Counting to Nine
Counting means giving each thing a number, one at a time. As you point to apples and count one, two, three, the last number you say is how many there are in all. The numbers 1 to 9 come in a fixed order, so you always know what comes just before or after, and zero means nothing at all. Add apples one by one with the slider, then compare two groups of stars with the greater-than and less-than signs.
To say how many things you have, you pair a number with each one. The last number you say is the total, and 1 through 9 keep a fixed order so you can name the next and the one just before. We call the empty case 0, so presence and absence sit on the same line while you learn to count and to compare. With that order you can write which side has more.
The first picture lays out as many apples as you choose with the slider, and each apple has its number written on it, starting from 1. Under the apples is a number line from 0 to 9: the numbers up to your count are bold and orange, and the larger ones stay faded. The second picture puts orange stars on the left and blue stars on the right, with >, <, or = in the middle. The side with more stars has the greater number, and when both sides have the same number of stars, = appears in the middle.
If you think counting starts only at 1, you have no number for none at all. 0 means nothing, and 0 also sits at the front of the number line. The slider picks apples from 1 to 9, but you still keep none on that same line so before, after, and size stay connected. Pointing with a finger one by one is the same idea as leaving the empty case as 0.
Counting to 9 and comparing with signs is the same work you will do with larger counts. Pairing a number with each thing, taking the last number as the total, and finding the neighbor just before or after all carry into the next lesson, up to 50. Once 0 through 9 and the signs >, <, and = feel familiar, you can write more and less on the same kind of line even when the piles grow.
When a question asks for the numbers between two values, walk from the next number after the smaller one up to the number before the larger one, and leave the ends out. When it asks for the number that is 1 less, look at the place just before, then pick >, <, or = to compare it with another number. Checking the number line once more before you write keeps counting and comparing on one line.
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