Arithmetic tables vs. straight equations and finger counting

Hello. The purpose of the tables is manifold. They allow a child to prove a fact before having to memorize it, give her time to notice patterns (this helps establish number sense as well as a sense of wonder), and aids in the transition between working in the concrete, mental work, and pure number.

Please do re-read the Overview of Lessons section that starts on p. 10 for more detail. This section helps parents decide which portions of lessons may be skipped, when to advance, and offers tips for those who have students that have advanced beyond the need for concrete objects.

Some things to think about:
1) We don’t want the building of the tables to overshadow the idea of the math lesson. At the same time, discoveries can be made during the physical act of building them.

2) The child who doesn’t want to use concrete objects can place pencil dots or even numbers in the grids of the math notebook in the same way the addition table is shown. Dots on the gridded dry erase board work well, too.

3) Some children love the creative act of writing. While notation is important in arithmetic, be sure your child isn’t focusing on this creative act rather than the idea of the lesson (learning her math facts).

4) The math facts are to be memorized. If you believe your child has had sufficient time working in the concrete, use only the questions in the lessons to work on these facts. More detail is given in that Overview of Lessons section.

5) Be sure your child isn’t simply guessing at the facts. If she gets an answer wrong while working mentally here, ask her to prove it to you using pennies, beans, or other objects.

6) There are two bookmarks provided. If you need to liven the lessons up, you may move onto a new idea/concept while continuing to solidify the math facts – building speed and accuracy.

As far as seeing the number of objects, we aren’t working on subitizing. Research shows humans will, over time, visually register about five objects without counting. When the addition and subtraction tables are made in this way, it is the design and repetition of building that usually alerts the child to know she is working with 1-10 in descending order.

I hope this helps you decide how to progress with your daughter. You are right, you want to move at her pace and not the book’s.

A note: Since you skipped the majority of Book 1, just be sure your daughter has an understanding of place value, as our money work and notation in Book 1 is where we began laying that foundation. If you didn’t, you might want to cover the Place Value section as well as #100 from Book 1 unless she already has a firm foothold in units, tens, and hundred.

Richele