Ray's New Higher Arithmetic · Misc. Exercises 1–35 · Unit 29: Miscellaneous Exercises

125. Miscellaneous exercises, part 1

Goal: Your student chooses the right method for mixed problems from the whole book, without being told the chapter.

⏱ About 45 minutes · 7 steps

Open it at the Internet Archive ↗

You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Chapter XXIII, Miscellaneous Exercises: problems 1 to 35 on gain and loss, fractions, work and time, and other topics. Answers are printed.

The lesson, step by step

  1. Set the scene

    SayThese problems are not labeled. Part of the work is deciding which method fits.

  2. A plan for each problem

    Teach a routine: 1) Read the problem twice. 2) Say in your own words what is asked. 3) Name the chapter it belongs to. 4) Estimate the answer. 5) Work it. 6) Compare with the estimate and the printed answer.

  3. Work one together

    Choose one of the first few problems on the page and talk through the routine out loud, step by step.

  4. Guided practice

    Do two more together. Let your student lead and you only ask questions.

  5. Independent practice

    Your student works five to eight problems alone. Many have fractions; keep them as fractions until the end.

  6. Check

    Compare with the printed answers. For any miss, ask your student to find which step went wrong.

  7. Wrap-up

    Ask: Which problem was hardest to start? What finally gave you the way in?

Afterwards

Spread these over several days, a handful at a time. They make good review all year.

@teddyrookbook GitHub