## Preschoolers and Number Sense: Summertime Ideas

June 14, 2015

One of the most important math skills students need to learn is number sense. It is the bases for more completed math skills we learn through elementary. I have included some games you can play this summer to build number sense while having fun!

Preschool number activities often involve counting, but merely reciting the number words isn't enough. Kids also need to develop "number sense," an intuitive feeling for the actual quantity associated with a given number.That's where these activities can help. Inspired by research, the following games encourage kids to think about several key concepts, including:

CCSS.MATH.CONTENT.K.CC.A.1: Count to 100 by ones and by tens.

CCSS.MATH.CONTENT.K.CC.A.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

CCSS.MATH.CONTENT.K.CC.A.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). K.CC.B:

Count to tell the number of objects.

CCSS.MATH.CONTENT.K.CC.B.4: Understand the relationship between numbers and quantities; connect counting to cardinality.

CCSS.MATH.CONTENT.K.CC.B.4.A: When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

CCSS.MATH.CONTENT.K.CC.B.4.B: Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

CCSS.MATH.CONTENT.K.CC.B.4.C: Understand that each successive number name refers to a quantity that is one larger.

CCSS.MATH.CONTENT.K.CC.B.5: Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

Compare numbers.

CCSS.MATH.CONTENT.K.CC.C.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

CCSS.MATH.CONTENT.K.CC.C.7: Compare two numbers between 1 and 10 presented as written numerals.

Most activities use a set of cards and counting tokens. Here’s what you need to get started. Preparing for preschool number activities:

Cards will be used in two ways, (1) as displays of dots for kids to count, and (2) as templates for kids to cover with tokens. Make your cards from heavy-stock writing paper, marking each with an Arabic numeral (1-10) and the corresponding number of dots.

Make your dots conspicuous, and space them far enough apart that your child can easily place one and only one token on top of each dot. The larger your tokens, the larger your cards will need to be.

In addition, you might make multiple cards for the same number--each card bearing dots arranged in different configurations. For example, one “three” card might show three dots arranged in a triangular configuration. Another might show the dots arranged in a line. Still another might show the dots that appear to have been placed randomly. But whatever your configuration, leave enough space between dots for your child to place a token over each dot.

Tokens

Kids can use a variety of objects for tokens, but keep in mind two points.

1. Children under the age of three years are at special risk of choking, so choose big tokens. According to the U.S. Consumer Product Safety Commission, a ball-shaped object is unsafe if it is smaller than a 1.75” diameter golf ball. Other objects are unsafe if they can fit inside a tube with a diameter of 1.25” inches.

2. Kids can get distracted if your tokens are too interesting, so it's best to avoid the fancy plastic frogs or spiders

Start small. It’s important to adjust the game to your child’s attention span and developmental level. For beginners, this means counting tasks that focus on very small numbers (up to 3 or 4).

Keep it fun. If it’s not playful and fun, it’s time to stop. Be patient. It takes young children about a year to learn how the counting system works.

Place a card, face up, before your child. Then ask your child to place the correct number of tokens on the card—one token over each dot.

After the child has finished the task, replace the card and tokens and start again with a new card. Once your child has got the hang of this, you can modify the game by helping your child count each token as he puts it in place.

Choose two cards, each displaying a different number of dots, taking care that the cards differ by a ratio of at least 2:1. For instance, try 1 vs. 2, 2 vs. 4, and 2 vs. 5. You can also try larger numbers, like 6 vs. 12.

Next, set one card in front of your child and the other in front of you. Have your child cover all the dots with tokens (pretending they are cookies) and ask her

After she answers you, you can count to check the answer. But I’d skip this step if you are working with larger numbers (like 6 vs. 12) that are beyond your child’s current grasp. You don’t want to make this game feel like a tedious exercise.

As your child becomes better at this game, you can try somewhat smaller ratios (like 5 vs. 9).

And for another variant, ask your child to compare the total amount of cookies shared between you with the cookies represented on another, third card. In recent experiments, adults who practiced making these sorts of “guesstimates” experienced a boost in their basic arithmetic skills.

Instead of playing with the tokens, have your child place the cards side-by-side in correct numeric sequence. For beginners, try this with very small numbers (1, 2, 3) and with numbers that vary by a large degree (e.g., 1, 3, 6, 12).

Choose three toy creatures as party attendees and have your child set the table—providing one and only plate, cup, and spoon to each toy. Then give your child a set of “cookies” (tokens or real edibles) and ask her to share these among the party guests so they each receive the same amount. Make it simple by giving your child 6 or 9 tokens so that none will be left over.

As always, go at your child’s pace and quit if it isn’t fun. If your child makes a mistake and gives one creature too many tokens, you can play the part of another creature and complain. You can also play the part of tea party host and deliberately make a mistake. Ask for your child’s help? Did someone get too many tokens? Or not enough? Have your child fix it. Once your child gets the hang of things, try providing him with one token too many and discuss what to do about this "leftover." One solution is to divide the remainder into three equal bits. But your child may come up with other, non-mathematical solutions, like eating the extra bit himself.

Play the basic game as described above, but instead of having your child place the tokens directly over the dots, have your child place the tokens alongside the card. Ask your child to arrange his tokens in the same pattern that is illustrated on the card. And count!

For this game, use cards bearing dots only--no numerals. To play, place two cards--each bearing the same number of dots, but arranged in different patterns--side by side. Ask your child to recreate each pattern using his tokens. When she’s done, help her count the number of tokens in each pattern. The patterns look different, but they use the same number of dots/tokens.

Even before kids master counting, they can learn about the concepts of addition and subtraction. Have a puppet “bake cookies” (a set of tokens) and ask your child to count the cookies (helping if necessary). Then then have the puppet bake one more cookie and add it to the set. Are there more cookies or fewer cookies now? Ask your child to predict how many cookies are left. Then count again to check the answer. Try the same thing with subtraction by having the puppet eat a cookie.

Don’t expect answers that are precise and correct. But you may find that your child is good at getting the gist. When researchers asked 3-, 4- and 5-year olds to perform similar tasks, they found that 90% of the predictions went in the right direction.

As your child begins to master the first few number words, you can also try these research-tested preschool number activities for teaching kids about the number line. Games can be very useful for reinforcing and developing ideas and procedures previously introduced to children. Although a suggested age group is given for each of the following games, it is the children's level of experience that should determine the suitability of the game. Several demonstration games should be played, until the children become comfortable with the rules and procedures of the games.

Materials: 15 dot cards with a variety of dot patterns representing the numbers from one to five and a plentiful supply of counters or buttons.

Rules: One child deals out one card face up to each other player. Each child then uses the counters to replicate the arrangement of dots on his/her card and says the number aloud. The dealer checks each result, then deals out a new card to each player, placing it on top of the previous card. The children then rearrange their counters to match the new card. This continues until all the cards have been used.

Variations/Extensions:

Each child can predict aloud whether the new card has more, less or the same number of dots as the previous card. The prediction is checked by the dealer, by observing whether counters need to be taken away or added.

Increase the number of dots on the cards.

Memory Match (5-7 years) 2 players

Materials: 12 dot cards, consisting of six pairs of cards showing two different arrangements of a particular number of dots, from 1 to 6 dots. (For example, a pair for 5 might be Card A and Card B from the set above).

Rules: Spread all the cards out face down. The first player turns over any two cards. If they are a pair (i.e. have the same number of dots), the player removes the cards and scores a point. If they are not a pair, both cards are turned back down in their places. The second player then turns over two cards and so on. When all the cards have been matched, the player with more pairs wins.

Variations/Extensions

Materials: A pack of 20 to 30 dot cards (1 to 10 dots in dice and regular patterns), counters.

Rules: Spread out 10 cards face down and place the rest of the cards in a pile face down. The first player turns over the top pile card and places beside the pile. They then turns over one of the spread cards. The player works out the difference between the number of dots on each card, and takes that number of counters. (example: If one card showed 3 dots and the other 8, the player would take 5 counters.) The spread card is turned face down again in its place and the next player turns the top pile card and so on. Play continues until all the pile cards have been used. The winner is the player with the most counters; therefore the strategy is to remember the value of the spread cards so the one that gives the maximum difference can be chosen.

Variations/Extensions:

Try to turn the spread cards that give the minimum difference, so the winner is the player with the fewest counters. Roll a die instead of using pile cards. Start with a set number of counters (say 20), so that when all the counters have been claimed the game ends. Use dot cards with random arrangements of dots.

Preschool number activities often involve counting, but merely reciting the number words isn't enough. Kids also need to develop "number sense," an intuitive feeling for the actual quantity associated with a given number.That's where these activities can help. Inspired by research, the following games encourage kids to think about several key concepts, including:

- Relative magnitudes
- The one-to-one principle of counting and cardinality (two sets are equal if the items in each set can be matched, one-to-one, with no items left over)
- The one-to-one principle of counting (each item to be counted is counted once and only once)
- The stable order principle (number words must be recited in the same order)
- The principle of increasing magnitudes (the later number words refer to greater cardinality)
- The cardinal principle

#### Common Core Standards These Games Target:

Know number names and the count sequence.CCSS.MATH.CONTENT.K.CC.A.1: Count to 100 by ones and by tens.

CCSS.MATH.CONTENT.K.CC.A.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

CCSS.MATH.CONTENT.K.CC.A.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). K.CC.B:

Count to tell the number of objects.

CCSS.MATH.CONTENT.K.CC.B.4: Understand the relationship between numbers and quantities; connect counting to cardinality.

CCSS.MATH.CONTENT.K.CC.B.4.A: When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

CCSS.MATH.CONTENT.K.CC.B.4.B: Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

CCSS.MATH.CONTENT.K.CC.B.4.C: Understand that each successive number name refers to a quantity that is one larger.

CCSS.MATH.CONTENT.K.CC.B.5: Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

Compare numbers.

CCSS.MATH.CONTENT.K.CC.C.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

CCSS.MATH.CONTENT.K.CC.C.7: Compare two numbers between 1 and 10 presented as written numerals.

Most activities use a set of cards and counting tokens. Here’s what you need to get started. Preparing for preschool number activities:

__Cards__Cards will be used in two ways, (1) as displays of dots for kids to count, and (2) as templates for kids to cover with tokens. Make your cards from heavy-stock writing paper, marking each with an Arabic numeral (1-10) and the corresponding number of dots.

Make your dots conspicuous, and space them far enough apart that your child can easily place one and only one token on top of each dot. The larger your tokens, the larger your cards will need to be.

In addition, you might make multiple cards for the same number--each card bearing dots arranged in different configurations. For example, one “three” card might show three dots arranged in a triangular configuration. Another might show the dots arranged in a line. Still another might show the dots that appear to have been placed randomly. But whatever your configuration, leave enough space between dots for your child to place a token over each dot.

Tokens

Kids can use a variety of objects for tokens, but keep in mind two points.

1. Children under the age of three years are at special risk of choking, so choose big tokens. According to the U.S. Consumer Product Safety Commission, a ball-shaped object is unsafe if it is smaller than a 1.75” diameter golf ball. Other objects are unsafe if they can fit inside a tube with a diameter of 1.25” inches.

2. Kids can get distracted if your tokens are too interesting, so it's best to avoid the fancy plastic frogs or spiders

#### Games to play

One you have your cards and tokens, you can play any of the preschool number activities below. As you play, keep in mind the points raised in my evidence-based guide to preschool math lessons:Start small. It’s important to adjust the game to your child’s attention span and developmental level. For beginners, this means counting tasks that focus on very small numbers (up to 3 or 4).

Keep it fun. If it’s not playful and fun, it’s time to stop. Be patient. It takes young children about a year to learn how the counting system works.

__The basic game: One-to-one matching__Place a card, face up, before your child. Then ask your child to place the correct number of tokens on the card—one token over each dot.

After the child has finished the task, replace the card and tokens and start again with a new card. Once your child has got the hang of this, you can modify the game by helping your child count each token as he puts it in place.

__The Tea Party: Relative magnitudes__Choose two cards, each displaying a different number of dots, taking care that the cards differ by a ratio of at least 2:1. For instance, try 1 vs. 2, 2 vs. 4, and 2 vs. 5. You can also try larger numbers, like 6 vs. 12.

Next, set one card in front of your child and the other in front of you. Have your child cover all the dots with tokens (pretending they are cookies) and ask her

__“Which of us has more cookies?”__After she answers you, you can count to check the answer. But I’d skip this step if you are working with larger numbers (like 6 vs. 12) that are beyond your child’s current grasp. You don’t want to make this game feel like a tedious exercise.

As your child becomes better at this game, you can try somewhat smaller ratios (like 5 vs. 9).

And for another variant, ask your child to compare the total amount of cookies shared between you with the cookies represented on another, third card. In recent experiments, adults who practiced making these sorts of “guesstimates” experienced a boost in their basic arithmetic skills.

__Bigger and bigger: Increasing magnitudes__Instead of playing with the tokens, have your child place the cards side-by-side in correct numeric sequence. For beginners, try this with very small numbers (1, 2, 3) and with numbers that vary by a large degree (e.g., 1, 3, 6, 12).

__Sharing at the tea party: The one-to-one principle__Choose three toy creatures as party attendees and have your child set the table—providing one and only plate, cup, and spoon to each toy. Then give your child a set of “cookies” (tokens or real edibles) and ask her to share these among the party guests so they each receive the same amount. Make it simple by giving your child 6 or 9 tokens so that none will be left over.

As always, go at your child’s pace and quit if it isn’t fun. If your child makes a mistake and gives one creature too many tokens, you can play the part of another creature and complain. You can also play the part of tea party host and deliberately make a mistake. Ask for your child’s help? Did someone get too many tokens? Or not enough? Have your child fix it. Once your child gets the hang of things, try providing him with one token too many and discuss what to do about this "leftover." One solution is to divide the remainder into three equal bits. But your child may come up with other, non-mathematical solutions, like eating the extra bit himself.

__Matching patterns: Counting__Play the basic game as described above, but instead of having your child place the tokens directly over the dots, have your child place the tokens alongside the card. Ask your child to arrange his tokens in the same pattern that is illustrated on the card. And count!

__Matching patterns: Conservation of number__For this game, use cards bearing dots only--no numerals. To play, place two cards--each bearing the same number of dots, but arranged in different patterns--side by side. Ask your child to recreate each pattern using his tokens. When she’s done, help her count the number of tokens in each pattern. The patterns look different, but they use the same number of dots/tokens.

__The cookie maker: Making predictions about changes to a set__Even before kids master counting, they can learn about the concepts of addition and subtraction. Have a puppet “bake cookies” (a set of tokens) and ask your child to count the cookies (helping if necessary). Then then have the puppet bake one more cookie and add it to the set. Are there more cookies or fewer cookies now? Ask your child to predict how many cookies are left. Then count again to check the answer. Try the same thing with subtraction by having the puppet eat a cookie.

Don’t expect answers that are precise and correct. But you may find that your child is good at getting the gist. When researchers asked 3-, 4- and 5-year olds to perform similar tasks, they found that 90% of the predictions went in the right direction.

__The Big Race: Increasing magnitudes and the number line__As your child begins to master the first few number words, you can also try these research-tested preschool number activities for teaching kids about the number line. Games can be very useful for reinforcing and developing ideas and procedures previously introduced to children. Although a suggested age group is given for each of the following games, it is the children's level of experience that should determine the suitability of the game. Several demonstration games should be played, until the children become comfortable with the rules and procedures of the games.

__Deal and Copy (4-5 years) 3-4 players__Materials: 15 dot cards with a variety of dot patterns representing the numbers from one to five and a plentiful supply of counters or buttons.

Rules: One child deals out one card face up to each other player. Each child then uses the counters to replicate the arrangement of dots on his/her card and says the number aloud. The dealer checks each result, then deals out a new card to each player, placing it on top of the previous card. The children then rearrange their counters to match the new card. This continues until all the cards have been used.

Variations/Extensions:

Each child can predict aloud whether the new card has more, less or the same number of dots as the previous card. The prediction is checked by the dealer, by observing whether counters need to be taken away or added.

Increase the number of dots on the cards.

Memory Match (5-7 years) 2 players

Materials: 12 dot cards, consisting of six pairs of cards showing two different arrangements of a particular number of dots, from 1 to 6 dots. (For example, a pair for 5 might be Card A and Card B from the set above).

Rules: Spread all the cards out face down. The first player turns over any two cards. If they are a pair (i.e. have the same number of dots), the player removes the cards and scores a point. If they are not a pair, both cards are turned back down in their places. The second player then turns over two cards and so on. When all the cards have been matched, the player with more pairs wins.

Variations/Extensions

- Increase the number of pairs of cards used.
- Use a greater number of dots on the cards.
- Pair a dot card with a numeral card.

__What's the Difference? (7-8 years) 2-4 players__Materials: A pack of 20 to 30 dot cards (1 to 10 dots in dice and regular patterns), counters.

Rules: Spread out 10 cards face down and place the rest of the cards in a pile face down. The first player turns over the top pile card and places beside the pile. They then turns over one of the spread cards. The player works out the difference between the number of dots on each card, and takes that number of counters. (example: If one card showed 3 dots and the other 8, the player would take 5 counters.) The spread card is turned face down again in its place and the next player turns the top pile card and so on. Play continues until all the pile cards have been used. The winner is the player with the most counters; therefore the strategy is to remember the value of the spread cards so the one that gives the maximum difference can be chosen.

Variations/Extensions:

Try to turn the spread cards that give the minimum difference, so the winner is the player with the fewest counters. Roll a die instead of using pile cards. Start with a set number of counters (say 20), so that when all the counters have been claimed the game ends. Use dot cards with random arrangements of dots.

Have a great time playing this games this summer that target important math skills. Happy playing!

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Great tips and ideas. Thanks.

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