Measuring with Hand Spans, Steps and Cubes

Ask your child how to find out whether two books are the same length. Put them side by side, with their ends lined up. Now try comparing a table and a bed. You cannot easily bring those together, but you can carry a measurement between them.

Choose something to repeat

A unit is the small thing you use again and again. It might be one cube, one paper clip, or one hand span. To measure a length, find how many equal units fit from one end to the other.

Gather linking cubes or paper clips of one size. Line a few up beside a book. Point along the book as you say, "We are finding how long it is." Length runs from end to end. Height runs from bottom to top. Width runs across, from side to side. Let your child show you each direction on a box.

Keep small loose pieces away from mouths.

Say what you counted

Suppose nine cubes fit exactly along your book. Touch each cube once while counting together. Then say, "The book is 9 cubes long."

The answer needs a number and a unit. If your child answers "Nine," ask, "Nine what?" Nine steps cover much more ground than nine cubes. Naming the unit tells someone else what the number means.

Let your child draw the book and its cube row. You can write the words while your child writes the number. Keep a cube from the set beside the drawing to show which size you used.

Compare things in different places

Measure the table with your hand span, then measure the bed with the same hand. If the table is seven spans long and the bed is ten, the bed is longer. Count on from seven to ten: "Eight, nine, ten." That is three more spans.

A strip of paper can carry a length too. Mark a strip to match a small shelf. Take it to the place where you want to put the shelf. Hold the marked length against the space. Counting units adds a number you can save and compare later.

Place a pencil on the table with a pile of matching paper clips nearby. Tell your child, "We will find how many clips fit along the pencil." Lay the pencil still while you build the row beside it.

Line up, then count

1. Start the first clip exactly at the pencil's flat end.
2. Place the next clip so its end touches the first.
3. Keep adding clips in a straight line beside the pencil.
4. Stop when the row reaches the pencil's tip.
5. Touch each clip once as you count.

In this example, six clips fit exactly. Say, "The pencil is 6 paper clips long." Check both ends before taking the row away. A row starting partway along misses some pencil. A row sticking out past the tip includes extra length.

Spot spaces and overlaps

Leave spaces in the row and let your child look. The spaces use up some of the pencil's length, so fewer clips reach the tip. A count with gaps is too small. Push the clips together and see how much pencil is left to measure.

Now slide the end of one clip over another. Each clip covers less new length, so you need more clips. Overlaps make the count too big. Keep the row straight too: a zigzag takes a longer route beside the pencil.

Ask, "Can you find where our row needs fixing?" Let your child move the pieces before counting again.

When a whole unit will not fit

A book might reach past seven cubes but stop before the eighth cube ends. Say, "The book is between 7 and 8 cubes long," or "a bit more than 7 cubes long." Counting that last part as a whole cube would hide what you saw.

For a ribbon, lay it straight before measuring. A curled ribbon does not show its full end-to-end length. Moving or turning a straight pencil does not change its length. If two pencils seem different after one is moved, line their ends up again.

Measure upward

Stand a teddy bear on the table. Build a tower of cubes beside it, starting on that same table. Stop at the top of the bear's head. A tower reaching its head at ten cubes shows, "The teddy is 10 cubes tall."

For a long row, count with your child. You can join the first ten cubes and count on from ten. Measure once more to check any count you are unsure of.

You can measure even when you have only one unit. The important part is keeping the place where that unit ends. Your child then starts the next placement at exactly that spot.

Use a hand span

A hand span runs from the thumb tip to the little-finger tip when the hand is stretched wide. Show your child those two ends.

Put your thumb at the table's edge and stretch your hand along it. Hold the little finger's place with your other hand. Move your thumb to that place, stretch again, and count another span. Keep the stretch steady each time.

Let your child try while you help hold the ending spot. If the thumb lands before or after that spot, the spans overlap or leave a gap. Move it back before continuing.

Use heel-to-toe steps

For a room, start with the heel at one side. Place the next heel against the toes of the foot in front. Keep going in a straight line, counting each foot length. Say, "The room is about 15 of my feet long."

A foot length runs from the back of the heel to the longest toe. Ordinary walking steps vary in size. Heel-to-toe steps keep the repeated length steadier. Use one person's feet throughout a measurement.

Use one craft stick

Put the stick at the edge of a coffee table. Mark its far end with a small piece of removable tape. Move the stick so its starting end meets the mark. Count each placement and make the next end mark.

Suppose you place the stick five times and still see a little table left. Record, "A bit more than 5 sticks long." Count placements, not all the marks. A start mark plus five end marks makes six marks, but only five stick lengths. Let your child point to each space between marks to see why.

Body units belong to the person using them. Your larger hand span covers more table than your child's smaller span, so you need fewer spans. When comparing two objects, have the same person measure both. If you want someone else to repeat a measurement, share the same stick or set of cubes.

Set out some new crayons and some short, worn crayons. Ask your child to match them by length. They may all be crayons, but they do not all cover the same distance.

Equal pieces make a useful count

Every unit in one measurement must be the same size. "Five cubes long" means five equal cube lengths. If some pieces are longer, the count no longer tells you how many equal lengths fit.

Before measuring, place paper clips side by side with their starts lined up. Their far ends should match. Do the same with sticks or crayons. For cubes, check that their sizes match and that the same-sized face runs along the object.

Color does not matter to a length measurement. A red cube and a blue cube can be equal units. What matters is the length each one adds.

Repair a mixed row

Suppose your child puts two craft sticks and three cubes along a shoe. The row has five objects, but saying "5 long" leaves out their different lengths. Five craft sticks and five cubes would give very different rows.

Ask, "Which one thing shall we use?" Remove the mixed pieces. Lay matching cubes from the shoe's heel to its toe, touching end to end. Now the count can be named in cubes.

Even using one kind of object needs a size check. One child may fit four long crayons along a book. Another may fit seven short crayons. Those counts use different crayon lengths. Measure both books with the same matching set before comparing them.

Keep a body unit steady

A hand that stretches wide, then curls a little, changes its span. Practice holding the same stretch. Ordinary walking steps also change length. Use one person's heel-to-toe steps to repeat a steadier foot length.

Ask your child to explain a row they have made. You might hear, "I used matching cubes. They touch, and none is on top of another." That explanation shows what made the count useful.

Equal units matter in other jobs too. Use the same full cup for each pour. Use matching flat tiles to cover a surface. On a balance, use units that all weigh the same. In each case, every counted unit must stand for the same amount.

Put a book on the table and measure its length with craft sticks. Then leave the book in place and measure with cubes. Your child can see that the book stays the same while the count changes.

More small pieces fit

A smaller unit covers less length each time. You need more of it to reach the end. A bigger unit covers more length, so you need fewer. This rule is about the same length measured in different units.

For example, a book is three craft sticks long and twelve cubes long. Each stick reaches as far as four cubes. Lay the cubes beside the sticks to show how both rows reach the same end. You can count the cubes one at a time; no new counting method is needed.

Before changing units, ask, "Will we need more cubes or fewer cubes?" Then let your child check the prediction with the actual pieces.

A bigger count can describe the same thing

It is easy to hear twelve and think "longer than three." Here the units explain the difference. Twelve cubes and three sticks describe one book. The book did not grow.

Your larger hand span and your child's smaller span work the same way. The table needs more of the smaller spans. Keep each person's hand stretch steady while measuring. Different people's ordinary steps also give different counts because their steps cover different lengths.

If a rug is eight cubes long and a mat is six sticks long, the numbers alone cannot tell you which is longer. Measure both with the same cubes, or both with the same stick. Then compare the counts.

Choose a unit that shows the end clearly

A book might be "a bit more than 3 sticks long." Smaller cubes can show that leftover length more closely. They may give a whole-unit answer where the sticks leave a large part to describe.

There is a trade-off you can show with objects: very small units make a long row hard to count. Try the smaller unit when you need to describe a short leftover piece. Use a larger, easy-to-repeat unit for a long distance.

When you share results, share the unit too. Two people using the very same stick can repeat the measurement. Hands and feet vary from person to person. This is why people use agreed units when measurements need to mean the same thing to everyone.

Choose a measuring job together. A small crayon suits cubes or paper clips. A table suits hand spans or craft sticks. A room suits heel-to-toe steps. The unit should be easy to repeat and easy to count.

Match the unit to the job

A paper clip is useful beside a crayon. Along a hallway, it would take so many clips that your child could lose count. A foot length makes a steadier, more manageable choice for that distance.

A unit can also be too big. A crayon shorter than one step gives only "less than 1 step." Small cubes tell you more about that short length. Put a cube and a foot beside the crayon so your child can see the difference.

Save the number with its unit

Make a short list, or let your child draw the objects. For example:

• Shoe: 7 cubes.
• Book: 9 cubes.
• Pencil: 6 cubes.

You can write the names and units while your child adds the numbers. Use the same cubes for all three. Later, the list tells you the book is longest and the pencil shortest, even after the rows are packed away.

Find how much longer

Suppose a rug is nine of your child's foot lengths long. A mat is five of the same foot lengths long. The rug is longer. To find the difference, count on from five: "Six, seven, eight, nine." Four counts show it is four foot lengths longer.

You can make the difference visible too. Build one cube row to match each of two measured lengths. Line the rows up at the same start. Pair the cubes along the shared part. The extra cubes on the longer row show how much longer it is.

Put three things in order

Use one person's hand to measure a shelf, table, and bed. If the counts are seven, ten, and thirteen spans, the order from shortest to longest is shelf, table, bed. Count past ten together if your child needs help.

Use the words that fit what you measured: "longer," "shortest," "taller," or "the same length." Keep "about" in the record when an end falls between units. A rounded description such as "about 8 cubes" should stay an approximate answer when you compare it later.

Choose a small cup and an empty jug. Ask, "How many of these cupfuls will fill the jug?" Capacity means how much a container can hold. The cup is your unit for finding out.

Make each pour equal

Work over a tray or sink to catch spills. Use the same cup every time. Fill water level with its rim, pour all of it into the jug, and count one cupful. Repeat until the jug is full.

In one example, six full yogurt cups fill a jug. Your child can say, "The jug holds 6 yogurt cups." This names the everyday cup used; a different cup can give a different count.

Dry rice, sand, or lentils work too. They can pile above the cup's rim. Sweep the top flat with a finger or stick before each pour. A heaped cup holds more than a level one, so mixing the two makes unequal units.

Keep track of the pours

Place one block in a bowl after each full pour. When the jug is full, count those blocks. Each block stands for one cupful already poured. This helps when your child is busy pouring and loses the spoken count.

Partly filled cups give too little water for the same number of pours. Spilling some water means the full counted amount did not reach the jug. Empty it and start again when a spill changes the measurement.

You can also start with a full container and scoop water out. Count equal full cupfuls until it is empty, describing any part left at the end.

Describe the last part

Sometimes four full cups fit and there is still room. Part of a fifth cup fills the bowl. Say, "The bowl holds between 4 and 5 cups." If that last part is about half a cup, say, "About 4 and a half cups."

The half describes the last cupful, not half of the whole bowl. Let your child look at that part in the cup before pouring it.

Use a spoon for a little bottle lid or egg cup. A cup suits a larger pot or bucket. For a small box, equal cubes can show the space inside. Pack the cubes closely, filling all the space they can fit into. Take them out one at a time to count every cube, including hidden ones.

Set a tall, narrow container beside a short, wide one. Ask your child which will hold more. Height can be misleading: a wide bowl can hold more than a taller vase. Measure to find out.

Compare matching cupfuls

Fill each container from empty using the same small cup. Keep every cupful full and count the pours. Suppose a vase holds two cups and a bowl holds five. The bowl holds more, even though it is shorter.

To find how much more, count from two to five: "Three, four, five." That is three more cupfuls. Make two rows of counters, one for each cup count, if your child wants to see the difference.

You can order three containers this way. If a bottle holds three cups, a jug six, and a pot ten, the bottle holds least and the pot holds most. Keep the same cup for every container in the comparison.

Try a direct pouring test

Fill one container completely. Pour all its water into the other empty container, catching any overflow in a tray.

• If water overflows, the first container holds more.
• If the second container still has room, the second holds more.
• If it fills exactly, they hold the same amount.

This test shows which holds more. Counting equal cupfuls can then tell you how much more.

Follow the same water

Pour three cupfuls into a tall glass. Transfer all that water into a wide bowl without spilling. The water looks lower, but there is still the same amount. Scoop it back out with the same cup to check: three cupfuls.

Ask, "Did we add water or take any away?" The shape and level changed; the amount did not. Also notice that the water in a partly filled container does not show its whole capacity. You must fill it to find everything it can hold.

A smaller cup or a spoon gives a bigger count for the same capacity. A mug may hold three yogurt cups or eighteen spoonfuls. Both counts can describe the same mug. Keep the unit name with the count, and use one unit for containers you want to compare.

Lay a placemat on the table. Ask your child how many square paper tiles will cover it. Area means how much flat surface something covers. To measure it, cover the whole surface with equal tiles and count them.

Fill the surface, not just an edge

Choose square notes or paper tiles of one size. Begin at a corner. Place tiles side by side, touching without overlapping. Continue across, then start another row. Reach all the edges.

Suppose two rows of three sticky notes fit the placemat exactly. Touch each note once, moving along one row and then the next. Count, "One, two, three, four, five, six." Say, "Six sticky notes cover the placemat."

Counting just the first row would miss the rest of the surface. Your child can put a small removable marker on each tile as it is counted if keeping track is hard.

Check the covering

Look for bare spaces between tiles. Those spaces are surface you have not measured. Look for tiles lying over each other too. An overlap counts some surface twice. The tiles should touch edge to edge.

Square and rectangular pieces fit together without gaps. Round coins leave spaces between them, so they cannot make a complete covering. Let your child try a few circles and squares to see those spaces.

If whole tiles do not fit the edge, describe the result with "about" or "a bit more than." Do not count a tiny uncovered corner as a whole extra tile without saying it is an estimate.

A long edge can fool you

Make a long strip covered by one row of six equal squares. Make a shorter, wider mat covered by two rows of three of those same squares. Count each covering. Both have an area of six squares, although the strip has a longer edge.

Now try smaller tiles on the same placemat. More small tiles are needed because each covers less surface. Compare two surfaces using the same kind of tile. If a book cover takes four playing cards and a tray takes nine of the same cards, the tray has the larger area.

Invite your child to hold a big bag of cotton balls and a small stone. Ask, "Which feels heavier?" Size alone does not tell you weight. Weight means how heavy something is; your child's school may also use the word "mass."

Start with a level balance

A pan balance has a beam with a pan at each end. The beam tips around the middle. Check it with both pans empty. They should hang level before you add anything.

If an empty pan already hangs lower, fix the balance first. Otherwise, you would be reading a tilt that was there before the objects arrived.

You can make a simple balance with two matching cups hung from a coat hanger. Hang each cup the same distance from the middle. Suspend the hanger so it can tip freely, then check the empty cups are level.

Read the settled beam

Place an apple in one pan and an orange in the other. Take your hands away and wait for the beam to stop moving.

• The heavier side goes down.
• The lighter side goes up.
• A level beam shows the same weight on both sides.

If the orange's pan goes down, say, "The orange is heavier than the apple." Invite your child to say it the other way too: "The apple is lighter than the orange."

The pan that rises is easy to notice first. Help your child follow the lower pan back to its object. That is the heavier load.

Check a guess about size

Compare the cotton balls and the stone on the balance. A large, light object can rise while a smaller, heavier one goes down. Let the balance settle before deciding. Holding objects gives a useful first guess, especially when the difference feels large. A balance helps check weights that feel nearly the same.

Order three objects

Compare an orange with an apple, then the apple with a lemon. If the orange is heavier than the apple and the apple is heavier than the lemon, place them from lightest to heaviest: lemon, apple, orange.

Choose a small object and a set of identical cubes. A balance can tell you how many of those cubes weigh the same as the object. Use cubes of one kind, with the same weight each.

Add one unit at a time

Check the empty balance is level. Put the object in one pan. Add cubes to the other pan, one at a time. Let the beam settle after each addition. When it is level, count the cubes in the pan.

For example, an apple balances eight cubes. Record, "The apple balances 8 cubes." The cubes are units of weight here. You are matching the two loads, not lining the cubes along the apple.

Keep hands off the pans while reading. A finger pushing down changes the result. Count only cubes actually in the pan; a cube left on the table adds no weight to that side.

When the beam tips past level

With eight cubes, the apple's pan may still be lower. Add a ninth cube. If the cubes' pan now goes down, the apple is heavier than eight cubes but lighter than nine.

Say, "The apple weighs between 8 and 9 cubes." The ninth cube has taken the load past the apple's weight. It did not give an exact match. Remove that cube and add it again so your child can watch the change.

Compare using one kind of cube

Suppose an apple balances eight cubes and an orange balances eleven of the same cubes. The orange is heavier. Count on from eight to eleven: "Nine, ten, eleven." It is three cubes heavier.

All the units must weigh the same. A pan holding a mix of cubes and marbles has a count of objects, but each object adds a different weight. Use a matching set and weigh again.

A lighter unit gives a bigger count for the same object. The apple might balance eight wooden blocks or twenty light plastic cubes. Neither count means the apple changed. To compare two objects, use the same units for both. With those matching units, more cubes means a heavier object.

Show your child a cube and a book. Ask, "About how many cubes will fit along this?" An estimate is a thoughtful guess made before measuring. Your child can use what they can see and what they have measured before.

Give the guess something to grow from

Hold one cube at the book's edge. Help your child picture more of those cubes along the book. You can place the first two or three, then ask how many more might be needed. Stop before completing the row so there is still something to estimate.

A known length is useful too. Suppose a book measured nine cubes. A tray looks about as long as two of those books. You might say, "I think the tray is about 18 cubes long." If that count is too much for your child, keep the comparison simple: "The tray looks longer than the book, so more than 9 cubes."

Ask, "What helped you choose that guess?" Listen for a link to the unit or to something already measured. You can model that thinking aloud without choosing the child's answer for them.

Say and save the estimate

Write down the guess before measuring. You can record, "Estimate: about 8 cubes," while your child draws the object. Leave space beside it for the measured result.

Useful words include "about," "nearly," "more than," "fewer than," and "between." They show the guess does not claim an exact count. Keep the unit name in the estimate, just as in a measurement.

Guess about filling, covering, or weight

Hold a cup beside a bowl and ask how many full cupfuls it might hold. Show a square tile beside a book cover and ask how many will cover it. Let your child hold a toy, then guess how many cubes will balance it.

A thoughtful estimate can miss the exact answer. If your child guesses seven and finds eight, talk about what helped the guess. You might say, "You pictured the cubes along the book."

After saving an estimate, measure with care. Write the result next to the guess. Ask your child what they notice about the two numbers, then use what you found to answer the original question.

Compare the guess with the result

Suppose you guessed eighteen cubes for a tray and measured sixteen. The guess was two cubes too many. Count from sixteen to eighteen to show the difference.

Think about that difference beside the whole length. Two cubes is a small part of a sixteen-cube tray. A guess two cubes away from a crayon only three cubes long misses by a much bigger part of the object. Lay out the rows to make that visible.

Keep the tray's measured length in your record. Next time, hold the tray beside another object to guide a new estimate.

Will it fit?

A doll is nine cubes long. Its shoebox bed has eight cubes of inside length. The doll is one cube too long to lie straight inside. Show this with nine cubes beside a row of eight.

For a toy box, compare its outside size with the space where you want it. Use the same person's hand span for both. A box five spans long has one span of room in a six-span gap along that direction. Check its other directions too before putting it in the space. The inside space matters when you put an object into a container.

Is there enough?

A watering can holds five of your small cupfuls. A plant needs three of those cupfuls. One full can is enough, with two cupfuls left. Pour the three cupfuls into a separate container first so your child can see what remains.

Check the method when counts disagree

If the same object gives very different counts with the same units, look at the setup. Did the row start at the end? Are there gaps or overlaps? Did each cup contain the same amount? Was the balance settled?

Ask your child to show the method while explaining: "I used cubes. I put them end to end. The shoe is 7 cubes long." You can then find the place that needs fixing and measure again.