Counting by Groups: Making Ten

Look at your two hands. Ten fingers, right? Every time you count past ten, you're really counting how many groups of ten you have, plus a few extra. That's the big secret of numbers!

- How to group objects into sets of ten - Why 23 means '2 tens and 3 ones' - How to use ten-frames to see numbers faster - How to add two small numbers by making a ten first

Imagine counting 47 crayons one at a time: 1, 2, 3... it takes forever and it's easy to lose count! Instead, put the crayons into little cups of 10. If you fill 4 cups and have 7 crayons left over, you know right away: 4 tens and 7 ones is 47. This is exactly how our number system works. Every two-digit number is made of tens and ones. The number 32 is 3 tens and 2 ones. The number 58 is 5 tens and 8 ones.

A ten-frame is a simple box with 10 spaces, arranged in two rows of 5. When you fill in dots for a number like 7, you can instantly see it's '5 and 2 more' without counting one by one. This is called subitizing — recognizing a small amount at a glance instead of counting it. Once you're comfortable with one ten-frame, two ten-frames side by side can show any number up to 20, which makes teen numbers much less confusing.

A classroom has 34 pencils. The teacher puts them into cups of 10. She fills 3 cups completely and has 4 pencils left over. So 34 = 3 tens + 4 ones. If 6 more pencils arrive, she now has 3 tens + 10 ones — and since 10 ones makes a new ten, that becomes 4 tens + 0 ones, or 40!