In a recent blog, I mentioned the value of games involving lots of counting and calculation. This blog lists some commercial games, available in most toy/game stores.

• Chutes & Ladders (sometimes titled Snakes & Ladders): the classic dice game of moving your piece to the 100th square, hoping to avoid the downward chutes and trying to land on the upward ladders.

– variation on Chutes & Ladders: as your child gets older and learns how to subtract and multiply, after the dice are rolled allow each player to choose whether to add, subtract, or multiply the two numbers. A player rolling a 5 and a 3 could move either 8 (from 5 + 3), or 15 (from 5 x 3), or 2 (from 5 – 2), or even -2 (from 3 – 5). This variation helps kids realize there are more relationships between two numbers than always just adding.

• Mancala: remember this? – moving stones around from your side of the board to your end zone – counting, estimating, visualizing moves.

• Monopoly: lots of practice both with the counting of your piece across the board as well as use of play money, making change, buying and paying and renting.

• ParcheesiSorry: these traditional games involving lots of counting and moving pieces. From sheer experience of lots of counting, players learn to look for shortcuts, counting on, counting back, etc.

• Ring-A-Round: another game of three regular six-sided dice to find expressions equal to number goals from 2 to 18, in a ring around your own colored post. Players can use any combination of +, –, x, or ÷ to find a number goal – for example, rolling a 3, 4, 5 could results in 12 (from 3 + 4 + 5), or 17 (from 5 + 3 x 4, or from 5 x 4 – 3), or 11 (from 3 x 5 – 4), or 3 (from[5 + 4] ÷ 3), or 6 (from 5 + 4 – 3), etc.

• Backgammon: the ancient dice game allowing players to decompose sums into desired parts in order to move all pieces to their own goal.

• Yahtzee: there’s no better dice game allowing so many intriguing combinations and arrangements of numbers.

• Cribbage: the pegging game of counting points with pairs, three of a kind, cards adding to 15, strategizing to reach 31.

• Kenken: this game is available as a board game but is more commonly found in newspapers, magazines, and booklets. Kind of like Sudoku but with arithmetic thrown in.

• The Game of 24: use each of the four numbers on a card exactly once each to create an expression equal to 24 – for example, a card with the numbers 2, 2, 6, 8 would have a solution of (6 + 8 – 2) x 2. Each box has dozens of such cards, with each card marked with degree of difficulty.

There certainly are other games of computation that I haven’t included here. Write me at info@AlgebraForKids.com with your favorite counting/calculating game for kids.

Recently I had an aha! moment that connected, I believe, with why so many students in middle school and high school have difficulty getting meaning from written directions.

My challenge in this blog is to connect that aha moment with algebra. Here goes.

My aha was partially birthed in several elementary classrooms in which I was a substitute teacher recently. In the early elementary grades (1st through 3rd or even 4th grade), it’s understandable that kids have some degree of challenge understanding what the written directions both say and mean.

During several substitute teaching assignments, quite a few 2nd or 3rd graders kept saying to me about the written directions on a worksheet (or quiz or test), “I don’t get it.”

I found myself defaulting to the tried and true strategy of re-wording what the directions meant – “Kids, what it means is…”

No doubt my re-worded explanation was brilliant. No doubt it helped some to many kids, of course.

But as I pondered what had just happened, I began to think about some things that were really going on here when I orally re-worded the written directions.

One element that was present was I was subtly teaching kids that they didn’t have to pay attention to the written directions! Why pay attention to what the words say – why learn to decode the meaning of the written directions at all – when the teacher is just going to step in (sooner or later) and say, “What this means is…”

That inference is not a good thing for kids to learn.

So I tried taking a different approach the next time students told me they didn’t understand the written directions: I was going to “drag them through” the exact wording of the written directions.

What this meant was examining how the directions were structured:

• We examined the verbs, especially command verbs like underline, draw, explain, solve, simplify, group, match, etc. Along the way we happened upon the distinction between an action verb like explain and a stative verb like is or were.

• We pinpointed the subject and object of the verbs – which often were the nouns and pronouns of the directions. Write a fraction that is equivalent to the percentDescribe the similarities and differences between… Simplify the improper fraction and then change it to a mixed number.

• I pointed out how common it is to see prepositional phrases that contain nouns (like the capital of the country) – but how that noun country isn’t the subject of the sentence.

In other words, I gave a grammar lesson from the directions. Whether the subject matter was English or history or math or science – it didn’t matter.

We focused on getting meaning from written directions by “dragging ourselves through the English of the written directions” – without re-wording those written directions (at least at first).

Of course, providing synonyms for certain words is helpful at times. It’s unavoidable and part of language. But I didn’t end at the synonym. I always went back to the exact wording of the directions to ensure that students were getting meaning from that exact wording.

Several students summarized an important truth about certain kinds of problems in saying, “The hardest part about problem solving in math isn’t the numbers. It’s the English.”

Getting meaning from written directions – a lifelong skill. A skill we can help our kids develop. Such kids become better learners, more self-reliant learners, more capable problem-solvers.

Drag kids through the exact wording of written directions. It’s the educational equivalent of a well-known adage that I’m revising here: Give a child the decoded meaning of the written directions and you provide help for today. Teach a child how to decode written directions and you provide help for a lifetime.

Consider the following examples of details versus big picture:

Detail: What’s the answer? Big Picture: What’s the question?

Detail: How much is 9 x 6? Big Picture: 9 x 6 is somewhere less than 10 x 6.

Detail: Do I add or multiply? Big Picture: What does add mean? What does multiply mean?

Detail: Is this inches or square inches? Big Picture: How are perimeter and area different? Similar?

Detail: How do I add 2/7 + 3/7 ? Big Picture: What does 2/7 mean?

Detail: What is 3/4 as a percent? Big Picture: What does percent mean?

Detail: Is it true that 5 + 3 = 2 x 4? Big Picture: What does the equal sign mean?

Detail: Is 11 x 13 equal to 93? Big Picture: Since 10 x 10 = 100, then 11 x 13 should be more than 100.

Detail: (5 x 2 – 10) x 172 is a long problem. Big Picture: (5 x 2 – 10) is 0, and 0 times anything is 0.

Too often, kids learning math can be sidetracked to focus primarily on the details of math. Such details include the exact values of basic facts, the placement of the decimal point in a multiplication exercise, or converting fractions to percents.

Such details are important. As important as they are, however, details are not the only thing that’s important in math.

It’s also important that kids learn how to see the big picture, the larger perspective. Seeing the big picture requires non-math skills, such as overfamiliarity, impulse control, knowing definitions, practicing patience, knowing multiple ways to think about how much a number is or how to solve a problem, etc.

So what helps kids learn how to think with the big picture in mind? Here are some suggestions:

Teach definitions of things, but keep definitions brief. Add means put together with. Equal means is the same value as. Percent means out of 100 or for every 100.

Use those definitions. Ask your child regularly and repeatedly for the meaning of key terms like add, divide, equal,

Aim for overfamiliarity – shoot for your child becoming overly familiar with, not just acquainted with, basic facts. Teach and play lots of math-type games – games involving lots of counting and calculation (more on those kinds of games in the next blog).

Ask kids questions that go beyond details. See all of the Big Picture questions above. Encourage them to ask questions too.

It’s time to re-introduce one of the most popular math games that I know of: the card game called SET.

SET is a card game of logic, geometric shapes, and visual perception. It’s a fast moving game in which neither age nor academic excellence is necessarily an advantage. SET is simple and clever: each of the 81 cards has one to three icons that can be any of 3 different colors (red, green, purple), any of 3 different amounts (single, double, triple), any of 3 different shades (solid, hollow, striped), and any of 3 different shapes (diamond, oval, squiggle).

For example, a single card could have two red striped diamonds, and another card could have three purple solid ovals. Three different possible variations on each of four criteria is 3•3•3•3 = 81 different cards.

Lay the 12 or 15 cards out in a rectangular grade. The goal is to find three cards (always three) that are either all three the same or all three different for each of the four criteria (color, amount, shade, shape).

The game is actually easier to play than it is to explain, and while SET is not hard to learn, it still continues to challenge both experienced players  and novices of all ages. Because SET can be played alone or in groups of 2 or more, it is a great activity for a classroom tournament, or a family game night, or a solitaire session on a dull afternoon.

I first taught my younger son to play the game at age 7. Although I was no slouch at playing SET, this… kid… consistently beat the pants off me. Both of us delighted in a young boy being able to beat Dad so convincingly.

   SET earned Game of the Year awards from numerous game organizations and magazines in the early 1990s. This game is for adults, adolescents, and kids as young as age 7.

SET isn’t a game involving quantitative math (numbers, ratios, calculations, etc.) – but it is a math game because it involves logic, perception, and visual discrimination. Visual discrimination is the ability to look at a group of items and then group or re-group – or even un-group – them according to some specific criteria. In SET, players have to find three cards that can be grouped together according to four separate criteria. The multi-tasking involved in keeping track of four separate criteria is great brain building. For the most part, all that brain-building is dominated by a game that is sheer, challenging fun.

This is a blog I’ve published before, and it’s worth posting again.

As I’ve written elsewhere, I’m convinced that the skill of skip counting is an extremely important pillar in building a strong foundation for success in arithmetic and mathematics. Recall that skip counting is counting in multiples of a number – 6, 12, 18, 24, 30, etc., or 4, 8, 12, 16, 20, 24, etc.

Skip count songs are catchy, fun songs that help plant those number-word sequences firmly into a child’s memory. We have two different skip counting albums that we carry, with different lyrics and melodies for each of the numbers from 2 through 10.

My younger son Trevor started hearing the skip count songs when he was about 16 months old.  We played one in the car and the other for the house, and we played the songs a lot – in the car during trips, sometimes at bedtime, sometimes at lunch, and often simply just in the background when Trevor was playing with toys and with friends. The catchy songs started getting stuck in his head, and before he was two years old, he could count to 20 by 2’s.

Now here, the question has to be asked: did he know what he was really doing? I’d say, No – of course not. He was just repeating a series of number-words that he knew from the skip count song for 2’s. But here’s the important piece: at least that series of number-words was firmly embedded in his memory in the proper order.

He kept hearing the songs at various times throughout his day as he grew older, and over the next 3+ years, he eventually mastered all the skip count choruses from 2 through 10. When he turned 5 years old with his summer birthday, my wife Sarah took him in for his kindergarten checkup. The nurse checked his ears and eyes and throat, and then she asked him, “Trevor, can you count?”

Trevor looked at the nurse and said, “How?”

The nurse didn’t understand what he meant and replied, “Well, I’ll just make a note that he can’t count.”

Since my wife was there, she spoke up, “No, he means what he said when he said How?”

The nurse was still puzzled, and so Trevor asked her, “How do you want me to count? By 2’s or by 8’s or by 9’s or by 4’s?”

At this point, the nurse looked at him with astonishment and said, “You can count by 4’s?!”

So Trevor replied in a sing-song-y voice, “Sure – four, eight, twelve, sixteen, twenty, twenty-four, twenty-eight, thirty-two, thirty-six, forty days Goliath had to wait.”

At this point, the nurse turned back to her check-up form and said, “I’ll put down that he can count…”

Here was a young boy who had mastered all the sequences of skip counting for each of the numbers from 2 through 10 – going into kindergarten. This was a perfect set-up for success in so many areas of elementary arithmetic.

Trevor is now an adult. He didn’t go into math or a math-related field in college. But the impact of skip count songs on this guy is noticeable. He has excellent mental math skills and great number sense. From paying attention to skip count song numbers as a child, he’s also learned to pay attention to details all over the place. He’s a very savvy young man. Other things contributed to that, and listening to skip count songs was a piece of that.

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