Mathematics 2 Ms. Meek Review of Addition and Subtraction

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Mathematics 2 Ms. Meek Review of Addition and Subtraction. Review: Addition Vocabulary . Words to know: sum – the answer to an addition problem. add – to find the sum of two or more numbers. addends – any of the numbers that are added together. Strategies . Count On to Add:

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Mathematics 2Ms. Meek

Words to know:

• add – to find the sum of two or more numbers.
Strategies

When adding 1, 2, or 3 to a larger number, an easy way to add is to count on.

Strategies

Doubles and Doubles Plus 1:

When adding the same number twice, we call it a doubles fact.

If you memorize your doubles facts, solving addition problems with consecutive numbers is a snap!

Ex: 6 + 6 = 12

That means… 6 + 7 = 13…the doubles answer plus 1!

Strategies

Making a 10:

If we work to learn all of the ways we can make a sum of 10 when adding, we can more easily remember how to solve other problems. Ways to make 10:

1 + 9, 2 + 8, 3 + 7, 4 + 6, and 5 + 5

Making a 10

If you have a problem like:

7 + 4

We know that 7 + 3 is 10

4 is 1 more, so our answer is 1 more.

7 + 4 = 11

Example:

1 + 2 + 3 =

Then, take the sum of the first two and add it to the third addend for a total sum.

Example:

3

^

1 + 2 + 3 =

3 + 3 = 6

Add one number at a time:Example:

3

^

1 + 2 + 3 + 4 =

3 + 3 =6

6 + 4 = 10

3 7

^ ^

1 + 2 + 3 + 4 =

3 + 7 = 10Adding sets of addends works when there is an even set of addends.

Review: Subtraction

Subtraction is the operation of finding the difference between two numbers.

There are many strategies used when learning how to subtract numbers.

Subtraction Vocabulary

Words to know:

• difference – the answer to a subtraction problem.
• subtract – to find out how many are left when a number of items are taken away from a group.
Strategies

Count Back:

When subtracting 1, 2, or 3 from a larger number, an easy way to subtract is to count back.

Ex: 5 – 2 = 3

Strategies

Thinking of subtraction as the inverse of addition:

If you have learned your addition facts, you can do subtraction facts!

Strategies

Thinking of subtraction as the inverse of addition:

Examples:

6 – 4 =

To solve this work backward, think:

What + 4 = 6

2 + 4 = 6

That means… 6 – 4 = 2

Strategies

Thinking of subtraction as the inverse of addition:

Examples:

8 – 5 =

To solve this work backward, think:

What + 5 = 8

3 + 5 = 8

That means… 8 – 5 = 3

Look at: 4 + 7 = 11

If you can add 4 plus 7 and come up with an answer of 11 then you are on your way to understanding some more facts as well!

Let us take a look at the other facts we can make with numbers 4, 7, & 11.

First, we can turn the addends around:

We had 4 + 7 = 11

7 + 4 = 11 as well!

This is the commutative property.

Now our two subtraction facts:

• subtract either of the other two
• the third number is the difference

11 – 4 = 7

And

11 – 7 = 4

Now our two subtraction facts:

We can also look at these facts another way, on a fact triangle!

create a fact family using 5, 9, 4:

remember:

• With subtraction, you begin with your largest number.

addition facts:5 + 4 = 9 AND 4 + 5 = 9

subtraction facts:9 - 4 = 5 AND 9 - 5 = 4

When adding numbers that have more than one digit, you add each column starting with the ones and move left.

To solve:

• write the problem vertically
• add any additional columns left ofthe tens one at a time

Ex: 36 + 23

Write vertically:

36

+23

add the ones column: 6 + 3 = 9

36

+23

9

Add the tens column: 3 + 2 = 5

36

+23

59

If the numbers in the ones column add up to more than 9, then we have to regroup.

When we have a ten, it must move to the tens column.

Example: 37

+26

• When we add the ones column we get 13, but we cannot write 13 in the ones column.
• 13 is really 1 ten, and 3 ones.
• Write the number 3 in ones column and bring the remaining 1 to the tens column.

Write 1 above 3 in the tens column as shown below. This is what we call regrouping or carrying over.

Then, add all three numbers in the tens column.

Subtraction With Multiple Digits

When subtracting numbers that have more than one digit, you subtract each column, starting with the ones and move left.

To solve:

• write the problem vertically
• subtract the ones column
• subtract the tens column
• subtract any additional columns left of the tens, one at a time

Subtraction With Two Digits

Ex: 36 - 23

Write vertically:

36

-23

subtract the ones column: 6 - 3 = 3

36

-23

3

subtract the tens column: 3 - 2 = 1

36

-23

13

Subtraction With Regrouping

If the number on top is smaller than the number on the bottom we cannot continue.

In such cases when we do not have the bigger number on top, we have to borrow from the tens column.

Subtraction With Regrouping

Example: 34

-18

When we try to subtract the ones column, we realize that we cannot take 8 away from 4.

Now, we will borrow a ten from the tens column, and add it to the ones column.

Subtraction With Regrouping

Borrow one from the 3 in the tens column and add it to the ones column.

Strike off 3 and write 2. Add that borrowed number 1 (actually 10) to 4 to make it 14.

Subtraction With Regrouping
• Now you can subtract these two numbers in the ones column, 14-8=6
• Write 6 in the 'ones' column.
Subtraction With Regrouping

Now look at the digits in the tens column. We have 2 above and 1 below.

So, 2-1=1. Write 1 in the tens column.

Review: Estimating Numbers to Find Sums and Differences

Example:

36

+22

Rather than working this out, we can round both addends to get an estimate of the sum.

36  40

+22  20