"No math concept is beyond the grasp of a child, if it is presented at the child's level." ~Jerry Mortensen

Mortensen Math 

Addition 20 minute video on how to do addition, subtraction, and play What’s Under the Cup.

http://youtu.be/Msug39k5cCs

+ means “and.”

The numbers being added are called “addends.” The total is called the “sum.”

The highest number you can count to is 9. Once you get past 9, you start over.

All numbers are made from other numbers.

1 + 0 = 1 1 + 1 = 2 1 + 2 = 3 3 + 1 = 4

Image taken from the Completely Cool Curious Counters Compendium.

All numbers want to be 10. Ten is one in the next largest column (place value).

When adding, make a 10, then add what is left over. 5 + 6 is one 10 and one 1 (unit).

1

"No math concept is beyond the grasp of a child, if it is presented at the child's level." ~Jerry Mortensen

7 + 6 is one 10 and three 1s (units).

Image taken from the Completely Cool Curious Counters Compendium.

2

"No math concept is beyond the grasp of a child, if it is presented at the child's level." ~Jerry Mortensen

Image taken from the Completely Cool Curious Counters Compendium.

During multi-digit addition, remember you can only add (count together) things that are the same.

It is very important that students know the addends of 10. Spend as much time as needed so these

are instantly recalled.

The best thing is for students to know all 45 addends. This ensures they can do mental arithmetic.

The Associative Law of Addition

(a + b) + c = a + (b + c)

The Commutative Law of Addition

a + b = b + a

The Distributive Law of Addition

a(b + c) = ab + ac

3

"No math concept is beyond the grasp of a child, if it is presented at the child's level." ~Jerry Mortensen

Subtraction There are two ways to think about subtraction:

1)The difference between two numbers. This is commonly thought of as “take away” or “minus.”

2)Making zeros. Using “have” and “owe” is easy for most students to understand. If I have $5 and owe $5,

how much do I have after I pay what I owe. Owing money is a bad thing and we call bad thing negative.

There are two ways to show this. You can either turn the “take away”/“owe” block upside down next to the

“have” blocks, or you can put the “take away”/“owe” block on top of the “have” blocks. Either way, where

there are two blocks, side-by-side or stacked, you have a zero.

Representational Model of Subtraction

Dynamic Subtraction:

First question - “is there enough?” If not, regroup (decompose) a unit of higher value to get the

addend of 10, then add it to the unit of lower value in the minuend.

4

"No math concept is beyond the grasp of a child, if it is presented at the child's level." ~Jerry Mortensen

Image taken from the Completely Cool Curious Counters Compendium.

Here is another example:

5

"No math concept is beyond the grasp of a child, if it is presented at the child's level." ~Jerry Mortensen

Negative Numbers

If you must use a number line, draw a vertical number line.

Start with money. “If you have $10, are you in a positive place or a negative place?” “If you have to

borrow ten dollars (debt), are you in a positive place or a negative place?”

“If you owe your Mom $5, and borrow $10 from your Dad, how negative (how much in debt) are

you?” [-5 + (-10)]

“If I owe you $5, and give you $10, how much change should I get?” [-5 + 10]

3 + (-1) = 2 Adding a debt of 1 3 - (-1) = 4 Removing a debt of 1

(-3) X 3 = (-3) + (-3) + (-3) = -9 (-10) ÷ 2 = -5 Debt is split between 2 people

When the student understands those, you can talk about ladders and holes. “If you fall in a hole that

is 20 ft deep and I throw down an 8 ft ladder, how tall is the top of the ladder?”

Citations:

Images taken from “The Completely Cool Curious Counters Kindergarten Compendium”, and

“Supremely Simple Subtraction” by Crewton Ramone. You may purchase these books in PDF form by

using the links.

6