Early Numeracy and Arithmetic - Math Material

"The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree."

Aristotle

Outline first five activities and explain the reason for the sequence in which they are presented.

1 - Large Number Rods (fixed quantity)

2 - Sandpaper Numerals (fixed symbols)

3 - Large Number Rods and Cards (fixed quantity and loose symbols)

4 - Spindle Box (fixed symbols and loose quantity)

5 - Cards and Counters (loose quantity and loose symbols)

are the five activities in the sequence of their presentations.

The sequence of these introductory activities for numbers 1 to 10 starts with, 

1- oral counting of numerals 1 to 10 and visualizing the length on large number rods, 

2- recognizing the numerals 1 to 10 on sandpaper numerals

3- corresponding loose symbols to fixed quantity on large number rods and cards

4- corresponding loose quantity to fixed symbols on spindle box

5- corresponding loose quantity to loose symbols on cards and counters

Large number rods activity is an introduction of numbers 1 to 10 in form of fixed quantities.  It helps in visualizing the variation in length and colour coded segments of equal length.  The child develops a sense of order of numbers from shortest to largest or from largest to shortest.  While counting the segments orally, he/she understands that one is the smallest number, 2 is greater than 1 and 10 is the largest number.  The control of error is there to put rods in sequence to build a stair.  

Sandpaper numerals are the introduction of oral numbers 1 to 10 in their particular formation.  Through large number rods, the child has already developed the sense that the numerals will begin with 1 as first and the smallest number and ten will come in the last.  Through this activity, the child learns the recognition of numerals and is prepared for writing by tracing them with the index and middle finger.

After the first two activities, the child is able to recognize the numerals and understands their sequence from smaller to greater.  

The third activity, Larges number rods and cards, reinforces the concepts of numerals by their correspondence to the correct number rod, randomly and then in sequence.  In large number rods with cards, the child places the cards (symbol) to the rods (fixed quantity).

Spindle box consists of a wooden box with numerals 0 to 9 written on the back (fixed symbols) and 45 spindles (loose quantity).  The child compares the loose quantity which is spindle with fixed symbols which is numerals.  In addition to pairing numerals with spindles, it introduces the concept of zero for nothing or empty.

Cards and Counters in sequence to learning numerals, reinforces the child’s ability to recognize, count and compare the loose quantities with loose numerals.  This activity can be an introduction to the concepts of ‘more and less’ and ‘even and odd’.

Outline the sequence of exercises and pre-requisite in golden bead material.

1 - Teaching the names of the quantities

      Golden beads for one unit, one ten, one hundred and one thousand

      Three-period lesson

2 - counting through quantities

      Golden beads for 9 units, 9 tens, 9 hundreds and 1 thousand

      Starting from units, counting down to 9 and adding one more to start the column of 10.

      Starting with tens, counting down to 9 tens (90) and adding one more ten to start the 

      coloumn of 100.

      Starting with hundreds, counting down to 9 hundreds and adding one more hundred to start 

      the column of 1000.

3 - Bead practice

      The bank of golden beads

4 - Naming the symbols - Large Number Cards 

      A set of cards showing 1 unit, 1 ten, 1 hundred and 1 thousand

      Three period lesson

      

5 - Counting through with symbols

      Set of Large Number Cards - all quantities 1 to 9 - new column starts at 10

6 - Practice with the symbols

      Set of Large Number Cards - overlapping cards to make large figures

      Reinforcement of Ex # 4 and 5

7 - Combining quantity (beads) with symbols (LNC)

      Set of Large Number Cards and quantity of Golden Beads (the bank)

      Collect beads and then corresponding LNC

      Reinforcement of Ex # 3 and 6

8 - Combining quantity and symbols in sequence - Bird's Eye View

      Golden Beads - all quantities in 45 pieces and set of LNC

      Stacking up number cards in hierarchical order and then the corresponding beads

      Reinforcement of Ex # 2 and 5

9 - Changing unlimited quantities and carrying over

      A bead bank, set of Large Number Cards

      Introducing the idea of carrying over when beads are add up to 10 or higher number.

Pre-requisite for golden bead material, 

- The child can count and can recognize numbers 1 to 10.

- He/she has the ability of corresponding between symbols and quantities.

List down the exercises for early addition and early subtraction.

Early Addition Activities

1 - Snake Game (Initial and Complex)

     2 sets of short bead stairs, box of 10 x 10 golden beads, bead marker

     Reinforcement of the concept of conservation and reversibility

     Introducing adding numbers to 10

     

     5 sets of short bead stai, box of 25 x 10 golden beads, 1 black and 1 white stair, marker

     Introducing carrying a number over

2 - Addition with Small Number Rods

     2 sets of small number rods

     Practicing addition

     

3 - Addition with the Short Bead Stair

     Short bead stair, marker, exercise cards/sheet, pen/pencil

     recording addition and writing answers

4 - Addition Strip Board

     Strip board, 2 sets of number cards, stage 3 card, pen/pencil

     Counting up to 18

Early Subtraction Activities 

1 - Subtraction with Short Bead Stair

      Short bead stair, marker, exercise cards

      recording subtraction

2 - Subtraction Strip Board

      Subtraction strip board, a blank strip, set of number strips 1 to 9, exercise card, pencil

      Subtraction up to 18

Outline Seguin Board exercises in sequence.

1 - Seguin Board A - Exercise 1 - naming quantities 11 - 19

      Golden beads - 9 tens, short bead stair

      The child builds short bead stair, take 1 ten and unit from short bead stair

       Three period lesson

2 - Seguin Board A - Exercise 2 - naming symbols 11 - 19

      Seguin Board A with numeral cards

      Introducing written symbols from 11 - 19

      Combining quantity and symbols  

      

3 - Seguin Board A - Exercise 3 - combining quantities and symbols 11 - 19

      Seguin Board A and numeral cards, box of 9 tens, box of short bead stair

      Building numbers with beads and then on board.

      

      

4 - Seguin Board B - Exercise 1 - naming quantities 10 - 90 

     Golden beads - 45 x 10s

      Introducing numbers 10 - 90 - ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety

      Three period lesson

      

5 - Seguin Board B - Exercise 2 - naming symbols 10 - 90

      Seguin Board B

      Introducing written symbols from 10 - 90

6 - Seguin Board B - Exercise 3 - combining quantities and symbols 10 - 90

      Seguin Board B, Golden Beads 45 x tens
      Reinforcement of numerals 20 to 90
   

7 - Seguin Board B - Exercise 4 - combining quantities and symbols 10 - 99

      Seguin Board B, Golden Beads 9 x tens and 9 x units
      Using quantities and symbols to experience numbers 10 - 99