Back to School Refresher

Did you know your student could lose anywhere from two to two and a half months worth of math knowledge over the summer months? By enrolling your student at Mathnasium now, they can move ahead in their class and continue to learn new things.

Refresh their (and your) knowledge with key terms from the Mathnasium Glossary below.

addition counting “how many altogether.” The process of forming a whole.

complement “the rest of it.” the remaining part with respect to the whole.

counting the process of determining quantity (how many, how much).
denomination the collective name of a group of similar things (apples, dogs, inches).

division counting “how many of these are there inside of that.” The process of separating a whole into equal parts.

fraction the result of breaking a whole into equal parts; one or more of those equal

group one or more of the same thing (1 apple, 9 dogs, 5 inches, 8 things).

half the first fraction. A whole divided into two equal parts; one of those parts. “Two parts the same.”

interval the distance from one number (or unit) to another. The space between two numbers.

Law of SAMEness It is only possible to add and subtract things of the same kind, things with the same name, the same denomination (an apple plus a banana is not a “banapples”).

mathematics the study of wholes and parts, and the relationship between them.

matrix literally, “mother.” That which gives form, origin, or foundation to something enclosed or embedded in it. A place of origin and growth. Related words include environment, framework, womb, structure, model; enclosed, enveloping, surrounding.

measurement the determining of quantity.

multiplication counting “in equal groups.” The process of forming a whole from equal groups.

part a component of the whole. A fragment, fraction, section, portion, region; a piece broken off.

percent literally, “for each 100,” “parts per hundred,” “how many for each hundred.”

proportion literally, “according to amount.” The relation of one part to another or to the whole; relative size. Comparison, analogy, balance, symmetry.

ratio a comparsion of two numbers by division.

subtraction counting “how far apart two numbers are” and “how much is left.” The process of removing a part(s) from a whole.

whole undivided. The one composed of the many. That which can be broken–down into parts. All of the quantity under consideration.

zero the number that counts none. That which has no parts.   

- Larry Martinek

Friday Afternoon Cartoon

Want to make change? This cartoon illustrates how making change for a dollar can be an exercise in computation. Try it with your kids, but aim for 5 different ways to make change, not 293!

Numerical Fluency Tips – Addition/Subtraction Facts

The first few times a child looks at addition and subtraction problems can be a confusing experience. It is very important for children to be able to effortlessly recall reliable methods to answer number facts.

One excellent method is Filling in the Gap. Take a look at the following example.

8 + ___ = 13

To find the missing number, we can fill in the gap between 8 and 13 by solving:

8 +___ = 10       and      10 +___ = 13

Once the two easier problems are solved, adding the two answers together will give the child the desired result. Take a look.

Since 8 + 2  = 10 and 10 + 3 = 13, the “gap” is 5 (2 + 3).

Check the result: 8 + 5 = 13.

And in words…

How far is it from 8 up to 10 (2) — how far is it from 10 up to 13 (3)? From 8 up to 13 is 5 (2 + 3) so 8 + 5 = 13.

Now try this:

7 + ___ = 16

7 + ____ = 10 and 10 + ____ = 16

7 + ___ = 16  
Since ____ + ____ = ____, the “gap” is ____.

So, 7 +____ = 16

The ability to use this “up to and over 10” method relies on the student knowing a series of prerequisite skills.  Here is a list of those skills.  When mastered, these skills will enable students to have effortlessly recall of addition and subtraction facts.
For each tip, I will also provide practice problems.

ADDITION TIPS

1)    Doubles

5 + 5 =                                             9 + 9 =

2)    Doubles plus/minus 1

5 + 6 = 5 + 5 + 1 =                        8 + 7 = 8 + 8 – 1 =

3)    Counting on (start at x and count up by y)

7 + 2 =                                              8 + 3 =

4)    Breaking down numbers

6 + ___ = 9                                        7 + ___ = 11

5)    How far apart are two numbers? (How far is it from x up to y?)

How far apart are 6 and 10?

How far is it from 9 up to 12?

6)    Combinations that make 10

8 + 2 =                                              6 + 4 =

7)    10 plus a number

10 + 7 =                                           10 + 9 =

8)    10 plus what number?

10 + ___ = 16                                  10 + ___ = 19 

SUBTRACTION TIPS

1)    How much is left?
Use the notion of “how much is left” when the numbers are fairly far apart, and count down.
For example, 12 – 3 is best thought of as “counting down from 12 by 3.”

2)    How far apart are the two numbers (how far is it from the smaller number up to the bigger number)?
Use the notion of “how far apart are the two numbers” when the numbers are fairly close to each other, and count up.

For example, 12 – 9 is best thought of as “how far is it from 9 up to 12.”

For the following examples, decide which method you would use: How much is left or How far apart

100 – 98 =                       100 – 3 =                          100 – 87 =                       100 – 15 =

Stay tuned for my next Blog posting to learn some more tips to effortlessly recall number facts.