small blocks, pennies,
beads, or beans
When you get stuck on a story problem,
use manipulatives to help solve it.
Isabel T.
Math - Ms. Pliner
1. 4 4 3
+ 1 2 6
5 6 9
2. 4X
3=12
1 2 3 4
5 6 7 8
9101112
3
4
Lena
ms. Janke
1. Greta picked 12 apples
but kay picked only
half as many. How
many apples did Kay
pick?
Kay picked 6 apples.
Terrific Triangles
When you need to memorize math facts, triangle-shaped
flash cards can point you in the right direction.
Triangle flash cards help you master fact families. With these cards, you do more than just memorize math facts. You also see how addition is related to subtraction and how multiplication is related to division.
A single set of cards is used for both addition and subtraction. One point of a
card shows a sum (the total, or the answer to an addition problem), and the other two points show the addends—the numbers that add up to the sum.
Here’s how each card works.
sum
addend
addend
Quiz yourself by covering the sum with
your thumb. Look at the two addends,
and think out or call out the sum.
7 + 6 = 13 6 + 7 = 13
Quiz yourself by covering one addend.
Look at the sum, and subtract the
addend that’s not covered to figure out
the addend that’s hidden. Then cover
the other addend and do it again.
13 - 6 = 7 13 - 7 = 6
Another card set is used for both multiplication and division. One point of each
card shows a product (the answer to a multiplication problem). The other two points show factors—the numbers you multiply together to get the product.
product
factor
factor
Practice multiplication facts by
covering the product.
4 × 6 = 24 6 × 4 = 24
Practice division facts by covering
one of the factors. Cover the other
factor, too, so you can memorize
both division facts on the card.
24 ÷ 6 = 4 24 ÷ 4 = 6
In math, paying attention to patterns pays off. Triangle flash cards help you learn
addends and sums, and factors and products, as groups of numbers that go
together. Thinking about math facts in these groups will take you farther than
just memorizing math answers. When you make sense of numbers this way,
it can make learning math so much easier!
Clever Calculator
Use your calculator to perform math magic!
Favorite Number
1. Tell a friend to name her favorite number from 1 to 9.
2. Give your friend your calculator, and instruct her to multiply the number
she picked by 9.
3. Then tell her to multiply the result by 12,345,679 (the numbers 1 through 9
in order, without the 8).
4. Ask her to show you the calculator.
You both will see a 9-digit number in which every digit is
the number your friend selected. If she chose 3, for example,
the calculator will show 333333333.
Mind Reader
1. To prepare for this trick,
write the number 73 on a slip of
paper and put the paper in your pocket.
2. Then ask a friend to choose any 4-digit number and remember it.
3. Tell her to type her number into your calculator
twice in a row. (For example, if she chose 3,356,
she enters 33563356.)
4. Then tell your friend to divide the number
she entered by 137.
5. Finally, tell her to divide the number she has
now by her original 4-digit number.
6. Take the paper from your pocket, unfold it,
and ask, “Is this the number you see on
the calculator?”
The calculator
will read 73,
just like your
paper!
The Story of Math
Math teachers always say, “Show your work!”
Here’s what makes it so important.
You have a story in mind. It’s a wonderful, funny, interesting story. And you decide
to tell it. So you write,
She lived happily ever after. The end.
That’s not much of a story, is it?
Math problems are like stories. The work you use to figure out the answer to a
problem is as important as all the twists and turns of a good tale. When you do
math, you want to get the correct solution, but it’s usually more important to be
able to explain how you got it. You have to tell the whole story!
Elsa