Forming First Impressions: Kindergarten Math

The Explorer, 5, recently told me that his favorite subject is Math.  At this age he’s forming early impressions on the blank canvas that will become his Math Education.  Developing a strong base is important, but so is lighting a spark of interest.  Led partly by his fascination levels, I focus on three areas with my Kindergartener: math facts, new concepts, and problem solving.

1. Math facts

Mastery of the math facts will greatly reduce frustration for him down the road with things like muti-digit multiplication, long division, and many other areas.  It’s important that he learn the concept behind the idea.

I start him on skip-counting by introducing a hundred number chart.  After he’s learned to count to 100 (by ones), we learn the two’s, five’s and ten’s.  We then cover both odd and even numbers and what digits each type will end in.

We recently learned the three’s. For example:  I have him start at zero and count up three, and then cover the number with a rectangular counter stopping at 30 – for starters.  The idea is that he’ll begin to notice a pattern.  [He observed that the three’s have both odd and even numbers.]

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Hundred number chart, counting by 3’s starting at 0.

Then he removes the counter and writes down the numbers – beginning at zero then up to 30.  (If he gets frustrated writing the numbers down, I just have him read them while I write them for him.) What I like about this is that not only does he learn to count by three’s, but he also realizes that it starts at zero.  He reads them forward and backwards a few times.  Then we focus on memorizing.

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Recording the 3’s as he removes them

After he’s mastered the 3’s starting at zero, I then have him pick another starting number – say one.  We then count up by 3’s but notice that our numbers are now different depending on our starting point.

So far this year, we’ve covered the one’s (0 to 100); two’s (0 to 100); three’s (0 to 30); five’s (0 to 100); ten’s (0 to 100), the hundred’s (0 to 1000) and the odd numbers (1 to 21).  Next week we plan to start the four’s (0 to 40).  How many we’ll cover depends; I use his interest level to help guide me about how far to go.  It is not a race, though, and it’s far more important to me that he understands the idea.

2.  New Concepts

By this I refer mainly to the learning of the arithmetic operations:  addition, subtraction, multiplication, and division.  I often use a curriculum as my guide, and some of my favorites are Singapore Math, MEP Math, and Miquon Math.  However, I believe that any curriculum is a tool that should help and not hinder.  I often find myself filling in concepts that I think a curriculum should have spent more time on.  I use a Place Value Activity Kit to demonstrate all four operations.

We start by learning the plus and minus facts up to 10 (all the combinations), then we expand it up to 20.

Interestingly, we recently learned three different methods for subtraction. For example, consider:  15-8 = 7.

 Method 1: Start at 15 on our number line and count back 8 steps.  We stop at 7.

 Method 2: Think of 15 as a number bond of 10 and 5.  I ask my son if we can take 8 away from 5. (We’ve not learned negative numbers yet.)  He replies that we cannot, but we can take 8 away from 10.  So we calculate (10-8) and we still have our 5 from before so our answer is 2 + 5 = 7.

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Method 2 demonstrated with place value kit

 Method 3: Start at 15.  Think about where our nearest ten is when subtracting. Answer:10.  Think about how many units we would take away from 15 to get to our nearest 10.  Answer: 5.  Then subtract 5 from 15 and next subtract 3 more. (15-5-3=7)

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Method 3 explained.

Having learned three different methods hopefully causes him to analyze, compare, and develop a greater number sense regarding subtraction.

So far we’ve worked though the concepts of addition and subtraction mainly, and also a good start in multiplication.

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Multiplication demonstrated with place value kit, and noting that ‘x’ means ‘groups of’.
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More multiplication showing that multiplying can be thought of as repeated addition.

Having already introduced multiplication (with skip counting),  I then use examples like the one above with a place value kit to go into more depth by showing that multiplication is repeated addition and that ‘x’ can be thought of as ‘groups of’.  For division, I only introduce it with the place value kit and show how division is related to multiplication.

[As an aside: If a student is confused by a concept, I recommend trying another curriculum to explain it a different way.  Use the curricula that best helps your child understand OR simply explain it in your own words how you understand it.]

3.  Problem Solving

How I interpret it, problems solving means that a student has enough mastery of a concept that he can apply it to solve a problem.

Thus far for this type of activity, my favorite curricula are Singapore Math Intensive Practice and Challenging Word Problems workbooks.  What I like best about these are the way they encourage a child to visualize the problems in order to better understand and solve them.  Also, questions are asked from many different angles so that the child has to really think about what is being asked.

Recently we worked on a problem where he had to think about how a larger number can be made out of two smaller numbers to solve puzzle-like problems related to subtraction.  We pulled out our Cuisenaire rods to help visualize the combinations that make 10: (1,9); (9,1); (2,8); (8,2); (3,7); (7,3); (6,4); (4,6); and (5,5) – to remind us of our math facts. (Hopefully he sees the pattern that addition is commutative). Manipulatives can be a great addition when solving a complicated problem.

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Looking for a pattern and using C-rods to visualize.

Of course, problem solving can also bring feelings of frustration. During these trials of deep thought, he grows in knowledge and develops math endurance.  I’ve found that giving praise when he’s solved a problem works wonders, and it’ll likely light a fire and make him want to learn more.

Overall, our plan is that we cover math fact practice and new concepts daily.  Problem solving (puzzle-type questions) may only happen two or three days per week.  We touch on all three areas every week.

It’s my intention that Math time be fun for him at this age.  Demonstrating that problem solving can be both rewarding and enjoyable [hopefully] paints a positive first impression.

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