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Living Math- Practical Geometry
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Hi! I was wondering which math concepts & skills a student would need to have to be prepared to begin Practical Geometry? How far should a student be in working with fractions, decimals, etc before beginning? Thank you for any insight you may offer!
With gratitude,
Erika
If you use the Hall & Stevens “Experiments in Practical Geography” your child should have been introduced to fractions and decimals before beginning. Fractions and decimals in Arithmetic would then be carried alongside the weekly lesson in Practical Geometry as the student will be meeting with them in that branch as well.
If you are thinking of Strayer-Upton, one would follow along with the planned Scope & Sequence of the book as it is carefully integrated. I haven’t found a modern practical geometry textbook that utilizes a straightforward approach consistent with Mason’s philosophy and principles but I have been looking. HTH.
Warmly,
Richele
Hi Richele,
Thank you very much for your response. We are currently working out of Strayer Upton Book 2, but are still in the section on multiplying fractions. I am planning to use the Hall and Stevens geometry book. I guess it may be a while before we are ready for it though. Do you recommend completing the geometry section in Strayer Upton prior to beginning Hall & Stevens, or do you think it’s best to switch over for the weekly geometry lesson at that point and continue with Strayer Upton on arithmetic lesson days? Also, this is my daughter’s 5th grade year. I’m wondering if we are “behind” and if she will get enough of the practical geometry in for Form 2 with not having started it yet. Thank you very much for your time & insight.
With gratitude,
Erika
Oh, Erika, you are in a very good place. I would say that many PNUS students during Mason’s time did not even have 12 years of school so there is some flexibility in the maths timeframe. More important is that Practical Geometry takes place once a week for two years before formal geometry.
(And if anyone is reading this that is further along grade-wise even a term of Practical Geometry will have given practical knowledge and lend interest to the study of proof-based Geometry. The H&S book could then be taken alongside formal geometry).
You may decide to just carry on as usual with Strayer-Upton, doing some of the geometry problems as you come to them (remember, S-U has many more problems than needed throughout). Has your daughter had paper-sloyd during handicraft? Sloyd is definitely a good first step in getting ruler work and dexterity before Practical Geometry.
We live in a highly regulated state for homeschool and any classes taken before 9th grade cannot be counted on a high school transcript. We took practical geometry at a relaxed 30-minutes, once a week pace so as to begin Algebra and Geometry in 9th grade. One of my favorite things about Miss Mason and math is that she lays a very firm foundation upon which a superstructure can be built if so wished.
One note, if you continue on to Book Three (Blue Book) of Strayer-Upton for Consumer Math, Elementary Algebra, and Geometry, your student will need to be able to solve for x in the later geometry section of S-U. Therefore, you will want your student to have that introduction to algebra as laid out in the book before continuing. The consumer math part can be taken separately. Does that make sense?
Warmly,
Richele
Hi Richele! Thank you for your insight and encouragment. We are struggling in this area. I wonder if we should continue working sequentially with the Strayor Upton and continue through the summer instead of taking that time off of math. Do you have any thoughts on continuing math through the summer or taking a break from it? If a student ended up having to take Practical Geometry alongside their proof-based Geometry, what would that look like to schedule across the week? My daughter has been doing Sloyd. We just started it this school year. I also started it with my 9 year old daughter & 6 year old son. Should I continue trying to keep everyone together for this subject or would it help to let my 11 yo daughter work ahead of the younger children?
This is almost embarrassing to admit, but this point my older daughter has reached (fractions, decimals, percenta, geometry, etc) is where my own math understanding really started unraveling. I am struggling to keep up with her & help/guide her while keeping the lessons “living” and enjoyable. She may have been better prepared to begin the Practical Geometry on schedule were it not for that. I’m trying to work a few lessons ahead of her in the Strayor-Upton but haven’t been able to get the time to be much further than that. I’m just concerned not wanting my weakness in this area to hinder her. Do you have any suggestions? Also, is there a possibility of another math DVD & guide to help with middle school & high school CM math?
With much gratitude,
Erika
Hi Richele! Thank you for your insight and encouragement. I really appreciate it. We are really struggling in this area. My older daughter has reached the pint where my own math understanding really began to unravel. I’m trying to keep a few lessons ahead of her in the Strayer-Upton, but even that is a challenge with everything else going on many weeks. Do you have any suggestions? Is there any chance of another math DVD demonstrating the middle school and high school concepts? I do feel that my daughter may have been prepared to begin Practical Geometry on schedule if it wasn’t for my difficulty with these areas (fractions, decimals, percents, geometry). I really don’t want my weakness in this area to be a hindrance to her but am struggling to keep the lessons “living” and enjoyable while I’m floundering around myself.
We began Sloyd as a family this year, which is when we were introduced to your DVD and guide book. I have 4 children and have been doing Sloyd with the 3 school-aged children together as a group lesson. The other 2 children are 9 and 6. I’m wondering if they should be working at individual levels for Sloyd, and especially wondering if I should allow my 11 year old daughter to be working ahead of her younger siblings in this.
If a student had to compete Practical Geometry alongside their proof-based geometry, what would that look like scheduled across the week? I’m wondering if we should continue with math through the summer instead of taking time off so that we continue to make slow, steady progress. Do you have any thoughts on that?
With much gratitude,
Erika
Hi Erika,
Have you happened to listen to the podcasts from A Delectable Education where I was interviewed regarding Middle & High School Math? If you haven’t, I have linked to Episode 56 and then Episode 57 follows. I’m wondering if we cannot ease some of your own math fear so that you are able to better clearly see the path. Please forgive me if I have misspoken but I myself am a recovered math-ophobe. Speaking personally, I had to recognize that fear would be coming along for the ride but also determined that it would, under no circumstances, be allowed in the driver’s seat (reserved for the Lord). When fear lacked power it left.
Regarding year-round math, if I understand correctly, Charlotte’s schools had school breaks but the summer break did not exceed 8-weeks. According to PNEU philosophy, school breaks were considered precious and were both profitable and pleasurable. School breaks and formal education each serve to make the other more enjoyable, and parents were not meant to amuse and entertain the children. Parents were to provide children with a “multiplicity of interests” which gave a child freedom while helping them think and act profitably. In a Parents’ Review, J.S. Mills said we should not fear brain drain as a child would only forget superficially the lessons of a term. School breaks were seen as a time for children to develop their “senses, observation, and experience of life.”
Please know that I’m not saying you should adhere strictly to Mason’s break schedule at all. What I am saying is there might be very important reasons to have an 8-week break in the summer, 4-weeks over Christmas holidays and 4-weeks over Easter (or whatever works best for your family). You may want to ruminate on the above paragraph and note how important a break is to enjoying the school year, etc. There are certainly a “multiplicity of interests” in the summer that can help your children retain their math so they and you don’t feel like their youth is spent in all work and no play. To name just a few:
cooking lessons
learn a new handicraft
go on an expedition and make a detailed study, producing rough maps
classify and arrange collections in a home museum
grow a garden
Fractions and Decimals: If you have the DVD’s you may want to review the introduction of fractions via Mason. As you continue in fractions and decimals, this is a place that I think the Strayer-Upton books really shine and you will come out understanding them yourself like never before. The use of money here is really important. I don’t like turning living lessons into 1. 2. 3.-type lessons as a groove can quickly become a rut but at this point you may want to structure your lessons thus (and not in this particular order) 1. work in newest concept 2. review 3. mental math or rapid oral work. The “mixed review” section makes it simple to select a few problems for review. Your daughter’s rapid oral work could be solidifying math facts, reducing fractions, turning mixed fractions into improper fractions or vice versa. Here is a sample I shared recently:
Reducing improper fractions the stale way: “To reduce an improper fraction to a whole number or to a mixed number, divide its numerator by its denominator.” (p. 68 S/U Book Two). Memorize the rule and do the problems. Now, on to a more life-giving method taken from ? #11. p. 69 of Book II: If you have 3 quarters in one pocket and 2 quarters in another, how much money have you in all? Your child may be able to tell you this easily without even having money out but, if no aft, get the quarters out. Orally this would be 3 quarters + 2 quarters = 5 quarters or 1 dollar and 1 quarter. It looks like this written “3/4 + 2/4 = 5/4″ so your child may write the problem out once solved. Your child will already know from his/her previous math lessons that a) there are 4 quarters in 1 dollar and b)that line (between the numerator and denominator) is another way to express division. Now, you may work another simple problem orally and then have him write one once he has solved it. He may then tell you himself that he is dividing the numerator by its denominator.”
I spoke with a home educated math curriculum writer a few years ago and both her parents are accountants. She related how her mother had no problem teaching math to her but literature and grammar were another story. She recalls her mother praying aloud and asking the Lord for help in the middle of these lessons and how her mother learned alongside her in high school. This had a profound and positive effect on this young woman and her relationship with both her mother and the Lord.
As for having your children together for Sloyd, only you can answer that. Your 11-year-old will be working more quickly than your 6-year-old which means if you are working together she may be doing more projects. Does that make sense? Maybe one project you give orally and the second project she is reading directions while you are working with the youngers. Just an idea. You may consider more.
Erika, you could easily hold off on Practical Geometry with your 11-year-old for two more years and then teach your then 13-year-old together with your then 11-year-old. You really are not behind here.
Peace x 1000 from the One who put all laws, including mathematical, into place,
Richele
Hi Richele,
Thank you so much for such a gracious and informative response. I really appreciate it. I love A Delectable Education podcasts and was thrilled that you were on for those math episodes. I have heard them a few times but will relisten in light of what you just shared with me. My husband and I also attended your session at the Grace to Build retreat, and that was wonderful as well. You have already been such a blessing to our family!
You are absolutely right about my math fears and I appreciate the encouragement to trust in the Lord & His sovereignty in this area too, and to know that you had felt similarly with math and His grace was sufficient for that as well. Thank you!
I really appreciate how you gave me an idea of what the math lesson could look like at this point. That is such a help!
If my daughter started her first year of Practical Geometry next year, what would her math schedule for the week look like the following year, which is when she would also begin proof-based geometry?
With much gratitude,
Erika
Hi Erika,
Oh, I hadn’t realized with whom I was speaking -you and your husband are unforgettable, in the best way! I even remember your last name and where you are from, which I won’t mention here but you can quiz me if we meet again.
Mason’s PNEU programmes of study specify that “In home schoolrooms where there are children in A as well as in B, both forms may work together, doing the work of A or B as they are able.” It is also noted that “…in mathematics there must be no gaps. Children must go on from where they left off, …” So, how about if we use the PNEU schedule of math study as a roadmap while allowing your daughter’s understanding to determine the speed? With consistent, daily work and no pushing you will be amazed at her forward movement.
It may be helpful to look at this as rungs on a ladder and each step depends on the one before it. In arithmetic, you are going to want your daughter to have been introduced to fractions and decimals before beginning to work in Practical Geometry. She’s working in fractions so she has had that introduction and, if you have been working with money, she has had an introduction to decimals as well. We won’t know where she ends this year until the school year is over.
If you are breaking for the summer, use that for some prayerful school scheduling with your husband. What I am about to lay out is just one scenario as only you know the details of your lives and you will be the one seeing your child’s progress up that ladder. Next year (hypothetically): If you have a year of Practical Geometry once a week and carry on in Arithmetic your daughter should gain real firmness in her understanding of fractions, decimals, percents, etcetera. This will leave her in good stead for her introduction to Elementary Algebra in 7th. She could continue in Practical Geometry in 7th grade while she is learning to solve for x, which she will need in Formal Geometry.
This means she is in a rather good place for doing Algebra x 2 and Geometry x 2 in 8th & 9th grades which frees up 10th, 11th, and 12th for a slow and steady climb in advanced math topic(s) of your choosing. 8th could include one day of arithmetic, gaining competence in computations and ratio and proportion and 9th could include one day of consumer math. Having multiple streams of math going means you don’t need the big review between Algebra I and II, etc. You also want to be cognizant of your district, state and possible college requirements. This is not cause to worry but is something of which we all need to be aware.
My sister has four children in four different Forms and I believe she round robins with 20 minutes of math time together with a child then goes to the next while the first finishes up with 10 minutes of work on his/her own then on to the next. Does this all make sense? Again, this is just my view from here.
Kindest regards to you and your husband,
Richele
Hi Richele! Thank you so much for your kindness! I shared your message with my husband & we both agree the same about you (unforgettable, in the best way :). It would be our joy to ever run into you again.
Thank you for such thoroughly explained practical suggestions for our family! We really appreciate it & pray the Lord would bless your family and school planning as well, and as you so kindly wished for us, that the grace & peace of the Prince of Peace would abound in your hearts as home as well.
With joy & gratitude,
Erika S.
Richele,
When you say to follow Scope & Sequence in Strayer Upton, do you mean to just go through in the order they have it laid out? So keep doing fractions until we get to decimals, not both at the same time?
Again, thank you so much!
Patty
Hi Patty,
Help me be sure I’m understanding the question correctly. In CM math, utilizing the Strayer Upton text, a child will have been introduced to decimals via money before fractions -though the formal study of decimals follows fractions in SU. Once a child has confidence in fractions and the four operations in Strayer Upton then the formal study of decimals follows with more work in fractions incorporated, such as changing fractions to decimals and vice versa.
Does that answer your question?
Best,
Richele
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