Mental Math with Singapore 2B

I may have Willow start doing all her math in her head.

For a few weeks now, Willow and I have been working on adding one- and two-digit numbers using carrying. We visualized the process by setting up the equations with Base 10 blocks--

--then trading up and physically carrying the ten bars over to the next place before adding everything together, and finally moving into the conventional method of carrying while working arithmetic problems on paper.

 There was a lot of grumping, a lot of Base 10 block pattern building--

--and a lot more grumping, and the concept just didn't catch on. I'm pretty sure that the concept didn't catch on not because the kid didn't understand the concept, but rather because she was too busy grumping and pattern building to put the concept into her brain, but nevertheless, that's a lot of grumping and a lot of repetition just to learn (or NOT learn) carrying.

So we're just not going to learn that--not exactly, at least--right now.

In related news, last week my local indie teaching supplies store, which is normally too expensive for me to shop in, had their mid-summer sale, bringing their prices down to slightly more typical levels, and so I came home with the following:

• one postage stamp collector's album for Willow
• one book of world map post-its
• one book of hundred grid post-its
• one book of multiplication table post-its
• a set of coin rubber stamps
• the practice books for Singapore 1B and Singapore 2b

I avoid math curriculums because I have no problem teaching elementary math, but I do like the idea of having a logical order to work with, and I do like some of the mathematical concepts that Singapore math, in particular, teaches, so the reasoning behind purchasing just the practice books is that I can pretty easily figure out the concept that's being practiced, teach it on my own, and reinforce it with the books.

Singapore 2B has a lot of review in it for Willow, but I'm not opposed to drill and repetition, and there are a few key concepts in it that she hasn't explored yet, so that's why we settled there for her. Singapore 1B looks like a good fit for Sydney overall, so yay there for her.

My point with this digression is that, right there in the Singapore 2B practice book, front and center just before a money review and some new exploration of fractions, is a series of mental math practice problems that involve a different method of solving one- and two-digit addition problems, mentally, WITHOUT carrying. Here's what it looks like:

First, she's rounding the one-digit number to the nearest ten, and finding the difference, which is an easy subtraction problem. She's going to hold that number in her head. Second, she's adding the ten to the two-digit number, using skip-counting. Third, she's subtracting the difference from that new number, and it's another easy subtraction problem to the answer!

Now, do not even get me started on whether or not this method takes more steps than simply carrying the ten (it does), because for the little miss, that's not the point. The point for the little miss is, apparently, the fact that the steps are broken down into simple problems that she can do in her head. While the connection to the concept of what you're physically doing with the numbers isn't as clear, to me, as it is with carrying on paper, especially as visualized using Base 10 blocks, it IS still connected to the concept, just in a different way that seems to appeal more to the miss.

So this method, combined with simple "counting on" when the units to be added will add up to less than ten, gives Willow all the tools that she needs to mentally add one- and two-digit numbers to each other, abilities that we've been practicing with a homemade deck of laminated number cards:


And thus we can put aside that dreadful carrying altogether, to be brought back up at some point in the near future, preferably after the little miss has forgotten her grumps about it!

Skip Counting with Coins on the Hundred Grid

Our family is going to be participating in Lemonade Day in our town this Spring, and to that end I've reintroduced the money math unit that we first began some months ago when Willow got interested in coin collecting for a while.

My goal is (taking extra care with pricing, of course) for Willow to be able to do all the math and make all her own change at the girls' lemonade stand--whether or not this goal is realistic, I have no idea!

First step: skip counting by each of the coin denominations, followed immediately by keying the counting to the denomination. In other words, I want both girls to be able to easily skip count by fives, tens, and 25s at least up to 100, to count by hundreds up to at least 1,000, and to recognize that skip counting by fives, say, is the same as counting nickels.

The girls have been creating their own skip counting reference sheets using, of COURSE, our ubiquitous hundred grid. For nickels, for example, one day's schoolwork was simply to count off the fives and color in each five in their hundred grid. The next day's schoolwork (and the next!) was to memorize the fives, until they could recite it easily.

When a girl had her fives down cold, I gave her a new hundred grid, asked her to put a nickel down on each five, and then use the chart as a reference to solve a page of math problems:

The problems are all just iterations of how much a certain number of nickels equals. To solve the problem, the kid can either skip count over that many nickels, or just count over that many nickels, and then move aside that nickel. The number underneath is the correct answer!

Once the kiddos have all the skip counting and coin denominations memorized, I'm going to send them through the math drills in our Kumon money math workbook as well as some fun projects from my Money Math pinboard. And then when Lemonade Day comes around, providing I can convince the children not to price their lemonade at 63 cents or $1.07 or something else that will require a child to do twenty minutes of abacus work for every transaction, I think we may just have it made!

P.S. It's just occurred to me that I should also teach them to count by tens when beginning at 5. AND I should be mixing more subtraction drills into the prep work, especially two-digit subtraction.

Or I could just encourage the girls to price everything they make at one dollar?

Homeschool Math: Our DIY Roll to a Hundred Game

I have a strict Montessori-style policy that I do not discourage my children from doing academic work that is "too easy" for them. If Willow wants to play the Jump Start Kindergarten CD-Rom that I checked out from the public library for Sydney, then that's okay. If Sydney wants to spend the afternoon working color-by-number pages, then that is totally fine by me. If Willow suddenly develops a passion for those old First Chapter Books that she first read two years ago, and reads them all again, then good for her!

It's an important part of my homeschool philosophy that repetition reinforces skills, internalizes concepts, and builds the feelings of mastery that reward children for learning, and the confidence to take on more learning challenges.

Therefore, although our DIY Roll to a Hundred Game highlights skills that both my girls have already learned, we LOVE this game! It's excellent reinforcement for number recognition, sequencing, counting, and addition concepts. The unpredictable nature of the roll of the die prepares the girls for future lessons on statistics, graphing, and averages. The coloring requires fine motor skills, and is also graphing, and pattern-building.

Oh, and the game is based on a die, so the little one can win as often as the big one does, hallelujah.

To play Roll to a Hundred, you will need:

• a copy of a Hundred Grid for each person. You can use either a labeled hundred grid, or a blank hundred grid that the child labels for herself--this turns the potentially tedious activity of labeling a hundred grid into a useful activity that a child might choose to do for herself, by the way!
• one die
• crayons

1. Decide who goes first. The first player has the advantage, so it's important to remember to take turns.

2. During her turn, a player rolls the die--

--and then colors the same number of squares as pips on the die:

3. Change crayons each time so that you can see each individual roll on your hundred grid, and the first person to reach one hundred--

Wins!!!

We play such that you have to roll to reach 100 exactly--waiting for that perfect roll gives everyone time to catch up and makes the game a little more exciting.

Ways to modify the game:

• Use two dice, or a 20-sided die, etc.
• Play on a 200 number grid. 
• Play on a number line.
• Play Roll to Zero, where the game is subtraction!
• Multiply each roll by two.
• Assign a different mathematical operation to each number: One must be subtracted, Two gets doubled, Three gets added to the previous roll, Four gets divided by two, etc.
• Have everyone graph their rolls to see how many times each person rolled each number.

It's certainly not a bad way to spend a rainy afternoon!

Sydney Masters the Hundred Grid

We're big fans of the hundred grid around here--it's such a versatile math tool! You can use it to help you add and subtract, with skip counting, with coin calculations. Because Sydney likes puzzles, she also occasionally enjoys using our big laminated hundred grid with some overhead transparency number tiles that, even though I bought them at different times and places, happen to be exactly the same size--score!

I especially like the transparency of the overhead tiles, because if a child is still working on number recognition (and, as I learned while assisting Sydney through the most tedious three games of BINGO ever played at their 4-H club holiday party this week, we ARE still working on number recognition!), then that transparency allows instant self-correction.

During our most recent play with this board, I witnessed Sydney unlock one of the patterns implicit in the number grid. No more random seek-and-find for her--watch this girl go!

I was pretty thrilled that I was there to see it happen.

Syd has a lot of focus, and although she wearied a bit of the task near the end, she kept working, because she wanted to see it through:

Success!

Pretty proud kid, right?

We have an old garage sale BINGO set of our own, and I think that we'll be playing a lot of fun at-home BINGO games this week, because not only is Syd clearly ready for number recognition up to 100, but I'm not taking her near another BINGO party game until she has it down--geez Louise, what a nightmare!

How Many Pennies in One Dollar?

I re-branded the hundred grid as a dollar grid, so let's see...

This many!

It looks so cool that I considered having Sydney glue the pennies down to the grid so that we could keep it...

And then I thought, "Heck, no! I'm not wasting a whole dollar!"

The girls have recently wearied of all this talk of coins and commerce, so our math is moving on to geometry. Geomags, constructive triangles, spirograph, geoboard, patterns blocks and mirrors--that ought to hold us for a while!