Sharing Fairly and Doubling

A fair share gives everyone the same amount. With blocks of one size, that means the same number. Put 2 blocks on your child's mat and 2 on yours. Say, "We each have 2. Our shares are equal."

Match the shares

Line up your blocks in a row. Ask your child to put one of theirs across from each of yours. Every block needs a partner in the other row. If every block has a partner, the numbers are equal. A block without a partner shows which row has more.

Try a new arrangement with 4 blocks for you and 3 for your child. Match three pairs. Your row has one block left without a partner. Ask, "Who has more? How can you tell?" This check works before your child can compare number words quickly.

Count to check

Touch each block once while counting. Compare the last number for each share. Say, "You have 3 and I have 4. I have more." Then try three toy plates with 2 blocks each. Check every plate; a fair share must work for everyone.

Move the blocks on one plate farther apart. The row now looks longer, but the count has stayed the same. Let your child match or count again. Spreading things out does not add anything.

Choose things you can compare

Use matching objects for counting games. One large piece of dough and one tiny piece are one piece each, but they do not give the same amount of dough. For pieces of one whole thing, compare their size.

Listen for, "It's fair because we both got some." Ask your child to show whether both shares have the same number. Two nonempty plates can still hold different amounts. Invite a full answer: "It is unfair because this plate has more."

Give two toys different shares and invite your child to put them right. Start with 4 blocks for Fox and 2 for Duck. Keep all 6 blocks on the table so your child can follow every move.

Move one and check

Ask, "Who has fewer?" Move one block from Fox to Duck. Fox now has 3 and Duck has 3. Match the blocks or count each share. One move was enough, because it changed both sides: Fox lost one and Duck gained one.

Reset with 5 blocks and 1 block. After one move the shares are 4 and 2. They are still unequal. After a second move they are 3 and 3. Let your child decide when to stop by checking after each move. Moving another block would make the shares uneven again.

Notice what stays the same

Count all the blocks before and after moving them. There are still 6. Moving a block changes where it belongs, but no block joins or leaves the game.

Swapping the whole piles does not fix an unfair share. The toy with more has changed, but the two numbers are still different. Bring the rows together so your child can see which blocks still lack partners.

Try another fair fix

A spare box gives you more choices. If Fox has 2 stickers and Duck has 3, give Fox one more from the box. Both now have 3. You could also put one of Duck's stickers away. These fixes change the number in the game; moving between shares keeps it unchanged.

With 7 toy cars between two toys, a whole car will remain after making 3 each. Moving it back and forth gives 4 and 3, then 3 and 4. Save that car beside the shares. The uneven total needs a leftover plan.

Ask your child to describe a successful fix: "Fox had more. I moved one to Duck. Now they each have 3." Let the objects support the explanation.

Set out a small pile and one plate for each toy. Sharing means giving each toy part of the pile. To make the shares equal, everyone needs the same number.

Give everyone a turn

Use 6 blocks and two plates. Ask your child to give one to each plate, in the same order each time. Say, "One for Bear, one for Cat." After the first round, each plate has 1 block and 4 remain in the pile.

Go around again. Each plate now has 2 blocks and 2 remain. One last round gives each plate 3. The pile is empty. Count both shares and say, "6 shared between 2 is 3 each."

For three toys, put down three separate mats. Share 9 blocks by visiting every mat once in each round. After three rounds, every mat has 3. With 8 blocks and four mats, two rounds give 2 each.

Keep the turns easy to follow

Name each toy while giving its block. This helps your child notice a skipped plate. If the shares stop matching, pause and check who missed a turn. A handful can hide unequal amounts; one block at a time makes each turn clear.

Giving two at a time can work too. Share 8 blocks between two plates by giving 2 to each plate in a round. Repeat once. Both plates have 4. Each full round must give everyone the same amount.

Check the shares and the whole pile

First count each share. Then count everything together, including anything left beside the plates. The shares and leftovers must account for the starting pile. If a block rolled away, the total check helps you notice it.

Try sharing the same 6 blocks between two toys, then three toys. Each toy gets 3 in the first game and 2 in the second. More people never gives each person more from the same pile. Sometimes each gets the same as before: 4 blocks give 1 each to either three or four toys, with a leftover in the three-toy game.

A leftover is something that remains after everyone has had the same number of turns. There are too few things for another full round. Put leftovers beside the plates so your child can see them.

Find where to stop

Share 7 blocks between two toys. Three full rounds use 6 blocks, giving 3 to each toy. One block remains. Giving it to one toy would make the shares 4 and 3. The sharing was done correctly; there simply is not another whole block for both toys.

Try 10 blocks between four toys. Two full rounds give 2 each and use 8. Two blocks remain, but another full round would need four. Both extra blocks belong beside the shares.

Agree on a fair plan

Ask, "What shall we do with the ones left over?" You can save them, return them to the box, or give them to someone outside the sharing game. Adding enough blocks for another full round also works. For 7 blocks between two toys, add 1 block to make 8, then give one more to each.

Food that can be cut offers another choice: split the leftover into equal pieces. Whole toys cannot be shared that way. The child who dealt the things does not automatically get the extras; that would give them more.

Look for a pattern between two

Try the numbers from 1 to 10 with two plates. The numbers 2, 4, 6, 8, and 10 leave nothing over. These are even numbers. The numbers 1, 3, 5, 7, and 9 leave one over. These are odd numbers. Keep the objects beside the number as your child spots the pattern.

The number of people matters too. Six blocks share with nothing left between two or three toys. Between four toys, they give 1 each with 2 left. Before a new game, invite a prediction: "Will there be any left?" Let your child test it with the pile.

Your child can also make groups of a chosen size. Put 8 crayons on the table and ask, "How many children can have 2 crayons each?" Here you know the size of each group. You are finding how many groups you can make.

Build one full group at a time

Count out 2 crayons and set them together on a mat. That is one group. Make another group of 2 beside it. Keep going until all 8 crayons are used. Count the groups: there are four, enough for four children.

Keep a finger on each group as you count it. Counting every crayon answers how many crayons there are. Counting the separate groups answers how many children can receive a group.

Now try 6 blocks, with 3 blocks in each tower. Build one tower of 3, then a second tower of 3. There are two towers. Ask the two questions separately: "How many blocks are in each tower?" and "How many towers did you make?"

Check every group

The agreed size stays the same. If a tower has 2 blocks when each tower needs 3, it is not full. Compare the towers or count each one before counting how many full towers you made.

With 7 blocks in towers of 2, your child can build three full towers. One block remains. Keep it beside the towers; a single block is not another full tower of 2.

Find pairs at home

A pair is a group of two. Line up 10 socks in pairs and count five pairs. You can count the socks two at a time: "2, 4, 6, 8, 10." Shoes and mittens give other chances to make pairs.

Both games end with equal groups. Listen for whether your child is counting the things inside each group or the groups themselves.

Half is one of two equal shares. Help your child find half of a group by sharing it between two toys. Each toy's share is half of the starting group.

Share and name one half

Put 8 toy cars in a pile. Give one to each of two toys in turn. After four rounds, each toy has 4 cars. Say, "Half of 8 is 4." Point to one share as you say "half," then bring both shares together to show all 8 again.

Make the shares 3 and 5. Ask whether they are halves. They are two parts, but they are not equal parts. Move one car from the larger share to the smaller share and check again. Both shares must match before either can be called half.

Practice the small halves

Build each whole pile before sharing it. These are the halves of the even numbers to 10:

• Half of 2 is 1.
• Half of 4 is 2.
• Half of 6 is 3.
• Half of 8 is 4.
• Half of 10 is 5.

Your child may connect the word "half" with the number two and answer "2" every time. Two tells you how many equal shares to make. Count one share to find how many are in that half.

When a whole thing remains

Try sharing 5 pretend apples. Each toy gets 2, with 1 apple left. Whole apples alone cannot finish the two equal shares. Show how cutting the last apple into two equal pieces gives each toy 2 apples and half an apple. With real food, an adult handles the knife.

Keep the meaning of half clear in everyday talk. Eating a few bites is eating some; it is half only when the eaten amount and the amount left are equal. You can show this with a flat piece of dough split into two equal amounts.

Ask your child to point to the whole group, then to one half. Saying "Half of 6 is 3" names both the starting amount and the size of one share.

One whole thing can be shared too. A paper square, a sandwich, or a flat piece of dough gives your child something to split. Fair pieces hold the same amount of that whole.

Fold and match

Give your child a square sheet of paper. Bring one edge over to the opposite edge. Help the edges meet exactly, then press the fold. Open it and point to the two equal parts. Each part is half; together they are halves of the sheet.

Fold again along the crease. One part covers the other exactly. This checks the two parts without needing to count objects. For a straight cut through the center of a square, rectangle, or circle, you can lay one piece on the other. Turn or flip a piece if needed to make them fit.

Two pieces need to be equal

Tear a different paper square into one large and one small piece. There are two pieces, but they are not halves. One person would get more paper. Avoid asking for "the bigger half": halves of the same whole have equal amounts.

A square can be halved in different ways. A straight cut down the middle gives two rectangles. A cut from corner to corner gives two triangles. Each way shares the square equally. A triangle half and a rectangle half of the same-size square hold equal amounts, even though their shapes differ.

Keep track of the whole

Fit two halves back together. The original whole returns. Breaking one half into smaller pieces does not add more paper or more food. More pieces can still be the same amount.

For four toys, fold a sheet in half, then fold it in half again. Open it to see four equal parts. Each part gives one toy the same amount. Check the folds line up so the pieces match.

You can also try "one cuts, one chooses" with dough. One child makes the two pieces; the other chooses first. Ask the cutter how to make either choice feel fair.

To double, make the same number again and put both groups together. Double 3 means 3 and another 3. Your child can build, draw, or use fingers to show both equal groups.

Build the same again

Build a tower with 2 blocks. Ask your child to make another tower just like it. Count both towers together: 4 blocks. Say, "Double 2 is 4." Keep the towers separate at first so your child can see the two matching groups.

Now build a row of 4 blocks and copy it below. Match the blocks across the rows. There are 4 in each row. Count all the blocks to find 8. If your child knows the first row has 4, they can keep counting through the second row: "5, 6, 7, 8."

Show a double another way

Hold up 3 fingers on each hand. Both hands show the same number, and together they show 6. Draw a ladybug with 2 spots on one wing and 2 on the other. Ask your child to name the double and count its total.

A mirror can show the same number again. Put two toy cars in front of it. Your child sees two real cars and two reflected cars, making four cars to look at. The reflection shows a double picture; the actual toys have stayed on the table.

Check the second group

If your child adds just one block to a group of 4, they have made 5. Ask them to build another full group of 4 for a double. "The same again" is a useful phrase while they copy the first group.

If they add 2 because the word double makes them think of two, point to the groups. Double needs two groups, each holding the starting number. Match each new block to one in the first group.

Before counting, ask, "Will we have more than we started with?" Doubling any of the numbers 1 to 5 makes a larger total. Let your child show why with their two groups.

Small doubles become familiar through pictures, fingers, and quick games. Start with facts your child can see easily, then return to the less familiar ones with blocks.

Say each whole fact

Use these five doubles:

• "Double 1 is 2."
• "Double 2 is 4."
• "Double 3 is 6."
• "Double 4 is 8."
• "Double 5 is 10."

Show the starting number on each hand as you speak. Double 5 uses all ten fingers. Double 4 can use four fingers on each hand, with both thumbs down. Saying the starting number and its double together helps your child connect them. Reciting "2, 4, 6, 8, 10" alone leaves out which double made each total.

If your child already recognizes plus and equals signs, show a fact beside its model:

Read it as, "3 and 3 make 6." The blocks or fingers still show what the marks mean.

Build a staircase

Use one color for the first group and another for its matching group. Build towers with 1 and 1 blocks, then 2 and 2, up to 5 and 5. The tower totals are 2, 4, 6, 8, and 10. Each next tower grows by 2: one extra block in each color.

Split any tower back into its two color groups. They are equal. Every double you built can share between two with nothing left. These totals are the even numbers to 10.

Play for recall

Draw cards showing one to five dots. Turn one over and ask your child to say its double. They can show both groups on their fingers to check. Start with doubles of 1, 2, and 5, then mix in 3 and 4.

Look for dominoes with the same number of dots at both ends. Your child can name the double before counting the total. If a total is one too high or low, touch every dot once to check. Keep the game relaxed so remembering grows from knowing what the double means.

Doubling and halving undo each other. When your child makes a double, they join two equal groups. When they halve that total, they separate it into those two equal groups again.

Build, join, and share

Make a tower of 4 blocks. Copy it with 4 more blocks and count all 8. Say, "Double 4 is 8." Mix the blocks, then share them between two toys. Each toy gets 4. Say, "Half of 8 is 4."

Keep the two actions visible. Doubling starts with one group's number and finds the total. Halving starts with the whole total and finds one equal share. Asking, "What are we starting with?" helps your child choose which action to take.

Use a fact you know

If your child knows double 3 is 6, ask how many each toy gets from 6 blocks. They can answer 3, then share to check. A known half works in the other direction too: half of 10 is 5, so two groups of 5 make 10.

The linked facts are:

Listen to the story

"Two toys each need 2 blankets" asks for the total: double 2 is 4. "Four blankets go equally to two toys" asks for one share: half of 4 is 2. Act out both stories and let your child point to what the answer counts.

If your child doubles when asked to halve, return to the whole pile. Sharing it between two gives each toy fewer than the starting total. Making the same pile again gives more.

When doubles come quickly, try a nearby addition. Put 3 red blocks beside 4 blue blocks. Show 3 and 3 first: that makes 6. One blue block remains, making 7. The known double gives your child a starting point for finding the new total.