Jun. 15, 2009 - Ray's Arithmetic Teacher Guide
Category • Math
I have planned to use Ray's Arithmetic for our math curriculum since I first thought about homeschooling, more than 5 years ago. Since we started actually using it two years ago, though, I've been struggling to figure out how it was intended to be used. The books don't have instructions for the teacher, and the teacher guide that comes with the reprints, by Ruth Beechick, did not satisfy me. I have several posts on this blog where I've analyzed Charlotte Mason's arithmetic recommendations and explained how I've adjusted Rays to fit those, but I still didn't think I was using the material as effectively as I'd like. (Fortunately, my oldest has natural math ability so she hasn't been bothered too much by all this.)
On the Ray's Arithmetic Yahoo group I learned some time ago about the Eclectic Manual of Methods, which is a teacher guide for a variety of materials including the McGuffey Readers and Rays Arithmetic. I found working from a pdf copy of the book to be off-putting so I never really approached it. In fact, I didn't even look closely enough to realize that the arithmetic section of that manual was quite short . (It begins on page 105 of the pdf copy.) I did try to find a hardcopy, but they are few and far between. (The only one I can find right now is located in Germany and would cost me over $20 including shipping.)
I finally sat down with the text copy and the pdf copy of the manual and created a Word document with just the arithmetic section. I've included all of it except one long table of exercises that I just couldn't bring myself to type in--that part you'll have to go to the pdf copy to see.
I haven't yet read through this in detail and tried to compare it with CM's recommendations, but from my cursory review while editing I would say that it generally does follow the same outline that CM recommended in Volume 1. I'm sure I'll post more about this as I dig into it further--I'll be using at least years 1 and 3 of this guide very soon.
• 1 Comments • Post A Comment! • 9:51 PM
Feb. 17, 2009 - Ray's Arithmetic Status Update
Category • Math
We are still using Ray's Arithmetic as our math text, having just finished Term 2 of Ambleside's Year 2 with my newly 8 yodd. We have completed addition, subtraction, multiplication, and division, and I am extremely pleased with dd's understanding of the math processes involved. She still needs drill to have fluency with the math facts, but we will continue to drill using Peggy Kaye's Games for Math and our math wrap-ups as well as practicing with real-life situations whenever possible.
This year we have added a weekly lesson from Edward Zaccaro's Primary Grade Challenge Math. This excellent, living math book introduces concepts like fractions and decimals and percents that we otherwise wouldn't reach for years, and it also adds an element of intellectual stimulation that arithmetic lacks.
One thing I would still like to do is to study the Manual of Methods that went with the original Ray's Arithemetic (which differs substantially from the Parent-Teacher Guide by Ruth Beechick that comes with the Mott Media set).
I also regret not having been faithful in implementing the measurement exercises recommended by CM. They are not hard to do, but I just didn't make them a priority. Picking those up again would be valuable, I believe.
• 0 Comments • Post A Comment! • 9:23 PM
Jan. 30, 2008 - Year 1 Math Update
Category • Math
We are using Ray's Arithmetic for math, but modifying it to fit the plan laid out by CM in Volume 1. We are now almost finished with Term 2 of Year 1, so we've been schooling for almost 24 weeks, approximately. We've finished the addition and subtraction lessons, although I think we need some review to cement the information. I suspect that I discontinued the use of counters sooner than I should have, mostly because I was on bedrest and using the counters was inconvenient. We have done the first three multiplication/division lessons, and so far they have gone very well. This seems to be because dd has already grasped the concepts without the lessons, though.
I do think I'm going to add in some addition/subtraction review activities, probably games, so that we don't lose those facts and to help improve her grasp of them. But yes, so far I'm pleased with the way these lessons have worked out.
• 2 Comments • Post A Comment! • 10:34 PM
Oct. 2, 2007 - Math Progress
Category • Math
Our formal math lessons are still working through addition and subtraction. We've covered up through the 7's, I think. I don't present more advanced math concepts usually because I want to make sure we follow an orderly progression that helps develop strong numeracy. Sometimes, though, dd figures things out on her own (which is fine).
A week or so ago she told me that she really preferred numbers that had two in them, like 4, which had two 2's, or 6, which had 4 and 2. After we talked about this a bit, I told her about even and odd numbers. She was able to explain the difference in the result when you add two even numbers versus two odd numbers or one of each.
Another night in the car she asked me what half of 2 was. We talked about that and how to figure it, and she went on to tell me what half was for all the even numbers up through twenty. Then she asked about half of 9, so we talked about why we couldn't do half of 9 without using a number in between 4 and 5. I didn't bring up whole numbers as a concept.
DH surreptitiously asked me if we had covered this stuff in school, and I told him we had not. Sometimes these concepts come up while we are doing other things, so it's not as though we never discuss them, but we aren't formally learning them. For instance, dd offered up the fact that 16 and 16 are 32. Well, upon questioning her, I learned that she got that fact from a lullaby on a CD they listen to at night sometimes. I knew that but had forgotten, and she took that lyric and filed it away in her math facts.
• 0 Comments • Post A Comment! • 5:21 AM
Jun. 3, 2007 - Revised Plan for Ray's New Primary Arithmetic
Category • Math
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.
• 4 Comments • Post A Comment! • 10:01 PM
Jun. 3, 2007 - More CM Math from Volume 1, pp. 259-60 - Weighing and Measuring
Category • Math
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.
• 0 Comments • Post A Comment! • 9:49 PM
Jun. 3, 2007 - More CM Math from Volume 1, pp. 258-259 - Place Value
Category • Math
"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."
• 0 Comments • Post A Comment! • 9:41 PM
Jun. 2, 2007 - Tentative Plan for Ray's New Primary Arithmetic
Category • Math
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.
• 0 Comments • Post A Comment! • 9:07 PM
May. 31, 2007 - CM Multiplication and Division Question
Category • Math
I'm trying to go through Volume 1's arithmetic section and make an outline of the steps recommended. I can get through the addition and subtraction parts just fine (I think - see this post for my analysis), but I have a question about the multiplication and division parts from pages 256-257.
For addition and subtraction, there's a three-step process for each line of the addition table, followed by the same three-step process for the same line of the subtraction table. First work the whole line with counters, then with word problems, then with mental numbers.
For multiplication and division (page 257), there appears to be just a one-step process for each line of the multiplication table, followed by a one-step process for the same line of the division table. It seems we're just supposed to work out the line using counters and then go on to the next one. But after working out both tables all the way through, with counters, then she recommends moving to complex word problems that involve both multiplication and division within one problem, without any mention of ever having done the simpler word problems in the course of working through the multiplication and division tables.
Do you think this is what she meant or did she mean us to do the three-step process here as well before moving on and just omitted mention of it?
• 2 Comments • Post A Comment! • 9:24 PM
May. 31, 2007 - Modifying Ray's Arithmetic
Category • Math
I have for years now planned to use Ray's Arithmetic when my dd was ready for formal math. That time is now, and I'm finding as I look closely at both Ray's New Primary Arithmetic (this links to a copy of the actual text) and Charlotte Mason's math recommendations (page 253 at the link) that the two are not exactly in sync. I prefer to follow CM's recommendations, but I'm hoping I can modify Ray's to fit so that I don't have to create the whole shebang from scratch.
I think we can follow this course for the first several lessons. My lessons are numbered with Arabic numerals; Ray's are numbered with Roman numerals.
Lesson 1 - Lesson XI - work out the table at the top with counters and drill over that, with counters
Lesson 2 - Lesson XI - drill on the word problems, orally
Lesson 3 - Lesson XI - drill on the word problems, orally, but phrase them as arithmetic problems (2+1 instead of using the word problem format)
Lessons 4-6 - Lesson XXV - repeat three steps above
Lessons 7-60 - Repeat this process for each of the next arithmetic lessons, alternating addition and subtraction lessons. Optionally skip the last arithmetic lesson since it works with 10 and the implication from CM is that we would stop at 9.
Lesson 61 - Lesson XXXIX - work out the table at the top with counters and drill over that, with counters
Here I'm at a loss because I'm not sure if we should drill with word problems, as above, or continue straight to addition. Any thoughts are welcome.
• 3 Comments • Post A Comment! • 9:24 PM
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