Sunday, June 3, 2007

Revised Plan for Ray's New Primary Arithmetic

How much of this is completed in Year 1 remains to be seen.  Ruth Beechick’s Parent-Teacher Guide assumes only addition and subtraction are covered in first grade, but she also uses lessons I-X, which I am omitting as not being in line with CM’s recommendations.  Besides which, we don’t need the practice learning the actual numbers conceptually that those lessons would provide, and I don’t want to work on writing numbers before moving on.  I’ll fold that into our penmanship work.  The concrete lessons on weights and measures will follow the model outlined by CM in Volume 1 and described in a post below.

_____ Lesson XI – Addition 1
_____ Lesson XXV – Subtraction 1
_____ Lesson XII – Addition 2
_____ Lesson XXVI – Subtraction 2
_____ Lesson XIII – Addition 3
_____ Lesson XXVII – Subtraction 3
_____ Lesson XIV – Addition 4
_____ Lesson XXVIII – Subtraction 4
_____ Lesson XV – Addition 5
_____ Lesson XXIX – Subtraction 5
_____ Lesson XVI – Addition 6
_____ Lesson XXX – Subtraction 6
_____ Lesson XVII – Addition 7
_____ Lesson XXXI – Subtraction 7
_____ Lesson XVIII – Addition 8
_____ Lesson XXXII – Subtraction 8
_____ Lesson XIX – Addition 9
_____ Lesson XXXIII – Subtraction 9
_____ Lesson XX – Addition 10
_____ Lesson XXXIV – Subtraction 10
_____ Lesson XXI – Addition Review
_____ Lesson XXXV – Sub Review
_____ Lesson XXII – Addition Review
_____ Lesson XXXVI – Sub Review
_____ Lesson XXIII – Addition Review
_____ Lesson XXXVII – Sub Review
_____ Lesson XXXIX – Multiplication 1
_____ Lesson XL – Multiplication 2
_____ Lesson LIII – Division 2
_____ Lesson XLI – Multiplication 3
_____ Lesson LIV – Division 3
_____ Lesson XLII – Multiplication 4
_____ Lesson LV – Division 4
_____ Lesson XLIII – Multiplication 5
_____ Lesson LVI – Division 5
_____ Lesson XLIV – Multiplication 6
_____ Lesson LVII – Division 6
_____ Lesson XLV – Multiplication 7
_____ Lesson LVIII – Division 7
_____ Lesson XLVI – Multiplication 8
_____ Lesson LIX – Division 8
_____ Lesson XLVII – Multiplication 9
_____ Lesson LX – Division 9
_____ Lesson XLVIII – Multiplication 10
_____ Lesson LXI – Division 10
_____ Lesson XLIX – Mult review
_____ Lesson LXII – Division review
_____ Lesson L – Multiplication review
_____ Lesson LI – Multiplication review
_____ Lesson LXIII – Mult/Div review
_____ Lesson LXXIX – US money
_____ Lesson LXXX – British money

Add concrete exercises in weights and measures.

More CM Math from Volume 1, pp. 259-60 – Weighing and Measuring

We are to work with measures by actually measuring.

"On the same principle, let him learn ‘weights and measures’ by measuring and weighing; let him have scales and weights, sand or rice, paper and twine, and weigh, and do up, in perfectly made parcels, ounces, pounds, etc. The parcels, though they are not arithmetic, are educative, and afford considerable exercise of judgment as well as of neatness, deftness, and quickness."

I’m not sure I even know how to do up such a parcel, but maybe it would be sufficient to do it in plastic containers without actually wrapping a parcel?  Or would that be leaving out an important part of the process?  I suppose it would since CM mentions that the parcels themselves provide training in valuable skills.

"In like manner, let him work with foot-rule and yard measure, and draw up his tables for himself."

What does it mean to let him draw up his tables himself?

"Let him not only measure and weigh everything about him that admits of such treatment, but let him use his judgment on questions of measure and weight. How many yards long is the tablecloth? How many feet long and broad a map, or picture? What does he suppose a book weighs that is to go by parcel post? The sort of readiness to be gained thus is valuable in the affairs of life, and, if only for that reason, should be cultivated in the child."

We should take every opportunity to estimate and then test the accuracy of the estimate.

"While engaged in measuring and weighing concrete quantities, the scholar is prepared to take in his first idea of a ‘fraction,’ half a pound, a quarter of a yard, etc."

And we should use these exercises to introduce fractions in a gentle way.

All my Charlotte Mason math posts.

More CM Math from Volume 1, pp. 258-259 – Place Value

"When the child is able to work pretty freely with small numbers, a serious difficulty must be faced, upon his thorough mastery of which will depend his appreciation of arithmetic as a science; in other words, will depend the educational value of all the sums he may henceforth do. He must be made to understand our system of notation. Here, as before, it is best to begin with the concrete: let the child get the idea of ten units in one ten after he has mastered the more easily demonstrable idea of twelve pence in one shilling."

So after we work with basic arithmetic and achieve mastery of the four operations with small numbers, we move to working with money for a time to introduce the concept of place value.  Two skills are drilled during this process:  converting a quantity of one coin into larger coins, and noting on paper the value of the whole.
"Let him have a heap of pennies, say fifty: point out the inconvenience of carrying such weighty money to shops. Lighter money is used––shillings. How many pennies is a shilling worth? How many shillings, then, might he have for his fifty pennies? He divides them into heaps of twelve, and finds that he has four such heaps, and two pennies over; that is to say, fifty pence are (or are worth) four shillings and two pence. I buy ten pounds of biscuits at fivepence a pound; they cost fifty pence, but the shopman gives me a bill for 4s. 2d.; show the child how to put down: the pennies, which are worth least, to the right; the shillings, which are worth more, to the left."

Then we introduce place value.

"When the child is able to work freely with shillings and pence, and to understand that 2 in the right-hand column of figures is pence, 2 in the left-hand column, shillings, introduce him to the notion of tens and units, being content to work very gradually."

"We have but nine figures and a nought: we take the first figure and the nought to express another number, ten; but after that we must begin again until we get two tens, then, again, till we reach three tens, and so on. We call two tens, twenty, three tens, thirty, because ‘ty’ (tig) means ten. But if I see figure 4, how am I to know whether it means four tens or four ones? By a very simple plan. The tens have a place of their own; if you see figure 6 in the ten-place, you know it means sixty. The tens are always put behind the units: when you see two figures standing side by side, thus, ’55,’ the left-hand figure stands for so many tens; that is, the second 5 stands for ten times as many as the first."

We must drill with this concept, just using the tens and ones, for a time until the child is completely comfortable with the idea.

"Let the child work with tens and units only until he has mastered the idea of the tenfold value of the second figure to the left, and would laugh at the folly of writing 7 in the second column of figures, knowing that thereby it becomes seventy. Then he is ready for the same sort of drill in hundreds, and picks up the new idea readily if the principle have been made clear to him, that each remove to the left means a tenfold increase in the value of a number."

Then we move on to larger units, and drill again.  However, we do not work any problems with large numbers until the concept of place value for that number has been mastered.

"Meantime, ‘set’ him no sums. Let him never work with figures the notation of which is beyond him, and when he comes to ‘carry’ in an addition or multiplication sum, let him not say he carries ‘two,’ or ‘three,’ but ‘two tens,’ or ‘three hundreds,’ as the case may be."

All my Charlotte Mason math posts.

Saturday, June 2, 2007

Tentative Plan for Ray's New Primary Arithmetic

Here’s my tentative plan for Ray’s New Primary Arithmetic, just through multiplication and division.

_____ Lesson XI – Addition 1
_____ Lesson XXV – Subtraction 1
_____ Lesson XII – Addition 2
_____ Lesson XXVI – Subtraction 2
_____ Lesson XIII – Addition 3
_____ Lesson XXVII – Subtraction 3
_____ Lesson XIV – Addition 4
_____ Lesson XXVIII – Subtraction 4
_____ Lesson XV – Addition 5
_____ Lesson XXIX – Subtraction 5
_____ Lesson XVI – Addition 6
_____ Lesson XXX – Subtraction 6
_____ Lesson XVII – Addition 7
_____ Lesson XXXI – Subtraction 7
_____ Lesson XVIII – Addition 8
_____ Lesson XXXII – Subtraction 8
_____ Lesson XIX – Addition 9
_____ Lesson XXXIII – Subtraction 9
_____ Lesson XX – Addition 10
_____ Lesson XXXIV – Subtraction 10
_____ Lesson XXI – Addition Review
_____ Lesson XXXV – Sub Review
_____ Lesson XXII – Addition Review
_____ Lesson XXXVI – Sub Review
_____ Lesson XXIII – Addition Review
_____ Lesson XXXVII – Sub Review
_____ Lesson XXXIX – Multiplication 1
_____ Lesson XL – Multiplication 2
_____ Lesson LIII – Division 2
_____ Lesson XLI – Multiplication 3
_____ Lesson LIV – Division 3
_____ Lesson XLII – Multiplication 4
_____ Lesson LV – Division 4
_____ Lesson XLIII – Multiplication 5
_____ Lesson LVI – Division 5
_____ Lesson XLIV – Multiplication 6
_____ Lesson LVII – Division 6
_____ Lesson XLV – Multiplication 7
_____ Lesson LVIII – Division 7
_____ Lesson XLVI – Multiplication 8
_____ Lesson LIX – Division 8
_____ Lesson XLVII – Multiplication 9
_____ Lesson LX – Division 9
_____ Lesson XLVIII – Multiplication 10
_____ Lesson LXI – Division 10
_____ Lesson XLIX – Mult review
_____ Lesson LXII – Division review
_____ Lesson L – Multiplication review
_____ Lesson LI – Multiplication review
_____ Lesson LXIII – Mult/Div review

Each lesson will be covered in at least three parts, first with manipulatives, then with word problems, then with numeric problems worked mentally (without manipulatives).  I tentatively plan to do one lesson each week, but some lessons will probably move faster than that while others will take more time.