Complete Guide to Addition/Subtraction Within 20 for Grade 1

Master addition and subtraction within 20: definitions, rules, methods, examples, and practice exercises for 1st grade students.

Solution: Addition Exercises 1 to 3
1 Basic Addition
Exercise 1
8 + 7 = ?
Definition:

Addition: Combining two or more numbers to find the total

Addition method:
  1. Start with the larger number (8)
  2. Count up by the smaller number (7)
  3. Count: 8, 9, 10, 11, 12, 13, 14, 15
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First Number
8
Second Number
7
Sum
15
Step 1: Identify the numbers

We need to add 8 and 7

Step 2: Use counting strategy

Start at 8 and count up 7 more: 9, 10, 11, 12, 13, 14, 15

Step 3: State the answer

8 + 7 = 15

8 + 7 = 15
Final answer:

8 + 7 = 15

Applied rules:

• Counting on: Start with the larger number

• Make ten strategy: 8 + 2 = 10, then 10 + 5 = 15

• Always verify: Count to double-check

2 Addition with Regrouping
Exercise 2
9 + 6 = ?
Definition:

Regrouping: Breaking numbers to make addition easier

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First Number
9
Second Number
6
Sum
15
Step 1: Break down the second number

Think of 6 as 1 + 5

Step 2: Make ten first

9 + 1 = 10

Step 3: Add the remaining part

10 + 5 = 15

Step 4: Verify by counting

Count: 9, 10, 11, 12, 13, 14, 15

9 + 6 = 15
Final answer:

9 + 6 = 15

Applied rules:

• Make ten strategy: Add to make 10 first

• Decomposition: Break numbers into parts

• Counting verification: Always check your answer

3 Addition with Doubles
Exercise 3
7 + 8 = ?
Definition:

Near doubles: Adding numbers close to doubles

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First Number
7
Second Number
8
Sum
15
Step 1: Recognize near doubles

7 + 8 is close to 7 + 7 = 14

Step 2: Adjust from double

7 + 7 = 14, so 7 + 8 = 14 + 1 = 15

Step 3: Alternative strategy

Think: 8 + 8 = 16, so 7 + 8 = 16 - 1 = 15

Step 4: Verify with counting

Count: 7, 8, 9, 10, 11, 12, 13, 14, 15

7 + 8 = 15
Final answer:

7 + 8 = 15

Applied rules:

• Near doubles: Use known doubles to solve

• Alternative strategies: Try different approaches

• Multiple verification: Check with different methods

Complete Summary: Addition/Subtraction Within 20
\(a + b = c\) and \(a - b = d\)
Basic Operations Within 20
Key definitions:

Addition: Combining two or more quantities to find the total

Subtraction: Taking away one quantity from another to find the difference

Sum: The result of adding numbers together

Difference: The result of subtracting numbers

Within 20: Results must be between 0 and 20

Addition methods:
  1. Counting all: Count all objects together
  2. Counting on: Start from one number and count up
  3. Make ten: Break numbers to make 10 first
  4. Doubles: Use known doubles facts
  5. Near doubles: Use doubles to solve nearby problems
Subtraction methods:
  1. Counting back: Start from the larger number and count backwards
  2. Counting up: Count up from the smaller to the larger number
  3. Fact families: Use related addition facts
  4. Take from ten: Break numbers to make subtraction easier
Tip 1: For addition, always start with the larger number when counting on.
Tip 2: Learn doubles facts (2+2, 3+3, etc.) to help with near doubles.
Tip 3: For subtraction, think "what number plus the smaller equals the larger?"
Tip 4: Practice making ten: 8+2=10, 7+3=10, 6+4=10, 5+5=10.
Common errors: Forgetting to regroup, counting incorrectly, confusing addition with subtraction.
Success strategies: Use visual aids, check answers, practice regularly.
Key rules to remember:

• Commutative property: 3 + 4 = 4 + 3

• Associative property: (2 + 3) + 4 = 2 + (3 + 4)

• Addition/subtraction relationship: 5 + 3 = 8, so 8 - 3 = 5

• Adding zero: Any number plus zero equals itself

• Subtracting zero: Any number minus zero equals itself

ADDITION
8 + 7 = 15
SUBTRACTION
15 - 7 = 8
Detailed Learning Summary:

Core Concepts: Addition and subtraction within 20 require understanding number relationships and flexible thinking.

Strategies: Use multiple approaches: counting, making ten, doubles, and fact families.

Memory Aids: Learn doubles facts, practice making ten, and connect addition to subtraction.

Checking Work: Always verify answers using different methods.

Progression: Start with concrete objects, move to visual representations, then abstract symbols.

Visual Addition/Subtraction Guide
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Counting Strategy
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

For 8 + 7: Start at 8, jump 7 spaces: 8→9→10→11→12→13→14→15

Make Ten Strategy

For 8 + 7: Think 8 + 2 = 10, then 10 + 5 = 15

8 + 7 = 8 + 2 + 5 = 10 + 5 = 15
Solution: Subtraction Exercises 4 to 5
4 Basic Subtraction
Exercise 4
15 - 7 = ?
Definition:

Subtraction: Taking away one number from another to find the difference

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Starting Number
15
Number to Subtract
7
Difference
8
Step 1: Identify the numbers

We need to subtract 7 from 15

Step 2: Use counting back strategy

Start at 15 and count back 7: 14, 13, 12, 11, 10, 9, 8

Step 3: Use fact family strategy

If 8 + 7 = 15, then 15 - 7 = 8

Step 4: Verify the answer

Check: 8 + 7 = 15 ✓

15 - 7 = 8
Final answer:

15 - 7 = 8

Applied rules:

• Counting back: Start with the larger number

• Fact families: Use related addition facts

• Verification: Always check with inverse operation

5 Subtraction with Regrouping
Exercise 5
13 - 8 = ?
Definition:

Take from ten: Breaking numbers to make subtraction easier

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Starting Number
13
Number to Subtract
8
Difference
5
Step 1: Break down the starting number

Think of 13 as 10 + 3

Step 2: Subtract from ten first

10 - 8 = 2

Step 3: Add the remaining part

2 + 3 = 5

Step 4: Verify the answer

Check: 5 + 8 = 13 ✓

13 - 8 = 5
Final answer:

13 - 8 = 5

Applied rules:

• Take from ten: Break the minuend to make subtraction easier

• Decomposition: Separate numbers into manageable parts

• Verification: Use addition to check subtraction

Complete Learning Summary: Addition/Subtraction Within 20
\(a + b = \text{sum}\) and \(a - b = \text{difference}\)
Operations Within 20 Framework
Key definitions:

Addition: Combining two or more groups to find the total

Subtraction: Taking away one group from another to find what remains

Minuend: The number being subtracted from

Subtrahend: The number being subtracted

Difference: The result of subtraction

Addition strategies:
  1. Counting on: Start with the larger number
  2. Make ten: Break numbers to create 10
  3. Doubles: Use known double facts
  4. Near doubles: Build on double facts
  5. Number line: Move forward on the line
Subtraction strategies:
  1. Counting back: Move backward from the starting number
  2. Counting up: Count from smaller to larger number
  3. Fact families: Use related addition facts
  4. Take from ten: Break numbers to make subtraction easier
  5. Number line: Move backward on the line
Tip 1: Addition facts to memorize: doubles (1+1, 2+2, etc.) and make-ten combinations.
Tip 2: Subtraction facts are connected to addition facts through fact families.
Tip 3: Use visual aids like counters, number lines, or drawings to support understanding.
Tip 4: Always verify your answers by checking with the inverse operation.
Common mistakes: Confusing addition with subtraction, miscounting, forgetting to regroup.
Success strategies: Practice regularly, use multiple methods, ask for help when needed.
Important facts to memorize:

• Doubles: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, 6+6=12, 7+7=14, 8+8=16, 9+9=18

• Make-ten: 1+9=10, 2+8=10, 3+7=10, 4+6=10, 5+5=10

• Near doubles: 4+5=9, 5+6=11, 6+7=13, 7+8=15, 8+9=17

• Fact families: If 3+4=7, then 4+3=7, 7-3=4, 7-4=3

Mastering Operations Within 20:

Understanding: Addition and subtraction within 20 build the foundation for all future math.

Flexibility: Use different strategies depending on the numbers involved.

Connection: See the relationship between addition and subtraction as inverse operations.

Practice: Regular practice builds fluency and confidence.

Application: Apply these skills to solve word problems and real-world situations.

Strategy Selection Guide
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Choose the Best Strategy
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COUNT ON
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MAKE TEN
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DOUBLES
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TAKE FROM 10
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FACT FAMILY

Questions & Answers

Question: I get confused when adding numbers like 9 + 6. How can I make it easier?

Answer: Great question! Here's a helpful strategy called "make ten":

  • Think: "How much more do I need to add to 9 to make 10?" (Just 1!)
  • Take 1 from the 6, leaving 5
  • Now you have: 9 + 1 = 10, and 10 + 5 = 15

So: 9 + 6 = 9 + 1 + 5 = 10 + 5 = 15

This strategy works because adding to 10 is usually easier to remember!

Question: What are the most important facts my child should memorize for addition and subtraction within 20?

Answer: Focus on these foundational facts first:

  • Doubles: 1+1, 2+2, 3+3, 4+4, 5+5, 6+6, 7+7, 8+8, 9+9
  • Make-ten: 1+9, 2+8, 3+7, 4+6, 5+5 (and their reverses)
  • Near doubles: 4+5, 5+6, 6+7, 7+8, 8+9
  • Plus one/two: Adding 1 or 2 to any number

Once these are mastered, your child can use them to figure out other problems more easily!

For example: knowing 6+6=12 helps with 6+7=13 (just add one more).

Question: Why do I need to learn subtraction if I already know addition?

Answer: Addition and subtraction are opposite operations that help us solve different kinds of problems:

  • Addition: When we want to find the total when things are combined
  • Subtraction: When we want to find what's left after taking some away

They also help each other! If you know that 5 + 3 = 8, then you also know that 8 - 3 = 5 and 8 - 5 = 3.

Think of them as two sides of the same coin - both are important for solving math problems!