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- Math at Home, or How Parents Can Help Their Children
- Basic Facts Strategies
- Plus 2
- Doubles and Plus Tens
- Adding Near Doubles or 'Neighbor Numbers'
- Adding 'Neighbor in the Middle' Numbers
- Make a Ten
- Adding Hungry Eights and Hungry Nines
- Multiplying by Zero and by One
- Multiplying by Two
- Multiplying by Three
- Multiplying by Four
- Multiplying by Five
- Multiplying by Six
- Multiplying Squares
- The Dreaded 7 x 8
- And the rest....
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Math at Home, or How Parents Can Help Their Children
It is critical that students have a working command of the basic arithmetic
facts in fifth grade. The computation work will be more easily accomplished
and less prone to errors if students have quick rote recall of facts in
addition, subtraction, multiplication, and division. We will have some
practice drills on these skills, but our curriculum does not provide time to
teach these skills since they are covered in previous grades.
In Reading, students must be able to read 98% of the words in a text in
order to comprehend at least 70% of the material. Similarly, in Math a
student must have nearly 100% accuracy in basic facts in order to solve
problems. Math facts that are shown to be deficient on a timed test will be
sent home for practice. Time for painless practice of basic facts can be
found throughout the day: at school, in the car, during chores like table
setting and clearing/washing dishes and folding laundry, or during
television commercials.
The Math Newsletter, which will be posted in the Newsletter section of this
site, will explain ways to practice the current unit's skills at home.
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Basic Facts Strategies
Students generally know most of the facts, but once they start working on
multiplication and division, their addition and subtraction facts slip.
Since much of our work involves some mental math facility, students need to
keep their addition, subtraction, multiplication, and division skills sharp.
Students know their +0 and +1 facts.
Using strategies, students actually learn all 100 facts on a 1-10 Hundreds
Chart except 4 facts. Because addition is commutative (the order of the
factors does not change the sum) there are really only 2 facts to learn
since 3 + 6 is the same as 6 + 3 for example. The 'unknown facts' that must
be learned are: 3 + 6 and 4 + 7.
Subtraction facts are found by using Fact Families, just like students found
in the primary grades. 7, 8 and 15 are a Fact Family: 7 + 8 = 15, 8 + 7 =
15, 15 - 7 = 8 and 15 - 8 = 7.
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Plus 2
The +2 facts are found by skip counting to the next even or odd number
depending on the other addend. Practice skip counting by twos using even
numbers or odd numbers. Start at a different point each time, like 39, 41,
43, 45, 47 etc.
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Doubles and Plus Tens
Students know the doubles facts from playing board games and they can add
ten by increasing the tens digit by one.
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Adding Near Doubles or 'Neighbor Numbers'
Another strategy, Neighbor Numbers, is used when the addends are consecutive
numbers on the number line, like 5 + 6. The strategy is based on a known
doubles fact: 6 = 5 + 1, so 5 + 6 is the same as 5 + 5 + 1 or 11.
Try laying out pennies or other objects: five in one group and six in the
next group. By moving one penny from the group of six to the side, students
can see the 5 + 5 fact. Repeating this activity for other Neighbor Number
pairs helps students to internalize the concept.
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Adding 'Neighbor in the Middle' Numbers
Another strategy works for numbers separated by one place on a number line
like 6 + 8. I call these facts Neighbor in the Middle facts since the sum of
the two numbers is the Doubles fact for the Neighbor in the Middle on the
number line, or 7 in this case. So, 6 + 8 = 7 + 7 or 14.
Try laying out pennies or other objects: six in one group and eight in the
next group. By moving one penny from the group of eight to the group of six,
students can see the 7 + 7 fact. Repeating this activity for other Neighbor
in the Middle pairs helps students to internalize the concept.
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Make a Ten
Make Ten is usually an easy strategy for most students. They learn the
combinations that make ten: 1 + 9, 2 + 8, 3 + 7, etc.
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Adding Hungry Eights and Hungry Nines
My last strategy is Hungry Eights and Hungry Nines. In lower grades, this
strategy is taught using blocks that link together. To use Hungry Eights,
students have a 'train' of eight blocks hooked together. Eights are always
hungry for two more blocks ... which will make them a ten. Students take two
from the other addend to put with the eight and make a ten. The remaining
amount from the second addend is added to ten. For example, 8 + 7 would mean
that students should take two from the seven. That makes a ten and five more
or fifteen. The same strategy works for Hungry Nines, which are always
hungry for one more to make them a ten. So, to add 9 + 5, take one from the
five to make a ten and add the remaining four for fourteen.
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Multiplying by Zero and by One
Zero times any number means we have that number zero times and the product
will always be zero. This is known as the Zero Property of Multiplication.
The Identity Property of Multiplication, or Identity Property, says that any
number times one means we have that number one time, so one times any number
is that number.
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Multiplying by Two
The twos facts are the same as the Doubles in addition, so students should
already know the twos. Twos facts are always even numbers, so they are
divisible by 2 and end in 0, 2, 4, 6, or 8.
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Multiplying by Three
Multiplying by three means three sets of a group. Students can find threes
by building from their twos. Three sets are like doubles plus one more set.
So, for example, 6 x 3 can be three sets of six -- 6 + 6 = 12, 12 + 6 more =
18 or double six is twelve, plus one more six is eighteen.
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Multiplying by Four
To multiply by four, students have already learned to double the Doubles
fact. A mnemonic story can also help students to skip count by fours: Four
ate twelve sixteens going down Easy Street when Thirty-Two and Thirty-Six
passed him doing Forty. The diagram that accompanies the story shows a
caricature character Four eating Sixteens. He already has a 3 x 4 array in
his tummy, but one number is missing from a corner -- it is the twelfth
sixteen being eaten. Easy Street is a row of townhouses with house numbers
20, 24 and 28 for easy skip counting. Two more caricature characters, Thirty-
Two and Thirty-Six are riding tandem on a scooter by a speed limit sign that
reads 40 mph. So students recall the skip counting multiples: 4, 8, 12, 16,
20, 24, 28, 32, 36, 40.
Numbers that are divisible by four are numbers whose two rightmost digits
form a multiple of four. This is only helpful about half the time ;-)
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Multiplying by Five
Skip counting by fives has been done so often that most students already
know the fives facts. Multiples of five always end in zero or five with even
multiples being the zero in the ones place and odd multiples ending in the
five.
Students can also use the tens facts for even multiples of five -- 5 x 6 can
be found from 10 x 6 = 60. Since 5 is half of ten, 5 x 6 is half of 10 x 6
or 30. Some students see a pattern in the even multiples: cut the even
factor in half and tack on a zero for the ten. It's the same idea, but the
student cuts in half before making the ten multiple :-)
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Multiplying by Six
Just as we double the twos facts for the fours, we double the threes facts
for the sixes. Numbers that are divisible by six are even numbers whose
digits add up to a multiple of three.
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Multiplying Squares
A number times itself is a square number because it can be represented in a
square array, and squares are usually easily recalled by most fifth graders,
like 4 x 4 = 16 and 5 x 5 = 25.
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The Dreaded 7 x 8
This fact is considered the most challenging for students to learn. I tell
students about my teacher who shouted "5 - 6 - 7 - 8" in my face when I
couldn't immediately supply the answer to 7 x 8. Unfortunately for me, I had
been absent the day before when she taught students to say "five, six,
seven, eight" for 56 = 7 x 8.
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And the rest....
Nine facts use 'tricks' like the hand trick and the pattern trick. We use
these in class.
Tens are easy to skip count and form an easy pattern.
That just leaves the sevens and eights. Most of them are already known since
students know the commutative facts for the factors 1-6, like 7 x 4 = 4 x 7
and that's a double the doubles fact. So students need to learn 7 x 6, 7 x
8, and 8 x 6.
Students know many of these 100 multiplication facts already also, and they
should know the math property that applies. Once students know a
multiplication fact, they can figure out the related division fact.
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