Homeschool Math Blog

I don't want to leave out one of the best manipulatives there is for first and second graders: a simple "school" abacus that has 10 wires and 10 beads on each wire. I don't mean a Chinese or Japanese abacus with a special counting system. I am talking about using a simple 100-bead abacus for counting, and treating each bead as 1. You don't have to learn any of these sophisticated systems that have been in use with various abacuses. Just consider each bead being 1, period. Then you have 10 tens, or a hundred, in your abacus, and that goes a long way explaining tens and ones or 2-digit place value to first graders. It is best if the abacus has the first five beads colored differently from the next five, in each row, like on the right. Then the child will easily recognize 6, 7, and 8 beads without counting. Also, let's say you choose 6 beads on one wire and 8 on the next one. You can show how the five and five on those two wires makes ten, ...

I've received several questions about abacus usage in Math Mammoth curriculum. Here are some thoughts about it: The only way the abacus is used in my books is so that each bead counts as one. Nothing fancy. It is NOT used like Chinese or Russian abaci where one bead might count as 5, 10, or 100. A 100-bead abacus or school abacus simply contains 10 beads on 10 rods, a total of 100. Each bead simply represents one. The 100-bead abacus lets children both see and touch the numbers. First and foremost, the abacus is used in the place value chapter in 1st grade where children learn about tens and ones (numbers up to 100). We use it to show how 45 is made up of 4 tens and 5 ones, for example. Secondly, you can use the abacus with addition and subtraction problems in 1st and 2nd grade: Show the child additions and subtractions with whole tens. For example, to solve 50 + 20, first make 50 on the abacus. Then add 20 more. Add a two-digit number and a single-digit numbe...

Let's be reminded first of all that there are two basic "interpretations" of division: 1) Sharing division. In it, you think that 16 / 2 means "If there are 16 beads divided between 2 people, how many does each one get? 2) Quotative division. In it, you think how many groups of the same size you can form. Or, "how many times does the divisor fit into the dividend?" For example, 16 / 2 is interpreted as: "If you have 16 beads, how many groups of 2 beads can you make?" Sharing division is easy to understand as a concept, but it's hard to do without the knowledge of multiplication tables. Just imagine, if a child who doesn't know their times tables is trying to find the answer to the question, "If there are 56 strawberries and 8 people, how many will each one get?" It'll take some guesswork, trying and checking. But quotative division is easy for children to do with the help of manipulatives (or by drawing pictures). Just make...

I've been doing math lessons with my 3-year old using the 100-bead abacus . Usually we do a few problems where she tells me a two-digit number to make, and I tell her a number to make, back and forth. Today she asked me to make 51, and I asked her to make 68. These went smoothly since she's getting pretty good at this now. Then we did a few "more than" problems. I said, "Let's say your sister has 5 cookies and you have one more than her . How many do you have?" This is a new concept to her, so we need to do it slowly and carefully with the abacus: first make her sister's cookies, then let her have the same amount, then give her one more. Then we did a few subtraction problems such as 7 − 4. She moved 7 beads, then "took away", or moved the other way, 4 beads. How many were left? 3 beads. I also showed her the subtraction 50 − 10 = 40. She started working on her own problem, "Let's do 9 − ..." and while she was thinki...