Ray's Arithmetic · Book 1 · 1877

Ray's New Primary Arithmetic

89 short lessons, from counting to ten to money and measures, for children about 5 to 7. Each one has a guide you can follow step by step, with the right page of the book beside it.

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How to use it

  • A little, often. About 15 minutes a day, three to five days a week. That covers the book in about a school year.
  • Repeat freely. Most table lessons take two or three days before the facts come easily. Move on when they do, not before.
  • Real things first. Have a cup of about 40 counters ready (dried beans, buttons or pennies), and a slate, small whiteboard or paper.
  • Out loud. Ray's children said every answer in a full sentence: “3 and 2 are 5.” The guides keep that habit.
  • Skip what's history. A few lessons near the end teach old measures (English money, troy weight). They're marked optional.

Unit 1 Counting and writing numbers

Count real things to 10, then read and write every number to 100. Lessons 1–6.

  1. 1Counting to ten and the figures 1 to 10Lesson I✓
  2. 2Numbers from 11 to 40Lesson II✓
  3. 3Numbers from 41 to 70Lesson III✓
  4. 4Numbers from 71 to 100Lesson IV✓
  5. 5Reading figures from 1 to 100Lesson V✓
  6. 6Writing numbers from dictationLesson VI✓

Unit 2 First number facts with counters

Put small groups together and take them apart with beans or buttons, before any tables. Lessons 7–10.

  1. 7Putting small groups togetherLesson VII✓
  2. 8Facts up to 8: together, apart and in groupsLesson VIII✓
  3. 9Facts up to 10Lesson IX✓
  4. 10Counting the birds: adding with a pictureLesson X✓

Unit 3 Addition

The addition tables, one number at a time, each with short story problems. Lessons 11–23.

  1. 11Adding 1 (sums to 11)Lesson XI✓
  2. 12Adding 2 (sums to 12)Lesson XII✓
  3. 13Adding 3 (sums to 13)Lesson XIII✓
  4. 14Adding 4 (sums to 14)Lesson XIV✓
  5. 15Adding 5 (sums to 15)Lesson XV✓
  6. 16Adding 6 (sums to 16)Lesson XVI✓
  7. 17Adding 7 (sums to 17)Lesson XVII✓
  8. 18Adding 8 (sums to 18)Lesson XVIII✓
  9. 19Adding 9 (sums to 19)Lesson XIX✓
  10. 20Adding 10 (sums to 20)Lesson XX✓
  11. 21Review of addition, and counting by 2s, 3s, 4s and 5sLesson XXI✓
  12. 22Adding three numbersLesson XXII✓
  13. 23Story problems with additionLesson XXIII✓

Unit 4 Subtraction

Taking away: the subtraction tables, then adding and subtracting together. Lessons 24–37.

  1. 24Taking away: the owls and the batsLesson XXIV✓
  2. 25Subtracting 1Lesson XXV✓
  3. 26Subtracting 2Lesson XXVI✓
  4. 27Subtracting 3Lesson XXVII✓
  5. 28Subtracting 4Lesson XXVIII✓
  6. 29Subtracting 5Lesson XXIX✓
  7. 30Subtracting 6Lesson XXX✓
  8. 31Subtracting 7Lesson XXXI✓
  9. 32Subtracting 8Lesson XXXII✓
  10. 33Subtracting 9Lesson XXXIII✓
  11. 34Subtracting 10Lesson XXXIV✓
  12. 35Review of subtractionLesson XXXV✓
  13. 36Adding and subtracting togetherLesson XXXVI✓
  14. 37Counting back, and story problems with two stepsLesson XXXVII✓

Unit 5 Multiplication

Equal groups, then the times tables from 1 to 10, with reviews. Lessons 38–51.

  1. 38Equal groups: the swallowsLesson XXXVIII✓
  2. 39Multiplying by 1Lesson XXXIX✓
  3. 40Multiplying by 2Lesson XL✓
  4. 41Multiplying by 3Lesson XLI✓
  5. 42Multiplying by 4Lesson XLII✓
  6. 43Multiplying by 5Lesson XLIII✓
  7. 44Multiplying by 6Lesson XLIV✓
  8. 45Multiplying by 7Lesson XLV✓
  9. 46Multiplying by 8Lesson XLVI✓
  10. 47Multiplying by 9Lesson XLVII✓
  11. 48Multiplying by 10Lesson XLVIII✓
  12. 49Review of multiplication, and three numbersLesson XLIX✓
  13. 50Adding, subtracting and multiplying in a chainLesson L✓
  14. 51Mixed story problemsLesson LI✓

Unit 6 Division

Sharing and grouping: how many times one number is contained in another. Lessons 52–63.

  1. 52Sharing: the geese and the ducksLesson LII✓
  2. 53Dividing by 2Lesson LIII✓
  3. 54Dividing by 3Lesson LIV✓
  4. 55Dividing by 4Lesson LV✓
  5. 56Dividing by 5Lesson LVI✓
  6. 57Dividing by 6Lesson LVII✓
  7. 58Dividing by 7Lesson LVIII✓
  8. 59Dividing by 8Lesson LIX✓
  9. 60Dividing by 9Lesson LX✓
  10. 61Dividing by 10Lesson LXI✓
  11. 62Review of division, and chains with dividingLesson LXII✓
  12. 63Finding the price of oneLesson LXIII✓

Unit 7 Signs, bigger numbers and mixed problems

The signs + − × ÷ =, adding and subtracting past 20, and story problems that use every operation. Lessons 64–78.

  1. 64The signs + − × ÷ =Lesson LXIV✓
  2. 65Adding past 20Lesson LXV✓
  3. 66Adding past a tenLesson LXVI✓
  4. 67Story problems with bigger numbers: addingLesson LXVII✓
  5. 68Story problems with bigger numbers: taking awayLesson LXVIII✓
  6. 69Add, add, then take awayLesson LXIX✓
  7. 70Spending, change and agesLesson LXX✓
  8. 71Multiply, then subtractLesson LXXI✓
  9. 72How many times? (up to 32)Lesson LXXII✓
  10. 73How many times? (up to 100)Lesson LXXIII✓
  11. 74Mixed story problemsLesson LXXIV✓
  12. 75Buying, selling and paying in goodsLesson LXXV✓
  13. 76Trading: paying with something elseLesson LXXVI✓
  14. 77Trading, work and "if this, then that"Lesson LXXVII✓
  15. 78Counting by 2s to 9s, forward and backLesson LXXVIII✓

Unit 8 Money, weights and measures

The old tables of money, weight, length, area and time. Some are history now; each guide says which still matter. Lessons 79–89.

  1. 79United States moneyLesson LXXIX✓
  2. 80English money (history) optionalLesson LXXX✓
  3. 81Troy weight (gold and silver) optionalLesson LXXXI✓
  4. 82Pounds and ouncesLesson LXXXII✓
  5. 83Dry measure: quarts, pecks and bushelsLesson LXXXIII✓
  6. 84Liquid measure: pints, quarts and gallonsLesson LXXXIV✓
  7. 85Long measure: inches, feet, yards and milesLesson LXXXV✓
  8. 86Square measure: areaLesson LXXXVI✓
  9. 87Time, and other tablesLesson LXXXVII✓
  10. 88Dozens, scores and other old measures optionalLesson LXXXVIII✓
  11. 89Review of tablesLesson LXXXIX✓

The book itself

Ray's New Primary Arithmetic

1877 · Beginners, about ages 5 to 7

Counting, reading and writing numbers to 100, then the addition, subtraction, multiplication and division tables, story problems, and the tables of money and measures. 89 short lessons with pictures.

🧑‍🏫 Teaching guides ⬇ Download PDF (1.6 MB) Internet Archive ↗

Scanned by Google from a Harvard University copy.

Lesson numbers match the book's Roman numerals: Lesson 3 is the book's Lesson III. The guides are written for this site; the book is in the public domain.

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