Prob

points, but to develop the idea of units of measure. lems: 1. How many times did you apply the longest measure? 2. How many times did you apply the shortest measure? 3. How many times did you apply the other measure? 4. Which did you apply the greater number of times, the longest measure or the shortest measure?

Use the pint, quart, and gallon as units of measure.

Have the pupils find how many different units of measure can be applied to a pile of twelve counters; to a pile of eight, six, nine, seven, five, and eleven counters. Have them select the number of counters as high as twelve, that can be measured with two counters without a remainder. Associate this list with counting by 2's. Even and odd numbers will be recognized by this test, and the pupil should become familiar with them through this experience.

Use the flash cards for recognition of units. The group for five is two 2's and 1, five 1's, or one 5; the group for six is two 3's, three 2's, six 1's, one 6, one 4 and one 2. The pupil may not be able on account of the arrangement of disks to see the group 5 and 1. No attempt should be made to have the pupils memorize these facts.

LESSON VII-INCHES, FEET, AND YARDS

Foot and Yard. ILLUSTRATION. Draw on the board two vertical lines nine feet apart, or such distance apart as can be measured with the foot rule and the yard stick without a remainder. Letter the lines a and b. Problems: 1. How far is it from line a to line b, Frank? 2. How far do you think it is, Henry? 3. Alice, how can we find out how far it is? 4. Shall I measure it with a string? 5. Tell me of some measure I can use to measure it.

6. Does any one know of any other measure that can be used? 7. Fred and Walter may measure it with the yard stick. Martha may write their answer on the board. 8. Are they measuring it correctly, class? 9. Henry and John may measure it with the foot rule. Lottie may write their answer on the board. 10. With which measure do you think it is easier to measure it, Ethel? 11. Why? 12. Measure the yard stick with the foot rule. 13. How many foot rules could be made of a yard stick, Belle? 14. How many feet long is the yard stick? 15. How many feet are there in one yard? 16. Which is it better to use in measuring the length of the room, the foot rule or the yard stick? 17. Who can name something that is sold by the yard? rule is marked off into little spaces. called? 20. How many inches are marked on the foot rule? 21. How many are there on the yard stick? 22. What are inches for? 23. Why do we want so many different measures to tell length and distance? 24. Did you ever hear any one tell how far it is from your home to the school house? 25. Did he tell it in yards, inches, or feet?

18. The foot 19. What are these

Use the yard stick and the foot rule in measuring other distances in which there is no remainder. Measure the distance between two lines four feet apart with the yard stick. Measure the part remaining with the foot rule. Measure in the same way five feet, seven feet, ten feet, eleven feet, etc. Mark the feet on the yard stick. Measure three feet six inches with the yard stick, to show the pupils how the yard stick may be used to find the exact measure in inches, feet, and yards. Give practice in measuring yards, feet, and inches with the foot rule and the yard stick. Give practice in drawing lines one foot

long, two feet long, and one yard long. Test these by measuring. Give practice in estimating short distances. Test these estimates. Much interest will be aroused by measuring the height of the children. Lead the pupils to see the necessity of longer units of measure to measure greater distances. Mention the rod and the mile as such units. Upon the completion of this work, the pupils should know that there are twelve inches in one foot, and three feet in one yard. They should be able to draw lines to represent these measures with a fair degree of accuracy. They should be able to use these measures in finding the length of the room, the height of other children, etc.

LESSON VIII-PINTS, QUARTS, AND GALLONS

Use the pint, quart, and gallon measures in giving this lesson. The pupils should be led to see the necessity for measuring things that are bought and sold. They should also see the necessity for fixed units of measure, and for units of measure of various sizes. They should see that such indefinite units as half a basketful, half a sackful, half a pailful, etc., cannot be fixed units for buying and selling.

Before taking up this lesson the teacher should provide a definite quantity of water, say eleven pints. ILLUSTRATION. Problems: 1. Harry, how much water is there in this pail? 2. Alice, how much water do you think there is in this pail? 3. How much do you think there is, John? 4. How can we find out how much water there is in it? 5. What shall we measure it with? 6. Select one of the measures for this purpose. 7. This is called the pint measure. 8. Is there a pint of water in the pail? 9. Are there two pints of water in it? 10. How many

pints of water do you think there are in it, George? 11. Measure it. Mary may write the number of pints on the board. 12. Could we measure it in anything but pints? 13. Select the quart measure. 14. Do you think there is enough water to fill this measure? 15. How many quarts of water do you think there are in the pail? 16. Measure it in quarts. 17. Do you think there is enough water to fill this larger measure? 18. Will it fill it twice? 19. Who can tell what this large measure is called? 20. Measure it with the gallon measure. 21. Is there enough left over to fill the pint measure? 22. Is there enough left over to fill the quart measure? 23. Fill the quart measure. 24. Is there a pint of water left in the pail? 25. Fill the pint measure. There was one gallon, one quart, and one pint of water in the pail. 26. What is sold by the pint? By the quart? By the gallon?

The pupils should become familiar with the names of the measures through hearing them used. They should learn the relative sizes of the measures by actual experience with them, by using one as a measure in filling the other, etc. The ratio of the several measures should also be perceived. A quart of water is twice as much as a pint of water. Its ratio to a pint is two. A pint of water is one half as much as a quart of water. Its ratio to a quart of water is one half. If this stands for a pint of water, what will stand for a quart of water? If stands for a quart of water, what will stand for a gallon of water? Use counters to represent the measures, so the pupils can handle them.

At the completion of the work suggested in this lesson the pupils should be familiar with the pint, the quart, and the gallon as units of liquid measure. They should know

that a quart equals two pints, that a gallon equals four quarts, that a gallon equals eight pints, that a pint equals one half of a quart, that a quart equals one fourth of a gallon.

LESSON IX-FORMS

Teach pupils to distinguish the following geometrical forms the circle, the square, the oblong, and the triangle. To guard against the common error of associating these names with the lines which form the perimeters of these surfaces instead of with the surfaces themselves, attention should be directed to surfaces which stand out in contrast to surrounding areas. If the blackboard is used to show these forms, the surfaces should be shaded, thus:

Cut circles, squares, oblongs, and triangles out of cardboard, and have the pupils tell what the forms are. Have the pupils draw these forms on paper. These surfaces should be shaded.

Problems: 1. What is the shape of the window panes ? 2. What is the shape of the door? 3. What is the shape of the blackboard? 4. What is the shape of the top of your desk? 5. What is the shape of this piece of paper? 6. What is the shape of this book? 7. What is the shape of the top of this table? 8. What is the shape of this picture? 9. Name something in the room that is a square. 10. Name something that is a triangle. 11. Name something that is a circle. 12. A square has