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Category: Math

For her fourth grade math class, Satori’s homework involved making a math puzzle that she would put on the wall for the other students to solve. She had some ideas, but wanted my help “making it creative”. Last week I helped her write a poem to put on the wall in a creative way, so I guess she figured I’d make this project look cool too. Although I really shouldn’t help so much with her homework in the future, I couldn’t resist.

We have her a mystery five digit number. In between the purple lines are clues to fill in all the digits. The creative touches to our number puzzle include magnetic numbers, we included just the five digits of her final number, but the person doing the puzzle would have to snap them in place. We used real coins as well as a real foam polygon shape. The picture is Satori and her teacher I took on the first day.

Number Puzzle

 Who can guess the Number Puzzle?!

This is Part II of a 3-part series demonstrating how we use Singapore Math, Part I was finished earlier today. This post will show how we use the extra books – Extra Practice, Intensive Practice, and Challenging Word Problems. All the books are smaller than average size, approximately 7.5 x10.5 inches, just high enough to peek out of a Desk Apprentice. In addition to the stack below, we also keep 1A Intensive Practice workbook around. A total of eight books for one program seems a bit too much, but we typically work with 3 or less books at a time. I guess I think of it as a lot of content, but in smaller, manageable books that we can take out as needed.

HIG Scheme of Work

First of all, while it isn’t that hard to figure out which pages to schedule to go along with your current lessons, the Singapore HIG (spiral-binded book above) does include the Extra Practice and Tests page suggestions to go along with your lessons. (Click image below to see larger size.) As you can see, it also schedules out the Textbook, Workbook and the Guide itself, broken down into suggested Weeks (18 weeks for 1A, 17 for 1B, total of 35 weeks). We do not use Singapore Tests yet, but I may end up purchasing them for Singapore Level 2.

We’ve finally decided how we’re going to incorporate the three extra books. Our way is just one way, your family may decide to do it differently, or may only use one (or none) of these extras. If we finish our main lesson early, we’ll pull out some of these books. I have scheduled Singapore Math to be 30 minutes. Yesterday we finished our lesson in 5 minutes, so we did a lot of the extras. Today we finished in 15 minutes, so half our time was spent in the extra books. We use this extra time as review and/or added challenge.

Extra Practice Book

We use the Extra Practice as a review, staggered slightly behind our actual lessons, working about 2-3 units behind our current work. The content is similar to what you’ll find in the Workbook. Answers are in the back of the book. This is a very optional book, I can see many families not purchasing it. If you do, you may prefer to use it alongside your current lessons instead of a review as we do. Or you may wish to only use certain pages that your child needs work in.

Extra Practice books are offered per year, so you only need one for the entire Singapore year, rather than buying both 1A and 1B. Another nice thing is that it is offered for both Standards edition (which we use) and U.S. Edition. The worksheets are perforated, so you can take out just what you need. It is a big book, over 200 pages, so I’m thinking I might want to ProClick it and bind it myself so the pages lie flat. They are $13.30 on and $12.50 on Rainbow Resource. “They can be used to review for tests or to review concepts taught a while ago, or as a summer math book to keep concepts fresh.  Although each unit contains “friendly notes” reviewing the topics of that unit, the notes are strictly for review, and the concepts are not developed as thoroughly as in the textbooks, so it is not recommended as a replacement for the textbook.”

As we use Extra Practice as a review, it’s an easy refresher for us and I can catch what may need to be worked on before we continue further in the program. Below are the examples.

There are four total Extra Practice pages for Chapter 6: Subtraction Within 100. There are five lessons covered in Chapter 6. Other chapters may include several note pages for review before hitting the problems. Unit 14 on Multiplication has 2 pages of notes and 6 pages of practice.

Intensive Practice

We usually try to fit in a few pages of Intensive Practice, but we’re staggering this a whole half level behind what we’re studying. Unfortunately for us, currently they are only offered in U.S. Edition, although we haven’t noticed any issues with that yet. You do have to purchase both A and B for the year, for a total of $18.60 from or $16.30 from Rainbow Resource. The pages are not perforated. Total pages are 152 for Intensive Practice 1B, with answers in the back.

Satori enjoys this book but there are a few here and there that she needs my help to figure out. She’s not a math genius, but if you have an extremely mathy child, I can see them loving to independently figure out these puzzles. In addition to typical math problems, you’ll also find a variety of interesting and diverse problems and puzzles.

The books include a “Topical Review” that exposes students to a variety of questions and then plenty of “Take the Challenge” that develop more mathematical reasoning and higher-order thinking skills.  The book concludes with a “Mid Year or End of Year Review”. The very end of the books includes “More Challenging Problems” to further challenge the child to think critically and creatively.

As you see, it includes word problems, but if you are really craving word problems, take a look at the book below.

Challenging Word Problems

I’ve heard such great things about this book, I even purchased this book a entire year before we even started using Singapore Math. There is one book per level, and it works with either Standards or U.S. Edition. It is $10 on or $8.75 on RR. My book (2010) matches exactly to the book on their website, but has a different cover. I hear there are earlier editions, and I am not sure how they differ from this. Book 1 is 218 pages with answers in the back. The pages are not perforated.

The book includes 17 chapters, plus a chapter on Miscellaneous Problems and a chapter with the Answers. The chapters begin with a few Worked Examples such as below.

It then gets into Practice Questions, at a level similar to the normal text/workbooks.

Then you’ll get into the Challenging Problems, which also include a few Worked Examples. Here is an example problem from the beginning of the book:

“A class had 3 fewer boys than girls. After 2 girls left the class, only 5 girls remained. How many boys were there?”

Here’s an example from the middle of the book, in the Multiplication section:

“An ant has 6 legs. A spider has 8 legs. A beetle has 6 legs. There are 2 ants, 2 spiders, and 1 beetle. What is the total number of legs”

Here’s a page toward the end.

Not Using Singapore Math?

Many families still pick up a copy of Challenging Word Problems and maybe even Intensive Practice. In fact, that was our initial plan before we ended up using Singapore as our main math. Hopefully I’ve given enough information for you to see if these books might be suitable for your current math program.

There have been lots of questions about Singapore Math so hopefully a short series of blog posts will help answer some of those questions. Since I took a lot of screenshots, I’ll break it up into 3 parts. Part I (this post) will cover a day in Singapore Math 1B, using the Home Instructor’s Guide, Text, and Workbook – the core lesson only. Part II will cover the extra materials – Extra Practice, Intensive Practice, and Challenging Word Problems and how our family ended up incorporating them into our lessons. Part III will cover more about why we like the HIG book and a few differences between the Standards and U.S. Editions.

Singapore Math Part I

Singapore Primary Math Level (grade) 1 covers 19 Units. We are currently on Unit 18: Numbers to 100 | Chapter 6: Subtraction Within 100 | Lesson 2 (Subtract ones with renaming). If you use the Home Instructor’s Guide (referred to as HIG from now on), pages 98-99 will introduce Chapter 6 – informing you of the content to be covered, basic strategies used, what the child should already know, and Materials used (Base-10 blocks, Multilink cubes, and playing cards). By this time, Satori should instantly know her subtraction facts through 10, and also either know instantly (or be able to figure out quickly) her facts through 20 (such as 17-8).

singapore math 1B HIG

Before we start our lesson, I pull out our table-top whiteboard and a small bin with Place-Value blocks. We use these pretty much everyday. MUS blocks, base-10 blocks, or cuisenaire rods can be used, whatever you have and feel comfortable with.

Page 101 (on the right side) covers the actual day’s lesson: (2) Subtract ones with renaming. You can click on the image to see it larger. This lesson is mostly a review, but using numbers over 40 up to 100.

The lesson goes over a few problems, illustrating how to approach the answer using either base-10 material (our place value rods/cubes) or using number bonds. I start the lesson using our white board and blocks and put up a problem on the board. Satori usually just answers it all in her head, but to reinforce/check her solution, it just takes a moment to go through the two methods to find the solution. Here we break off one ten from the 70, now thinking of it as 13-5. We take away 5 from one of 10-rods, leaving 5 ones and the original 3 ones. That’s a total of 8 ones, plus the remaining 6 tens – which is 68. I am probably making this sound more confusing than it really is, but once you understand it, it makes it so much easier to do in your head, as Satori is able to do effortlessly now.

Then we tackle it another way using number bonds.

In the HIG, there is a shaded area which shows how to coordinate the Textbook and Workbook with the current lesson. I find this super handy.

Sometimes the HIG offers extra sections to reinforce or challenge the child further. This lesson did not.

After we do our lesson using manipulatives and the whiteboard with just the HIG, we move on to the Textbook. This is the only book that is colorful. It shows the basic idea, but never goes beyond the basic idea. I actually find this the least helpful book in the program, even though you’d think it would be the most important. We usually quickly review what we just learned in the textbook, and it is typically 1-3 pages. You can see illustrations of children thinking in their head how to approach the problem.

After that, it’s on to the Workbook to try it out on her own! For this lesson, we are supposed to do Exercise 21 on pages 169-170. Workbook pages are usually 2-4 pages.

After that, we’re done with the lesson! Yesterday our lesson just took 5 minutes, today it took 15 minutes. I schedule 30 minutes a day for Singapore Math. Sometimes I add on a second lesson, but that can get too much, so I’m trying to stop it there. We will add the extra workbooks, which I’ll cover in Part III of Singapore Math.

Just in case you haven’t heard, Math Mammoth is on sale now at the Homeschool Buyers Co-op for half off! I blogged about this last month, but the actual sale wasn’t on until this month of March. It hit the 50% off mark sometime last week and the offer is good through this Thursday (3/31). This is a worksheet-based program that teaches math straight to the student. I have not found a better combination of affordable, easy, and effective math for the elementary years.

We’ve been using Math Mammoth Light Blue 1A/1B as a supplement, but there are tons of families happily using it for their main math program. We’re now ready for MM grade 2, so we’ll be getting the Light Blue Series Package PDF download. This includes the complete elementary mathematics curriculum for grades 1-6 for just $64.00 (plus $1.95 service fee). That’s $11 per year of very effective math program! It includes the Soft-Pak bonus software where you can generate even more worksheets.

There are other packages to choose from, including the Blue Series, Download or CD options, and more. Head on over and check it out!

Shortly after starting Singapore Math just under two weeks ago, I realized we had better go back to 1A to get the basics of subtraction and various thinking strategies that were introduced in the first half. For subtraction, 1A introduces two methods of subtracting: taking away and part-whole. In 1B, we learned the comparison method of subtracting. We had not covered subtraction with RightStart, and I really wanted to give Satori a solid foundation starting Singapore. Even though I knew I could teach Satori the taking away and part-whole methods, we were still missing some of the mental math strategy basics that Singapore is so great at. So I ordered 1A Home Instructor’s Guide, Textbook, and Extra Practice (which covers both 1A/1B).

Satori got a 90% on her 1A placement test, but there were just some mental math strategies I wanted to go over. I think it will take us one week (the whole 7 days) to cover 1A at an accelerated pace. As of today, we’re already well over halfway through the book. Satori has been very eager to do math, and both of us are enjoying our Singapore math time, so we have been spending an entire hour per day on math this week! We’ve never spent an hour at math. Here’s what we’ve learned this week.

  • Make 10: Split one of the numbers up in order to make a ten with the other number
  • Subtract From the ten: To subtract ones from a ten and ones where there are not enough ones, subtract the ones from the tens and add that result to the ones

To introduce the topic, we did a lot of concrete, hands-on work to demonstrate how it works. We used 10-frames, linking cubes, and here we pulled out our MUS blocks. We haven’t played with our MUS blocks in almost two years! Satori totally forgot she ever used them.

Here we are solving for 14-8. We have a ten rod (1-ten) and 4 singles (4-ones) to represent 14.

Since the ones we are subtracting (8) is greater than the ones being subtracted (4), we will be using the following strategy.  In the pink marker, you see we broke the 14 up into 10 and 4 as a number bond. We then subtract the 8 from the ten, which is two, so we substitute 2 blocks for our previous 10.

Now we’re left with 2 blocks and 4 blocks, giving us a total of 6. (orange marker)

We’ve been working on such problems, including 20 minus 4, where we break the 20 up into two 10’s and subtract the 4 from one of them, and then adding that number to the other 10, to make it easier to think of these larger problems in our head. We’re also using the 1A Mental Math drills, some of which are even more complicated than 1B. We’re also working in the Singapore Extra Practice book, Satori just loves her new math workbooks. She doesn’t doodle like she used to in her Math Mammoth worksheets. She actually asks to work in her Singapore books. By the weekend, I think she’ll have finished the entire Singapore Extra Practice book for the 1A problems.

Here Satori tells us what she’s learned yesterday.

Next week we’ll have finished Singapore 1A, and then we can resume at a normal pace of 1B. Who knows, maybe we’ll finish that quickly too? She’s really surprising me with her new fascination with math. She’s already planning Daddy’s lessons this weekend on showing him how to subtract. 🙂 Monday we were at the car shop for an hour, and all she wanted to do was Singapore-style math problems. She begged to go over multiplication (she has a strange preoccupation with learning her times tables already). Instead of writing stories in her journals, she’s including math problems as well. Maybe this kid will turn out to be more “mathy” than I thought she was…

I honestly think this all started once I started watching my Khan Academy videos to re-educate myself. I’m in Algebra 1 now, and she listens to it now and then. I guess it’s made me a great role model, having a mother so excited about math. Then we get a shiny new math curriculum that is fun and challenging that gives us the ability to go through it at an accelerated pace. It’s all about MATH in the Satori household this week!

As I mentioned a few days ago, we are switching our primary math program to Singapore Math 1B. We very happily used RightStart, but mom was ready for a change. Before we decided on their 1B level, I gave Satori their placement tests. She scored 90% on 1A (first part of Grade 1). We didn’t even attempt 1B (second part of Grade 1), because there was so much we haven’t covered yet halfway through RightStart B (subtraction, multiplication…) So last week I ordered 1B and we started Sunday.

Singapore Primary Mathematics 1B

At first I found it confusing what exactly to order. There’s a gazillion different books, supplementary materials, manipulatives, etc… For Primary Mathematics (grade 1-6), you first have to choose between US and Standards version. Since the program is from Singapore, you might think you’d need US, but both versions use customary U.S. measurement and metric measurements. I suggest the Standards edition (2008), it is the same as the U.S. edition (2003), but with a different sequence of topics, all textbooks in color, additions on several topics, additional sections on mental math, additional problems. They even say on their website that Standards is a little more challenging than U.S., due to the additional topics. I’m all for a more rigorous math program!

Thanks to several folks on the WTM forums, I decided to get the Home Instructor’s Manual (HIG). I almost didn’t, but am so relieved I did. You do not need the Teacher’s Guide (meant for classroom instruction). Some families use just the Singapore Textbook and Workbook (some just the text!), but they miss the crucial aspects of what makes Singapore Math “Singapore”. Unless you are very familiar with Asian math and are comfortable coming up with examples on your own, the HIG is necessary. It not only holds my hand telling me how to teach the lesson, but also breaks the lessons up into easy chunks and tells me what Textbook and Workbook pages to do along with the lesson (complete with answers). The HIG provides the concrete introduction, provides background notes, and emphasizes where concepts are taught differently than most US texts. The HIG gives suggestions and mental math practice on how to memorize math facts.

Singapore Math consists of three parts. Primary Mathematics follows a concrete to pictorial to abstract sequence of instruction.

  1. Concrete introduction to the concept – You, as the teacher teach the lesson using the HIG as a guide and different manipulatives
  2. Followed by pictorial representation – textbook supplies colorful pictures and abstract aspects
  3. Independent practice and review – with the workbook(s)

I have bumped up our usual 20 minute math session to 30 minutes now. So far, we’ve done Singapore Math 4 days and it’s going great. I start by glancing at the HIG to see how to introduce the day’s topic.  After a short review of 1A, right away we were learning subtraction for the first time, so I used math counters and a whiteboard. This is our second subtraction lesson and it had Satori pair up the counters and write the subtraction equation.

We did this a few more times and then moved to the textbook. Satori is excited by the cute, colorful pictures. We haven’t had this in any math program we’ve used so far. Here, we’re using transparent counters to help with subtraction. She loves them.

Finally, we take out the workbook. It isn’t the same exercises over and over, so I doubt Satori will get bored. Usually, each lesson will have her do 2-4 pages, which may have just a couple exercises on each page.

This week the HIG said we should have all our simple addition/subtraction facts memorized by Unit 3. (I think this is Unit 13 in 1B.) In the back of the HIG, they have Mental Math exercises. Satori already has her addition facts memorized, so we’ll be working on subtraction facts. Basically, we go through one column a day, and she orally tells me the answer. We do this quite quickly.

Some children may need more practice than just what the above offers, so there are extra books. In the HIG’s Scheme or Work pages in the beginning of the book, they provide page numbers for Extra Practice Standards Edition book 1 (covers both 1A/1B) and Tests (1A and 1B are separate). I don’t intend to use these extras, but we’ll see as we go. Instead, we’ll use the more advanced supplements…

One of the great things about the Singapore program is their extra books on Challenging Word Problems (CWP) and Intensive Practice (IP). Even before I decided upon using Singapore, I had purchased CWP based on so many people loving them. Even Math Mammoth encourages using Singapore Math’s CWP book. The Intensive Practice books are great and some people use them as a review. I purchased both 1A and 1B (right now they only come in U.S. Edition, but Standards will be coming), and we plan to use these if we finish our main math lesson early and we’ll use the remaining time doing pages from Intensive Practice and CWP. Today we did 5 pages out of IP 1A. The exercises were extremely engaging and several are fun puzzles.

Math is fun!

So this was just our first week with Singapore, but here are our thoughts. Mom loves them because they’re actually fun and easy to teach, yet I know they’re extremely effective at teaching my daughter great math. It is a program I can teach every single day without getting frustrated or bored. Satori was excited the first day to start her “colorful” math. The second day she actually started the day bringing me all the Singapore books and begged to do math. The third day she said “I love this book!” after working from her Intensive Practice book. The fourth day (today) I asked her if she liked her new Singapore Math and she yelled “I LOVE IT!”

She’s excited to learn several things that Singapore is teaching her right away. She can’t wait to get into multiplication. She noticed multiplication as I was watching my Khan Academy videos so she knows kinda what it’s about already. She can’t wait to get into graphing, which she noticed is covered in the next lesson.

I am happy that it looks like we’ve found a math program to take us all the way through high school. I’m glad it’s an Asian math program, and will continue with the great foundation RightStart gave us with doing mental math. All the different books (if you buy everything for one year) might be a lot to handle, but I think it will be okay. One thing I realized after looking through all of 1B carefully, is that we missed the extremely important “regrouping” concepts in 1A. Regrouping is thinking of an addition problem like 8+7 in terms of giving 2 to the 8 to make it a 10, and then ending up with 10+5 instead. For that reason, I did end up purchasing the 1A HIG and textbook so we can learn those lessons.

We will be switching to Singapore Primary Mathematics 1B this week and in planning the lessons, I started organizing our math manipulatives. Then I went on to clean and organize the whole Learning Loft. This includes our Math Manipulative Closet which I don’t think I ever mentioned it before. I’ve gotten a few emails asking where I store/organize everything, so hopefully this will help others who are looking for ideas.

The narrow closet is just off our loft area. It works perfectly to hide all our manipulatives. Since I’ve entertained using quite a handful of math programs, I ended up with lots of math manipulatives, starting with our MUS blocks. I admit that I’m a helpless addict to this kind of stuff. In this closet, I try to keep the supplies Satori might want to take out to play with on her own on the lower shelves that she can reach. She just loves playing with her math manipulatives.

The lowest shelf holds our MUS blocks, ManipuLite Pattern Blocks and Color Cubes, Geometric foam solids, Math Links, Linking Cubes, 1″ wooden blocks, Cuisenaire Rods, Math dice games, Place Value Kit, 1″ plastic square tiles and a few other various counting items like shiny rocks and beads. (To see any photo larger, just click on it.)

Next shelf holds more manipulatives and some logic games. We’ve got Tangoes Tanagrams, Large Rubber Vehicle Counters, smaller Kid and Wild Animal counters, transparent disc counters, plastic coins, tanagram shapes, blue and multicolor centimeter cubes, Unifix cubes and disc counters. We’ve got a few logic games up here, but we keep some in our game closet downstairs. Here you’ll find Mighty Mind, Logic Links, Block Buddies, Rory’s Story Cubes, Hundred Mat, and magnetic fractions. You can see I went wild with the labeler!

On the floor rest our math balances and scales, time clock and long pointy thingies like yard sticks, big thermometer, and a pointer.

Top shelf holds science and social studies stuff: Microscope and slides, Animal flashcards, timelines, Magnet kit, Little Passports suitcase… The shelf below it holds workbooks we’ll be using very soon. I’m entertaining moving ALL our math and logic games and storing them on the second shelf, but I’m not sure there would be enough room.

Things we use on a daily basis are taken out of the closet and stored on the bottom shelf of a small bookcase we have in the middle of our Learning Loft. The red tote holds our math manipulatives and math cards so we can easily take it all out while we do math. The abacuses we use all the time are also within convenient reach. I’ve decided to store our Singapore math books down here too as they are shorter than our normal binders and workbooks that we store elsewhere. We put a children’s dictionary here too, Satori uses it often. A new manipulative we’ll be using soon are the Unifix and linking cubes.