A Comparison of 1st Grade
I was able to take a long and (relatively) uninterrupted look at Singapore Math in Focus Grade 1. I had the Teachers Guides, Textbook, and Workbook. I own the Singapore Math Standards edition with HIGs of first grade and Math Mammoth Light Blue 1A and 1B so I compared the programs. Here are my observations.
- Scope and Sequence
MIF and Singapore Primary Standards cover basically the same material. They both start out with counting to 10 and cover addition and subtraction facts to 10, shapes, ordinal numbers and position. They move onto numbers to 20 and addition and subtraction facts to 20. The later half of the year they cover graphs, numbers to 100, and addition and subtraction facts to 100.
Math Mammoth has a more narrow focus and starts at a more advanced place. It covers addition and subtraction facts within 10 in the first book. In 1B it covers place value, skip counting, clocks, measuring, money, and +/- facts within 100.
Some differences are that MIF covers mental math strategies explicitly in a separate chapter while these techniques are folded into the addition and subtraction chapters in Primary Math Standards Edition. Primary math includes capacity while MIF does not. Also, Primary Math covers halves and fourths and I didn’t find that in MIF.
They both cover the fundamental concepts of multiplication as repeated addition and division as sharing equally. However, Primary Math actually uses the word multiplication whereas MIF does not. It emphasizes 5 fours =20. It would say 2+2+2= 3 twos = 3 groups of 2 = 6. Also in MIF they compare numbers with words but don’t use >, or < signs that I could find. There is no multiplication or division in Math Mammoth 1 that I could find.
Singapore Primary Math doesn’t include as much terminology as you would see in Math Mammoth or MIF. In Math Mammoth they use terms like addend, minuend and subtrahend in the text. In MIF these terms as well as the properties (like commutative or identity properties) are present in the teachers text but not in the student text or workbook.
One interesting thing I notes was that Primary Math HIGs say renaming, MIF says regrouping, and MM uses terms like making 10s, within 10s, or make 10s.
I grew up with borrowing and carrying so I have no idea what I am going to use. I used regrouping with my older ds and that worked well so I will probably stick with that.
I picked the topic of subtraction with 10s to compare how each program presents the lesson.
For MIF the teacher guide has the fundamentals. They start in the TG with emphasizing how subtraction is related to the part-whole concept taught in addition. It goes on the list the strategies they use to teach subtraction – taking away, counting back, counting on, and using number bonds. The chapter planning guide breaks down the chapter into 45 minute instructional blocks(days) and tells you what resources to use each day. Each lesson starts with a 5 minute warm up and then moves to guided practice. Frequent use of manipulatives and/or pictoral representations is provided. They focus on manipulatives that directly assists with the lesson like the 10-frame, linking cubes, and place value charts. One or two games are included in the student text but they would be more fun with more than one kid participating. The lessons proceed logically and clearly and no leaps are made or expected of the student. The concept is taught, reinforced in the text, and finally workbook exercises that coincide directly with what was taught are assigned. Answers are provided to everything in the TG. Problems with missing subtrahends and minuends are provided and a challenging problem or two are presented in the text and workbook for every lesson. The chapter ends with a two page summary of what you have learned explicitly written out to the student in the text and very helpful.
In the Singapore US Standards edition the text isn’t as helpful if you are having problems. There is little explicitly stated and the pictures are large and cartoon like.
The HIG emphasizes taking away and part to whole but other strategies aren’t explored explicitly. Fact families are emphasized as the most important concept. The HIG explicitly states to commit facts to memory and this isn’t found in MIF. The teaching in the HIG is fairly unconnected to the text. That being said, I think Singapore is a strong program and for a math intuitive mom and/or kids this program would be easy to accelerate.
In Math Mammoth 1A subtraction is presented as taking away with pictoral representations emphasizing that. Counting back is presented in the context of a number line an explicit work with jumping back on the number line is illustrated multiple times with many opportunities for the student to practice this. MM works with number before for example ____,55 and ___,___,55. Counting back is taught and missing subtrahend and minuend problems are presented. Fact families are taught and comparing with > and < are explicitly asked of the student. For example 3-2 ____ 5 or compare 8-5___2+1.
Math Mammoth also explicitly teaches the student that you can’t subtract a bigger number from a smaller number without going into debt.
Of the three MIF seems the clearest with the best presentation. It is visually very clean and the TG is excellent. It isn’t as challenging as Math Mammoth and some of the problems seen in the Singapore Editions of IP and CWP are a good deal more difficult to do. Math Mammoth is easy to implement and covers things well but the presentation is more appropriate to a more mature student. The text and pictures are small and there are a lot of problems on the page, which appears very overwhelming. MIF is more thorough and explicit in its’ instruction and it would be easy to teach from just the text and workbook with a mathy dc in first grade.
I am going to look over the regrouping lessons when I get a chance so I might have more comparisons to post later.