Unit 1 · Counting and Numbers

Mia has some apples on the table. She touches one apple and says one. She touches the next and says two. Then three. Each apple gets one number. This is one-to-one counting.

Sometimes we count too fast. We say five but only touch four apples. Slow down. Touch each thing. Move it to the side after you count it. Then you will not count it twice.

Leo counts his crayons. He says one, two, three, four, five. He stops at five. So Leo has five crayons. The last number tells how many.

Now Leo moves the crayons around. He puts them in a circle. Does he have to count again? No. It is still five. Moving things does not change how many.

Try it. Count seven coins in a row. Now spread them out. Count again. Still seven. The number does not change.

Jo has a plate. There are three cookies on it. She eats one. Now there are two. She eats one more. Now there is one. She eats the last cookie. Now there are none. We say zero. We write 0.

Zero is a number. It comes before one. Count down: 3, 2, 1, 0. An empty box has zero toys. An empty hand has zero coins.

Max has 5 stickers in a pile. He knows there are 5. He gets 3 more. He does not start at one. He says five, then six, seven, eight. Now he has 8 stickers. This is counting on.

Start at the number you know. Say the next numbers. Start at 12: 13, 14, 15. Start at 27: 28, 29, 30. Counting on saves time.

A dime is worth ten cents. Ten pennies make one dime. Count dimes by tens: 10, 20, 30, 40, 50. Five dimes are 50 cents. Say it fast. Ten, twenty, thirty, forty, fifty.

Keep going up. 60, 70, 80, 90, 100. Ten tens make one hundred. Counting by tens is a skip count. You skip the numbers in between.

Hear the pattern. Each word ends the same way. Twenty, thirty, forty. Each one is ten more than the last.

Socks come in pairs. A pair is two socks. Count socks by twos. 2, 4, 6, 8, 10. Five pairs are 10 socks. Each jump adds two.

Your hand has five fingers. Count fingers by fives. 5, 10, 15, 20. Four hands are 20 fingers. A nickel is worth five cents. Count nickels by fives too.

Tia has 4 red cubes. Ben has 6 blue cubes. Line them up. Put one red next to one blue. Two blue cubes have no partner. So Ben has more. Tia has fewer.

Now count instead. 6 is bigger than 4. So 6 cubes is more than 4 cubes. If both had 4, the groups would be the same. Matching and counting both work.

We write numbers two ways. We write the numeral 5. We write the number word five. Both mean the same amount. Count 5 fingers. Write 5. Write five.

Here are the words from 0 to 10. Zero, one, two, three, four, five, six, seven, eight, nine, ten. Then come the teens. Eleven, twelve, thirteen, fourteen, fifteen.

Some numbers are tricky to write. A 6 and a 9 look alike upside down. Watch the direction. Practice writing 0 to 20 on a line.

Ali has ten straws. She counts them. 1, 2, 3, up to 10. She puts a rubber band around them. Now she has one bundle. One bundle is one ten. It is still ten straws.

Ten ones make one ten. That is the big idea. When we have ten small things, we can group them. Then we count groups. It is faster.

Ken has 14 grapes. He makes a group of ten. Four grapes are left over. So 14 is one ten and four ones. Say it: ten and four more.

Every teen number works this way. 11 is ten and one. 12 is ten and two. 15 is ten and five. 19 is ten and nine. The 1 in front means one ten.

Watch the words. Fourteen sounds like four and ten. Sixteen sounds like six and ten. Eleven and twelve are the odd ones. Just remember them.

A ten frame is a box with ten spaces. Two rows of five. Put one dot in each space. When it is full, you have ten. You do not need to count.

Rae shows 13 with frames. She fills one frame. That is ten. She puts 3 dots in a second frame. Ten and three is 13. One full frame and 3 more.

A ten frame also shows how far to ten. If 7 spaces are full, 3 are empty. So 7 needs 3 more to make ten.

The class has 64 pennies. Six bags of ten. Four loose ones. We write 64. The 6 is in the tens place. The 4 is in the ones place. Six tens and four ones.

Look at 37. The 3 means three tens. That is 30. The 7 means seven ones. 30 and 7 is 37. Now look at 73. Is that three tens? No. 73 is seven tens and three ones. Order matters.

A common mistake is to mix up the places. 25 is not the same as 52. Say the tens first. Two tens and five ones is 25. Each digit has its own job.

Math blocks called base-ten blocks help us count. A small cube is one. A long rod is ten. The rod is ten cubes stuck in a row. Count rods by tens. Count cubes by ones.

Show 45 with blocks. Take 4 rods. That is 40. Take 5 cubes. Count on: 41, 42, 43, 44, 45. Four rods and five cubes show 45.

Now show 45 another way. Use 3 rods and 15 cubes. 30 and 15 is 45. Same number. You can trade ten cubes for one rod.

Which is bigger, 52 or 38? Look at the tens. 5 tens beats 3 tens. So 52 is greater than 38. Write 52 > 38. The open side faces the bigger number.

Now 43 and 47. The tens are the same. Four and four. Look at the ones. 3 is less than 7. So 43 is less than 47. Write 43 < 47.

If both digits match, the numbers are equal. 29 = 29. A common mistake is to look at ones first. 19 has a 9, but 21 is bigger. Tens come first.

Nia has 34 stickers. She gets 10 more. Add one rod. 3 tens become 4 tens. The ones stay at 4. So 34 and 10 more is 44. Only the tens digit changed.

Now she gives away 10. Take away one rod. 4 tens become 3 tens. 44 take away 10 is 34. That is ten less. The tens digit goes down by one.

You do not need to count by ones. Find ten more than 57. It is 67. Ten less than 57 is 47. A common mistake is to change the ones digit. The ones stay the same.

A hundred chart shows 1 to 100. It has ten rows. Each row has ten numbers. The first row is 1 to 10. The second row is 11 to 20. The last row ends at 100.

Find 25. Move one box right. You see 26. That is one more. Move one box down. You see 35. That is ten more. Move up instead. You see 15. Ten less.

Look at a column. 4, 14, 24, 34, 44. The ones digit stays 4. The tens digit goes up by one. The chart shows the pattern.