Name of Activity: Formation of Complex Numbers Area: General: Mathematics Specific: Decimal System Materials: 3 work mats, trays with container for unit beads, 1 set of large number cards for 1-9, 10-90, 100-900, and 1000. Aims: Direct: To assist the development of the Mathematical Mind. Indirect: To associate beads with cards, assisting the child in moving towards abstraction. Preparation: All previous decimal system work. Age: Second year child Presentation of the Lesson: Presentation #1: Introduction Gather together a small group of children. Unroll mat #1 on one side of the room and invite 1-2 children to lay out the card layout (only the thousand card is used in this exercise). Place mat #2 in another area of the classroom, sufficiently far to create movement within the exercise. The teacher lays out the bead material equivalent to the number cards on mat #1. Mat #3 is used for combining the materials. Begin the activity by choosing a unit card from mat #1 (6 units). Place the card on the tray. Show the card to the child and say, “This card says 6 units, please go to the mat and fetch 6 units.” Bring child to mat #2 with tray and card to fetch the units. Bring the tray with the units and card to mat #3. Lay the number card on the mat and carefully count the six units, aligning them below the card. Return the units to mat #2 and the card back into the card layout on mat #1. Invite the children to take turns finding a number and fetching the quantities.
Note: Zero is not demonstrated in this exercise. The is on the possible combinations to make a number. Presentation #4: Commutative Law (Order Principle) and pencil are required for this lesson. Lay out the material for the lesson. Think of a number (7). Write the number at the top of the page. Place the 1 blue strip on the board. Now place the 6 red strip on the board to make 7. Now the 6 blue strip on the board and the 1 red strip and say, “We have made a discovery; 1+6=7 and 6+1=7.” Record the equations. Explain that this is called the commutative law. (It is sometimes called the Principle - the order of the numbers added does not matter.) Work of the Teacher: Points of Emphasis: Careful layout of the materials, clear, simple language so that the child understands the concept of addition. Language: Woven into the lesson. Points of Interest: Discovering new work, discovering combinations to make numbers. Work of the Child: Points of Consciousness: Numbers can be added together, the same numbers added in reverse order give the same answer. Control of Error: The answers can be found at the top of the board. Variations: Extensions: Note: There are other versions for laying out the strips. Consistency within the school or classroom may take precedent. The above placement reflects the layout of the number rods (9 on top, 1 on bottom, left edge aligned).
Memorization: Multiplication Charts Multiplication Chart (control chart of tables) A rectangular wooden board divided into one hundred small rectangles. On this board the complete multiplication table is written in sequence, one equation to a rectangle, from 1 x 1 = 1, to 10 x 10 = 100. The multiplicands and multipliers are written in black, the products in red. The child uses this chart as a control chart. Multiplication Chart 2 (control chart with duplicates removed) This chart is similar to multiplication chart 1, but commutative equations have been eliminated. Equations with the same multiplier appear in the same column. Squares of numbers form the diagonal. As with multiplication chart 1, multiplicands and multipliers are in black, products in red. The child also uses this chart as a control when she understands that multiplication is commutative. To check a problem like 6 x 3, she must be able to reverse the order of the addend and find 3 x 6 on the chart. Multiplication Chart 3 (complete finger chart) A square wooden board divided into one hundred small squares. The top row of squares is blue and contains the numerals 1 to 10. The column on the far left is red and contains the numerals 2 to 10 (preceded by 1 in the top left corner). Each remaining square contains the product of a multiplicand (red column) and a multiplier (blue row). The child uses this chart to practice multiplication. Procedure of use: Have a box of prepared multiplication tickets (made on yellow paper, because multiplication is yellow) and have the child choose a ticket (i.e., 3 x 7 = ). The child places her left index finger on the multiplicand (3) in the red column and her right index finger on the multiplier (7) in the blue row. She slides one finger down a column and the other across a row until they meet. The product lies in the square where the column and row intersect (in this example, 21). Multiplication 4 (half finger chart) This chart is similar to multiplication chart 3 except that commutative products (those above and to the right of the ‘squared’ products along the diagonal) have been eliminated. The child uses this chart to practice multiplication.