Place Value, Grade 1 teaches students two-digit numbers, or place value with tens and ones.
The initial lessons that introduce tens and ones use a 100-bead abacus extensively. A 100-bead abacus or school abacus simply contains 10 beads on 10 rods, a total of 100. It is not a special abacus as used by the Chinese or the Russians. In the school abacus, each bead simply represents
one. The 100-bead abacus lets children both "see" the numbers and use their touch while making them.
If you cannot obtain a real abacus, you can probably use this virtual abacus:
The abacus is not the only model used in the book. We also use a visual model of blocks where ten of them "snap" together to form a stick-like stack. If you already have so-called "base-ten blocks", you can use them along with the visual exercises, if you want to.
The book also uses the 100-chart and number lines. Number lines help to visualize how the numbers continue indefinitely and also connect with the concept of measuring. The 100-chart helps the child to be familiar with the numbers below 100 and find patterns in the number system.
When children count, they basically just learn numbers as some kind of continuum that goes on and on. With simple counting, your student might not catch on to the inherent structure and how it goes into groups of tens and hundreds and thousands.
For children to understand place value, they first need to know their numbers up to 10, do simple addition with small numbers, and understand about counting in groups. Our whole number system is based on the idea that if you have lots and lots of objects, the efficient way is to count them in groups of tens, hundreds, and thousands - not individually.
The crucial point in understanding the concept of place value is that a certain position represents a certain-size group. Then the digit in that position tells you how many groups of that size there are. For example, in the number 2,381, the 8 represents eight tens, and not just "8". The number 3 represents three hundreds, and not just "3". The placing or positioning of the digit tells us what size the group is, and the digit itself tells how many groups of 8 there are. In this book, children learn this idea for just two digits.
The two lessons in the end, about tally marks and graphs, are included as real-life applications of two-digit numbers. The last lesson about regrouping is optional.
I wish you success in teaching math!
Maria Miller, the author