order of operations/middle school math/ pre-algebra

[kristin0713]

Ok so my main question is, when is order of operations generally introduced and then thoroughly mastered?  I'm trying to decide on 5th grade math for my DS and this one topic has me stuck.

DD 12 is finishing up MLFLE 6 and has been very successful with it. But she still has done very little with order of operations!  Not at all in MFLE 6. This is after grades 2-5 with Singapore and Math Mammoth as a supplement.  She hit a wall in 5th grade and was extremely ill, and we played catch-up all summer to get her ready for 6th grade. MM 6 was excruciating at the beginning of the year, and MLFLE was exactly what she needed for a successful year. I think I'm going to put her in Principals of Mathematics for 7th grade.  Or, any other suggestions?

DS 10 just finished Singapore 4b.  He is strong in math, but needs a year of reinforcing fractions and decimals.  He is totally on track for 5th grade, and he could probably do algebra in 8th very successfully.  He is my engineering minded STEM kid.  He complains a lot about work but he is good at it.  I think that Singapore does not give enough problems, but MM is a little too much for him.  I was thinking of putting him in MLFLE and supplementing with MM.  I really wish they introduced order of operations, but maybe that is not necessary in 5th grade? 

Help me think through this!

[Lecka]

In public school my son started it in 6th grade and reviewed it at the beginning of 7th grade, as far as I know.  I am not aware of him doing it before 6th grade.  

[almondbutterandjelly]

We covered order of operations in Horizons Pre-Algebra.

[Sherry in OH]

Does your child's math program not include multi-step problems or is that the term 'order of operations,' isn't used?

My children encountered problem sets such as 

(2 + 4) x 6

2 + (4 x 6)

2 + 4 x 6

almost as soon as mulitiplication was introduced.  Other elements of the order of operations were added in when those concepts were taught.  I believe exponents were the last element taught, sometime between 4th and 6th grade.

[rjand6more]

MM introduces this very early. Grade 3/4.

[mytwomonkeys]

My children learned the PEMA acronym in 6th grade for the order of operations. It was not taught before then. 

[TheAttachedMama]

 

Singapore math also introduces order of operations very early.  (But you probably already know that.)  I can't remember what book they introduce it in.   Maybe level 3 or 4?  But then it is reviewed each year and practiced.   (They just add decimal or fractions to the problems.)  

For you 10 year old son, I would NOT move him from Singapore just because he needs more practice.  Especially if you are considering a STEM path for him.  And especially because it is working well for him.   :)   And especially because you are almost finished with the primary math sequence...why not stick it through?   (In full disclosure, i am a math snob, but I love Singapore math!)    I agree with you that math mammoth is also a very strong math program, but sometimes the sheer amount of problems can kill a child's love for math.   (Of course, you don't have to assign every problem in math mammoth.   But I know from experience that it can sometimes be a lot of work to sort through and pick out your child's assignment each day.  And I feel like the answer key in math mammoth makes grading more difficult than singapore.)  

So, let me ask you some questions (about the 10 year old specifically):

Is he currently doing all of the textbook and workbook problems?  (All of the reviews, practices, mental math for HIG, etc.)    (If not, start doing both of those.  That is the bare minimum.)   

Is he currently fixing his math each day and correcting missed problems until 100%?   (That is an easy way to provide more practice, and from my experience a very useful tool in teaching math.)  

If he is currently doing both the textbook and workbook problems (and fixing his math each day), then it might be time to add in one of the extra Singapore books.  The reason they have so many books is so you can completely customize the amount and type of practice your son needs and come up with a perfect math solution.

Here are just a few of the most common "extra" books people order:

• Extra Practice books.  These are going to be more problems just like the workbook.  These are for kids who just need more practice of the same.
• Intensive practice / challenging word problems:   These are for kids who don't find the regular workbook problems challenging enough.   
• Process Skills:  Does he need help with word problems or bar diagrams?
• Mental math books:   self-explanatory
• Tests book:   I know a lot of people who use the tests book for extra practice too.  I feel like they are a bit easier than the regular workbook because many of the problems are multiple choice.  But they are great, quick reviews.

 

My kids also need a little bit of extra review and practice.  I try my best to constantly keep sniffing out weak areas in their understanding.    I use the cumulative textbook and workbook reviews (at the end of each unit in the standards version of Singapore) to snuff out any weak areas of understanding.    If I notice that they are missing a lot of the same types of problems (or have forgotten how to do it and have to ask for a review)---then I re-teach the concept and start assigning 1-2 of those types of problems per day to practice.

Another easy way to add in extra practice is Prodigy math.  I don't know how you feel about screens, but it is a fun, online math video game that is actually pretty useful in reviewing math concepts.   (It is NOT a good primary teaching tool.)   It is free too.   You can assign topics for targeted review (ex. order of operations, finding the area of different shapes, dividing fractions, etc.) or you can just have them work on grade specific spiral review.  

 

 

 

[kristin0713]

8 minutes ago, TheAttachedMama said:

 

Singapore math also introduces order of operations very early.  (But you probably already know that.)  I can't remember what book they introduce it in.   Maybe level 3 or 4?  But then it is reviewed each year and practiced.   (They just add decimal or fractions to the problems.)  

For you 10 year old son, I would NOT move him from Singapore just because he needs more practice.  Especially if you are considering a STEM path for him.  And especially because it is working well for him.   :)   And especially because you are almost finished with the primary math sequence...why not stick it through?   (In full disclosure, i am a math snob, but I love Singapore math!)    I agree with you that math mammoth is also a very strong math program, but sometimes the sheer amount of problems can kill a child's love for math.   

So, let me ask you some questions (about the 10 year old specifically):

Is he currently doing all of the textbook and workbook problems?  (All of the reviews, practices, mental math for HIG, etc.)    (If not, start doing both of those.  That is the bare minimum.)   

Is he currently fixing his math each day and correcting missed problems until 100%?   (That is an easy way to provide more practice, and from my experience a very useful tool in teaching math.)  

If he is currently doing both the textbook and workbook problems (and fixing his math each day), then it might be time to add in one of the extra Singapore books.  The reason they have so many books is so you can completely customize the amount and type of practice your son needs and come up with a perfect math solution.

Here are just a few of the most common "extra" books people order:

• Extra Practice books.  These are going to be more problems just like the workbook.  These are for kids who just need more practice of the same.
• Intensive practice / challenging word problems:   These are for kids who don't find the regular workbook problems challenging enough.   
• Process Skills:  Does he need help with word problems or bar diagrams?
• Mental math books:   self-explanatory
• Tests book:   I know a lot of people who use the tests book for extra practice too.  I feel like they are a bit easier than the regular workbook because many of the problems are multiple choice.  But they are great, quick reviews.

My kids also need a little bit of extra review and practice.  I try my best to constantly keep sniffing out weak areas in their understanding.    I use the cumulative textbook and workbook reviews (at the end of each unit in the standards version of Singapore) to snuff out any weak areas of understanding.    If I notice that they are missing a lot of the same types of problems (or have forgotten how to do it and have to ask for a review)---then I re-teach the concept and start assigning 1-2 of those types of problems per day to practice.

Another easy way to add in extra practice is Prodigy math.  I don't know how you feel about screens, but it is a fun, online math video game that is actually pretty useful in reviewing math concepts.   (It is NOT a good primary teaching tool.)   It is free too.   You can assign topics for targeted review (ex. order of operations, finding the area of different shapes, dividing fractions, etc.) or you can just have them work on grade specific spiral review.  

 

 

 

 

Thank you so much, this is very helpful!

I don't remember either of them doing order of operations in Singapore.  We haven't seen it in 4a or 4b this year.  We only did a little of book 5a, before my DD fell apart last year, so I haven't been through level 5 with them.  MM 6 has it at the beginning but we switched to MFLE after chapter 1.  Other than that, we have only used MM topics for reinforcement--division, fractions, and decimals--so neither of them have been through a full grade level of MM. 

He usually only does the problems in the workbook.  We actually have barely opened the textbook this year.  Most of the time, when I sit down with him, I take out the textbook to teach him but he pretty much knows everything already.  He will say, oh yeah, I know this from hearing you work with *sister*.  He barely needs instruction and get most of the problems correct. Yes, anything that is wrong, we go over it and he fixes it. The reason why I feel like there is not enough is because he often forgets things when we circle back to them in the review chapters. I absolutely LOVE the review section in MLFLE.  Everyday there has been a review with at least one problem from every concept we have worked on and that has been awesome for showing me what my DD has really mastered and what she's still struggling with.  And I really prefer the format of MM or MLFLE with the teaching built into the student text. I have a feeling 5a and 5b won't be so easy for him, but I want the teaching to be in the text in front of him so he can see it after he pushes me away and says he knows it already.

So maybe my answer is to use MM, but not have him do all the problems...?  BTW, we have a subscription to Reflex Math and that has helped both my kids master their multiplication and division facts up to 12. Maybe we could try Prodigy for the summer or next year. 

[TheAttachedMama]

If you like MM, then go ahead and use that!  I think it is a very strong program.  :)     (I am not familiar with MLFLE...that is why I am not mentioning it.  Maybe it is great too!?) 

FYI...Here is the scope and sequence of when things are introduced in Singapore:   https://www.singaporemath.com/v/vspfiles/assets/images/SSUSandSTD2009.pdf

 

[LMD]

My son just completed order of operations in chapter 2 of grade 5 maths. 

[blue plaid]

My son has recently started learning order of operations in 4th grade CLE math.

[YodaGirl]

I know we did order of operations in Math in Focus 5A/5B this year, and I'm almost positive we discussed it last year in 4A/4B.

[kristin0713]

18 hours ago, TheAttachedMama said:

If you like MM, then go ahead and use that!  I think it is a very strong program.  :)     (I am not familiar with MLFLE...that is why I am not mentioning it.  Maybe it is great too!?) 

FYI...Here is the scope and sequence of when things are introduced in Singapore:   https://www.singaporemath.com/v/vspfiles/assets/images/SSUSandSTD2009.pdf

 

A lot of people say MLFLE is not rigorous enough. I have found it to be great for my English minded DD but I really do wish more pre-algebrea was included in the 6th grade level.  I think my DS will thrive in anything.  Now I'm wondering if I should have my DD do MM 6 and 7 through 7th and 8th. I think she could handle it now after a year of MLFLE. Or have her quickly go through Singapore 5 and 6.  Or MM topics to fill in gaps?  UGH!  I don't know. 

 

8 hours ago, YodaGirl said:

I know we did order of operations in Math in Focus 5A/5B this year, and I'm almost positive we discussed it last year in 4A/4B.

Are you doing US or Standards?  We have only used US, I think that might be the difference. So now I'm wondering if I should switch to Standards for my DS for level 5!

[YodaGirl]

1 hour ago, kristin0713 said:

Are you doing US or Standards?  We have only used US, I think that might be the difference. So now I'm wondering if I should switch to Standards for my DS for level 5!

I'm honestly not sure how Math in Focus compared to US or Standards or how the latter two compare to each other. MiF is the Singapore approach, and if I had to guess, I'd say it probably fits in more closely to the US.  From what I've read, I don't think there's a big difference between any of them. 

[YodaGirl]

According to the product description here, Singapore US discusses order of operations in 5A.

 

According to the pdf posted earlier, standards introduced order of operations in 4a and will go over it again in 5a.  If you check it again, you should be able to see the differences between the two easier.