PROGRESSIVE ARITHMETIC.

ONE

PART ONE.

Two

1. Show me one pencil, one block, one stick.
2. Raise one finger, one hand, one arm.

3. Point to one chair, one window, one door. 4. How many feet have you? How many eyes? 5. Show me two fingers, two hands, two books. 6. Take one stick. Take another stick. How many sticks have you now?

7. One stick and one stick are how many sticks?

8. Draw a line one inch long. Draw another line one inch long. How many lines have you?

9. One line and one line are

lines.

10. How long is the first line? How long is the second line? How long are both lines?

11. One inch and one inch are

inches.

12. Take two blocks. Give me one block. How

many blocks have you left?

13. Two blocks less one block is 14. How many are two less one?

15. One and one are two.

block.

Two less one is one.

16. Take one stick; now take one more.

times have you taken one stick?

17. Two times one stick are

How many

sticks.

18. Draw two parallel lines one inch long.

19. Draw a vertical line two inches long.

20. Draw one horizontal and one vertical line each

one inch long.

1

2

THREE

THREE.

AND

ARE

1. Take two sticks. Put one more stick with them. You now have three sticks.

2. Two sticks and one stick are

sticks.

3. Show me three fingers, three pencils, three books, three blocks.

4. If you have two sticks, how many more sticks must you take to have three sticks?

5. Take one stick; take one more stick; and then take one more. How many sticks have you?

6. One stick, and one stick, and one stick are

9. Take three blocks. Put 2 blocks back. How many blocks have you now?

10. 3 less 1 are 2. 3 less 2 is 1.

11. How many are 3 less 1?

This figure is called a triangle.

12. How many sides has this triangle? How many angles has it?

13. Take three sticks. Place them so that they form a triangle.

14. Draw three horizontal lines, three parallel lines, three vertical lines.

15. How many times must you take one block to have three blocks?

16. Three times one block are

blocks.

17. If I have three cents, to how many boys can I give one cent each?

18. How many ones are there in 3?

19. Two times one are two. Three times one are three.

them.

Put one more block with

You now have four blocks.
2. Three blocks and one block are
3. How many are three and one?
4. One stick and three sticks are

5. Two horses and two horses are
6. Take four sticks. Give me one stick.
sticks left. How many are 4 less 1?

7.

have

have

blocks.

sticks.
horses.
You have

Take four sticks again. Give me two sticks. You sticks left. How many are 4 less 2?

8. Take another four sticks. Give me 3 sticks. You stick left. How many are 4 less 3? 9. If you take 4 sticks and give me 4 sticks, how many sticks will you have left? have left? 4 less 4 are how many?

Take four sticks.

10. Arrange them in one horizontal line. How long is the line?

11. Arrange them in two equal parallel lines. How long is each line?

12. Make a triangle. How many sticks are left over? 13. If you take one stick at a time for four times, how many sticks will you have?

14. Four times one stick are

sticks.

15. If you take two sticks at a time for two times, how many sticks will you have?

16. Two times two sticks are

sticks.

17. If you have 4 pencils, how many times can you give me one pencil?

19. If you have 4 blocks, how many times can you give me 2 blocks?

3. Each side of this square is

4. This square is a 1-inch square.

5. The oblong has

6. The oblong has

corners.

sides.

7. Two of the sides of the oblong are longer than the

other two.

8. The oblong is

9. The oblong is

inches long.

inch wide.

10. Draw on paper a square and oblong the same size as those on this page.

11. Divide the oblong into inch squares. How many are there?

12. Draw another square and oblong, making each side twice as large as those on this page.

13. How long is the square? How wide is it? 14. How long is the oblong?

15. Draw a square 2 inches on a side. 16. Draw 2 squares 3 inches on a side. 17. Draw 3 squares 4 inches on a side.

18. Draw an oblong 2 inches long and 1 inch wide. 19. Draw an oblong 3 inches long and 2 inches wide. 20. Draw an oblong 3 inches long and 1 inch wide. 21. Draw an oblong 4 inches long and 2 inches wide. Take 4 inch-squares.

22. Arrange them so as to form a 2-inch square.

meant by one half He should cut into

NOTE. Be sure that the pupil understands what is before he is asked to find a half of any number of things. halves apples, balls of clay, etc. He should draw circles, squares, and oblongs, and divide them into halves. Care must be taken that the drawing is exactly divided into two parts that the pupil may get a correct mental picture of one half. When this correct idea of one half has been grasped he is then ready to find one half of any number.

1. Draw a square.

Divide it into two equal parts. One part is called one half. How many halves are there in the whole square?

2. Draw an oblong 2 inches long and 1 inch wide. Divide it into halves. How many inch-squares in each half?

3. Draw a line 2 inches long. parts. What is each part called? part?

Divide it into 2 equal
How long is each

4. One half of 4 balls is two balls.
5. One half of 4 pencils is

pencils.

6. Draw 4 inch-squares. Color one half of them red and one half blue.

7. Draw a line one inch long. Divide it into halves. Each half is one half of an inch long.

8. Draw 4 triangles. Color one half of them yellow. 9. Draw a two-inch square. How many square inches are there in it? How many square inches in one half of a two-inch square?

10. If one half of an apple is worth a cent, how much is the whole apple worth?