The forward slash is the end of a measure (also called a bar of music).
The number '1' at the beginning of each measure of music is the most stressed beat. The '&' sign is an unstressed beat.
Just a note about differences between clapping the meter and saying a line of verse, (which does not necessarily finish at the end of the measure): The first line of 'Jingle Bells' in 2/2 Time - "Dashing through the snow" has 5 syllables and the last 3 beats of the measure are rests. For singing one would rest quietly for those last 3 beats, but the meter would be clapped for all 8 beats.
Another example of combining verse and meter is to visualize soldiers marching along while singing a song. While natural pauses occur in the lines of song and verse, the soldiers just keep up the meter with their steady marching steps.
2/2 Time
1, 2, 3, 4, 5, 6, 7, 8 / etc.
The tempo is even and livelier than 4/4 time with twice as many claps per measure.
"Dashing through the snow,
In a one horse open sleigh,
O'er the fields we go,
Laughing all the way." - Jingle Bells
2/4 Time
1 & 2 & /1 & 2 & / etc.
Stressed claps on the numbers.
"Mary had a little lamb,
Little lamb, little lamb,
Mary had a little lamb, its
Fleece was white as snow." - Mary Had a Little Lamb
4/4 Time
1, 2, 3, 4, / 1, 2, 3, 4, / etc.
Evenly spaced claps. Count 1 stressed.
"From this valley they say you are going,
I shall miss your sweet face and your smile,
Just because you are weary and tired,
You are changing your range for a while." - Red River Valley
3/4 Time
1, 2, 3, / 1, 2, 3, / etc.
The claps are evenly spaced, but the number '1' of each measure is stressed.
"Rock-a-bye baby, in the tree top,
When the wind blows the cradle will rock,
When the bough breaks the cradle will fall, and
Down will come baby, cradle and all." - Rock-a-bye Baby
6/8 Time
1, 2, 3, 4, 5, 6, / 1, 2, 3, 4, 5, 6, / etc
Counts are evenly spaced, but counts 1 and 4 are stressed.
"Here we go 'round the mulberry bush, the
Mulberry bush, the mulberry bush.
Here we go 'round the mulberry bush, on a
Cold and frosty morning.
Links
What Is Your Child's Learning Style?
Kinesthetic Language Learning Homepage
More rhythmic practice in this text
Free to Move - Kinesthetic Learning
A comprehensive guide to teaching K-3 students kinesthetically, in a 102 page fully illustrated ebook, outlining body placement, rhythms, motor skills, dynamics, mini-lessons, and a 40-minute lesson plan divided into 5 minute segments.

I recommend this collection of piano music to practice clapping in meter while singing - from Amazon.com at this link
The Nursery Rhyme Book - Piano Music



