Ray's New Higher Arithmetic · Art. 52, Examples 1–19 · Unit 3: Addition
8. Adding: the rule, proofs and problems
Goal: Your student adds long columns accurately, checks by adding downward, and solves the book's practical addition problems.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
The rule for adding simple numbers, three methods of proof, then 19 examples for practice with answers, including sums of consecutive numbers and short business problems, and the book's suggestions about accuracy and speed.
The lesson, step by step
Warm-up
Mental: add 25, 25, 50 and 100. Then 19 + 21 + 30.
The rule
Read:
Write the numbers to be added, so that figures of the same order may stand in the same column
Begin at the right and add each column separately
Carry one for every ten, since ten units of each order make one unit of the order next higher
Proof
Read the first method of proof:
Add the figures downward instead of upward.
The book's other methods: split the numbers into groups and add the group totals, or add from the left. (Casting out nines comes later, in Art. 105.)
Guided practice
Do the first two together:
Of 76767; 7654; 50121; 775.
Of 97674; 686; 7676; 9017.
Check each by adding downward. (135317 and 115053, as the book prints.)
Independent practice
Your student works Examples 3 to 19. Numbers 5 to 8 are written in words first; 9 to 15 ask for the sum of consecutive numbers (write them all out, or look for a shortcut); 16 to 19 are short business problems.
Check
The book prints every answer. Cover them while working, then compare. Rework any miss without looking at the answer again.
Wrap-up
Read the book's suggestion together:
Two things are of the greatest importance in arithmetical operations, — absolute accuracy and rapidity.
Ask: Which one comes first? (Accuracy.)
Afterwards
If Examples 9 to 15 were slow, show the pairing trick: 119 + 131, 120 + 130... each pair makes 250.
Tip
Neat columns prevent most addition errors. Squared paper helps.