Comparing two objects

When you reach for it

Two things can be compared without any numbers: put them side by side so they start at the same place, and look at which one goes further. That gives longer and shorter, taller and shorter, or the same length; for containers, pouring one into the other shows which holds more. It comes right after a child can name what can be measured about an object, and it is about size, not about how many things are in a group.

Each day below takes about ten to fifteen minutes and uses things already in the room.

Day 1: Taller and shorter

You need: about 10 snap cubes or blocks, a flat table, a thick book.

Build two towers, one of 5 cubes and one of 3, and stand them side by side on the table. Ask, “Which tower is taller? Which one is shorter?” Let the child lower a flat hand slowly from above: the hand lands on the taller one first.

Now put the short tower on top of the book and ask again. Its top may now be higher, but the tower did not grow. Take it off the book and stand both towers on the table again. Say, “To compare how tall, both things have to stand on the same floor.” Then stand back to back with the child and ask a third person (or a mirror) to say who is taller.

Practice.

1. A tower of 6 cubes and a tower of 4 cubes stand on the table. Which is taller? Answer: the tower of 6, so the tower of 4 is shorter.
2. A child and a grown-up stand back to back on the floor, and the child’s head reaches the grown-up’s shoulder. Who is shorter? Answer: the child.
3. A milk carton and a toy truck stand on the table, and the carton’s top is higher. Which is taller? Answer: the milk carton.
4. One doll stands on the floor and another on a chair, and the second doll’s head is higher. Can you tell which doll is taller? Answer: not yet. Stand both dolls on the floor first, then look.

Day 2: Longer and shorter: line up the ends

You need: two paper strips of different lengths, crayons, a spoon, a piece of string.

Lay the two strips on the table with the shorter one pushed far to the right. Ask, “Which one is longer?” A child may point to the strip whose end sticks out. Then slide both strips so their left ends touch the edge of the table, and ask again.

Say, “Line up the ends, then look at the other end. The one that goes further is longer.” Lying flat, standing up, or lying on a slant, a strip keeps its length; only lining up the ends tells you which is longer. A bent string has to be pulled straight before it is compared.

Practice.

1. A crayon and a spoon have their ends lined up at the table edge, and the spoon reaches further. Which is longer? Answer: the spoon; the crayon is shorter.
2. In the top pair of the picture, which strip looks longer, and which really is? Answer: B looks longer because it starts further right; A is longer, as the bottom pair shows.
3. A string lies in a wiggly line next to a chopstick. Can you tell which is longer? Answer: not yet. Pull the string straight, line up one end with the chopstick’s end, then look.
4. Two shoes are put heel to heel against the wall, and the right shoe’s toe sticks out further. Which shoe is longer? Answer: the right shoe.

Day 3: The same length, and two ways to say it

You need: two strips cut to the same length, a straw, a paintbrush, the child’s own hand.

Line up the left ends of the two equal strips and ask, “Which is longer?” Neither one: both ends match. Say, “They are the same length.”

Next, line up the straw and the paintbrush, and ask for two sentences, for example “The paintbrush is longer than the straw” and “The straw is shorter than the paintbrush.” Both tell the same fact from opposite sides. Then hunt the room for something longer than the child’s hand, something shorter, and something about the same length, laying each one against the hand from the wrist.

Practice.

1. A marker and a toothbrush have their left ends lined up, and their right ends also match. What do you say? Answer: the marker and the toothbrush are the same length.
2. A belt is longer than a shoelace. Say it the other way. Answer: the shoelace is shorter than the belt.
3. A glue stick is shorter than a hand, laid from the wrist. Is the hand longer or shorter than the glue stick? Answer: longer.
4. A book is the same length as a ruler. Is the book longer than the ruler? Answer: no, neither is longer.

Day 4: Which holds more?

You need: a few containers of different sizes and shapes, dry rice or water, a tray to catch spills.

How much a container holds is something else you can compare. Fill one container to the top, then pour all of it into the other, empty one. Three things can happen, and each has a meaning:

• It spills over: the first one holds more.
• The second one is not full when the pouring is done: the second one holds more.
• It just fills the second one to the top: they hold the same amount.

Ask before pouring, “Which do you think holds more?” and after, “How do you know?” A tall, thin container can fool the eye, which is why the pouring settles it. Heavier and lighter are compared in another way, with the hands or a balance, in balancing to compare mass.

Practice.

1. A full mug is poured into an empty pot and the pot is not full. Which holds more? Answer: the pot.
2. A full pitcher is poured into an empty mug and water spills over the top. Which holds more? Answer: the pitcher.
3. A full spoonful of rice is poured into an empty cup and only covers the bottom. Which holds less? Answer: the spoon.
4. Two jars: one is filled and poured into the other, and it fills it exactly to the top. What do you say? Answer: the two jars hold the same amount.

Exercises

1. Look at the picture. Which strip is longer? Which strip is shorter? Ask the child how the dashed line helps.
2. Fill a small yogurt cup with dry rice and pour all of it into an empty measuring cup. Suppose the rice reaches only halfway up the measuring cup. Which one holds more, and how do you know?

Where this goes next

When two things cannot be put side by side, such as a rug and a doorway, a string can stand in for one of them: that is comparing with a middle object. Comparing heavier and lighter is balancing to compare mass, and seeing that water poured into a different glass is still the same amount is Volume does not change when it is poured. Laying small copies of one thing end to end to say how much longer grows into measuring with a unit.