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Place value charts are helpful for students who learn visually. This site shows you different options for place value charts, and how to make them for your classroom.

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Place value, in mathematics, describes the value of every digit in a number depending on its position. These positions start from the units place (ones place). The order of the place value of digits in a number from right to left is expressed as ones/units, tens, hundreds, thousands, ten thousands, and so on.

What is Place Value?

Place value is the value of each digit in a number. The value of every digit in a number is different based upon its position. A number might have two similar digits but different values, which is decided by the position that the digit holds in the number.

Place Value Meaning

Place value is the value of a digit according to its position in the number such as ones, tens, hundreds, and so on. For example, the place value of 5 in 3458 is 5 tens, or 50. However, the place value of 5 in 5781 is expressed as 5 thousands or 5,000. It is important to understand that a digit can be the same, but its value depends on its position in the number.

Example: Write down the place value of each digit in the number 543.

Solution: The correct place value of each digit in the number can be expressed as follows:

5 × 100 = 500 or 5 hundreds

4 × 10 = 40 or 4 tens

3 × 1 = 3 or 3 ones

Place Value Chart

Place value charts help us to make sure that the digits are aligned in the correct places. A place value chart displays the correct position or place of a digit in a number. To identify the positional values or worth of different digits in a number accurately, we first write the given digits in the place value chart to check their position. In order to make the process easier, the larger numbers are divided into periods that are separated with the help of commas. There are two types of place value charts that are most commonly used:

Indian place value chart

International place value chart

We can refer to the International or Indian place value chart based on the numeral system that both the charts follow. The Indian place value chart is based upon the Indian numeral system, while the International place value chart is based upon the Internationally accepted numeral system. The main difference between the Indian and the International numeral system is the placement of the separators (commas) and the nomenclature of different place values.

Indian Place Value Chart

The Indian place value chart is a table that is used to find the value of each digit in a number based on its position, as per the Indian numeral system. In this place value chart, a 10-digit number is grouped into periods of ones, thousands, lakhs, crores, and so on. These numbers are separated by commas following the rule of 3:2:2. This means starting from the right, the first comma is placed after 3 digits, then the next commas are placed after every 2 digits. For example, observe the commas in the following number: 5,43,13,62,283

Observe the Indian place value chart given below which shows the place value of digits till ten crores.

International Place Value Chart

The International numeral system is used worldwide in which we count in the order of ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, and so on. In this place value chart, the numbers are grouped into periods of ones, thousands, millions, and so on and they are separated by a comma after every 3 digits, starting from the right. For example, observe the commas in the following number: 135,912,332. Observe the International place value chart given below which shows the place value of digits up to hundred millions.
Printable Place Value Charts
Memorizing and solving problems on place value systems becomes easier using a printable place value chart. These charts have place values printed in a tabular form across blank spaces for each digit in a number. While referring to these charts for solving a problem, we can directly place the digits in their respective position according to the one in the number and evaluate their place values accordingly.

Place Value Chart with Decimals

The decimal place value chart shows the place value of the digits in a decimal number. A decimal number system is used to express the whole numbers and fractions together using a decimal point. This decimal point lies between the whole number part and the fractional part. While the whole number part follows the usual place value chart of ones, tens, hundreds, and so on, there is a slight difference in the place value of the numbers to the right of the decimal point. If we go to the right after the decimal, the place values start from tenths and go on as hundredths, thousandths and so on. The first place to the right of the decimal is on the one-tenth (1/10 th) position, the next one is 1/100 and it goes on. Observe the following place value chart for decimal numbers.

Place Value and Face Value

The face value of a digit in any number is the digit itself. Whether the number is single-digit, double-digit, or any number, each digit has its face value. Let us understand this using the following examples.

If 4 is the given number, the face value of 4 is 4, and the place value of 4 is also 4 (4 ones = 4 × 1 = 4).

For a given number 78, the face value of 7 is 7 and its place value is 70 (7 tens = 7 × 10 = 70).

For 52369, the face value of 3 is 3 while its place value is 300 (3 hundreds = 3 × 100 = 300).

Difference between Place Value and Face Value

Place value describes the position of a digit in a given number. On the other hand, face value represents the number itself. Let us take an example of a number say, 1437. The table given below explains the difference between the place value and the face value of digits in this number.

Place Value in Numbers

The place value in numbers can be expressed in two different ways. For example, the place value of 4 in 2458 can be expressed as 4 hundreds, or 400. In another example, the place value of 4 in 4681 is expressed as 4 thousands or 4,000.

In simple terms, if we need to express the place value in the number form we simply multiply the number with the name of the column under which it falls. For example, if we need to find the place value of 5 in 67538, we will first place the given number under the place value chart such that each digit is placed correctly under the respective column. In this case, we can see that 5 comes under the hundreds column. So, we can say that the place value of 5 is 5 × 100 = 500. Therefore, the place value of 5 is 500 in the given number.

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What is Place Value in Math?

Place value is the value of each digit in a number. The value of every digit in a number is different based on its position. A number might have two similar digits but different values, which is decided by the position that the digit holds in the number. For example, the place value of '9' in the number 8934 is 9 hundreds or 900 because 9 is on the hundreds place.

What is the Place Value of 6 in 64?

Since 6 is in the tens place, the place value of 6 in 64 is 6 tens, i.e., 6 × 10 = 60.

What is an Example of Place Value in Numbers?

Place value represents the worth of a digit in a number. A few examples of place values are given below:

What is the Place Value of 5 in 50?

Place value is the value of each digit in a number. The place value of the digit 5 in 50 is 5 tens, i.e., 5 × 10 = 50.

What is Place Value and Face Value with Example?

The face value of a digit in any number is the digit itself, while its place value is its position in the number. For example, the face value of 7 in 2769 is 7 while its place value is 7 hundreds or 700.

What is a Place Value Chart?

A place value chart is a table that is used to find the value of each digit in a number based on its position, as per the numeral system. In order to identify the worth of different digits in a number accurately, we place the given number in the place value chart so that the place value of each digit is seen. To make the process easier, the larger numbers are divided into periods that are separated with the help of commas. There are two types of place value charts that are most commonly used, the Indian place value chart and the International place value chart.

How to Make a Place Value Chart?

To make a place value chart, we can use the following steps:

Step 1: Draw columns showing different periods according to the type of numeral system: ones, tens, hundreds, thousands, and so on.

Step 2: Under each period, draw sub-columns to show the different place values.

You can refer to the Indian place value chart and International place value chart in the above sections for the different periods and place values of a digit in a number according to the type of numeral system.

Why is Place Value in Numbers Important?

The concept of place value in numbers is important because it gives the worth of every digit in a number according to its position. The essence of numbers as a whole can only be understood through the knowledge of place values.

What is the Place Value of Zero?

The place value of zero is always zero. For example, in a given number 4078, zero comes under hundreds place. So, this is expressed as, 0 hundreds, that is, 0 × 100 = 0.

How to Find the Place Value in Decimal Numbers?

In decimal numbers, the place value of the digits after the decimal is expressed in a little different way. We know that a decimal number consists of a whole number and a fractional part which is written after the decimal point. The whole number part follows the usual place value chart of ones, tens, hundreds. Now, if we go to the right after the decimal, the place values start from tenths and go on as hundredths, thousandths, and so on. For example, let us write the place value of all the digits in the following decimal number: 578.43

5 comes under the hundreds column, therefore, the place value of 5 is 5 hundreds, or 5 × 100 = 500

7 comes under the tens column, therefore, the place value of 7 is 7 tens, or 7 × 10 = 70

8 comes under the ones column, therefore, the place value of 8 is 8 ones, or 8 × 1 = 8

4 comes under the tenths column, therefore, the place value of 4 is 4 tenths, or 4/10 = 0.4

3 comes under the hundredths column, therefore, the place value of 3 is 3 hundredths, or 3/100 = 0.03

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Place Value - Charts, With Decimals | What is Place Value?

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Place value is the value of each digit in a number. It describes the value of every digit in a number depending on its position. These positions start from the units place (ones place). The order of the place value of digits in a number from right to left is expressed as ones/units, tens, hundreds,…

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This is an interactive number line by The Math Learning Center. This would be beneficial for hands on and visual learners.

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Number Line helps students visualize number sequences and demonstrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing.

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This site provides step-by-step instructions on how to complete operations using fractions.  It starts with fractions as numbers and moves step by step. Provides pictures as well, which would be helpful for visual learners.

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Slice a pizza, and we get fractions:

The top number says how many slices we have.
The bottom number says how many equal slices the whole pizza was cut into.

Have a try yourself:

Equivalent Fractions

Some fractions may look different, but are really the same, for example:

=

=

(Four-Eighths)

(Two-Quarters)

(One-Half)

=

=

It is usually best to show an answer using the simplest fraction ( in this case ). That is called Simplifying, or Reducing the Fraction

Numerator / Denominator

We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

You just have to remember those names! (If you forget just think "Down"-ominator)

Adding Fractions

It is easy to add fractions with the same denominator (same bottom number):

Another example:

Five-eighths plus one-eighth equals six-eighths, equals three-quarters

Adding Fractions with Different Denominators

But what about when the denominators (the bottom numbers) are not the same?

Three-eighths plus one-quarter equals ... what?

We must somehow make the denominators the same.

Three-eighths plus two-eighths equals five-eighths

There are two popular methods to make the denominators the same:

(They both work nicely, use the one you prefer.)

Other Things We Can Do With Fractions

We can also:

Visit the Fractions Index to find out even more.

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The top number says how many slices we have. The bottom number says how many equal slices the whole pizza was cut into. Some fractions may look different, but are really the same, for example: = = (Four-Eighths) (Two-Quarters) (One-Half) = = It is usually best to show an answer using the simplest fraction ( in this case ).

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Developing Effective Fractions Instruction for Kindergarten Through 8th Grade

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Developing Effective Fractions Instruction for Kindergarten Through 8th Grade

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From the What Works Clearinghouse, this article provides tips on Developing Effective Fractions Instruction for Kindergarten Through 8th Grade.

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This practice guide was prepared for the WWC by Mathematica under contract ED-07-CO-0062.

The following research staff contributed to the guide: Jeffrey Max, Moira McCullough, Andrew Gothro, and Sarah Prenovitz.

These videos were prepared by WestEd under the Doing What Works Contract (ED-PEP-11-C-0068).
All videos are based on recommendations from the WWC practice guides and are designed to complement the guides.

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developing effective fractions instruction for kindergarten through 8th grade

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WWC | Developing Effective Fractions Instruction for Kindergarten Through 8th Grade

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This practice guide presents five recommendations intended to help educators improve students' understanding of fractions. Recommendations include strategies to develop young children's understanding of early fraction concepts and ideas for helping older children understand the meaning of fractions and the computations involved.

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This contains the rules for each of the four operations in Math. It also has free downloads to use as study guides or in the classroom.

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Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

Let us understand each of the basic arithmetic operations in detail.

Basic Arithmetic Operations

The four basic arithmetic operations in Maths, for all real numbers, are:

Addition (Finding the Sum; '+')

Subtraction (Finding the difference; '-')

Multiplication (Finding the product; '×' )

Division (Finding the quotient; '÷')

Let us discuss all these four basic arithmetic operations with rules and examples in detail.

Addition Definition

The addition is a mathematical process of adding things together. The addition process is denoted by '+' sign. It involves combining two or more numbers into a single term. In addition process, the order does not matter. It means that the addition process is commutative. It can involve any type of number whether it be a real or complex number, fraction, or decimals.
Example: 4.13 + 3.87 = 8
The addition of more than two numbers, values or terms is also known as a summation of terms and can involve n number of values.

Addition Rules

The following are the addition rules for integers:

Addition of two positive integers is a positive integer

Addition of two negative integers is a negative integer

While adding positive and negative integers, subtract the integers and use the sign of the largest integer number

Subtraction Definition

The subtraction operation gives the difference between two numbers. Subtraction is denoted by '-' sign. It is almost similar to addition but is the conjugate of the second term. It is the inverse process of addition. The addition of the term with the negative term is known as subtraction. This process is mostly used to find how many are left when some things are taken away.

The term can also be re-written as 15 + (-7)
Adding terms we have, 8.
Read: Addition and Subtraction of Integers
Subtraction Rules

The following are the subtraction rules for integers:

If both the signs of the integers are positive, the answer will be the positive integer

If both the signs of the integers are negative, the answer will be the negative integer

If the signs of the integers are different, subtract the values, and take the sign from the largest integer value.

Multiplication Definition
Example: 2 × 3 = 6
Multiplication is known as repeated addition. It is denoted by '×' or '*'. It also combines with two or more values to result in a single value. The multiplication process involves multiplicand, multiplier. The result of the multiplication of multiplicand and the multiplier is called the product

Here, "2" is the multiplier, "3" is the multiplicand, and the result "6" is called the product.

The product of two numbers says 'a' and 'b' results in a single value term ' ab, ' where a and b are the factors of the final value obtained.

Multiplication Rules

The following are the multiplication rules for the integers.

The product of two positive integers is a positive integer

The product of two negative integers is a positive integer

The product of positive and negative integer is a negative integer

Division Definition
Example: 4 ÷ 2 = 2
The division is usually denoted by '÷ ' and is the inverse of multiplication. It constitutes two terms dividend and divisor, where the dividend is divided by the divisor to give a single term value. When the dividend is greater than the divisor, the result obtained is greater than 1, or else it would be less than 1.

Here, "4" is the dividend, "2" is the divisor, and the result "2" is called the quotient.

Read: Multiplication and Division of Integers

Division Rules

The following are the division rules for integers:

The division of two positive integers is a positive integer

The division of two negative numbers is a positive integer

The division of integers with different signs results in the negative integer.

Mathematical Operations

The basic mathematical operations are the four arithmetic operations that we have already learned in the above sections.

Addition and subtraction are inverse operations of each other. It means if the addition of two numbers gives the third number, then subtraction of an added number from the third number will result in the original number.

Now, if we subtract 7 from 11, we get;

Thus, we got the original number.

Similarly, multiplication and division are also inverse operations.

Thus, we can see, these mathematical operations are related to each other. Also, these operations are the simplest form of mathematical calculations, which can be easily understood by everyone.

Basic Arithmetic Properties

The basic arithmetic properties for real numbers are:

Commutative Property

This property is applicable only for two arithmetic operations, i.e., addition and multiplication.

Suppose A and B are two numbers, then, according to commutative property;

Thus, the order of numbers in addition and multiplication does not change the result.

Associative Property

Like commutative property, the associative property is also applicable to addition and multiplication.

Thus, if we change the grouping of numbers, the result does not change.

Distributive Property

According to the distributive property, if A, B and C are any three real numbers, then,

Example: 2 x (3 + 4) = (2 x 3) + (2 x 4)

Hence, proved.
Q.1: Add 23 and 40 and then subtract 20 from the sum.
Solved Examples

Solution: On adding 23 and 40, we get;
Q.2: Solve: 20 + 20 + 20 + 20 + 20.
Now subtracting 20 from the sum, we get;

Solution: Given, 20 + 20 + 20 + 20 + 20

It is clear that 20 is added to itself five times, thus, we can write;

5 times of 20 = 5 x 20 = 100
Q.3: Find the value of (6 x 4) ÷ 12 + 72 ÷ 8 - 9.
If we add them directly, the answer remains the same.

Solution: Given,

(6 x 4) ÷ 12 + 72 ÷ 8 - 9

⇒ (24 ÷ 12) + (72 ÷ 8) - 9 [BODMAS rule]

To learn more about numbers and different Maths-related concepts, visit BYJU'S- The Learning App.

Frequently Asked Questions on Arithmetic Operations

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Arithmetic Operation (Four Basic Operations in Maths)

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Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division. These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life.

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Interactive (color-coded) hundreds chart from The Toy Theatre. This can be color-coded however you want, and you can even remove some of the numbers completely by blacking them out.

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Interactive Hundreds Chart | Toy Theater

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Use this online hundreds chart to practice counting to one hundred, for modeling math problems, for skip counting, and more! Try it, it’s free!

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Anchor charts are great to create and hang in your classroom as reference points. Here are 17 anchor charts specific to place value.

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Grasping place value is a crucial step in understanding more complex mathematical concepts. Large numbers can be tough to comprehend, and this concept is fundamental to making sense of future math operations. Place value anchor charts using blocks, pictures, different number forms, and class activities are all helpful ways place value can be taught.

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Xtra math is a technology resource that provides additional practice for students in math. It would be very helpful for students to practice math facts. It is a good alternative to worksheets.

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View the research behind our ESSA Tier IV evidence

XtraMath worked with LeanLab Education to document the connections between using XtraMath and improving outcomes for students primarily in grades K-6.

Download our Logic Model to discover the research and evidence that demonstrates how using XtraMath enhances students' learning and performance, leading to better outcomes for both students and teachers.XtraMath worked with LeanLab Education to document the connections between using XtraMath and improving outcomes for students primarily in grades K-6.
Download our Logic Model

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XtraMath - 10 minutes a day for math fact fluency

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XtraMath is a free program that helps students master addition, subtraction, multiplication, and division facts.

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This is an article about the effectiveness of flash cards. Flash cards are a great way to promote math fact fluency.

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By Inez Zung and Megan Imundo

Flashcard use is often recommended as an effective way for students to learn. Popular media sources list flashcards as a fun and easy way to study (e.g., Smith & Weinstein, 2016) and researchers back this recommendation for a number of reasons (e.g., Hung, 2015). Perhaps in part due to these recommendations, undergraduate students report using flashcards as a common study strategy when preparing for exams (Wissman, Rawson, & Pyc, 2012). One such reason is that flashcards promote self-testing if used in the traditional method of putting a word or question on one side and the definition or answer on the other. Testing is beneficial for learning because it requires effortful retrieval of learned information, which in turn strengthens the memory for that information (e.g., Bjork, 1975; Roediger & Karpicke, 2006). In the typical flashcard format, students can test themselves by looking at the question or word side, generating an answer, and then checking to see if they gave the correct response by turning the flashcard over.

Using flashcards also promotes spaced learning. The spacing effect refers to the benefits to long-term learning from spacing studying across multiple sessions, as opposed to massing studying into one session (Carpenter, Cepeda, Rohrer, Kang, & Pashler, 2012). Spacing allows for some forgetting between sessions, which actually benefits long-term retention when retrieving the learned material again (e.g., Pavlik & Anderson, 2004). Though spacing is often thought of as simply incorporating multiple study sessions with a time delay in between, flashcard use can create spacing within a single study session. Studying other flashcards between iterations of a single flashcard creates spacing, and thus some forgetting, in between those iterations. As a result, students are more likely to be able to recall what they studied on those flashcards.

The act of making the flashcards themselves can also be a learning event. Generating words has been shown to be more effective for later recall than simply reading them (Slamecka & Graf, 1978). When students create flashcards, they generate the word-definition or question-answer pairs instead of passively rereading the textbook or their notes again.

While flashcard use can be extremely effective for long-term retention of information, there are also a few potential pitfalls if they are used ineffectively. Since flashcards can be made and used individually, students often use them for self-regulated study. Kornell and Bjork (2008) found that the effectiveness of such self-regulated study depends on the accuracy of metacognitive judgments, or students' own evaluations of how well they can remember the information they are studying. When students use flashcards on their own, they might make inaccurate judgments of their own learning. For example, some students prematurely stop studying a particular flashcard ("dropping" a flashcard) because they think they have learned the material, even though it has not yet been fully integrated into long-term memory. Students can also cheat themselves when studying with flashcards. Students may look at the other side of the flashcard without putting in much effort to recall the answer first, or they may tell themselves that they would be able to recall the full answer in the future, even if at the moment they can only partially recall the material.

There are a few ways students can get around the potential pitfalls of using flashcards in order to benefit from the robust, long-term effects of retrieval practice, spacing, and generation. Studying in groups or pairs by testing each other using flashcards might be an effective way to make sure you are truly retaining the information. Having a partner can also help you make better metacognitive judgments so that you do not prematurely drop flashcards that could benefit from more study. If you can't find anyone to study with or have to use flashcards on your own, keep yourself honest by actually reciting your full answer out loud before turning the flashcard over to evaluate your response.

Flashcards are an easy and effective way to study-if used correctly. Keep in mind why they work and the common mistakes people make when using them, and you might find your flashcard studying more efficient and helpful. Happy studying!

References

Bjork, R. A. (1975). Retrieval as a memory modifier: An interpretation of negative recency and related phenomena. In R.L. Solso (Ed.), Information processing and cognition: The Loyola Symposium (pp. 123-144). Hillsdale, NJ: Erlbaum

Carpenter, S. K., Cepeda, N. J., Rohrer, D., Kang, S. H. K., & Pashler, H. (2012). Using spacing to enhance diverse forms of learning: Review of recent research and implications for instructions. Educational Psychology Review, 24(3), 369-378.

Hung, H. -T. (2015). Intentional vocabulary learning using digital flashcards. English Language Teaching, 8(10), 107-112.

Pavlik, P. I., & Anderson, J. R. (2005). Practice and forgetting effects on vocabulary memory: An activation-based model of the spacing effect. Cognitive Science, 29, 559-586.

Roediger, H. L., & Karpicke, J. D. (2006). The power of testing memory: Basic research and implications for educational practice. Perspectives on Psychological Science, 1(3), 181-210.

Slamecka, N. J., & Graf, P. (1978). The generation effect: Delineation of a phenomenon. Journal of Experimental Psychology: Human Learning and Memory, 4(6), 592-604.

Smith, M., & Weinstein, Y. (2016, June). Learn how to study using... retrieval practice. The Learning Scientists. https://www.learningscientists.org/blog/2016/6/23-1

Wissman, K. T., Rawson, K. A., & Pyc, M. A. (2012). How and when do students use flashcards? Memory, 20(6), 568-579.

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Flashcards: Are you using them effectively when learning? - Psychology In Action

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By Inez Zung and Megan Imundo Flashcard use is often recommended as an effective way for students to learn. Popular media sources list flashcards as a fun and easy way to study (e.g., Smith & Weinstein, 2016) and researchers back this recommendation for a number of reasons (e.g., Hung, 2015).

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This is the grade 4 ODE model curriculum for mathematics from March 2015.   It provides instructional strategies and resources for teaching math, broken down into clusters. The section on fractions is particularly helpful.

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From the National Education Association, this is a resource with technology tools to teach fractions. It is a great way to bring technology into the classroom, and would be helpful to hands on learners.

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Talking about Free Tech Tools for Teaching Fractions

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There is much to learn from three elementary school teachers who meet weekly as a professional learning community (PLC). Together they identify free tech tools to support their struggling students using the rich resources in PowerUp WHAT WORKS .

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Khan Academy (Whole numbers as fractions)

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Khan Academy (Whole numbers as fractions)

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This video comes from Khan academy. It does an excellant job of showing how whole numbers relate to fractions and vice versa.

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If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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Whole numbers as fractions (video) | Khan Academy

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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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From Intervention  central. How To: Master Math Facts using Cover-Copy-Compare. The student looks at a math problem that has been solved. Next, they cover it. Then they copy and solve the problem. Finally, the student compares the new written problem to the original solved problem.

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This intervention promotes the acquisition of math facts. The student is given a sheet containing math facts to practice. The student studies each math fact with answer that appears on the sheet, covers the fact briefly and copies it from memory, then compares the student-copied math fact and answer to the original correct model (Joseph et al., 2011; Skinner, McLaughlin & Logan, 1997).
Materials:
Procedures: Here are the steps of Cover-Copy-Compare for math facts:

STEP 1: [Teacher] Create a Cover-Copy-Compare math fact sheet. The teacher selects up to 10 math facts for the student to practice during the session and writes those facts (including number sentence and answer) as correct models into the left column of the Cover-Copy-Compare Worksheet ( horizontal or vertical poblems). The teacher then pre-folds the sheet using as a guide the vertical dashed line ('fold line') dividing the left side of the student worksheet.

STEP 2: [Student] Use the Cover-Copy-Compare procedures. During the Cover-Copy-Compare intervention, the student is trained to follow these self-directed steps for each math fact:

Study the correctly completed math fact (model) that appears in the left column of the sheet.

Fold the left side of the page over at the pre-folded vertical crease to hide the original math fact ('Cover').

Copy from memory the math fact and answer, writing it in the first response blank under the 'Student Response' section of the Cover-Copy-Compare worksheet ('Copy').

Uncover the original correct model and compare it to the student response ('Compare'). If the student has written the math fact and answer CORRECTLY, the student moves to the next item on the list and repeats these procedures. If the student has written the math fact INCORRECTLY, the student draws a line through the incorrect response, studies the correct model again, covers the model, copies the model again from memory into the second response blank under the 'Student Response' section of the sheet, and again checks the correctness of the copied item..

Continue until all math facts on the sheet have been copied and checked against the correct models.

STEP 3: [Teacher] Log: items mastered by the student. The teacher should formulate an objective standard for judging that the student using Cover-Copy-Compare has 'mastered' a particular math fact (e.g., when the student is able to copy that fact with answer from memory without error on three successive occasions). The teacher can then apply this standard for mastery to identify and log items mastered in each session, using the appropriate Cover-Copy-Compare Log Sheet.

Variations: One modification of Cover-Copy-Compare that may make it even more effective is to have the student respond orally. The student covers the original math fact and orally states the fact and answer rather than putting it in writing (Skinner, Bamberg, Smith, & Powell, 1993). Because students can often respond more quickly by stating rather than writing their response, oral responding can speed the task and result in a larger number of effective learning trials in the time allocated.

References

Joseph, L. M., Konrad, M., Cates, G., Vajcner, T., Eveleigh, E., & Fishley, K. M. (2011). A meta-analytic review of the cover-copy-compare and variations of this self-management procedure. Psychology in the Schools, 49(2), 122-136.

Skinner, C. H., Bamberg, H. W., Smith, E. S., & Powell, S. S. (1993). Cognitive cover, copy, and compare: Subvocal responding to increase rates of accurate division responding. Remedial and Special Education, 14(1), 49-56.

Skinner, C. H., McLaughlin, T. F., & Logan, P. (1997). Cover, copy, and compare: A self-managed academic intervention effective across skills, students, and settings. Journal of Behavioral Education, 7, 295-306.

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This intervention promotes the acquisition of math facts. The student is given a sheet containing math facts to practice. The student studies each math fact with answer that appears on the sheet, covers the fact briefly and copies it from memory, then compares the student-copied math fact and answer to the original correct model (Joseph et al., 2011; Skinner, McLaughlin & Logan, 1997).

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National Center for Intensive Intervention

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National Center for Intensive Intervention

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From the National Center on Intensive Intervention. This has sample problems as well as downloadable resources, such as fraction tiles.

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These are math games that are specific to place value. Toy theater is a great resource to add to your classroom. Especially for learners who struggle with traditional worksheets and book work.

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Original & fun place value games aimed at helping kids understand the base ten system in the first grade classroom. Strategies for making ten, ten frames, 1-10 and 11-19, and more! Toy Theater is trusted by teachers around the world. Free to play, priceless to learn.

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Place Value Games | Toy Theater Educational Games

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Original & fun place value games aimed at helping kids understand the base ten system in the first grade classroom. Strategies for making ten, ten frames, 1-10 and 11-19, and more! Toy Theater is trusted by teachers around the world. Free to play, priceless to learn.

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Freckle Math is a computer program that promotes fact fluency with daily exercises. There is also the opportunity to dress your freckle character as you "level up"

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See the power of differentiated practice with Freckle