have both girls? How many more roses has Mary than Susan? How many roses does Mary lack of having 2 times as many as Susan? If Mary should give Susan 2 of her roses, how many would each girl then have?

How many are 1+1? 2+2? 3+1? 4+1? 1+3? 3+2? 4+0? 2+3? 2-1? 3-2? 5-3? 5 2? 4-3? 3-1? 4-2? 5-4? 4-4? 5X0? 5X1? 2X2? 4÷1? 4÷2? 3÷1? 2÷1?

NOTE. The teacher should improvise questions, similar to foregoing, after each lesson. No question, however, should involve a number greater than the subject of the last lesson. The preceding questions may be used with different numbers.

LESSON VI.

ABOUT THE NUMBER SIX.

What lesson is this? What is it about? Show me 6 planks. How many apples in each row of the picture? Is each row separated into two parts? How many apples in the two parts of the first row? In the two parts of the second row? Of the third row? Fourth row? Fifth?

Are the parts of the the first and fifth rows the same? Of

the second and fourth? What,
then, are the two parts of 6 apples?
a's, 2 a's and 4 a's, 3 a's and 3 a's.

Ans. 1 a and 5

5 and 1.

What are the two parts of 6? Ans.

4 and 2.

3 and 3.

ADDITION. - Uniting the parts.

How many are five apples and 1 apple? 1 apple and 5 apples? 4 a's and 2 a's? 2 a's and 4 a's? 3 a's and 3 a's?

What are the two parts of 6? What do they make when united? How many are 4 eggs and 2 eggs ? 5 cows and 1 cow? 3 baskets and 3 baskets? 1 orange and 5 oranges?

The two parts of a set of chairs are 2 chairs and 4 chairs; how many chairs in the set? 3 chickens and 3 chickens are the parts of a brood; how many chickens in the brood?

Copy and read: 5+1=6; 4+2=6; 3+3=6; 2+46; 1+5=6.

SUBTRACTION. - Taking away one part.

Six apples are together; how many apples would be left if 1 apple were taken away? If two apples were taken away? If 3 apples? 4 apples? 5 apples? 6 apples?

When one of them is

A squad of 6 men is

What are the two parts of 6? taken from 6, is the other left? divided into two parts; if 4 men are in one part, how many are in the other? 6 girls are in one class; part of them are standing, and part are sitting; if 3 are sitting, how many are standing? James had 6 birds in his cage, but 5 birds got out; how many had he left?

Copy and read: 6-1-5; 6—3—3; 6-5=1; 6-2-4;6-4-2;6-6=0.

MULTIPLICATION.—Uniting equal parts.

How many are 1, 1, 1, 1, 1, and 1? How many times is the part 1 taken? How many, then, are 6 times 1? How many are 2, 2, and 2? How many times is the part 2 taken? How many, then, are 3 times 2? How many are 3 and 3? How many times is 3 taken ? How many, then, are 2 times 3? Are 3 times 2 dollars more than 2 times 3 dollars?

John has 2 peaches, and Ben has 3 times as many; how many peaches has Ben ? Emma has 3 tulips and Rosa has 2 times as many; how many tulips has Rosa?

Copy and read: 6 x 1=6; 3 X 2=6; 2 × 3 = 6.

DIVISION.- Measuring by a part.

Does 6 contain its parts? Is 6 formed of 6 ones? Of three 2's? Of two 3's? How many times, then, does 6 contain 1? 2? 3? Make 6 a's. Now erase 1 a at a time. How many times did you erase? How many times, then, is 1 a contained in 6 a's?

Make 6 b's. Now erase 2 b's at a time. How many times did you erase? How many times, then, are 2 b's contained in 6 b's?

Make 6 c's. Now erase 3 c's at a time. How many times did you erase? How many times, then, are 3

c's contained in 6 c's?

Copy and read: 616; 62=3; 6 ÷ 3 = 2.

OBJECT EXERCISES.

Take 6 blocks, put them on a table, and call them

caps.

What stands for cap? Ans. c.

Now separate the caps into two parts, every way you can, calling the results thus: 1 c and 5 c's are 6 c's, etc. Now take off 1 cap at a time, calling the result thus: 1 c from 6 c's leaves 5 c's; 2 c's from 6 c's leave 4 c's, etc.

Now put on 1 cap at a time, calling the results thus: 1 time 1 c is 1 c; 2 times 1 c are 2 c's, etc.

Next take off 1 cap at a time, calling the results thus: 1 c contains 1 c,1 time; 2 c's contain 1 c, 2 times, etc. Now put on 2 caps at a time, calling the results thus: 1 time 2 c's is 2 c's; 2 times 2 c's are 4 c's, etc.

Next take off 2 caps at a time, calling the results thus: 2 c's contain 2 c's, 1 time; 4 c's contain 2 c's, 2 times, etc.

Now put on 3 caps at a time, calling the results thus: 1 time 3 c's is 3 c's; 2 times 3 c's are 6 c's.

Next take off 3 caps at a time, calling the results thus: 3 c's contain 3 c's, 1 time; 6 c's contain 3 c's, 2 times.

LESSON VII.

ABOUT THE NUMBER SEVEN.

What lesson is this? What is it about? How many

Ans. Parts of the whole. Can you put 6 books in one pile and 1 book in the other? 5 in one and 2 in the other? 3 in one and 4 in the other?

1 and 6,

What are the two parts of 7? Ans.

2 and 5,

3 and 4.

ADDITION.-Uniting the parts.

How many are 6 books and 1 book? 1 b and 6 b's? 2 b's and 5 b's? 3 b's and 4 b's? 5 b's and 2 b's? 4 b's and 3 b's?

What are the two parts of 7? When you unite them, do they make 7? How many are 5 girls and 2 girls? 4 pins and 3 pins? 1 hog and 6 hogs? 3 mugs and 4 mugs?

Ann has 3 prunes and John has 4 prunes; how many have both? 2 hogs are in one pen and 5 hogs are in another; how many in both pens?

Copy and read: 6+1=7; 4+3=7; 2+5=7; 5 +2=7; 3+4=7; 1+6=7.