Ideas on a Math curriculum

[Bryan B]

Hello Everyone,

 

I only started Homeschooling in Oct 2020 with my 6 year son.  We've been doing great, but over the past two weeks math has become a problem.  I've just been filling math in with Khan Academy, and he was doing fine.  He's in 2nd grade level on Khan, but he's just not getting carrying & borrowing.  He has all the other area's "mastered", but moving forward with carrying & borrowing doesn't seem to be happening.  The video's don't seem to help.  He also doesn't want to write anything down.  I've known I was going to find a better math curriculum than Khan, but I've been busy with family stuff. To be honest I realize.... A) I'm not the best math teacher B) I should have looked into a Math curriculum sooner.  

I'm leaning twords MEP Math.  But I'm also intrested in Rod & Staff, Singapore, and Math Mammoth.  Is there anyone could share some of thier experiences with those curriculum with me?

 

Thanks!

[Servant4Christ]

Rod and Staff is great at teaching mastery and as long as you use the teaching manual daily, it will give good review as well. It does implement writing which my son detests, but I find that this helps him retain the info and builds up his stamina in physical writing across all subjects. His handwriting also improved greatly. I do not make my son do every math problem. We do many on the white board together, but he does have to do a certain amount of my choosing on paper daily. Hope this helps.

Note: Rod and Staff focuses on straight arithmetic, not the other stuff that a lot of other programs teach. The other stuff comes much later to make sure the basics are mastered.

A set of base 10 blocks helped my son tremendously with carrying and borrowing. Not the kind that connect, but loose. Having to trade in 10 cubes for a rod of 10 made everything click. Pennies, dimes and dollar coins might work too if you happen to have a lot of change on hand.

Oh, and I just noticed your son's age. I learned the hard way not to accelerate just because he understands higher concepts. My son began to hate math because of the workload. If you stick to the grade his age dictates, the expected amount of physical writing is usually realistic.

Edited December 25, 2020 by Servant4Christ

[lulalu]

Rod and Staff goes slow. (That isn't a bad thing) but my son loves math and gets it quick so we ordered and only used some of it for three months because it was just too slow. It includes a lot of writing in 3rd and above as the workbooks stop. It focuses on arithmetic. So it feels lacking in comparison to other more updated programs. It does a great job at mastering facts. 

MEP didn't work for ME. Ds did fine with it and it offers a great challenge for math lovers. But the TM and all the little parts were too much for me. And when printing the page out there are tiny areas to write answers in. (If you are in the states you will need to format it to fit your paper size, of you use A1 size you don't need to format it at all). However, being that it is free I would start here and see if it works for you. 

Math Mammoth has lots of good samples that you could try too. We have used a few different units. I like it a lot, but do find the explanations are lacking a little. 

But take all that as you will- I have come to the conclusion that for us and elementary topics I do best making it all on my own 🙃 

[EKS]

The best thing you could do is spend some time improving your own understanding of math and how to teach it.  The book Elementary Mathematics for Teachers is a wonderful resource for this.  As for programs, you're going to want to find one that supports your own teaching.  Khan does not do this.  It is opaque, meaning that you can't easily look ahead, and so you're having to backfill on the fly.  I'd take a look at RightStart and Singapore math as they are both excellent elementary math programs that have built in teacher helps.  Another program to consider is Math U See.

[Not_a_Number]

29 minutes ago, EKS said:

The best thing you could do is spend some time improving your own understanding of math and how to teach it.  The book Elementary Mathematics for Teachers is a wonderful resource for this.  As for programs, you're going to want to find one that supports your own teaching.  Khan does not do this.  It is opaque, meaning that you can't easily look ahead, and so you're having to backfill on the fly.  I'd take a look at RightStart and Singapore math as they are both excellent elementary math programs that have built in teacher helps.  Another program to consider is Math U See.

Yep. This. 

As for carrying and borrowing, OP, I'd 

a) explain carrying WAY before borrowing. It's easier and 

and 

b) Clarify in your own head what carrying is all about. 

How would you explain it to him? 

[Amethyst]

We used Singapore for years which was very good, but we eventually transitioned to Teaching Textbooks which I loved. 
 

But at your son’s age, maybe he needs a different approach. Maybe some manipulatives? I used Games for Math by Peggy Kaye but I’m sure there are many many other math game books out there.
 

You’re smart to want to not move ahead until he has mastered the concept. That’s one of the benefits of homeschooling - go at the child’s pace. 

[wathe]

Have a look at the Education Unboxed videos.  They are very good for teaching you how to teach.  I spent a lot of time with my kids working on regrouping and place value with manipulatives (cuisenaire rods) instead than working a lot of written problems.  And I'd often scribe for them (and sometimes play dumb and write the wrong thing so they could correct me).  They were both writing resistant.  Writing resistance doesn't have to get in the way of math learning.

[Hilltopmom]

If you think of “carrying & borrowing” as “regrouping” instead (which is how it’s taught now), it is much easier to grasp the concept. Use base ten blocks for as long as it takes to understand the concept before moving onto doing the problems on paper.

There are good videos to explain the concept- search for 2nd grade math “double digit addition with regrouping” and “subtraction with regrouping using base ten blocks”.

For a 6 year old I wouldn’t push it and ruin his interest in math... spend time playing math games and mastering his math addition & subtraction facts rather than on the curriculum output (the writing).

Edited December 24, 2020 by Hilltopmom

[happypamama]

We do carrying and borrowing in terms of cookies because kids like cookies. 

 

The ones column is cookies on a plate (sometimes it's chocolates). But only nine can fit on a plate, so when there are more cookies, they get boxed into boxes of 10. Then those boxes get packed into large cartons of 10. Cartons get shrink-wrapped together onto forklifts of 10 cartons. Forklift loads get put into trucks of 10 forklift loads. Trucks get lined up in the parking lot of 10 trucks. Then it's 10 sections of 10 trucks. In reverse, it's, "Someone wants eight cookies, but there are only six on the plate. Where can we get more?  Well, we have three boxes.  Let's open one. Now we have two boxes and we take those ten cookies and add them to the six, so now we have sixteen on the plate, and we will have eight left after the person gets their eight.". The visual has really helped my kids grasp the concept. 

[EKS]

16 hours ago, Not_a_Number said:

As for carrying and borrowing, OP, I'd 

a) explain carrying WAY before borrowing.

I agree, but I'd start by backing up further to place value.

[mathmarm]

Op, get

 1,000 craft sticks
a bag of tiny hair bands
a bag of rubber bands.

and make 1s, 10s and 100s.
Teach your kiddo to count 1s, 10s, and 100s.

Each day do several related addition and subtraction problems that require regrouping.

Spend a couple of weeks where you model and solve problems with the manipulatives only, talking through each step.

Then once he's comfortable with that step, go ahead and write down the problem and solve it as you go. Continue to do this every day for a few months. The Regrouping Concept is vital. It is used not just in base-ten (whole numbers and decimals) but also is used in fraction arithmetic and converting measurements. It's worth investing time and energy to get that concept down gradually to the point of automaticity.

 

[mathmarm]

Using the sticks/bundles, make the regrouping a seperate step from the operations.
 

If you're doing 301 - 257, then analyze the problem first and do all the regrouping necessary.

We don't have enough 10s, and we don't have enough 1s.

So take 1-hundred and regroup it to ten 10s, then grab a 10 and regroup it to 1s. Now we have enough 100s, 10s and 1s. So now we can subtract.

 

 

[Not_a_Number]

1 hour ago, EKS said:

I agree, but I'd start by backing up further to place value.

Agreed, although I found that my kids needed to be really hands on to fully understand place value. Naming 10s and 1s didn’t cut it... they needed to actually do the regrouping while performing operations.

[EKS]

1 minute ago, Not_a_Number said:

Agreed, although I found that my kids needed to be really hands on to fully understand place value. Naming 10s and 1s didn’t cut it... they needed to actually do the regrouping while performing operations.

Absolutely--learning about regrouping is a great way to cement understanding of place value.  So is learning about and then working with bases other than ten.

[Not_a_Number]

Just now, EKS said:

Absolutely--learning about regrouping is a great way to cement understanding of place value.  So is learning about and then working with bases other than ten.

Yep — DD8 absolutely adored binary as a 5 and 6 year old.

[Drama Llama]

My kids all went through a phase when they loved monopoly.  I subbed pennies, dimes and dollar bills for the money, so there were lots of trades to be made. My youngest, in particular, would spend hours playing by himself, calling out to me as I did the laundry "Mom, do you want to buy Park Place?"  

[lulalu]

I will add cuisenaire rods are the BEST thing to use for understanding math. If I only had one thing it would be c-rods. Gattegno's books are free to read online and the second book teaches regrouping. It is a different method and I had to play with the rods first to understand. 

educationunboxed.com has videos to help see how to use the rods. 

And playing lots of games really helps too- Zeus on the Loose, Monopoly, Clumsy Thief, all are good ones for math. There are a lot more out there. 

Ds really got regrouping after getting addition and subtraction down within 100. 

[sweet2ndchance]

It could be that he just isn't developmentally ready to understand carrying and borrowing. He may just need more time for the idea to bounce around in his head before he is ready to understand and apply it. It is a very common developmental learning wall that young elementary kids get stuck at for a while until their brains are ready to comprehend. 

My youngest picks up math concepts quickly and easily but even he got stuck behind that developmental learning wall of carrying and borrowing. So we went sideways for a while. We explored multiplication for a while. We worked more on place value. We explored really really really big numbers like decillions and touched on decimals and fractions. And now, at a week away from 8 years old, he suddenly understands and can apply carrying and borrowing. We touched on it several times while we were going sideways just to keep it fresh in his mind but we didn't bog down on it or drill it every day until he got it. He just needed time to process and understand the concept.

We really like MEP math here. Math Mammoth is really good too. I would say go ahead and use MEP since it is free and you can research the others in the mean time to see if you want to try them out or not.

[Not_a_Number]

1 hour ago, lulalu said:

I will add cuisenaire rods are the BEST thing to use for understanding math. If I only had one thing it would be c-rods. Gattegno's books are free to read online and the second book teaches regrouping. It is a different method and I had to play with the rods first to understand. 

educationunboxed.com has videos to help see how to use the rods. 

And playing lots of games really helps too- Zeus on the Loose, Monopoly, Clumsy Thief, all are good ones for math. There are a lot more out there. 

Ds really got regrouping after getting addition and subtraction down within 100. 

I know I’m weird, but I don’t like C-rods and don’t use them. I like my small number manipulatives countable but my place value manipulatives uncountable. So I like cards/dice/fingers for small numbers, and differently colored poker chips for place value.

[wathe]

2 hours ago, lulalu said:

I will add cuisenaire rods are the BEST thing to use for understanding math. If I only had one thing it would be c-rods. Gattegno's books are free to read online and the second book teaches regrouping. It is a different method and I had to play with the rods first to understand. 

educationunboxed.com has videos to help see how to use the rods. 

And playing lots of games really helps too- Zeus on the Loose, Monopoly, Clumsy Thief, all are good ones for math. There are a lot more out there. 

Ds really got regrouping after getting addition and subtraction down within 100. 

I lovity-love c-rods.  They are the one math manipulative that we just kept on using. Right up to multiplying and dividing fractions. 

And they're lovely to look at.  They feel nice in the hand.  Mine even smell good (wood set).  They are, along side pattern blocks, one of the few schooly things I will probably keep "forever".

[Not_a_Number]

16 minutes ago, wathe said:

I lovity-love c-rods.  They are the one math manipulative that we just kept on using. Right up to multiplying and dividing fractions. 

And they're lovely to look at.  They feel nice in the hand.  Mine even smell good (wood set).  They are, along side pattern blocks, one of the few schooly things I will probably keep "forever".

Apparently, everyone loves them but me 😛 

[lulalu]

51 minutes ago, Not_a_Number said:

Apparently, everyone loves them but me 😛 

They just teach about everything! That's why I love them so much. And they aren't set to certain numbers. 

 

[Not_a_Number]

11 hours ago, lulalu said:

They just teach about everything! That's why I love them so much. And they aren't set to certain numbers. 

I like my numbers countable 😛 . I feel like the biggest lesson I teach my kids in math with integers is that all the operations are simply tricks for counting quickly, so representations of numbers that aren’t connected to counting don’t seem like the right thing to me. 

[daijobu]

I replicated the illustrations in the Singapore Math textbooks with little squares of construction paper on a labeled whiteboard:

(checking...can you see this image below?)

In this situation I would repeatedly ask my dds, "Is this a fair trade to exchange 10 ones for 1 ten?"  Has the number changed?  Same for exchanging 10 tens for 1 hundred.  Is that a fair trade?  Has the number essentially changed?

I used those same bits of construction paper squares (easier to cut than circles) for renaming in subtraction and to illustrate long division.  Singapore math is brilliant this way.    

 

Edited December 25, 2020 by daijobu

[Not_a_Number]

Just now, daijobu said:

In this situation I would repeatedly ask my dds, "Is it was a fair trade to exchange 10 ones for 1 ten?"  Has the number changed?  Same for exchanging 10 tens for 1 hundred.  Is that a fair trade?  Has the number essentially changed?

Yes, that's what we did! We've been using poker chips of different colors, but same idea, and I keep asking the same questions. 

We took a fairly circuitous path to long division, though. We did division in other ways first. 

[wathe]

We used the language of trading too.  And with c-rods, ten units lined up is the same size (length, volume, weight) as a 10 rod, so the kid can see that, without a doubt, he is getting a fair deal.   Very good for concrete thinkers.

[Bryan B]

On 12/23/2020 at 3:54 PM, EKS said:

The best thing you could do is spend some time improving your own understanding of math and how to teach it.  The book Elementary Mathematics for Teachers is a wonderful resource for this.  As for programs, you're going to want to find one that supports your own teaching.  Khan does not do this.  It is opaque, meaning that you can't easily look ahead, and so you're having to backfill on the fly.  I'd take a look at RightStart and Singapore math as they are both excellent elementary math programs that have built in teacher helps.  Another program to consider is Math U See.

Thanks!  I ordedred the book.  Is it that obivious I'm not that great at math? 😏

[Not_a_Number]

1 hour ago, Bryan B said:

Thanks!  I ordedred the book.  Is it that obivious I'm not that great at math? 😏

Nah, it’s her recommendation for everyone, lol!

[Servant4Christ]

2 hours ago, Bryan B said:

Thanks!  I ordedred the book.  Is it that obivious I'm not that great at math? 😏

No worries. There have been many times when I've thought, "Why on earth didn't my teachers teach me like this? I would've actually understood it!"

My Oldest recently picked up on a pattern while finding equivalent fractions that I was never taught. My jaw dropped when we tested his theory and it worked EVERY SINGLE TIME. I then had to think of a much larger numerator and denominator to get him to apply the lesson correctly rather than just skip count top and bottom. 🤣 

 

Edited December 28, 2020 by Servant4Christ

[Not_a_Number]

2 hours ago, Servant4Christ said:

No worries. There have been many times when I've thought, "Why on earth didn't my teachers teach me like this? I would've actually understood it!"

My Oldest recently picked up on a pattern while finding equivalent fractions that I was never taught. My jaw dropped when we tested his theory and it worked EVERY SINGLE TIME. I then had to think of a much larger numerator and denominator to get him to apply the lesson correctly rather than just skip count top and bottom. 🤣 

 

What was the pattern?

[Servant4Christ]

1 hour ago, Not_a_Number said:

What was the pattern?

He skip counts by the numerator, then skip counts by the denominator if that makes sense. So for 2/3, he skip counts by 2s on top and by 3s on bottom. I had to show him that yes this works, but for a fraction such as 12/31 it will be way harder to skip count, but multiplying both the top and bottom by the same number will work regardless. It was fun to see his brain work like that.

Ok, enough hijacking and back to the topic at hand...

[Not_a_Number]

5 minutes ago, Servant4Christ said:

He skip counts by the numerator, then skip counts by the denominator if that makes sense. So for 2/3, he skip counts by 2s on top and by 3s on bottom. I had to show him that yes this works, but for a fraction such as 12/31 it will be way harder to skip count, but multiplying both the top and bottom by the same number will work regardless. It was fun to see his brain work like that.

Ok, enough hijacking and back to the topic at hand...

Cool! Yeah, that comes down to multiplication anyway, lol, but it’s a good trick!!