One of the biggest ideas behind adding and subtracting is the putting together and taking apart of collections. The following help to support the understanding of addition and subtraction concepts. Use of these strategies help students develop confidence in their ability to deal with numerical situations with flexibility, ease and efficiency.

1. Part whole relationships: For children who are developing early number sense, the idea that any collection can be separated into parts, that each part can be represented by a number and that the same number can be thought of in parts and many different ways is an important stage in the development of understanding addition and subtraction. Early on children will often disagree that the same number can be partitioned in more than one way (that 3 and 5 is eight but so is 2 and 6).

Ways to help: Children need many experiences breaking up the same collection in different ways, for instance take a small collection of pennies (10) and play “Heads and Tails.” Drop the pennies on a board. Count the number of heads and count the number of tails. How many pennies do you have altogether? What do you think will happen if we do this again? Do you think we’ll have the same number of heads and tails? Repeat and keep track of all the combinations.

2. Anchors of 5 and 10- Knowing that numbers can be thought of in relation to 5 and 10 (and later in relation to 50, 100, 500, etc) helps children understand many other number relationships and further strengthens number sense. Knowing how 2 relates to 5, that it is 3 less, or that 7 is 2 more than five and 3 less than ten is helpful for children as they begin to learn their basic facts (see //How to Help Your Child with Basic Facts//). In addition, seeing 12 as 10 + 2, 13 as 10 + 3 and so on, helps build understanding of our base ten system.

Ways to help:“Plus Five Machine”- Use a calculator to practice adding five (or 10). Enter + 5 = on the calculator. Next, your partner enters any number (start with numbers five or less, then ten or less, then less than 20) and says the sum of that number plus five before pressing the = key. Continue with other numbers.

3. Composing and Decomposing numbers- Collections can be organized or grouped in different ways to make it easier to see how many. The standard way of grouping numbers is based on our place value system; that 334 can be partitioned into a variety of ways such as three hundred, three tens and four ones or, 33 tens and four ones, or 334 ones. Partitioning numbers in nonstandard ways helps us mentally compute more efficiently such as 334 = 234 + 100. Having this flexibility makes it easy to subtract 95.

4. Estimation Skills: Estimation skills are related to understanding of quantity. These skills help students with applying logic and reasoning in problem-solving situations and enable students to make sense of the problem. Without estimation skills, students cannot judge the appropriateness of an answer.

Ways to help: Because estimating is about making sense of the numbers ask questions that stay within the context of the situation such as :

More or Less than… questions, such as, Will it be more or less than 10 dollars? Are there more or less than 20 cookies on the plate? Is the yard more or less than 25 steps long?

Closer to or to _? Will it be closer to 10 dollars or 20 dollars? Will it be closer to 10 cookies or 30 cookies? Is the yard closer to 15 steps or 30 steps?

About _. Give choices of multiples of five: 5, 10, 15, 20, 25, 30…Ask, About how many dollars? About how many cookies? About how many footsteps?

## Addition and Subtraction

One of the biggest ideas behind adding and subtracting is the putting together and taking apart of collections. The following help to support the understanding of addition and subtraction concepts. Use of these strategies help students develop confidence in their ability to deal with numerical situations with flexibility, ease and efficiency.

1. Part whole relationships:For children who are developing early number sense, the idea that any collection can be separated into parts, that each part can be represented by a number and that the same number can be thought of in parts and many different ways is an important stage in the development of understanding addition and subtraction. Early on children will often disagree that the same number can be partitioned in more than one way (that 3 and 5 is eight but so is 2 and 6).Ways to help: Children need many experiences breaking up the same collection in different ways, for instance take a small collection of pennies (10) and play “Heads and Tails.” Drop the pennies on a board. Count the number of heads and count the number of tails. How many pennies do you have altogether? What do you think will happen if we do this again? Do you think we’ll have the same number of heads and tails? Repeat and keep track of all the combinations.2. Anchors of 5 and 10- Knowing that numbers can be thought of in relation to 5 and 10 (and later in relation to 50, 100, 500, etc) helps children understand many other number relationships and further strengthens number sense. Knowing how 2 relates to 5, that it is 3 less, or that 7 is 2 more than five and 3 less than ten is helpful for children as they begin to learn their basic facts (see //How to Help Your Child with Basic Facts//). In addition, seeing 12 as 10 + 2, 13 as 10 + 3 and so on, helps build understanding of our base ten system.Ways to help:“Plus Five Machine”- Use a calculator to practice adding five (or 10). Enter + 5 = on the calculator. Next, your partner enters any number (start with numbers five or less, then ten or less, then less than 20) and says the sum of that number plus five before pressing the = key. Continue with other numbers.3. Composing and Decomposing numbers- Collections can be organized or grouped in different ways to make it easier to see how many. The standard way of grouping numbers is based on our place value system; that 334 can be partitioned into a variety of ways such as three hundred, three tens and four ones or, 33 tens and four ones, or 334 ones. Partitioning numbers in nonstandard ways helps us mentally compute more efficiently such as 334 = 234 + 100. Having this flexibility makes it easy to subtract 95.4.

Estimation Skills: Estimation skills are related to understanding of quantity. These skills help students with applying logic and reasoning in problem-solving situations and enable students to make sense of the problem. Without estimation skills, students cannot judge the appropriateness of an answer.Ways to help: Because estimating is about making sense of the numbers ask questions that stay within the context of the situation such as :Top of Page