Ray's New Intellectual Arithmetic · Lesson IV · Unit 1: Adding and subtracting in your head
4. Adding to two-digit numbers
Goal: Your child adds a one-digit number to any two-digit number quickly, using what they know about the ones.
You'll need
- The book page (press “📖 Book page”, or use a printed copy)
- Paper for jotting, though the work is meant to be done in the head
What's in the book
Twenty-nine drills. The early ones review the facts to 12 + 12; the later ones add to numbers ending in 9, 8 and 7, such as “How many are 29 and 2? 49 and 2? 69 and 2?”
The lesson, step by step
Warm up
Ask three or four problems from the last lesson again, out of order. Your child answers and says why.
Show the reasoning
Show the pattern.
Say9 and 2 are 11, so 29 and 2 are 31, 49 and 2 are 51, 69 and 2 are 71.
The ones fact is the same each time; only the tens change.
Work the problems aloud
Read each problem on the page aloud. Your child answers, then explains in a full sentence, the way the book's model solutions do. The problems go like this:
Seven and 7 are how many? 7 and 12? 7 and 9?
How many are 29 and 2? 49 and 2? 69 and 2?
How many are 17 and 7? 27 and 7? 47 and 7?
Ask “Why?”
After each answer ask “Why?” or “How do you know?” Ray's wants the reasoning said aloud, not just the number. If your child stalls, go back to the model and say the first half of the explanation together.
Wrap up
Pick the two problems that were hardest today. Tomorrow, start with those as the warm-up.
Afterwards
Do the rest of the lesson's problems over the next day or two, a few at a time. Move on when your child can explain them without help.
Tip
The book notes that pupils who have done Ray's New Primary Arithmetic can begin here.