Ray's New Practical Arithmetic · Arts. 18–19 · Unit 2: Addition
8. Carrying, the rule and the proof
Goal: Your child adds long columns with carrying and checks the sum by adding the other way.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Why we carry when a column passes 9, the rule for addition, the proof, and a page of column examples with answers.
The lesson, step by step
Warm-up
Ask: 8 + 7? 9 + 6? 7 + 5 + 4? Say each answer as tens and units: 15 is 1 ten and 5 units.
Why carry?
Read:
When the sum of the figures in a column exceeds 9, two or more figures are required to express it.
SayWhen the units column makes 15, we write the 5 and carry the 1 ten to the tens column. Carrying is just adding tens to tens.
The rule
Read the rule together.
Write the numbers to be added, so that figures of the same order may stand in the same column.
Begin at the right hand, and add each column separately.
Work an example together
Work this one on the slate:
Add the numbers 3415, 503, 1870, and 922.
Units: 5 + 3 + 0 + 2 = 10, write 0, carry 1. Tens: 1 + 1 + 0 + 7 + 2 = 11, write 1, carry 1. Hundreds: 1 + 4 + 5 + 8 + 9 = 27, write 7, carry 2. Thousands: 2 + 3 + 1 = 6. Sum: 6710.
The proof
Read the proof:
Add the columns downward, commencing with the column of units.
SayIf adding down gives the same sum as adding up, the work is right.
Guided and independent practice
Do the first column example together. Your child does the next four or five alone and proves each one.
Check and wrap-up
Answers are printed under the examples; compare after proving. Mental finish: 25 + 25? 48 + 6? 99 + 7?
Afterwards
One or two column examples a day until carrying is automatic.