Ray's New Intellectual Arithmetic · Lesson X · Unit 1: Adding and subtracting in your head
10. Chains with + and −
Goal: Your child reads and works chains of plus and minus signs in their head.
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
About twenty-seven chains, starting with the model “3 minus 2 plus 1 equals 2”, up to long ones like 9 − 7 + 8 − 5 + 6 − 3 + 4 − 2 + 1.
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
Say3 minus 2 is 1; plus 1 is 2. So 3 − 2 + 1 = 2.
Go left to right, saying each running total. Have your child point along the line with a finger.
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:
8 − 4 + 6 − 5 = ?
1 + 2 + 3 − 4 + 5 − 6 + 7 − 5 + 9 = ?
9 − 7 + 8 − 5 + 6 − 3 + 4 − 2 + 1 = ?
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
Write a chain on paper and cover all but the first two numbers, sliding the card along as you go.