Addition and Subtraction Study Notes

First grade math introduces students to the fundamental concepts of addition and subtraction. These skills are crucial building blocks for all future math learning. We use numbers to count, compare, and solve problems in everyday life.

➕ Understanding Addition

Addition is when we put two or more groups of things together to find a total. It means "to combine" or "to add more."

What is Addition?

📌 Definition: Addition is the process of finding the total number of items when two or more sets are combined.

• The symbol for addition is the plus sign: \(+\).
• The symbol for the answer is the equals sign: \(=\).
• The answer to an addition problem is called the sum or total.

Example: If you have 3 apples and your friend gives you 2 more apples, you combine them to find how many you have in total.

\[ 3 \text{ apples} + 2 \text{ apples} = 5 \text{ apples} \]

Ways to Add

There are many ways to add numbers:

• Counting On: Start with the bigger number and count up the smaller number.
  💡 Example: For \(5 + 3\), start at 5 and count on 3 more: 6, 7, 8. So, \(5 + 3 = 8\).
• Using Objects or Drawings: Draw circles or use blocks to represent each number and then count them all.
  💡 Example: For \(4 + 2\), draw 4 circles and then 2 more circles. Count them: \(\circ \circ \circ \circ \quad \circ \circ\) = 6 circles.
• Using a Number Line: Start at the first number and jump forward the second number.
  💡 Example: For \(6 + 4\), start at 6 and jump 4 places to the right. You land on 10.
• Making Ten Strategy: Break apart one number to make a 10 with the other number, then add the rest. This is great for adding numbers up to 20.
  💡 Example: For \(8 + 5\):
  • We know 8 needs 2 more to make 10.
  • Break 5 into 2 and 3.
  • Now, \(8 + 2 = 10\).
  • Then, \(10 + 3 = 13\). So, \(8 + 5 = 13\).

Adding Three Numbers

Sometimes you need to add three numbers together. You can add any two numbers first, then add the third number.

Example: \(2 + 3 + 4\)

• Add \(2 + 3\) first: \(2 + 3 = 5\)
• Then add the result to the last number: \(5 + 4 = 9\)
• So, \(2 + 3 + 4 = 9\).

➖ Understanding Subtraction

Subtraction is when we take away part of a group to find how many are left. It means "to take away" or "to find the difference."

What is Subtraction?

📌 Definition: Subtraction is the process of finding how many are left when some items are taken away from a group, or finding the difference between two numbers.

• The symbol for subtraction is the minus sign: \(-\).
• The answer to a subtraction problem is called the difference.

Example: If you have 7 cookies and you eat 3 of them, you take away 3 to find how many are left.

\[ 7 \text{ cookies} - 3 \text{ cookies} = 4 \text{ cookies} \]

Ways to Subtract

Here are common ways to subtract numbers:

• Counting Back: Start with the bigger number and count backward the smaller number.
  💡 Example: For \(9 - 2\), start at 9 and count back 2: 8, 7. So, \(9 - 2 = 7\).
• Using Objects or Drawings: Draw the total number of items, then cross out the number being taken away, and count what's left.
  💡 Example: For \(6 - 4\), draw 6 stars: \(\star \star \star \star \star \star\). Cross out 4 stars: \(\xcancel{\star} \xcancel{\star} \xcancel{\star} \xcancel{\star} \star \star\). You have 2 stars left.
• Using a Number Line: Start at the first number and jump backward the second number.
  💡 Example: For \(10 - 3\), start at 10 and jump 3 places to the left. You land on 7.
• Thinking Addition to Subtract: Ask "What do I add to the smaller number to get the bigger number?"
  💡 Example: For \(12 - 5\), think "What plus 5 equals 12?" (\(? + 5 = 12\)). The answer is 7. So, \(12 - 5 = 7\).

🏡 Fact Families

Fact families show how addition and subtraction are related. They use the same three numbers to create two addition facts and two subtraction facts.

💡 Key Idea: Addition and subtraction are inverse operations, meaning they undo each other. Fact families help us see this relationship clearly.

Example: For the numbers 3, 5, and 8:

Addition Facts	Subtraction Facts
\(3 + 5 = 8\)	\(8 - 5 = 3\)
\(5 + 3 = 8\)	\(8 - 3 = 5\)

❓ Solving Word Problems

Word problems are math stories that require you to use addition or subtraction to find the answer. It's important to read carefully and understand what the story is asking.

Steps to Solve Word Problems:

1. Read the problem: Understand the story.
2. Find the numbers: What numbers are given?
3. Look for keywords:
   • Addition Keywords: "in all," "altogether," "total," "sum," "add," "both," "plus."
   • Subtraction Keywords: "how many left," "take away," "difference," "fewer," "minus," "how many more."
4. Choose the operation: Decide if you need to add or subtract.
5. Write an equation: Turn the word problem into a math sentence.
6. Solve the equation: Find the answer.
7. Check your answer: Does your answer make sense?

Example Word Problem (Addition):

Sarah has 6 red balloons. Her brother gives her 3 blue balloons. How many balloons does Sarah have in all?

• Numbers: 6, 3
• Keyword: "in all" (means addition)
• Equation: \(6 + 3 = ?\)
• Solution: \(6 + 3 = 9\)
• Answer: Sarah has 9 balloons in all.

Example Word Problem (Subtraction):

There are 10 birds sitting on a branch. 4 birds fly away. How many birds are left on the branch?

• Numbers: 10, 4
• Keyword: "how many left" (means subtraction)
• Equation: \(10 - 4 = ?\)
• Solution: \(10 - 4 = 6\)
• Answer: There are 6 birds left on the branch.