NOTE.-These exercises are intended for use with the Numeral Frame or with counters of some kind,―marbles, pebbles, kernels of corn, beans, or bits of pasteboard. The objects should be arranged in distinct groups, to represent each number indicated. 1. How many counters have we here? (1) 2. How many are 1 and 1? One taken away from 2 leaves how many? How many ones in 2? How many are two times 1? 3. How many are 2 and 1? How many are 1 and 1 and 1? How many are three times 1? 4. One taken away from 3 leaves how many? Two taken away from 3 leaves how many? How many ones in 3? 5. How many are 3 and 1? How many are 2 and 2? How many are 1 and 1 and 1 and 1? How many are four times 1? How many are two times 2? 6. One taken from 4 leaves how many? Two from 4 leaves how many? Three from 4 leaves how many? How many ones in 4? How many twos in 4? 7. How many are 4 and 1? How many are 3 and 2? How many are 1 and 1 and 1 and 1 and 1? are five times 1? How many 8. One from 5 leaves how many? Two from 5 leaves how many? Three from 5 leaves how many? Four from 5 leaves how many? How many ones in 5? LESSON II. 1. How many are 5 and 1. How many are 4 and 2? How many are 3 and 3? How many are six times 1? How many are three times 2? How many are two times 3? 2. One from 6 leaves how many? Two from 6? Three from 6? Four from 6? Five from 6? How many ones in 6? How many twos in 6? How many threes in 6? 3. How many are 6 and 1? How many are 5 and 2? How many are 4 and 3? How many are 3 and 4? many are seven times 1? How Three 4. One from 7 leaves how many? Two from 7? from 7? Four from 7? Five from 7? Six from 7? How many ones in 7? 5. How many are 7 and 1? How many are 6 and 2? How many are 5 and 3? How many are 4 and 4? How many are 3 and 5? How many are 2 and 6? 6. How many are eight times 1? How many are four times 2? How many are two times 4? 7. One from 8 leaves how many? Two from 8? Three from 8? Four from 8? Five from 8? Six from 8? Seven from 8? 8. How many ones in 8? How many twos in 8? How many fours in 8? LESSON III. 1. How many are 8 and 1? How many are 7 and 2? How many are 6 and 3? How many are 5 and 4? How many are 4 and 5? How many are 3 and 6? How many are 2 and 7? 2. How many are nine times 1? How many are three times 3? 3. One from 9 leaves how many? Two from 9? Three from 9? Four from 9? Five from 9? Six from 9? Seven from 9? Eight from 9? How many threes in 9? How many are 8 and 2? 4. How many ones in 9? 5. How many are 9 and 1? How many are 7 and 3? How many are 6 and 4? How many are 5 and 5? 6. How many are 2 and 8? How many are 3 and 7? How many are 4 and 6? 7. How many are ten times 1? How many are five times 2? How many are two times 5? 8. One from 10 leaves how many? Two from 10? Three from 10? Four from 10? Five from 10? Six from 10? Seven from 10? Eight from 10? Nine from 10? 9. How many ones in 10? How many twos in 10? How many fives in 10? DEFINITIONS. 1. A Unit is a single thing; as one, one book, one slate, one day. 2. A Number consists of one or more units. 3. Arithmetic treats of numbers, and is the art of computing by them. 4. Notation is the art of expressing numbers, by means of figures. 5. Figures are characters used to represent numbers. The following figures are used: 1 2 3 4 5 6 7 8 9 0 One two three four five six seven eight nine naught. The first nine are called digits, or significant figures. The cipher, or naught, expresses no value of itself, but is used to give different values to the significant figures by changing their location. All numbers can be expressed by these figures, or by combinations of them. 6. Numeration is the art of reading numbers. Any number less than ten is read by naming the figure representing it; all other numbers, by naming the figures, the places they occupy, and the period in which they stand. Nine (9) is the largest number that can be represented by one figure; ninety-nine (99), by two figures; nine hundred and ninety-nine (999), by three. 7. A Period may consist of three figures. In every period, the right-hand figure represents units, and occupies the first place in the period. The middle figure represents tens, and occupies the second place in the period. The left-hand figure represents hundreds, and occupies the third place in the period. Here, 5 in the first place is 5 units; in the second place, 5 tens or fifty units; in the third place, five hundreds, or fifty tens, or five hundred units. |