🔵Addition Within 10 - Using Pictures and Number Lines
What is Addition?
Addition is putting things together to find the total. When we add, we find out "how many in all?" The symbol for addition is + (plus). The answer is called the sum.
Example: 3 apples + 2 apples = 5 apples (3 + 2 = 5)
Parts of an Addition Sentence:
\[
3 + 2 = 5
\]
(addend) + (addend) = (sum)
Addition Within 10:
All the numbers we add and the answer are less than or equal to 10.
Using Pictures to Add:
Count all the objects together to find the total.
Using a Number Line to Add:
Start at the first number. Jump forward the number of spaces for the second number. Where you land is the sum.
Number Line Example:
To add 4 + 3: Start at 4, jump 3 steps forward → 5, 6, 7. So 4 + 3 = 7.
Addition Facts Within 10 (Practice These!):
- 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4, 1 + 4 = 5, 1 + 5 = 6, 1 + 6 = 7, 1 + 7 = 8, 1 + 8 = 9, 1 + 9 = 10
- 2 + 2 = 4, 2 + 3 = 5, 2 + 4 = 6, 2 + 5 = 7, 2 + 6 = 8, 2 + 7 = 9, 2 + 8 = 10
- 3 + 3 = 6, 3 + 4 = 7, 3 + 5 = 8, 3 + 6 = 9, 3 + 7 = 10
- 4 + 4 = 8, 4 + 5 = 9, 4 + 6 = 10
- 5 + 5 = 10
👀 See a worked example
Add using pictures: 4 + 3 = ?
- Draw 4 circles: ●●●●
- Draw 3 more circles: ●●●
- Count all circles: ●●●●●●● (7 circles)
-
Answer: 7 **Example 2:** Use the number line to add: 5 + 2 = ? *Solution:* - Start at 5 on the number line - Jump 2 steps forward: 5 → 6 → 7 - Land on 7 - **Answer:** 7 **Example 3:** Tom has 6 red balloons and 2 blue balloons. How many balloons does he have in all? *Solution:* - Red balloons: 6 - Blue balloons: 2 - Addition: 6 + 2 = 8 - **Answer:** 8 balloons
🤖 Vidi's Key Points
- Addition means putting things together (plus sign: +)
- The answer is called the sum
- Pictures help us count objects to add
- Number line helps us add by jumping forward
- Practice addition facts to 10 until you know them quickly!
🟢Addition Within 20 and Single-Digit Addition
Adding Single-Digit Numbers (Within 20):
When we add two numbers that are each 9 or less, the sum can be up to 18 (9+9=18) or 19 (9+10? 10 is two-digit). For Grade 1, we focus on sums up to 20.
Strategies for Adding Within 20:
| Strategy | How to Do It | Example |
|---|---|---|
| **Count On** | Start with bigger number, count up | 8 + 3 = 8,9,10,11 → 11 |
| **Doubles** | Memorize doubles facts | 6 + 6 = 12, 7 + 7 = 14 |
| **Doubles +1** | Double the smaller, add 1 | 5 + 6 = (5+5)+1 = 10+1 = 11 |
| **Make Ten** | Make a ten first, then add rest | 8 + 5 = (8+2)+3 = 10+3 = 13 |
Addition Facts to 20 (Practice These!)
| + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Horizontal vs. Vertical Addition:
| Horizontal Addition | Vertical Addition |
|---|---|
| 7 + 4 = 11 | 7 + 4 ─── 11 |
| Write across | Write on top of each other |
👀 See a worked example
Add using count on: 9 + 6 = ?
- Start with the bigger number: 9
- Count on 6 more: 9 → 10,11,12,13,14,15
-
Answer: 15 **Example 2:** Add using make ten: 7 + 5 = ? *Solution:* - 7 needs 3 to make 10 - Take 3 from 5, leaves 2 - 10 + 2 = 12 - **Answer:** 12 **Example 3:** Add vertically: 15 + 3 = ? *Solution:* - Write 15 and 3 in a column: 1 5 + 0 3 ───── 1 8 - Ones: 5 + 3 = 8 - Tens: 1 + 0 = 1 - **Answer:** 18
🤖 Vidi's Key Points
- Count on from the bigger number
- Doubles help you add two same numbers quickly
- Make ten is a helpful strategy for numbers near 10
- Horizontal addition writes across (4 + 5 = 9)
- Vertical addition stacks numbers (align ones and tens)
🟣Adding Two-Digit Numbers Without Regrouping
What Does "Without Regrouping" Mean?
Regrouping (also called carrying) is when the sum in a column is 10 or more. For now, we only add numbers where each column's sum is less than 10. This is called addition without regrouping.
Adding Tens and Ones Separately:
When adding two-digit numbers, we add the ones column first, then the tens column.
Steps for Vertical Addition (Without Regrouping):
1. Write the numbers in a column (align ones under ones, tens under tens)
2. Add the ones column (right side)
3. Add the tens column (left side)
4. Write the answer
Example: 23 + 14 = ?
| Tens | Ones |
|---|---|
| 2 | 3 |
| + 1 | 4 |
| ─── | ─── |
| 3 | 7 |
Answer: 37
Adding Two-Digit and One-Digit Numbers:
Just add the ones column; tens column stays the same.
Example: 42 + 5 = ?
- Ones: 2 + 5 = 7
- Tens: 4 (stays the same)
- Answer: 47
Horizontal Addition with Two-Digit Numbers:
Break into tens and ones: 32 + 25 = (30+20) + (2+5) = 50 + 7 = 57
👀 See a worked example
Add vertically: 32 + 46 = ?
- Write in column:
3 2
+ 4 6
─────
- Ones: 2 + 6 = 8
- Tens: 3 + 4 = 7
- Answer: 78
Example 2:
Add horizontally: 53 + 24 = ?
Solution:
- Break into tens and ones: (50+20) + (3+4)
- Tens: 50 + 20 = 70
- Ones: 3 + 4 = 7
- Total: 70 + 7 = 77
-
Answer: 77 **Example 3:** Sara has 42 stickers. Her friend gives her 35 more. How many stickers does Sara have now? *Solution:* - Add: 42 + 35 - Ones: 2 + 5 = 7 - Tens: 4 + 3 = 7 - Total: 77 - **Answer:** 77 stickers
🤖 Vidi's Key Points
- Without regrouping means no column sum is 10 or more
- Always add ones column first, then tens column
- Vertical addition helps keep place values aligned
- Break apart tens and ones for horizontal addition
- Write numbers neatly so ones line up under ones
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