches. I want to reach into my drawer, without looking, and pull out enough socks to guarantee I have a matched pair, but no more. What is the fewest number of socks I need to pull out to be certain I will get a match?

They discussed this at length, with Nigel going from two socks to four socks as his guess right at the beginning. After some discussion he settled on three as being his answer. They continued to talk about why that was for a few more minutes.

The next night, Dad asked what would happen if he had three legs and wanted to get a matching triplet of socks. After determining it would take five socks to guarantee a match, Dad started diagramming out the answers they had discovered so far. Nigel saw that it would take seven socks to get a matching quadruple before Dad got to writing that part of the chart, and stumbled a bit on adding twos to the odd numbers (wanting to switch to counting even numbers by twos), but was able to see the trend quite easily.

2014-09-27: Flow Free

After a group violin lesson, Nigel came to sit with Mom and Dad, who were involved in a Suzuki parents discussion that started at the same time. Seeing Nigel quickly becoming bored, Dad gave him his phone to play with, provided he could be silent with it. Nigel found Flow Free, a puzzle game in which the player attempts to find a way to route a number of different-colored pipes (or flows) between designated endpoints, without crossing the paths of any of the other pipes. He played this for nearly half an hour by himself, then at the conclusion of the class wanted to keep playing while Mom and Dad watched.

He has become quite good at finding the appropriate paths to take, doing more and more complex puzzles, including those introducing the idea of a bridge square, where a pipe can go straight across in one direction and a second pipe can cross the same square but in the perpendicular direction.

2014-08-24: Odd and Even

Today, Nigel and Dad discussed odd and even numbers during lunch.

2014-07-27: Dividing by 10

Nigel and Dad talked about place values and dividing by 10 tonight during Midnight Math. Dad proposed the question: What is 50,000 divided by 10?, and they talked through what that meant.

2014-07-26: Multiplying and Dividing by 10

Nigel and Dad talked about multiplying and dividing by 10 tonight.

2014-07-14: Dividing 10

Tonight, in Midnight Math, Dad started things off by asking how to use rods to find the center of another rod. He demonstrated this with a 2 rod and two 1 rods. He then asked Nigel to show him how to do the same thing with a 10 rod. Nigel got out a bunch of 1 rods and counted five on each end until they met in the center.

They then talked about averages with temperature and a thermometer, and said that an average is the middle. Dad asked what the middle is. Nigel replied, "The center." Dad asked what the center means, and provided the definition that the middle or center of something is the place where there is the same amount on each side of that place.

Dad next asked how many units to the middle of ten. "Five" was Nigel's answer.

Dad: If we divide 10 into two equal parts, how many will be in each part?

Nigel: Five.

Dad: That is the same as asking what is 10 divided by 2. What is 10 divided into five parts?

Nigel went for the red 2 rods to find out. A great guess.

2014-06-24: Reading Large Numbers

Continuing a recent theme, tonight's Midnight Math was about multiplying by 10 (adding a zero to the end), with some practice reading large numbers, as well.

2014-06-22: Math with Grandpa

Grandpa came over tonight for Midnight Math. Dad pushed to do too much, and it dragged out a bit too long, but Nigel had fun talking about it with Grandpa.

2014-06-16: Dividing by Zero

Nigel asked today, on the drive home from summer camp, about a million and a billion and a trillion and a quadrillion divided by a million, and that sparked a discussion that lasted for most of the drive. Dad told Nigel about the dividing by zero rule (that the answer is undefined), giving the example of trying to divide a group of apples into zero groups.

2014-05-31: Super War and Estimation

Dad and Nigel have played Super War a couple of times recently as a Midnight Math activity. This is the classic card game War, but with each player turning over a pair of cards each time and adding them together for comparison with the other player's total. Dad usually adds his cards (ex: "Two plus eight equals ten."), and asks Nigel to add his up, then they compare the results, but sometimes estimation is encouraged.

This night, while playing, Nigel said something to the effect of, "I just knew in my brain that if two of our numbers were the same, and the other of my numbers was one more than your other number, then if you had nine, mine would be ten." An excellent and spontaneous use of estimation.