Overview
This lecture covers the basics of addition using number lines, adding positive and negative numbers, carrying over digits, and stacking numbers for multi-digit addition.
Basic Addition Using Number Lines
- To add two numbers, start at the first number and move right by the value of the second number.
- Example: 5 + 3 means start at 5, move right 3 units to reach 8.
Adding Negative and Positive Numbers
- To add a negative number and a positive number, move right from the negative value by the amount of the positive number.
- Example: -6 + 4; start at -6, move 4 steps right to reach -2.
- Addition is commutative: 3 + 6 is the same as 6 + 3.
Adding Two-Digit Numbers
- Align numbers by place value (ones, tens) before adding.
- Add the units (ones) column first, then the tens column.
- Example: 43 + 25: 5 + 3 = 8 (ones), 4 + 2 = 6 (tens), answer is 68.
Carrying Over in Addition
- If the sum in a column exceeds 9, write the rightmost digit and carry over the next digit to the next column.
- Example: 47 + 38; 7 + 8 = 15, write 5, carry over 1 to tens place.
Adding Multi-Digit and Grouped Numbers
- Stack all numbers vertically and align by place value.
- Add column by column from right to left; carry over as needed.
- Example: 465 + 236 + 75; add all digits in each column and carry.
Key Terms & Definitions
- Number Line — A visual tool to add or subtract by moving right (add) or left (subtract).
- Carry Over — Moving a digit to the next left column when a sum exceeds 9 in a single column.
- Commutative Property — Addition order does not affect the sum (e.g., 3 + 6 = 6 + 3).
Action Items / Next Steps
- Practice addition problems using number lines and carrying over.
- Try adding numbers in groups to reinforce column addition skills.
- Use a calculator to check your answers.