Mixed Operations - First Grade
What are Mixed Operations?
Concept: Mixed operations means working with both addition (+) and subtraction (−) together. We learn how they are connected and how to solve problems using both!
What We'll Learn:
✓ Different ways to make numbers
✓ Finding the correct math signs
✓ Understanding fact families
✓ Solving word problems
💡 Tip: Addition and subtraction are opposites - they undo each other!
1. Ways to Make a Number
Concept: We can make the same number in many different ways by adding or subtracting! This helps us understand numbers better.
📝 Example: Ways to Make 10
Different ways to make the number 10:
0 + 10 = 10
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
5 + 5 = 10
All these different ways equal 10!
We can also use subtraction:
11 − 1 = 10
12 − 2 = 10
15 − 5 = 10
Why This is Important:
✓ Helps understand number relationships
✓ Makes mental math easier
✓ Builds flexibility in thinking
💡 Tip: Practice making your favorite number in different ways!
2. Which Sign Makes the Number Sentence True?
Concept: Sometimes we need to figure out if we should use + (plus) or − (minus) to make a math sentence correct!
The Two Math Signs:
+
PLUS SIGN
Means: ADD
Result: Number gets BIGGER
−
MINUS SIGN
Means: SUBTRACT
Result: Number gets SMALLER
📝 Practice Examples
Example 1: 5 ___ 3 = 8
Think: Is 8 bigger or smaller than 5?
Answer: 8 is BIGGER, so we ADD
5 + 3 = 8 ✓
Example 2: 10 ___ 4 = 6
Think: Is 6 bigger or smaller than 10?
Answer: 6 is SMALLER, so we SUBTRACT
10 − 4 = 6 ✓
💡 Tip: Look at the answer - is it bigger or smaller than the first number?
3. Fact Families
Concept: A fact family is a group of related math facts using the same three numbers. Each fact family has 2 addition facts and 2 subtraction facts!
Fact Family Triangle
9
3
6
Total
Parts
Top number (9) = Total (biggest number)
Bottom numbers (3, 6) = Parts
The 4 Facts in This Family
Addition Facts
3 + 6 = 9
6 + 3 = 9
Subtraction Facts
9 − 3 = 6
9 − 6 = 3
Fact Family Rules:
✓ Uses the same 3 numbers in all facts
✓ Has 2 addition facts (order doesn't matter)
✓ Has 2 subtraction facts (start with the biggest number)
✓ Shows how addition and subtraction are related
💡 Tip: If you know one fact in the family, you can figure out all the others!
4. Addition & Subtraction Facts - Numbers up to 10
Concept: These are the basic math facts we need to memorize! When we know them by heart, math becomes much easier and faster.
Addition Facts Chart (up to 10)
| + | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 2 | 3 | 4 | 5 |
| 1 | 1 | 2 | 3 | 4 | 5 | 6 |
| 2 | 2 | 3 | 4 | 5 | 6 | 7 |
| 3 | 3 | 4 | 5 | 6 | 7 | 8 |
| 4 | 4 | 5 | 6 | 7 | 8 | 9 |
| 5 | 5 | 6 | 7 | 8 | 9 | 10 |
Important Facts to Memorize:
0 + 0 = 0
1 + 1 = 2
2 + 2 = 4
3 + 3 = 6
4 + 4 = 8
5 + 5 = 10
💡 Tip: Practice these facts every day until you know them without counting!
5. Addition & Subtraction Facts - Numbers up to 18
Concept: As we get better, we learn facts for bigger numbers! These go up to 18 and help us with harder math.
Key Facts to Learn (Sums up to 18):
6 + 6 = 12
7 + 7 = 14
8 + 8 = 16
9 + 9 = 18
7 + 8 = 15
8 + 9 = 17
6 + 7 = 13
6 + 8 = 14
Subtraction Facts (from 18):
18 − 9 = 9
17 − 8 = 9
16 − 8 = 8
15 − 7 = 8
14 − 7 = 7
13 − 6 = 7
💡 Tip: If you know your facts to 10, learning up to 18 is easier!
6. Addition & Subtraction Word Problems
Concept: Word problems tell a story with numbers. We need to read carefully and decide whether to add or subtract!
Keywords to Look For:
ADDITION Words
• Total
• Altogether
• In all
• Combined
• Plus
• More
SUBTRACTION Words
• Left
• Remain
• Gave away
• Took away
• Difference
• Fewer/Less
📝 Example Problems
Problem 1 (Addition):
Sarah has 5 apples. Her mom gives her 3 more apples. How many apples does she have in all?
Keyword: "in all" → ADD
5 + 3 = 8
Answer: 8 apples
Problem 2 (Subtraction):
Tom had 10 candies. He ate 4 candies. How many candies are left?
Keyword: "left" → SUBTRACT
10 − 4 = 6
Answer: 6 candies
Steps to Solve Word Problems:
Step 1: Read the problem carefully
Step 2: Find the numbers
Step 3: Look for keywords (add or subtract)
Step 4: Write the number sentence
Step 5: Solve and write your answer
💡 Tip: Draw pictures to help you understand the problem!
7. Addition & Subtraction Terms
Concept: Every part of a math problem has a special name! Learning these terms helps us talk about math correctly.
ADDITION Terms
3 + 5 = 8
3
= Addend
+
= Plus sign
5
= Addend
=
= Equals sign
8
= Sum/Total
Addend: Numbers being added
Sum: The answer in addition
Total: Another word for sum
SUBTRACTION Terms
9 − 4 = 5
9
= Minuend
−
= Minus sign
4
= Subtrahend
=
= Equals sign
5
= Difference
Minuend: Number you start with
Subtrahend: Number being taken away
Difference: The answer in subtraction
General Math Terms:
Equation: A math sentence with an equals sign
Operation: The action (+ or −)
Number Sentence: Another word for equation
💡 Tip: Knowing the correct terms helps you understand math better!
Quick Reference Guide
| Concept | What It Means | Example |
|---|---|---|
| Ways to Make a Number | Different combinations to get same total | 5+5=10, 6+4=10, 7+3=10 |
| Fact Family | 4 related facts using 3 numbers | 3+4=7, 4+3=7, 7-3=4, 7-4=3 |
| Addition | Combining two or more numbers | 5 + 3 = 8 |
| Subtraction | Taking away from a number | 8 − 3 = 5 |
Important Math Formulas
Addition Formula
Addend + Addend = Sum
Subtraction Formula
Minuend − Subtrahend = Difference
Inverse Relationship
If a + b = c
Then c − b = a
And c − a = b
🎯 Tips for Mixed Operations Success 🎯
- ✓ Practice fact families to see how addition and subtraction are related
- ✓ Memorize basic facts up to 10 first, then learn up to 18
- ✓ Look for keywords in word problems to know which operation to use
- ✓ Use drawings or counters to help solve problems
- ✓ Practice every day to get faster and more confident
- ✓ Check your work by using the opposite operation
⭐ You're a Mixed Operations Expert! ⭐
Fantastic work learning about mixed operations! You now understand how addition and subtraction work together, can solve fact families, know your math facts, and can tackle word problems like a pro. These are the building blocks for all future math. Keep practicing, and remember - the more you practice, the easier it gets. You're doing amazing!