Math · Rung 4 of 7
Why the 2 in 25 means twenty: grouping in tens, and using that to add and subtract bigger numbers.
Where this sits
Our number system is built on tens. Ten ones make a ten, ten tens make a hundred, and where a digit sits tells you which it is. Once a child really sees this, adding 38 + 15 makes sense: ones with ones, tens with tens, and ten loose ones traded for a ten.
This rung covers numbers to 100 and then to 1000, and adding and subtracting two-digit numbers. Take it slowly with real bundles and trades before any carrying on paper.
These come from the Addition and Addition and subtraction rungs. Counting higher than 20 is part of this rung.
Each step builds on the one before. Most children spend weeks on some steps and days on others.
Bundle loose things into groups of ten. Count the bundles, then the loose ones.
3 bundles and 4 loose → 34
Say and write numbers as tens and ones. Zero holds a place when there are no ones.
47 is 4 tens and 7 ones; 40 is 4 tens and 0 ones
Count by tens from any number, forward and back.
7, 17, 27, 37 …
Compare the tens first, then the ones.
52 is more than 48: 5 tens beats 4 tens
Tens with tens, ones with ones, where no trading is needed yet.
34 + 25 = 50 + 9 = 59
Ten ones become one ten, and one ten can be broken into ten ones. On paper this is carrying and borrowing.
38 + 15: 13 ones is 1 ten and 3 ones → 53
Ten tens make a hundred. Read, build and compare numbers to 1000.
247 is 2 hundreds, 4 tens and 7 ones
Add tens and ones to build a number. When there are ten or more ones, trade ten of them for a ten.
You need: About 100 popsicle sticks or straws, rubber bands
Tip out a big pile. Bundle groups of ten with a rubber band. Count the bundles by tens, then the loose ones.
“How many bundles? How many loose? So how many altogether?”
You need: A hundred chart (1 to 100 in rows of ten), small coins or buttons
Cover a number while your child looks away. Which number is hidden? Talk about the patterns: every number below is ten more.
“What's the number right below 36? How did you know?”
You need: Two dice, paper
Roll two dice and decide which is the tens. Make the biggest number you can, then compare with another player.
“You rolled 3 and 6. Is 63 or 36 bigger?”
You need: Sidewalk chalk, a long path
Walk a path counting steps. Every tenth step, draw a chalk line. At the end, count the lines by tens and add the extra steps.
“10, 20, 30 … and 4 more. How many steps?”
You need: A place with lots of acorns, pebbles or shells
Collect as many as you can, then sort them into piles of ten on the ground. Count the piles, then the leftovers.
“Let's make piles of ten. How many piles did we make?”
You need: Play money in $1 and $10 bills (or paper slips), one die
Take turns rolling and taking that many $1s. As soon as you have ten $1s, trade them for a $10. First to $100 wins.
“You've got 12 ones. What can you trade?”
You need: Nothing
One player thinks of a number under 100. Others ask yes-or-no questions about tens and ones until they find it.
“Does it have more than 5 tens?”
They write what they hear. Build 47 with 4 bundles and 7 loose, then write the tens digit, then the ones.
Build both. The teens say the ones first ("six-teen"), which is why this is confusing.
Unbundle it and count it: 1 to 10. Then bundle it back up.
Trade with real bundles first ("ten ones for one ten") before writing a small 1 above the tens.
In 305 the 0 holds the tens place. Build it: 3 hundreds, no tens, 5 ones.
Tick them off as you see them. Saved on this device only.