Ray's New Intellectual Arithmetic · Lesson XXXII · Unit 4: Working with fractions
32. Adding and subtracting together: what is left?
Goal: Your child adds the parts used up, then subtracts from the whole to find what is left.
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
Sixteen problems: parts of a field in different crops, a book read over four days, a pole partly in earth, water and air, and money spent and lost. The model adds the parts given away, then takes the sum from the whole.
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
SayIf a boy gives away ¼ and then ⅓ of his pecans, he gives away 3/12 and 4/12, which are 7/12. He has 12/12 less 7/12, or 5/12, left.
The whole is always “1”, or as many parts as the denominator.
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:
A boy gave away ¼ of his pecans and then ⅓: what part had he left?
A pole is ¼ in the earth and ⅓ in the water: what part is in the air?
A man spent and lost parts of his money and had $8 left: how much had he at first?
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
Use the Key for answers; the fractions in this part of the scan are hard to read on screen.