Sorting, Counting and First Charts

A basket of laundry gives your child something real to sort. Start with a small collection you can both see. Sorting puts things together because they share something, such as color or kind.

Choose one question

Ask, “What do these socks look like?” Your sorting rule is the question you use for every item. Each answer makes a group, or category. You might have white socks, striped socks and blue socks.

Color, shape, size, kind and use all make useful rules. Toys could become cars, animals and blocks. Household things could become things to wear and things to eat. “The ones I like” works too, but someone else needs to ask your child which those are.

Sort together

1. Spread out the things and agree on the rule.
2. Put out a plate or a piece of paper for each group.
3. Add a word, a drawing or a sample to name each group.
4. Pick up one thing at a time and choose its place.
5. Look through each finished group to check the rule.

For a basket of 9 socks, you make groups of 4 white, 3 striped and 2 blue socks. The basket is empty when you finish. Each sock has one place, ready to count.

Make room for every item

An item that fits none of your named groups needs an other group. When sorting vehicles into cars, trucks and boats, put a toy airplane in “other.” Keep it in the collection.

Sometimes your names overlap. A blue sock with white stripes could fit both “blue” and “striped.” Agree that all striped socks go in the striped group. Tell your child this decision before sorting the next sock. Every sock can then have one clear place.

Keep the rule steady

A child sorting by color may suddenly start a pile of big things. Point back to the labels and ask, “What are we sorting by?” Then ask about the item: “What color is this one?” Let your child move it to the right group.

Invite a short explanation: “I sorted by size. The big ones go here.” You can check the sort together by taking one item from each group and asking the same question again.

Your child may notice a new way to group familiar things. Mix the collection together and try that rule. Re-sorting changes which things belong together without adding or removing anything.

Change the question

Use 8 buttons: 3 big red, 2 small red, 1 big yellow and 2 small yellow. First ask, “What color is it?” Put the red buttons together and the yellow buttons together. You have 5 red and 3 yellow.

Take a photo before mixing them. Now ask, “Is it big or small?” The big red buttons join the big yellow button. The small red buttons join the small yellow buttons. This time there are 4 big and 4 small buttons.

Compare the two sorts. The groups and their counts changed, but there are still 8 buttons. A new rule can also happen to give the same group counts. What matters is that each item follows the new rule.

Listen to someone else's rule

Let another family member choose the next question. Ask your child to repeat it before starting. If the rule is “has wheels,” color will not decide where a toy belongs.

A yes-or-no question gives two groups. For “Is it red?”, name them “red” and “not red.” Blue, green and yellow things can all belong in “not red.” They share the answer “no” to the same question.

Guess and check

Make two groups without naming your rule. Your child suggests what the things in each group have in common. Start with an easy-to-see feature, such as color. Swap roles so your child gets to make the groups too.

Try a new item with the suggested rule. Ask, “Where would this go? Why?” Sometimes several rules fit the first few things. Another item can help you see which rule the sorter meant.

Find an item that needs moving

Check a “things that roll” group holding a ball, an orange, a toy car and a book. Try rolling each item. The book needs a different place because it does not roll.

A quick drawing or photo keeps a record of a finished sort. Look back at it after re-sorting and talk about which things moved together. Accept a sensible rule your child chooses, even when you had a different one in mind.

Once your child sorts easily by one rule, try two questions together. This is a useful stretch for many children around ages 5 or 6. Begin with hoops or yarn circles that your child can move objects into.

Overlap two hoops

Make the hoops overlap. Label one “red” and the other “big.” For every block, ask, “Is it red?” and “Is it big?” Both answers decide its place.

• A big red block goes in the overlap, inside both hoops.
• A small red block goes in the red hoop outside the overlap.
• A big blue block goes in the big hoop outside the overlap.
• A small blue block goes outside both hoops.

These overlapping circles make a Venn diagram. Keep the things outside both circles nearby: they still belong to your collection.

Work through a whole collection

Set out 10 blocks: 2 big red, 3 small red, 4 big blue and 1 small blue. Place the big red blocks in the middle first. They satisfy both rules in that one place.

Next put the 3 small red blocks in the red-only part. Put the 4 big blue blocks in the big-only part. The 1 small blue block goes outside both hoops.

Count the whole red hoop, including the middle: it holds 5 blocks. Count the whole big hoop, including the middle: it holds 6. To count the collection, count each of the four separate places once. That gives 10 blocks. Adding the two whole hoop counts would count the middle blocks twice.

Try four boxes

A Carroll diagram uses a grid of four boxes. Label its rows “red” and “not red.” Label its columns “big” and “not big.” Follow both labels to find a block's box.

The grid records the same blocks as the hoops. “Not red” includes blue, and “not big” includes the small blocks in this collection.

Help with the tricky places

If your child puts a big red block in the red-only part, ask the second question: “Is it big too?” Slide it into the overlap. You do not need a second copy of the block.

A box or overlap can be empty. Sorting animal toys and toys with wheels may leave nothing in the overlap. Keep that space and count it as 0. Move to drawn hoops or a paper grid when placing the real things feels easy.

Counting tells your child how many things are in each sorted group. Work with one group at a time. Leave the other groups apart so that things do not get mixed in.

Give each item one number

Line the items up and touch each one while saying a number. Your child can also slide each counted item to the side. The last number said tells how many are in that group.

With 4 red cars, touch and say, “1, 2, 3, 4.” Then ask, “How many red cars?” Help your child answer, “4 red cars.” A number card beside the group keeps that count visible.

Spread those cars farther apart and ask again. The count stays 4. Nothing was added or taken away. If the longer row seems to hold more, count the cars in both arrangements together.

Put the counts in a table

A simple table has a place for the group name and a place for its count. Use words, little drawings or color patches to name the groups.

For 9 toy cars, you have 4 red, 3 blue and 2 yellow. Record one group on each row:

Point across each row as you read it aloud: “Blue: 3.” Let your child check the count against the cars before you move to the next row.

Keep a place for none

An empty group has a number too: zero, written 0. With a fruit collection and no pears, leave the pear label in place and write 0. It shows that you checked that group and found none.

Check the whole collection

Count the cars all together. Then count through the sorted groups without restarting at 1: “1, 2, 3, 4” for red; “5, 6, 7” for blue; “8, 9” for yellow. Both counts give 9.

If the counts differ, recount slowly. Look for an item skipped, counted twice or moved to a different group. A matching total is a useful check; still check that each item is in the right group.

Your child may see 2, 3 or about 4 things and know the count at a glance. That is called subitizing. Ask, “How did you see it?” Let your child point or count to show you. For a larger group, return to touching one item for each number word.

Your child can compare groups by matching things in pairs or by counting. Use the words “more,” “fewer” and “the same” while your child handles the objects.

Match one with one

Put 6 apples beside 4 bananas. Make a pair with one apple and one banana. Keep going until every banana has a partner.

There are 4 pairs, with 2 apples left over. The apples have more because some have no partner. There are 2 more apples than bananas and 2 fewer bananas than apples. Counting agrees: the apple count is 6 and the banana count is 4.

To find “how many more,” count the unpaired things. Counting all 6 apples answers “How many apples?” but not “How many more apples?” Point to the paired part, then to the extras.

Find most and fewest

With several groups, the biggest count shows the most. The smallest count shows the fewest. For 5 white beads, 3 blue beads and 1 green bead, white has the most and green has the fewest.

You may also hear “least” when adults talk with young children. “Fewest” is a useful word for things you can count.

Keep empty groups in view. If a labeled red group has 0 beads, red has the fewest of all four colors. Ask your child to include that label when checking the groups.

Notice equal groups

When every item has a partner, with none left over, the groups have the same number. We also say their counts are equal.

Two groups can share the most. With 4 white beads, 4 blue beads and 1 green bead, white and blue share the biggest count. Name both groups when your child asks which has the most.

Order and check

Ask your child to put groups in order from most to fewest. With counts of 5, 3 and 1, the order is white, blue, green. Reverse the order to go from fewest to most.

Large objects and wide gaps can fool the eye. A group of 3 big teddy bears takes up more room than 5 small marbles. To compare how many things there are, count them or match one bear with one marble. The extra marbles show which group has more things.

A chart can begin with the real objects your child has sorted. Give each group its own row and each item its own space. An object chart makes the counts easy to see side by side.

Build the spaces first

Make a grid with tape on the floor or draw boxes on paper. A muffin tin or an egg carton can also hold one item in each space. Make the spaces large enough for your objects.

Mark one starting line. Put a group name, drawing or sample beside the start of each row. Then place the objects one to a space, beginning at that line. Fill the spaces in order without gaps.

The spaces should be the same size in every row. A large object still takes one space, just as a small one does. If you use a sample as a label, keep it outside the spaces being counted.

Make a shoe chart

The shoes by the door include 5 sneakers, 2 sandals and 3 boots. Give each kind a row. You are counting individual shoes, so each shoe gets a space.

1. Place 5 sneakers in the first 5 spaces of their row.
2. Place 2 sandals in the first 2 spaces of their row.
3. Place 3 boots in the first 3 spaces of their row.

All three rows start together. The sneaker row reaches farthest, showing the most shoes. The sandal row is shortest, showing the fewest. Count through the rows to check that all 10 shoes are shown.

Fix a misleading row

A row that starts farther along can reach farther even with fewer things. Ask your child to bring the first object back to the starting line. If there are gaps, move the objects into the next empty spaces.

You may also hear “real graph” or “concrete graph” for an object chart. The important feature is that the things themselves make the display.

Let people make the lines

A living graph uses people as its chart items. Put up signs for apples and bananas. Each person stands behind the sign for their preferred fruit, with one person at each marked spot.

With 4 people behind apples and 3 behind bananas, the apple line has 1 extra person. Lines can also stand upright as cube towers. Use matching cubes, one for each item, and put the towers on the same flat surface.

Pictures let you keep a chart after putting the objects away. Your child can draw, add stickers or color squares. Each picture or block stands for exactly one thing.

Name the chart and its groups

Write a title that tells what you counted, such as “Our Lids by Color.” Label each row with a word, a color patch or a little drawing. Read the title and point to the row labels before adding the pictures.

A title tells the reader what the whole chart is about. A label tells the reader which group one row shows. Keeping both makes it possible for someone else to read your child's work.

Make the pictures match the objects

Set out 7 lids: 4 green, 2 purple and 1 orange. Make one sticker stand for one lid.

1. Put 4 stickers in the green row.
2. Put 2 stickers in the purple row.
3. Put 1 sticker in the orange row.
4. Count the lids and stickers for each color to check the match.

Use one same-size sticker in each equal box. Begin every row at the same starting line and leave no gaps. Your child can write the count at each row's end.

A picture chart is also called a picture graph, pictograph or pictogram. Pictures can be simple circles or faces. They need to show the right count, not detailed artwork.

Watch size and spacing

Two wide stickers can stretch as far as four narrow stickers. That makes different counts look equal. Equal boxes and same-size pictures help the lengths show the counts clearly.

If your child wants to draw large pictures in one row, offer a grid. Ask them to fit one drawing inside each box. Keep the label picture beside the row, separate from the counted pictures.

Try blocks instead

A block chart, also called a block graph, uses one colored square or cube for each item. Color the first 4 squares for green lids, 2 for purple and 1 for orange. Count the squares one by one to read the chart.

You can turn the display so its groups go up the page as columns. All columns start at the same bottom line. Build cube towers the same way, with matching cubes and one tower per group.

Read a chart with your child before asking for its biggest group. Start with the title and labels. They tell you what the pictures mean and which group each row shows.

Read one row at a time

A chart called “Our Favorite Fruit” shows 5 apple votes, 3 banana votes, 2 orange votes and 0 grape votes. Each picture after a row label stands for one person's choice.

Point to “apples,” then touch and count the 5 pictures after it. Say, “5 people chose apples.” Do the same for the other rows. Keep the empty grape row visible: it tells you nobody chose grapes.

A drawing used as a row label names the group. It is separate from the answer pictures. If your child counts it, point to where the row starts and count again from the first answer space.

Compare what is shown

With equal pictures, even spaces and a shared starting line, the longest row shows the most. Apples have the most votes here. Grapes have the fewest, with 0. Among the fruits people chose, oranges have the fewest, with 2.

Ask about the counts even if your child likes a different fruit. “Which fruit did most people choose?” asks about the collected answers. Your child's own favorite can be different from the winning group.

Find a difference

Match the apple and banana pictures one by one. Three apple pictures have banana partners. Two apple pictures remain, so 2 more people chose apples than bananas.

Bananas have 1 more vote than oranges. Ask your child to show the unmatched picture. Two rows with equal counts have no extras; if oranges had 3 votes, they would match bananas.

Count everyone and speak in sentences

Count through all the answer pictures without restarting at each row. There are 10 pictures, showing 10 people's choices. The empty grape row adds no pictures to that count.

Invite your child to finish a sentence: “The chart shows…” They might say, “Apples were chosen most,” or, “Nobody chose grapes.” For a difference, try, “2 more people chose apples than bananas.”

Vary the questions when you return to a chart: “How many chose oranges?” “Are any groups the same?” “How many answers altogether?” Let your child point to the part of the chart that helped them answer.

Choose a question your child wants to answer with family or friends. The answers you collect are data. Calling them “our answers” or “our information” works well while you talk together.

Make the choices clear

Try, “Which snack should we take to the park: apples, grapes or crackers?” A few choices, usually 2 to 4, make it easy to collect and sort the replies. Add “something else” when someone needs another choice.

Ask each person the same question and let them choose once. A question about everyone's favorite color needs replies from several people. “How old is Grandma?” has one fact to find out; you do not need a vote to answer it.

Give each answer a place

Label cups for the choices. Each person can put one block or clothespin into the cup for their answer. You could also use a sticker or sticky note in a labeled column.

Keep a list of the people you plan to ask. Check off each name when that person answers. Your child can help by carrying the list and watching as you make each check.

A favorite choice can be exciting. If your child wants several votes, hand them one block and say, “One person, one answer.” Each person's choice then contributes equally to the collection.

Check names and counts

Six family members answer a game-night question. Three choose a puzzle, 2 choose cards and 1 chooses a ball game. Count the answers: there are 6, matching the 6 people asked. Then check the name list to see that each person answered once.

A matching total is useful, but check the names too. One person could be missed while another answers twice. Those errors can leave the total unchanged.

If you find 7 answers from 6 people, recount. Look for a missed, repeated or misplaced answer and check how it was recorded. Use the list to trace who answered before changing the chart.

Collect things you observe

You can also gather information without asking people. Watch vehicle colors from a window or sort leaves from a walk. Decide what you will record, then record each car or leaf once. Your child can place one marker for each thing you observe.

A question feels worthwhile when the answer helps your child do something. Turn the collected answers into a chart, talk about the result and use it to plan an activity or prepare what people need.

Follow the answers into a chart

Ask your question, collect replies, sort them and count each group. Make one picture for each answer. Add a title and labels, then check every row against the counts you collected.

Seven people choose a craft: 4 choose painting, 2 choose clay and 1 chooses collage. Draw 4, 2 and 1 pictures in those rows. Ask, “Which did the most people choose?” Your child can point to painting and count its 4 votes.

Use the vote to choose the first craft. Painting has the most votes, so start there. Clay has the next most and could come next.

Say who the answer is about

Help your child say, “Painting got the most votes.” Four of the 7 people chose it; 3 chose something else. Saying “everyone wants painting” would hide those other answers.

The result describes the people you asked on that occasion. Another family might choose differently. The same people might choose something new next week. Name the group when you talk about your result: “In our family today…”

Use counts to prepare

A snack chart can tell you how many people want each fruit. Read each row when you make your shopping or packing list. That uses the counts for every choice, even choices that did not win a vote.

Keep the purpose in view. A vote on the first game helps choose one activity. A chart of snack requests helps prepare different things for different people.

Read charts around you

A weather chart records days instead of votes. With 3 sunny, 2 rainy and 2 cloudy days, there are 7 days shown. Sunny weather happened most often in that week. Rainy and cloudy days had the same count.

Look together at a chore chart or a classroom helper chart. Point to a name or picture and ask what it tells you to do. A picture sign showing where to go also gives information you can use.

Keep investigations short and tied to real life. A few minutes of asking, counting and talking can answer a useful question. Let your child suggest the next thing your family could find out.