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I would also like to ask a few follow up questions. I just watched the DVD last night and so many things clicked into place for me! The DVD truly helped me see the overall progression and course of the lessons and how they build upon one another- something I wasn’t quite able to grasp fully just reading the book. For the first time now I am excited about working on math with my daughter.
However, I do have a few questions:
1) I am confused by how far to take the number lessons. At first Richele indicated we would do the basic number lesson for numbers 1-100, but then at 10 we start using money, and then after that the bundles- it seemed like the structure of the earlier lessons was out. I couldn’t tell. In other words- how does a lesson look for say the number 34 or what about 58, for example?
2) I was confused when the addition tables were introduced, if I remember correctly, at the beginning of the second year. I don’t understand what new concept is being taught here. It seems like the mental problems are the same as when we worked through each number earlier. What am I missing?
3) Finally, how do I get started with my daughter when she already has some math under her belt? She clearly understands 1-9 and its sums. We’ve already done quite a bit of work with money. Does CM even teach skip counting? Or does that discovery happen naturally through the course of the lessons? It seems like all the books and checklists include- so I have felt the need to teach it! lol
Thank you for your insight and advice on these questions.
I forgot! I have one more question and this may be more for Sonya as she is the one who mentioned it in the Math DVD- so I hope she sees this too!
How can I make my own grid paper? Excel or Word? It looks like from the DVD that the lines of the grid are not completely straight, that there is some definition to them. How do I accomplish this? Is it even necessary?
Hi Lauren! I’m glad you are excited to guide your daughter in math. Per your questions:
Numbers, 1-100, would take the first year in Charlotte’s schools. Remember, this was a time of exploration, investigation, and building a comfort with numbers. While the child has added, subtracted, and even brushed into multiplication and division during her work with addition and subtraction, the formal learning of the “four rules and tables” didn’t take place in her schools until the child’s second year of arithmetic. There are some important ideas formally introduced at this time that they may connect with from that first year of Numbers. Tables were not constructed or committed to memory until that second year though. Addition and subtraction are found on p. 29 and multiplication/division begins on p.35.
This first year is also when a child learns the idea of place value and learns notation (how we write the digits 0-9 and then arrange them for the larger numbers). So, at the number “10” we will be formally introducing money into the lessons and also the ideas of units and ten bundles. We can’t go further into our investigation of number without them. They will also be the concrete tools or manipulatives used as it would be unwieldy to add say, 27 pennies and 24 pennies, but two dimes and seven pennies are easily added to 2 dimes and four dimes (or, if we are using craftsticks: two ten bundles and seven units added to two ten bundles and four units) with the units being bundled into a ten or changed for a dime and the remaining unit kept to the right.
In general, the lessons for 34 and 58 would look primarily the same as your initial numbers lessons with a few exceptions (starting at page 26, point 17 in the handbook:
Your child won’t be pointing out 34 of some thing in the room. By the number 11, she has most likely grasped that these symbols express ideas.
When working with ten bundles/dimes the child should always placed those to the left and the units/pennies to the right to emphasize the idea of place value.
See if the child can tell which number is coming next to see if they have grasped the idea of where it will occur in relationship to other numbers.
30-100 are taken in sets of ten. Each set will take approximately 7-10 days. They follow the same pattern of learning the symbol for the idea, learning how to write it, working with it with the aid of manipulatives, counting, and reviewing numbers already learned.
Counting was an important part in CM numbers lessons. Skip counting does take place during this time. To give you an idea of how it would look, let’s take the lesson on number eight. My child has learned the symbol “8”, written it, worked problems using manipulatives, and now will I will ask my child to:
-Count out eight beads.
– Count them frontward and back.
-Arrange the beads in groups of two.
-Count them in two’s.
-Arrange them in groups of four.
-Count them in groups of four.
-Count them again forward and backward.
Depending on time remaining (remember, these lessons are only 20 minutes long) my child will –during this lesson or the next– work some problems without manipulatives and also review numbers already explored. Writing is used sparingly but before going on to the next number, a problem involving its use was done orally and then written out in the math notebook.
Does this make sense? As far as where to place your child, I would take her just a bit further back than you think she should be, seeing if she has truly grasped the idea or is just working mechanically. Sometimes using the concrete object will open the idea up. Or it may be the act of making ten bundles and setting them to the left of the units that helps her make the connection of each number having its own place.
You are right, Sonya printed the grid paper. We’ll ask her if she made it from an online template or on her own via Word or the like.
I created my own using a WP application. I inserted a Table, made the cells the 1″ x 1″ size, and selected all the lines of the borders to be a solid color.
Thanks to you both for responding. Richele, if you do not mind I have one final question/clarification to ask of you that I believe is the source of my confusion when it comes to numbers 30-100. It’s taken me a few days to re-read and review materials to finally pinpoint the source of my confusion 🙂
I referenced your book, specifically on page 28, and then skimmed all of Ray’s arithmetic and still did not find specific examples of addition and subtraction for numbers 30-100. Basically- will I be asking my daughter to add two 2-digit numbers? I noticed in your first reply to my question you mentioned adding 27 to 24- but I want to make sure I am understanding correctly! When I get up to the 50-set, for example, is it unreasonable for me to ask her to add 30 to 25 to make 55? Or are we sticking with adding single digit numbers to the larger number?
Ray’s Primary (or Ray’s New Primary) does not follow the scope and sequence we set out in the dvd and book, which was drawn from Irene Stephens’ (Ambleside’s Lecturer in Mathematics) The Teaching of Mathematics to Young Children. Her paper was presented in 1911 and, following its publication, was the suggested reading for implementing CM’s methods in arithmetic.
In the appendix of the book, I’ve provided three variations on Form I scope and sequences based on various books offered for use by PUSchools. I am unsure which of Ray’s books has the double digit addition and subtraction, most probably either Ray’s Practical Arithmetic or Ray’s Intellectual Arithmetic. Personally, I’ve found Strayer-Upton’s First Book in the Practical Arithmetics series (red book) to be most helpful along with Ray’s New Primary for following Irene Stephen’s scope and sequence. Some choose to stick solely with Ray’s, following that scope and sequence but utilizing CM methods for each concept as it is introduced.
Yes, when your child reaches the 50-set, she will be able to use the ten bundles and units (manipulatives such as popsicle sticks, golf pencils, matchsticks, strung buttons and beads, etc.) to add 30+25 as she will be adding five units to zero units and three tens to two tens to reach her answer. Say you are using popsicle sticks: She would place three ten bundles on the left and no units to represent 30. Then she would place two ten bundles directly under the three ten bundles and five popsicle sticks (units) to the right of the two ten bundles to represent 25. Now, she sees that she has five ten bundles and five units, making 55.
A question could be: Sarah practiced piano 30 minutes yesterday and 25 minutes today. How long did she practice all together?
Or, Luca read thirty pages of his book in the morning and 25 pages in the evening. How many pages had he read all together?
Does that clear it up, Lauren?
I would like to ask another follow up question if that’s alright. We have progressed through our first semester basing our lessons on the CM approach as outline in the Living Math book and DVD by Richele. We’ve enjoyed our lessons and my daughter loves working with the bundles!
If I understand correctly, though, I do need to cover topics like measurement and weights as well. I can’t find anywhere that explains CM’s approach to these topics as well.
Please forgive my very tardy reply. “Weights and Measures” are covered on pp. 39-42 in Chapter 2, “Arithmetic” in the handbook Mathematics: An Instrument for Living Teaching. Weights and Measures was begun about 9 years of age, in Form IIB – in approximately our grade 4. If we aren’t looking at the age/grade, it would follow division and the simple introduction to fractions found on the dvd. Incidental lessons can take place at any time and anywhere and were considered an important part of exercising a child’s judgement.
A few posts ago you discussed numbers 30-50. When you got to 50 in first grade would you do an addition problem with regrouping such as
I had 27 cars and then received 7 more for Christmas. How many do I have now?
I am 36″ tall and little sister is 18″ tall. How tall would we be if she stood on my head?
Also did Charlotte ever discuss mental math strategies with her students. Not necessarily forcing them to use them but suggesting them to see what worked best for each student. For example in your head add 36+18 as 30+10 and 8+2+4 another way is to visualize the algorithm etc… Perhaps with older? Students?
Also how do you teach adding early on with objects? Counting all, counting on, visualizing 5s like right start?
I have been using right start a and have mostly liked it but I do like to go on my own and have found it unwieldy at times and am thinking of going to rays/ stayer upmyer and Charlotte’s scope and sequence. I am a teacher by training who is very suspicious of common core but also personally benifited from some of the math thinking strategies associated with it… I want my kids to like and truly understand math in a way I never did till my math education class in college (I actually enjoyed long division in bases other than 10…)psreitmomParticipant
Richele, I asked this on my thread about life skills for an 8th grader. Would this CM Living Math be a good resource for focusing on life skills (money, measuring, time and sequence) for my daughter, currently in 7th grade. Those are the areas the neuropsychologist said to focus on for her to function as an adult.
I can identify with Melissa. My daughter has dyslexia and has always struggled with math. We have tried so much different curriculum because I didn’t know how to deal with her struggles. We got some help in third grade and have made some progress, but now that my daughter is a teenager, I have to focus on what will help her as an adult. She is currently learning multiplication, although I’m not sure if she totally understands the concept. But, I don’t want to spend so much time on that when she needs to be able to count money and follow a recipe and be able to keep track of time, all areas that need work. The neuropsychologist said to let her use a calculator, but I am not ready to let her do that. I want her using her brain and learning as much as she can and not take the easy road if possible. She even has trouble counting coins with mixed values, like going from dimes to nickels. In my other thread I was told about the business math sold here at SCM. I think that will be a great resource. I like to have something to follow. So, would this work in our situation?
Good questions. Yes, Charlotte Mason’s methods included those problems of an interesting nature. The lessons were lively and engaging without the use of games.
I am aware of Visualization in RightStart, which is based on groups of fives. It is not a part of Charlotte Mason’s living teaching of math and, in fact, counting is considered quite important in part due to that hallmark of a CM education, the unfolding of ideas in a child’s mind. For example, two ideas counting imparts is 1) the idea of “a series of symbols denoting a series of quantities whose magnitudes continue to grow greater” and 2)the idea of an order of things.
In CM maths, due to the work students are engaged in, they may in fact discover themselves without being taught some of the thinking strategies I believe you are speaking of, such as adding in tens. The abacus is not something used in Mason’s maths. She disdained contrived manipulatives and her use of concrete objects allowed the child to prove the validity of math facts and the reason for the processes used, thus laying the groundwork for mathematics. They were a means to an end however and done away with before a child could grow bored with them. Children were encouraged to discard the concrete by working with imaginary objects (imaginary beans or sheep) before advancing to the abstract but an abacus was never kept in one’s head.
My view is that the underlying methods of CM maths, which rest firmly upon her 20 Principles, along with its overarching philosophy differs greatly from RightStart. You may want to do a side-by-side comparison to reach your own opinion though.
You may read an impartial review of “Charlotte Mason’s Living Math: A Guided Journey” at Cathy Duffy Reviews and I believe it will answer many of your questions. There are also numerous sample pages and video clips from the book and dvd series found in the bookstore here at SCM that will also give you a look inside Miss Mason’s methods and philosophy regarding mathematics.
Charlotte Mason tells us of the appeal of [her] principles and this method to every type of child in Vol. 6. I have one son with dyslexia, one without, and both have consistently progressed in the mountainous land of mathematics. I do think CM’s method for teaching multiplication facts is brilliant and I haven’t met it elsewhere. Math is just one part of the greater whole though. Time is begun with the child’s outdoor geography lessons, noting the movement of the sun, shadows, direction, etc. Money is the most important of the concrete objects used and there is a lot of practice with it. The biggest problem you may find is that it isn’t an open and go curriculum telling you what to do. I’ll be sure to let you know when there is one. This is also not a “life skills” curriculum but a method that uses problems found in the everyday.
I’m not sure if my answer is any help to you. I applaud you for not simply giving in to the calculator but wanting your daughter to learn to think mathematically herself. I believe you both can do that.
Hi Richele…My youngest of 5 has dyslexia. He will be 9 in March. He is progressing fabulously with All About Reading, enjoys reading, desires to write comics and stories, and is doing very well with his attempts at spelling. It’s his frustration with the entire world of mathematics that is the source of his greatest difficulties and angst. We’ve tried many programs but we always hit a wall when we come across a concept he can’t grasp. I feel my focus should be helping him to find a way to help him with addition and subtraction fact recall and comprehension, simple fractions, and time before we can progress to multiplication, rounding, etc. I would be overjoyed if he could begin to enjoy math like he is loving reading now. I’m wondering if this math program is what I’m looking for to help with his dyscalcula.
Oh, marmiemama, the last thing I want is for the book and dvd set to be just another resource that sits on your shelf and has wasted your money. Having led a now 9th grader and 7th grader in Charlotte Mason math –7th grader since day one of formal lessons– I can say without hesitation that her applied philosophy in mathematics is the same as in every other subject: quite groundbreaking. The icing on this cake is that the child is respected as a person. That means the child will also be respected as a person if part of their uniqueness is dyslexia or dyscalcula.
I have had to remain in constant conversation with the Lord in each lesson. What I have found is what Charlotte says, that a math lesson must not be drowned in verbiage. Nothing frustrates my dyslexic child more than an onslaught of words in an attempt to explain things. This has made CM maths particularly freeing but that doesn’t mean it is always easy. As mothers, one of our chief tasks is to not let traits become temperaments and that means helping him learn the way of the will and the ability to stay calm when he realizes a concept he has never met with is headed his way. The irony is his math sense is actually quite strong, especially in the area of solving spatial problems. I, too, have had to go along in a faith like potatoes sort of way. That is -not digging things up to see if they are growing, thereby killing any growth, but trusting the method of direct and simple teaching that cooperates with the Holy Spirit.
I don’t know if you listen to A Delectable Education podcasts. They have one on the special needs child, episode #58. Warning: have tissues on hand. I believe two of the three of them have dyslexic children and have found CM’s living teaching of math valuable in their experience. You may want to ask in a comment at the end of that podcast though. Sonya also has an insightful blog post that speaks to Mason Homeschooling with Special Needs Children, addressing some of the CM principles that have worked beautifully with her daughter. I point these out as not only a “don’t just take my word for it” but also that if we have seen the intended results in other areas, should we not trust CM’s methods for arithmetic as well?
I’ll leave you with a quote from one of our all time favorite books, Heidi. It is at the pint when Heidi is to begin lessons alongside Clara, who is homebound with frail health. Clara describes her kind tutor this way:
“But mind, when he explains anything to you, you won’t be able to understand; but don’t ask any questions, or else he will go on explaining and you will understand less than ever.”
Again, Charlotte definitely cautioned of drowning a math lesson with too many words and it seems especially detrimental for a dyslexic child. According to her philosophy every subject can be approached in a living way, in cooperation with the one who is Life, or in a stale and deadening way – which opposes life.
All my best to you as you venture in faith in this method of education.
Thank you, Richele, for your wise and kind words. My son and I were talking about math this morning and I was telling him we’ll keep trying different things till we find what works for him. He said with a big sigh, “I wish I could just count sticks for math.”
Out of the mouth of babes…
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