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Stow-Munroe Falls City Schools uses
the Investigations
in Numbers, Data, and Space
program
for elementary mathematics instruction. Our math coordinator, Mrs. Yoak, has
created an excellent website for parents and families. To get more information
on our math program, the units and expected learning outcomes at each grade
level, and tips for parents, please visit Mrs. Yoak's website www.smfcsd.org/math/inds.htm
If you ever have any questions about
your child's math homework or questions about the math program in general,
please do not hesitate to contact me.
Math Facts
Math fact mastery is something that
frustrates teachers and parents alike. I think everyone agrees that knowing
the basic addition, subtraction, multiplication, and division facts is
essentional for efficient higher level computation. . The expectation in
the Ohio standards is that students will be fluent (efficient, accurate, and
flexible) with all of the facts to 10+10, 20-10, 10 x 10, and 100 ¸ 10 by the
time they reach the end of third grade. The goal is that students can recall
any fact within three seconds and compute in a relatively short amount of time.
However, it seems that no matter how
often some kids practice, they still don't retain the memorization of their
math facts. I believe that to combat this problem, it is essential to teach
the students computation strategies instead of math facts in isolation. Listed
here are computation strategies for addition, subtraction, multiplication, and
division. I personally have found much greater success and retention by
teaching these to students. I would highly encourage you to look at these
examples and work on the flash cards using these strategies instead of just
drilling them.
When students know these strategies,
they are able to remember them and apply them to larger problems. The
computation becomes more tangible to them and they are able to solve harder
problems. (For example, my first grade son was struggling with 9 + 7 but was
able to solve it by saying, "In first grade I learned how to add my tens, so I
know that 10 + 7 would be 17, so 9 + 7 must be one less. It's 16." He also
told me that he knew that 8 + 7 was 15 because he used the strategy of
"doubles minus 1.")
Addition facts
-
One/two more (7 + 1 = 8 or 3 + 2 = 5
– think one/two more than the initial number)
-
Zeros (5 + 0 = 5 or 0 + 8 = 8 – think
“add nothing to the other addend”)
-
Doubles (4 + 4 = 8 or 9 + 9 = 18 –
think two groups of this number)
-
Make 10 (7 + 3 = 10 or 2 + 8 = 10 –
look for combinations that add to 10)
-
Near doubles (7 + 8 = 15 or 3 + 2 = 5
– think the doubles fact plus or minus 1 – 7 + 7 = 14, 14 + 1 = 15 or 3 + 3 =
6, 6 – 1 = 5)
-
Two apart facts (5 + 7 = 12 or 2 + 4
= 6 – think the doubles fact plus 2 OR the middle number doubled – 5 + 5 = 10,
10 + 2 = 12 OR 6 + 6 = 12)
-
Using 10 as a landmark (5 + 8 - think
5 + 5 = 10, 10 + 3 = 13)
-
Math families (3 + 4 = 7, 4 + 3 = 7,
7 – 4 = 3, 7 – 3 = 4 – given the numbers 3, 4, and 7)
Subtraction facts
-
One/two less (7 - 1 = 6 or 3 - 2 = 1
– think one/two less than the initial number)
-
Zeros (6 - 0 = 6 or 7 - 7 = 0 – think
“take away nothing” or “take away everything”)
-
Doubles (10 – 5 = 5 or 16 – 8 = 8 –
think half of this number)
-
Make 10 (10 – 2 = 8 or 10 – 4 = 6 –
look for what is left out of 10)
-
Near doubles (13 – 6 = 7 or 9 – 4 = 5
– think a nearby doubles fact plus or minus 1: 12 – 6 = 6, so 13 – 6 = 7, or
10 – 5 = 5, so 9 – 4 = 5 also)
-
Two apart facts (14 – 8 = 6 or 8 – 3
= 5 – think a nearby doubles fact plus or minus 2 OR the initial number split
in half plus or minus 1 – 16 - 8 = 8, so 14 - 8 = 6 OR half of 8 is 4, so
8 – 3 = 5: 3 and 5 are 1 more and
less than 4)
-
Using 10 as a landmark (15 – 6: think
15 – 5 = 10, 10 – 1 = 9)
-
Math families (3 + 4 = 7, 4 + 3 = 7,
7 – 4 = 3, 7 – 3 = 4 – given the numbers 3, 4, and 7)
Multiplication facts
-
Doubles (6 x 2 = 12 – think 6 + 6)
-
Tens (3 x 10 = 30 or 10 x 3 = 30 –
think 10 3’s, or 3 rows on 100 chart)
-
Zeros (7 x 0 = 0 or 0 x 5 = 0 – think
“no groups of ____ is still 0”)
-
Ones (8 x 1 = 8 or 1 x 2 = 2 – think
“one group of ____ is ____”)
-
Fives (7 x 5 = 35 – think half of
10’s fact – 7 x 5 is half of 7 x 10 – 35 is half of 70)
-
Nines (4 x 9 = 36 – think 10’s fact
minus one group – 4 x 10 = 40, 40 – 4 = 36)
-
Squares (7 x 7 = 49 or 9 x 9 = 81 –
think of a square with this side length, 7 or 9 here)
-
Squares and one more set (7 x 8 = 56
or 9 x 10 = 90 – think squares fact plus one group – 7 x 7 = 49, 49 + 7 = 56;
9 x 9 = 81, 81 + 9 = 90)
-
Threes (4 x 3 = 12 – think doubles
fact plus one group – 4 x 2 = 8, 8 + 4 = 12)
-
Fours (6 x 4 = 24 – think doubles
fact doubled – 6 x 2 = 12, 12 x 2 = 24)
-
What’s left? – these are the
“harder facts,” but they usually can be connected to other facts using the
strategies shown above
-
Math families (given the numbers 3,
4, and 7: 3 x 4 = 12, 4 x 3 = 12, 12 ÷ 4 = 3, 12 ÷ 3 = 4)
Division facts
-
Doubles (14 ÷ 2 = 7 – think 14 – 7 or
half of 14)
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Tens (50 ÷ 10 = 5 or 50 ÷ 5 = 10 –
think 50 split into 10 or 5 groups, or 5 rows on 100 chart)
-
Zeros (0 ÷ 9 = 0 – think “0 divided
into ___ groups gives 0 in each group” – We cannot divide by 0!
6 ÷ 0 is “undefined” because working
backwards, no number can be multiplied by 0 to get 6)
-
Ones (3 ÷ 1 = 3 – think “____ put in
1 group gives ____ in that group”)
-
Fives (45 ÷ 5 = 9 – double dividend
and divide by 10 – 45 + 45 = 90, 90 ÷ 10 = 9)
-
Nines (27 ÷ 9 = 3 – think next
multiple of 10 divided by 10 – 30 ÷ 10 = 3)
-
Squares (25 ÷ 5 = 5 or 4 ÷ 2 = 2 –
think of a square with this area – what is the side length?)
-
Squares and one more set (30 ÷ 5 = 6
or 56 ÷ 7 = 8 – think of a nearby square and take away one group – 25 ÷ 5 = 5,
so 30 ÷ 5 = 6; 49 ÷ 7 = 7, so 56 ÷ 7 = 8)
-
Threes (24 ÷ 3 = 8 – think next
lowest doubles fact – 16 ÷ 2 = 8, so 24 ÷ 3 = 8 also)
-
Fours (28 ÷ 4 = 7 – think half and
half again – 28 ÷ 2 = 14; 14 ÷ 2 = 7)
-
What’s left? – these are the
“harder facts,” but they usually can be connected to other facts using the
strategies shown above
-
Math families (given the numbers 3,
4, and 7: 3 x 4 = 12, 4 x 3 = 12, 12 ÷ 4 = 3, 12 ÷ 3 = 4)
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