Adding and Taking Away with Real Objects

Adding joins things so you can find how many there are altogether. Let your child move familiar things, such as blocks, spoons, or toy animals. Say what happens while they can see it.

More things arrive

Put 4 crackers on a plate. Let your child count them. Say, "I'm adding 1 more cracker," and put it beside the others. Ask, "Are there more crackers now, or fewer?" Then ask, "How many crackers are there altogether?"

Your child counts every cracker: "1, 2, 3, 4, 5." Say, "There are 5 crackers." The answer includes the crackers already there and the new one. If your child answers "1," bring the crackers close together. Point around the whole group as you ask again.

Words such as "more," "join," "in all," and "altogether" help describe adding. Match the word to the movement: "Two more cars are coming!" as you slide them over.

Two groups make one whole

You can also add when nothing new arrives. Set out 3 red blocks and 2 blue blocks. Ask, "How many blocks are there altogether?" Your child counts all 5 blocks. The colors show the two parts, but the question asks about every block.

Try joining 2 blocks to 3 blocks, then start again and join 3 to 2. Count each whole group. Both ways give 5 blocks. The joining order changed; the number of blocks did not.

What changes the number?

Adding some objects makes a group bigger. Adding none leaves the number the same. For example, "There are 3 cars. No more cars arrive." Your child can count the 3 cars to check.

Spreading a group out also leaves its number the same. Count some blocks, move them farther apart, and count again. No block joined or left. If the longer row looks like more, let your child bring it close together and check each block.

Taking away means some things leave a group. Your child then finds how many are still there. You may also hear the word subtracting for taking away.

Drive some cars away

Line up 6 toy cars on the table. Count them together, then drive 2 into a box garage. Say, "Two cars drive away." Ask, "Are there more cars on the table now, or fewer?"

Point to the cars that stayed. Your child counts, "1, 2, 3, 4." Say, "Four cars are still here." Open the garage afterward. The 2 cars inside and the 4 on the table are the 6 you started with.

"Left" means still there in these stories. Your child may think you mean their left hand. Try, "How many cars are left over?" or "How many are still here?" Point to the place named in the question.

Keep the two groups clear

A child may count the cars in the garage and answer "2." That tells how many went away. The question asks about the cars on the table. Keep the garage closed while your child counts those cars.

Use action words during play: "give away," "eat," or "fly away." The movement shows what the word means. Taking some objects away makes the starting group smaller.

None, all, and putting back

Taking away none leaves the number unchanged. If 3 cookies are on a plate and nobody eats any, 3 remain. Taking away all of them leaves none. The number name for none is zero. An empty plate can have zero cookies.

Adding can undo taking away. Drive the same 2 cars back out of the garage. Count every car on the table again: 6. Putting the cars back checks the starting group.

Split a group without losing anything

Taking apart is another way to look at a group. Set out 5 socks: 2 striped and 3 plain. Let your child sort them and count each part. There are 2 striped socks and 3 plain socks, with 5 socks in all. Nothing has left. Ask about the part you want your child to count, such as "How many socks are plain?"

Your child can solve an adding story by counting every object after the groups join. This is called counting all. Starting again at 1 is a correct way to find the answer.

Give every object one number

Set out 3 toy ducks, with 2 more nearby. Keep both groups visible as you tell the story: "Three ducks are here. Two more swim over." Let your child move the new ducks into the group.

1. Count the first group before anything joins.
2. Bring in the new objects.
3. Push the groups together or line them up.
4. Start at 1 and touch each object once.
5. Say the last number as the answer: "Five ducks!"

The last number tells how many there are in the whole group. If your child counts correctly and starts again when you ask "How many?", model the finish: "1, 2, 3, 4, 5. There are 5."

Keep hands and words together

Young children may say the number words faster than they touch the objects. Move one duck to the side for each number. The ducks already counted stay on one side; those waiting stay on the other.

If a duck gets counted twice, put the whole group back in a row. Count slowly together, with one number for each touch. A clear row helps your child see where to start and where to stop.

Try a bigger group

When smaller groups feel easy, build a tower of 6 blocks. Hand your child 3 more blocks for the top. Once all the blocks are in place, touch each block from bottom to top: "1, 2, 3, 4, 5, 6, 7, 8, 9." The tower has 9 blocks. If the tower hides blocks, lay them in a row to check.

Counting all also works when two groups were there from the start. You might set out white ducks and brown ducks and ask about all the ducks. Keep the parts visible, then count the whole group. Your child does not need to count on to solve either kind of adding story.

After taking objects away, your child counts the ones that stayed. Two counts have different jobs: count how many leave, then count how many remain.

Make the action exact

Start with 8 pretend grapes on a plate, using blocks as grapes. Ask your child to count the starting group. Tell the story: "Three grapes get eaten. How many are left on the plate?"

Have your child move the pretend grapes into a box, one at a time. Count "1, 2, 3" as they go. Stop after the third grape. Set the box apart, then count the grapes still on the plate: "1, 2, 3, 4, 5." Five grapes remain.

A handful can take away more than the story says. Counting each object as it leaves helps your child stop at the right amount. If they take the whole group, set it up again and pause after each object moves.

Point to what the question asks

If your child counts all 8 grapes again, the taken-away grapes may still look like part of the group. Keep the box closed and point to the plate. Ask, "How many are still on this plate?"

If your child answers "3," ask them to show what they counted. Three is how many went away. The answer about what remains comes from the 5 objects on the plate.

Count an empty group

Tell a story with 4 toy birds on a fence. Let all 4 fly away. Ask how many birds are still on the fence. There are no birds to touch or count. "None" and "zero" are both correct answers.

To check a taking-away story, put the removed objects back. In the grape story, return the 3 pretend grapes to the 5 on the plate. Count all 8 again. If the starting group does not return, check how many moved and whether each object received one number.

Once your child counts all with ease, they can try keeping the first number in mind. Counting on and counting back shorten the count while objects still show what happens.

Check that your child is ready

Your child needs to count to ten reliably and know that the last number gives the total. They also need to start from a number other than 1. Try, "Start at 4 and keep going." Listen for "5, 6, 7." Many children are ready around age 5 or 6; use what your child can do to guide you.

Count on for each new object

Show 5 cars and count them. Say "five" before moving anything. Add 2 cars, one at a time. Say "six" for the first new car and "seven" for the second. There are 7 cars.

If your child says "five, six" while adding the cars, they have used the starting number for a new object. Cover the first group and say, "Five cars are hiding here." The next car needs the next number, "six."

You can start with the bigger group to make fewer counting steps. For 2 shells and 6 shells, keep 6 in mind and touch the other 2: "seven, eight." Joining the groups in either order gives 8 shells.

Count back as objects leave

Show 6 apples and say "six" before taking any away. Remove 2 apples, one at a time. Say "five" as the first leaves and "four" as the second leaves. Four apples remain.

The starting number is not the first backward step. Saying "six" as the first apple leaves would leave the count one too high. Match each removal with the next number back.

Try a number path

Lay out paper spaces labeled 1 through 10. Start on 5 and move forward 2 spaces, landing on 7. Start on 6 and move back 2 spaces, landing on 4. The space you start on tells where you are before moving; it is not a move.

If a new counting method gives a different answer, uncover the objects and count all to check.

A number story is a short story with a question about how many. You may also hear "story problem" or "word problem." Use your child's name or favorite toys so the scene is easy to picture.

Pause at each part

Tell a changing story in three parts. First gives the starting group. Then tells what happens. Now asks about the group at the end.

Try, "First, 2 frogs sat on a log." Wait while your child places 2 toy frogs. "Then, 1 more frog jumped on." Let your child move it. Ask, "Now how many frogs are on the log?" Count the 3 frogs together.

Before counting, ask, "Will there be more frogs or fewer?" Your child can show that they understand the arrival before finding the exact number. Afterward, invite them to retell it: "Two frogs were here. One jumped on. Now there are 3."

Listen to the whole scene

Action words help, especially when paired with movement. Things may "come," "join," or "fly away." But a single word does not settle what to count. Ask your child to show the action and point to the place named in the question.

If they answer with the last number heard, such as "1," ask them to move the frogs and count the group now on the log. This ties the answer to what happened.

Some stories show parts

A number story can also describe two groups already there: "Here are 2 red cups and 3 blue cups. How many cups are there?" Count all 5 cups. No cup needs to arrive.

For a whole split into parts, ask about a part your child can see and count. "Here are some red and blue cups. How many are blue?" Let your child sort the actual cups and count the blue group.

Choose stories whose question asks about the end group, all the objects, or a visible part. Keep the sentences short, and give your child time to do each action before you continue.

Acting out lets your child turn a spoken story into something they can see. Start with numbers up to five, including the answer. Let your child move the toys while you tell one sentence at a time.

Play the bus game

Set out chairs as a pretend bus. Put 3 teddy bears aboard. Ask your child to count the passengers.

At the first stop, say, "One bear gets off." Your child moves 1 bear away and counts the passengers still riding: 2. Pause for the answer before the next stop.

Then say, "Two bears get on." Your child brings 2 bears onto the bus. Count all the passengers now: 4. The second story starts with the 2 bears who stayed after the first stop.

Ask, "How do you know?" Your child can point to each passenger and count again. Ask this after correct answers too, so checking becomes part of play.

Give your child a turn

If your child moves 3 bears when the story says 2, return to the start of that action. Say, "Show me 2 bears getting on." Wait for the two moves before asking about the passengers.

You can show the first action when your child is unsure. Move one bear yourself while saying what you are doing. Then hand the toys back and let your child try.

Use bodies and songs

Family members can sit on or leave a couch as pretend passengers. Your child can also clap or jump to act out a count. For a group that must stay visible, toys or fingers help keep track of it.

Counting-down songs give repeated taking-away stories. In "Five Little Monkeys Jumping on the Bed," one monkey falls off each verse. Hold up 5 fingers or line up 5 toys. Fold down a finger or move a toy away for each monkey that leaves, then count those still there. Keep the toy movements matched to the verse.

Fingers and quick drawings can stand for things in a story. Use them after your child is comfortable moving real objects. Bring the toys back whenever a story becomes hard to follow.

Add and take away on fingers

For 3 and 2 more, hold up 3 fingers on one hand and 2 on the other. Count every raised finger: "1, 2, 3, 4, 5." Each finger stands for one thing.

A number above 5 already uses both hands. To show 6 and 2 more, hold up one full hand and 1 more finger. Raise 2 more fingers on the second hand, then count all 8. One whole hand shows 5.

To take away, fold fingers down. Start with 5 raised fingers, fold down 2, and count the 3 still raised. If fingers bend or get counted twice, touch each raised finger to the table as you count. Your child can also use blocks again to keep the group steady.

Draw simple marks

A dot or circle can stand for each object. Your child does not need to draw detailed birds, cars, or animals.

For "Seven birds are here. Three fly away," draw 7 dots. Cross out 3, one at a time. Count only the dots without a line through them: 4. The crossed-out marks show the birds that left. If your child counts them too, point to each plain dot with a pencil.

To show adding, draw the first group of dots, add the new dots, and count all of them. Let your child tell you what each group stands for.

Give counters their own spaces

A five frame is one row of 5 boxes. A ten frame has two rows of 5 boxes. Put one counter in each box so the count stays clear. Choose counters large enough for your child to handle safely.

Put 4 counters in a five frame and add 1. Every box is filled, showing 5. Empty boxes show how many more counters would fill the frame. In a ten frame, a full row shows 5 and the other row holds up to 5 more.

If the marks or spaces distract your child from the story, solve it with objects first. Then make the drawing or frame together, matching one mark or counter to each object.

When stories to five feel easy, bring in larger groups up to ten. Keep the starting numbers and answers within ten. The actions stay familiar, but your child has more objects to track.

Keep the count clear

Line up objects, use two hands of fingers, or put counters in a ten frame. For 7 cookies and 3 more, show the 7 first. Add 3, then count all 10 cookies. Let your child move each object once as they count.

Try a taking-away story with 10 pretend bowling pins. Knock down 4. Ask, "How many pins are still standing?" Point to the standing pins and count 6. The fallen pins tell how many went down; the question asks about those still up.

Include groups and parts

Two groups need not move to be counted together. "Six children are in the sandbox. Two are on the swings. How many children are playing?" Use toy people for the two groups, then count all 8.

Taking apart starts with the whole group. Show 9 crayons: 4 red and the rest blue. Let your child sort by color and count the blue crayons: 5. Put both piles together again and count all 9. Sorting changed where the crayons were, without changing the whole group.

Keep zero in the stories

For "Eight balloons are here. Zero balloons pop," leave all 8 counters in place. Nothing goes away, so 8 remain. For "Six pancakes are here. All 6 get eaten," remove every counter. None remain: zero pancakes.

Your child may notice that 5 cars and 2 more make 7, just as 5 birds and 2 more make 7. The same numbers with the same action give the same answer. Changing the action changes the story: taking 2 from 5 leaves 3.

Mix the larger stories with small ones. If your child loses track, try a smaller group or lay the objects in a clearer row. Use what they can show and explain to choose the next story.

A small change during a daily routine can become a number story. Ask one question while your child can still see what is happening. A few minutes of play gives you time to listen and watch.

Use a moment already happening

At the table, say, "We have 4 forks. Grandpa is coming, so we need 1 more." Let your child add the fork and count all 5. At snack time, ask how many crackers remain after some are eaten. While tidying, ask about toys still waiting to go into the box.

Use the math words as you act: "You have 3 blocks. I'll give you 2 more. How many do you have now?" Your child hears "more" while seeing the group grow. Outside, leaves gathered into a pile or children leaving a playground can give another short story.

Wait for one answer before adding a new question. Stop while your child still enjoys the game. You can find another moment later.

Make the action part of a game

Stand up plastic bottles for bowling. After a roll, count the bottles still standing. Ask about the fallen bottles separately so your child knows which group to count.

A stuffed animal can be a pretend hungry monster. Put a small group of pretend snacks in front of it. Let the monster eat some by moving them aside, then count what remains.

A board game with a die and numbered spaces can practice counting on. Start moving on the space after the one holding the piece. Move once for each dot on the die. Counting the starting space as a move leaves the piece one space short.

Let songs carry the story

In "Five Little Ducks," one fewer duck comes back each time. Move a toy duck away as you sing. In "Ten in the Bed," one child rolls out in each verse until only the little one remains. Toys or fingers let your child show who is still there.

Notice careful work: "You touched every block as you counted." This tells your child what helped. Give them time to move the objects and explain, without turning the game into a race.

Swap roles so your child tells a number story and you solve it. Their words and movements show what they understand. You can also spot where a little help would make the next step easier.

Listen to your child's story

Invite your child to choose some toys. They might say, "Three dinosaurs were playing. One ran away." Move the dinosaur and count the 2 still playing. Ask your child to check your answer with the toys.

Now ask, "Can you show me another way?" They might raise 3 fingers and fold down 1, or draw 3 dots and cross out 1. Both show 2 remaining. Keep the starting group and action the same when changing the way you show it.

Watch where things go wrong

An incorrect answer tells you to look at the actions and counting. If your child moves the wrong number, tell one sentence at a time and wait. If the number words race ahead of the fingers, model one touch for each number. If they count the toys that left, point to the toys still in the named place.

Use smaller numbers when the whole story feels hard. Real objects can make the action clearer than fingers or a drawing. Show a first move yourself, then let your child continue.

Make checking playful

Count again even after a correct answer. For a taking-away story, put the removed toys back and see whether the starting group returns.

Occasionally make a small mistake on purpose: "Three frogs, and one more joins. That makes three!" Invite your child to show you with the toys. Let the count settle the answer.

Notice what is getting easier

Look for your child moving the toys without help, predicting more or fewer, counting accurately to five and then ten, and telling their own stories. Starting to count on is another sign to notice. Your child can understand the action well while still needing real objects. Choose the next game from what they can show you today.