Ray's New Intellectual Arithmetic · Lesson XXX · Unit 4: Working with fractions
30. Adding fractions
Goal: Your child adds fractions and mixed numbers by changing them to a common denominator first.
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
Word problems (a knife and a ball, parts of an orange, acres of corn and oats) and then abstract sums and mixed numbers, with a model solution.
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
SayOne-third and one-fourth: change both to twelfths. 4 twelfths and 3 twelfths are 7 twelfths.
For mixed numbers, add the whole numbers and the fractions separately, then put them together.
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:
Mary, Jane and William each get part of an orange: how much in all?
Thomas pays part of a dollar for a knife and part for a ball: how much did he spend?
Add 2½ and 3⅓.
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 fractions in this part of the scan are hard to read on screen, so check them in the book and use the Key for answers.