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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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slide1

Mathematics 2Ms. Meek

Review of Addition and Subtraction

review addition vocabulary
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
Strategies

Count On to Add:

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

You can use your fingers, count in your head, use a model, or a number line.

strategies1
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!

strategies2
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
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

adding more than two addends
Adding More Than Two Addends

Example:

1 + 2 + 3 =

When you have three addends, add the first two together.

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

adding more than two addends1
Adding More Than Two Addends

Example:

3

^

1 + 2 + 3 =

3 + 3 = 6

adding m ore t han three a ddends
Adding More Than Three Addends

Add one number at a time:Example:

3

^

1 + 2 + 3 + 4 =

3 + 3 =6

6 + 4 = 10

adding m ore t han three a ddends1
Adding More Than Three Addends

Add sets of two addends at a time:Example:

3 7

^ ^

1 + 2 + 3 + 4 =

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

slide11

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
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.
strategies3
Strategies

Count Back:

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

You can use your fingers, count in your head, use a model, or a number line.

Ex: 5 – 2 = 3

strategies4
Strategies

Thinking of subtraction as the inverse of addition:

Addition and subtraction are opposites.

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

strategies5
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

strategies6
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

addition and subtraction fact families
Addition and SubtractionFact Families

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!

addition and subtraction fact families1
Addition and SubtractionFact Families

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.

addition and subtraction fact families2
Addition and SubtractionFact Families

Now our two subtraction facts:

  • start with the largest number
  • subtract either of the other two
  • the third number is the difference

11 – 4 = 7

And

11 – 7 = 4

addition and subtraction fact families3
Addition and SubtractionFact Families

Now our two subtraction facts:

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

addition and subtraction fact families practice
Addition and SubtractionFact Families Practice

create a fact family using 5, 9, 4:

remember:

  • With addition, your largest number is your answer.
  • 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

slide22

Addition With Multiple Digits

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 the ones column
  • add the tens column
  • add any additional columns left ofthe tens one at a time
slide23

Addition With Two Digits

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

addition with regrouping
Addition With Regrouping

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.

addition with regrouping1
Addition With Regrouping

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.
addition with regrouping2
Addition With Regrouping

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

addition with regrouping3
Addition With Regrouping

Then, add all three numbers in the tens column.

slide28

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
slide29

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
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 regrouping1
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 regrouping2
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 regrouping3
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 regrouping4
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.

slide35

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

Estimated answer: 60

slide36

Estimation of Sums and Differences

Let’s use estimation to help us determine if a sum is reasonable.

48 + 35 = 71

Without doing the actual calculations, can we tell if this is a reasonable sum?

48  50

+35  40Estimated answer: 90Is 71 a reasonable answer: NO