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- A felt mat
- A plentiful assortment of bead bars.

Presentation 1

Presentation

1. Have the child bring the material to the table and unroll the mat
2. Take out the seven bar and place it on the left side of the mat horizontally.
3. Have the child count how many beads are on the bar by using the card counter.
4. Have the child place the answer (7) in a seven-bar vertically below the horizontal seven.
5. Ask, “How many sevens did he have?”
6. The child should answer: once.
7. Say, “7 times 1 is 7.”
8. Tell the child to take, “a seven-bar two times”.
9. Have him place two seven-bars horizontally to the right of the first seven-bar.
10. Using the card counter, count the beads. When he gets to ten, have him place a golden ten-bar vertically at the bottom of the mat and then count the rest of the beads (4). Place the corresponding colored bead bar to the right of the golden bead bar.
11. Say, “7 times 2 is 14.”
12. Repeat in this way up to 7 times 9.

See below for an example of up to 7 times 4:              Exercice
The child, over times, works as shown in the presentation with

Presentation 2

1. Have the child bring the material to the table and unroll themat. Place the box of beads above the mat.
2. Tell the child, “Today, we are going to do some special multiplication.”
3. Write 2 x 10 = on the piece of paper.
4. Ask the child to read the equation and to then build the two-bar ten times.
5. Have the child count the total number of beads by using the card counter. Each time the child reaches ten, have him place a ten-bar vertically under the lines of two-bars. Have him write the answer on the piece of paper next to the equation.
6. Write 6 x 10 =
7. Have the child build the six-bar ten times.
8. Have the child count as he did for the two bars.
9. Say to the child, “So 6 taken 10 times is 60. And 2 taken 10 times is 20.
10. Write 4 x 10 =
11. Have the child build as above and count as above. See below:

12.                                 13. If the child doesn’t see the pattern, highlight for the child that what ever the bar taken 10 times, will be that amount of tens. So if you have 9 taken 10 time, you get 9 tens, or 90.
14. Have the child write a few of the equations and write the answer without building it with the beads.

Presentation 3

1. Have the child bring the material to the table and unroll the mat. Place the box of beads above the mat.
2. “Let’s see if we can make 12.” Make 12 at the top of the mat.
3. Start with the two-bars by placing them below one another and counting as you place the bars until you reach twelve.
4. Comment that 2 times 6 is 12.
5. Do the same using the three-bars and four-bars.
6. Try to build 12 with the five-bars but when it doesn’t work, replace them in the box of bead-bars.
7. Build 12 using two six-bars. Then try with the other bars but replace them in the box when you see it will not work.               8. Bring the 6 two-bars down and the 2 six-bars next to the ten-bar and two-bar of 12.
9. Show the child that there are 6 two-bars to make 12 and 2 six-bars to make 12. Discuss how these are the same thing.
10. Repeat for the 4 three-bars and the 3 four-bars.

Purpose

Direct
- One of the Exercises connected with the memorization of
multiplication tables. This geometrical form of multiplication is very useful:

• In showing up that the multiplier is never a solid body as in the multiplicand – that it is only indicative of ‘how many times’ a given quantity is to be repeated.
• That a succession of lines creates a surface (that is why it is called geometrical).

- Preparation for division by helping the child to visualize the divisibility of numbers.
- The elasticity of these Exercises and the opportunity for setting his own sum pushes him towards discovery.

Indirect
- Their geometrical formation giving him an indirect preparation
for Exercises which follow later in connection with preparation for geometry and algebra.

Control of Error
The child

Age
5 1/2 - 6 years

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