Motivating Students & Recognizing Effort Keeps Kids Engaged

The Rocket Math Online Game app is a demonstrably effective intervention–meaning if students engage and participate, they will learn and improve achievement. However, assigning an effective intervention will improve achievement only if students are engaged and participate in the intervention. The key is by motivating students to reach higher goals.

In today’s world, many students do not habitually give you their best effort. When you praise and recognize only excellent outcomes, many students are not motivated. They doubt their own abilities and think they are out of the running for achievement awards. Motivating students, ALL students, including low performers to participate is essential. But how to motivate students to learn math? You need to begin by praising and recognizing participation and effort instead of success. A good intervention helps you do that.

Motivating Students by Praises and Recognizing Effort Instead of Achievement

Instead of reporting and recognizing on benchmarks of academic achievement, why not report on benchmarks of effort? The Rocket Math Online Game, gives you data on effort and participation. The Review Progress screen (see above) shows each time students login and start and complete a session. Sessions can be set at five, ten, or fifteen minutes in length. A mini calendar shows the number of sessions per day. As shown in this screenshot, the first student started 3 sessions and completed 1 session on the previous Friday. The student below neither started nor completed a session on Friday because the “F” for Friday is still showing.  We highlighted Wednesday for the third student. It shows 3 sessions started. The “W” for Wednesday still shows in the completed calendar, meaning no sessions were completed.

Who is working the hardest? The “Total” column shows the number of sessions over the last two weeks.  This is even more discriminative than the mini-calendar. Click at the top of the column to sort it to see who is logging in the most sessions. The first student shows 19 sessions started and 11 completed (all the way to the end of the session). The second student started 12 sessions, but completed only two. The third student also started 19 sessions, but completed, to the end of the session, 5 times. This total data tells us the level of effort students have been putting forth to learn their math facts. If you monitor this number and recognize students putting forth good effort, you’ll get more students participating.

What is a Good Effort and Participation?

 

You should expect, at a minimum. for students to usually complete a session four days a week at school. Eight to 11 sessions in the last two weeks indicates a good “C” effort.  A good “B” effort would be completing 12 to 15 sessions in two weeks. That many sessions translate into a session every school day and more than one session a day, half the time. Any student with 16 or more sessions in the last two weeks is putting forth a great “A” effort.  Be sure to praise and recognize them and hold them up as an example, no matter what they have accomplished.

Motivating Students with the Award Certificates to Recognize & Reward Effort

The Rocket Math Online Game has Award Certificates, available to print out. You can find these right from your dashboard. “Award Certificates” are on the blue tab on the left-hand “rainbow” navigation.

Screenshot of Rocket Math's reward cards.
Give out some Award Certificates once every two to four weeks. Give them to the students who are putting forth the most effort in your class. For it to be effective, you have to make it kind of a big deal to get one of these. Sign the awards and then give them out in a little ceremony.

To have a successful ceremony, we recommend these steps:

  1. Having two adults to award the certificates
  2. Calling each student up to the room individually
  3. Handing them the certificate and shake their hand
  4. Having the awarded student stand in a line at the front 
  5. Calling the next student and repeated the first three steps, but adding that they shake hands with their fellow classmates before joining the line beside them

 

Motivation is most effective for students who don’t get it!

When you reward students for their effort, students who are watching, realize they can do it. They know they can get an award if they try.  The benefit of the motivation is for the ones sitting in their seats watching. If you reward everyone, the ceremony will have no effect. The students watching the ceremony will feel motivated to win the next one. Rocket Math can guarantee you’ll get improved fluency because it is an effective intervention.

Note, you are not rewarding achievement. You aren’t measuring them on how fast they are. You are noting that they did accomplish the goal of finishing the Learning Track. Rocket Math guarantees they will have improved their fluency. The Learning Track certificates are also available on the Award Certificates tab in the main rainbow navigation bar. The same ceremony you’ve been using for the general awards can include awards for completing Learning Tracks.

We also have sets of these Award certificates on card stock and glossy print available on our supplements store site.

After Effort Improves Accomplishment, Begin Rewarding Accomplishment also

Soon after starting regular awards ceremonies for effort, you’ll see students beginning to complete Learning Tracks. As they work through a Learning Track they develop fluency with the math facts in that Learning Track. So you can start awarding Learning Track certificates for the accomplishment of completing a Learning Track.

This is a powerful process. Rewarding effort first, then rewarding accomplishment, leads to learning. Once you see how well this process works, you can apply this elsewhere. It works in any area of your curriculum where effort will pay off in improved accomplishments. Motivating students only works if they believe they can succeed. That is why it is so important to begin by recognizing “effort,” something that everyone can do.

Rocket Math Knows How to Motivate Students to Excel in Math 

Rocket Math Online Game and Worksheet programs will help students reach each grade level math benchmark while motivating students to reach higher goals with the award certificates. Systematically teaching students to develop math fact fluency will pay off. Students will not only succeed at but learn to enjoy math.

Counting Objects Worksheets for Kindergarten | Do They Work?

Much is made in teacher education classes about the importance of counting real objects vs pictures, but there is little empirical evidence to support this concern. What is much more important is for the counting to be first demonstrated by the teacher. The second most important thing is to be able to ensure that students focus on the right number of objects. These are very hard to do with manipulatives.

How to use counting objects worksheets in the classroom

Worksheets can ensure that students are focused on the right number of objects while the teacher demonstrates the counting exercise. Manipulatives, not so much! I have seen counting exercises (of manipulatives) lead students seriously wrong. Some students have the wrong number of manipulatives in front of them as the counting ensues while others change the amount during the exercise.

Step 1–the “I do” step: Always begin with a teacher demonstration

 

A screenshot of the Beginning Numerals Worksheet A with six boxes with images of frogs, hands, or dice in each.

Here is part of the Rocket Math–Beginning Numerals Learning Track: Worksheet A. This shows the top part of the worksheet which is the “I do” or teacher demonstration part of the worksheet. The teaching suggestion for the “I do” step for the teacher reads as follows:

Using the six boxes at the top of each worksheet, model how to touch
and count the items in each box–then show the students that the correct
answer is circled. Have them touch the circled number. Confirm the
name of the numeral. Check to see that all students are touching it.

At a small table for instruction, the teacher could hold the worksheet up on a clipboard, or for a larger group, a document camera would be needed. The teacher gets all eyes on the demonstration and then models touching and counting. Skilled kindergarten teachers know to be quick, perky, and interesting to keep their students attention. Here’s the recommended narration:

I can do this. Watch me count. One, two, three.
There are three frogs in this box. So they circled the three.
Touch here where the three is circled next to the three frogs. Good.
How many were in this box, everybody? Yes, three.
Now watch me do the next box.

Watch me count. One, two,.
There are two frogs in this box. So they circled the two.
Touch here where the two is circled next to the two frogs. Good.
How many were in this box, everybody? Yes, two.
Now watch me do the next box.

Step 2–the “We Do” step: Lead the students to make the correct responses

Once kindergarteners can say the numbers by rote, the hard part is to develop the one-to-one correspondence between the words and the touching. This is much more difficult to do correctly than you might think. For starters, counting to ten by rote may seem like to little ones like a couple of long words, “Onetwothreefourfive sixseveneightnineten.” To teach them to touch each object and say only one word for each, the task must be done together, slowly and correctly, many times.

We Do: Touch and count. Start at zero and count each star

Screenshot of the star system starting with 0 and going up to 3.

We Do: Narration to Count Objects in an Image

Every worksheet in the Rocket Math Beginning Numerals Learning Track has a “We Do” activity of counting stars.  Here’s the recommended narration for the counting star’s activity pictured above entitled “We Do:”

Our ‘We Do’ says to touch and count. Start at zero and count each star.
We are going to touch and count the stars. Put your counting finger on zero,
everybody. We are going to start at zero and count each star. Let’s count.
One, two, three. We counted three stars. That was great!
Let’s do it again! Fingers on zero, everybody. Let’s count. One…

It doesn’t take much imagination to see that students will get this counting exercise right with the teacher’s help. If not on the first pass, by the third time, students will be correctly counting the stars. This counting exercise occurs on every worksheet in this Learning Track and gradually builds to counting up to 12 stars.

 

Step 3–the “You Do” step: Students demonstrate their learning

Screenshot of Rocket Math's Counting Objects worksheet showing 15 boxes all with their own images, then two numbers next to the images for students to choose from.

In the “You Do” portion of Worksheet A of the Rocket Math Beginning Numerals Learning Track (see above) it asks students to count the objects and select, rather than produce or write, the correct number for the number of objects they see in the box. This is identical to the teacher demonstration exercise at the top of the worksheet. The teacher has demonstrated how to do this task already. Students just need to remember that from the demonstration a few minutes prior.

Students are asked to make that distinction, to choose between two and three, by circling the right one–as was done in the top six boxes in the teacher demonstration part of the worksheet. The demonstration answers at the top of the worksheet will be available for students to use as a model of the correct answer. Students learn from practicing the correct answer rather than from practicing errors, so error-free work is the goal.

Benefits of using counting objects worksheets for kindergarten

Counting objects worksheets can focus on one thing to learn at a time

In the “I do” worksheet demonstration, the teacher is helping students develop one discrimination and one only.  The task is learning to discriminate between counting two objects vs. counting three objects. The three different pictures demonstrate this; frogs, dice, and fingers. It becomes clear that the job is to get it right, to be able to tell the difference between two and three–that’s all. Students can learn one distinction like this with a high level of success.  The worksheet allows the teacher to move back and forth between two objects and three objects quickly.  Imagine how chaotic that would be to accomplish with manipulatives!

Counting objects worksheets can transition students to fingers and lines

Many lists of objectives include counting objects to 20. While the ability to count things up to 20 is important, that’s a lot of pictures. It is very easy to make a mistake in counting. It is much preferable to transition students to counting fingers, up to 10, and then to lines for numbers up to 20. A good worksheet program should include from the beginning pictures of fingers and lines to count instead of just cute objects. By introducing fingers and lines from the beginning, students will find it easy to transition to using only fingers or lines later.

Worksheets can properly space out the objects to be counted

A common issue in counting objects is to have the objects spaced far enough apart so that students are reliably not touching the same object twice in a row. In the “We do” portion of the worksheet, pictured above, it is clear that students will succeed by beginning with three stars spaced far enough apart that students have to move their fingers to count the next star. They won’t be confused as they can be by counting objects that are too close together.

A worksheet can establish a starting point for fingers before counting begins

Another problem in teaching counting is that students often begin counting by touching one of the objects they are counting. Then to begin counting they move to the second object and count, “One.” The end result will be off by one. Students must be taught to start with their counting finger somewhere else, and then move to the first object to be counted while saying, “One.” The Rocket Math Beginning Numerals (counting objects) worksheets always have students start with their finger on “zero,” which is pretty useful as a starting place. That’s where you start before you begin counting.  I expect the savvy teacher will be saying, as students are getting their fingers ready to count, “We are touching the zero.  Have we counted any stars yet? No!  So we have counted ZERO stars.  That’s why we are touching the zero.”

A worksheet can allow students to choose the correct answer rather than produce it

Counting worksheets that begin by requiring students to produce, or write, the numeral of the answer are asking too much of beginning students. When the written answer is wrong the teacher has no way of diagnosing whether the student counted incorrectly or forgot how to write the numeral. Much better to begin by having students select the correct answer from a limited number of choices. Teaching students (1) how to write numerals and then (2) write them from dictation are two different skills that should be taught in different instruction.

Worksheets can limit displays to numbers the students have learned.

Another advantage of worksheets is the ability to limit the examples to numbers of objects that students have already learned. When a teacher allows students to use manipulatives the ability to control the number of objects to count is lost. Instead, as shown in the “You Do” portion of Worksheet A, shown above, students only need to be able to distinguish two objects from three objects.

By having the answers present to choose from, the worksheet limits the distinctions that the students need to make. Many beginning kindergarteners confuse 4 and 5 early on. Therefore that distinction, between 4 and 5, should not be required until 1, 2, 3, and 4 are well established and at mastery. You see here on Worksheet A students are only required to distinguish between 2 and 3 objects. They make the same distinction between several examples of different objects.

Rocket Math Beginning Numerals (counting objects) worksheets will start kindergarten students out successfully

The Beginning Numerals Worksheets is the first of over 25 math worksheet Learning Tracks available as part of the Rocket Math Worksheet Universal Level Subscription. See all the other Learning Tracks available in the Worksheet Program. Go here to get a 60-day trial subscription for $15 with a money-back satisfaction guaranteed offer direct from the author, Dr. Don

 

 

 

 

Math Benchmarks: How to Help Your Students Meet Them

Every year, students enter a new math level with new math facts, but what should the students know by the end of each grade? How do teachers measure the success of their students? By using math benchmarks, teachers have a reference point to assess their students’ progress. Rocket Math Online Game and Worksheet Program are great tools to help students meet math benchmarks in every grade.

 

What are Math Benchmarks?

Math benchmarks are standard reference points that can be measured and assessed. Teachers use benchmarks in math to help understand where their students are in their math education and know where they need to be in order to succeed in their grade level.

 

1st Grade Math Benchmarks 

In 1st grade, students focus on learning addition and subtraction up to 20, whole number relationships and grouping, linear measurement and lengths, and geometric shapes.

1. Addition and subtraction up to 20.

1st grade students learn strategies to build math fact fluency for adding and subtracting whole numbers up to 20.

2. Whole number relationships and grouping in tens and ones.

1st grade students learn to compare the whole numbers at least to 100 and be able to understand and solve problems involving their relative sizes.

3. Linear measurement and measuring lengths.

1st grade students learn to understand the meaning and process of measuring including the concepts of iteration and transitivity principle for indirect measurement.

4. Compose and decompose geometric shapes.

1st grade students learn how to compose and decompose geometric shapes, like creating a quadrilateral by putting two triangles together. 

 

2nd Grade Math Benchmarks

In 2nd grade math students focus on developing students’ knowledge of base-ten notation, their fluency with addition and subtraction, standard units of measure, and analyzing shapes. 

1. Base-ten system

2nd grade students learn to count by fives, tens and multiples of hundreds, and learn to recognize which digits represent amounts of thousands, hundreds, tens or ones. E.g. 456 is 4 hundreds + 5 tens + 6 ones.

2. Addition and Subtraction up to 1000

2nd grade students develop their math fact fluency in addition and subtraction up to 1000.

3. Standard units of measure

2nd grade students learn standard units of measure and how to use rulers and other measuring tools.

4. Analyze Shapes

2nd grade students learn how to examine shapes by their sides and angles, and decompose and combine them.

 

3rd Grade Math Benchmarks

In 3rd grade students focus on developing their multiplication and division math facts up to 100, understanding fractions, understanding the structure of rectangular arrays and are, and how to analyze two-dimensional shapes.

1. Multiplication and division math facts up to 100

3rd grade students develop their math fact fluency of multiplication and division of whole numbers up to 100.

2. Fractions and unit fractions

3rd grade students learn unit fractions and fractions and are able to use them to represent numbers equal to, less than, or greater than one.

3. Attribute of two-dimensional regions

3rd grade students learn to find the area of a shape which shows the students how to connect the area to multiplication and how to use multiplication to determine an area of a rectangle.

4. Analyze and compare two-dimensional shapes

3rd grade students compare and classify two-dimensional shapes by their angles and shapes.

 

4th Grade Math Benchmarks

In 4th grade, students focus on developing their math fact fluency in multi-digit multiplication and division, learn math operations with fractions, and understanding geometric figures.

1. Multi-digit multiplication & division

4th grade students understand place value to 1,000,000 and know how to apply multi-digit multiplication and multi-digit division to mentally calculate quotients.

2. Fraction equivalence and operations

4thd grade students learn that two fractions can be the same (e.g. 12/16 = 3/4) and learn how to add, subtract, multiply and divide fractions.

3. Geometric figures

4th grade students learn to describe, analyze, compare and classify two-dimensional shapes. 

 

5th Grade Math Benchmarks 

In 5th grade, students focus on developing fraction operations, learn operations with decimals to 100, and develop an understanding of volume.

1. Math fact fluency of fraction operations

5th grade students learn to apply their understanding of fractions and fraction models to calculate sums and differences of fractions in addition, subtraction, multiplication, and division.

2. Relationship between decimals and fractions

5th grade students learn to multiply and divide between decimals and fractions, and to compute quotients of decimals to 100.

3. Volume

5th grade students learn that volume is an attribute of three-dimensional space and can be measured by finding the total number of units that are needed to fill the space.

 

Not meeting Benchmarks: what should it mean?

When students score as “not meeting benchmark,” it means the school should provide some intervention to help the students learn.  When it comes to learning math facts, most students have had no opportunity to learn them in a systematic way. Unless they have had an extraordinary school or an unusual teacher, they have not received structured, systematic learning opportunities to memorize math facts. After three decades in schools, I know this to be the case. Without systematic practice and effort, most students will not meet math fact benchmarks. They won’t meet the Common Core expectation that students will “know [math facts] by memory.” Whose fault is that? It is not the student’s fault nor the parent’s fault. 

 

Are you certain your fluency intervention is effective?

The teacher and the school should provide, not just any “intervention” but should provide an effective intervention. Some so-called “interventions” do not reliably produce increased fluency. An essential part of using an intervention is to measure its effectiveness. [That’s why IEP goals are supposed to have measurable short-term objectives!] The best way to measure the effectiveness of a fluency intervention is with timed, curriculum-based fluency assessments.

By measuring the same way for the same amount of time period, you can see if fluency increases. If the student can complete more items during the timed test each time you measure, you can see their fluency increase. When a vast majority of your students, or all of your students, improve in fluency, then you can be certain that the intervention is effective.

 

Rocket Math Online Game is effective

Screenshot of Rocket Math's average student scores.

As students work through the levels in each Learning Track in the Rocket Math Online Game, they are periodically assigned fluency tests.  Students are tested after completing levels A, i, and R, and then after they finish level Z. Each test is a 1-minute fluency test of a random selection of facts taught in that Learning Track. Therefore the scores are comparable, and when the number goes up at each point in the curriculum, you can be sure that students are increasing in fluency. As you can see from the site-wide data shown here, students consistently improve in fluency as they work through the Rocket Math Online Game. You would not expect students to meet benchmarks until they have completed Set Z in the Learning Track.

 

Math fact fluency benchmark in the Online Game: 20/minute

Screenshot of Rocket Math's 1 minute results.

The 1-minute RACEs in the Rocket Math Online Game are a good way to measure math fact fluency. You can see from the site-wide averages above that on average, students exceed 20 per minute correct at Set Z, and the average at the beginning is much less. So a reasonable benchmark is 20 correct problems per minute.

The teacher can assign a 1-minute RACE at any time, and the student will need to do it upon their next login. The results will be available in the Review Progress screen and export from the button that gives “Results from Assigned races.” However, the best measure of whether students can meet the benchmark is after Set Z, when they have completed the Learning Track. By clicking on the pink button for exporting “Results from Scheduled races,” the score will appear.

A screen shot of an Excel spreadhseet that shows studen'ts multiplication benchmark progress.To the right is a screenshot of an example of the results from scheduled races from one class of upper elementary students. You can see the Account Average shows improvement at each level. If you set a benchmark at 25, you see all but one of the students met that by the end of Level Z. However, we do see several students who began above that level. (They need not have gone through the Learning Track, but most improved anyway.) After Set Z, those scores show that nearly all students are proficient by the end of the Learning Track. So we know that the Online Game is an effective intervention. But there’s a catch. For this display, we eliminated a lot of students who had not completed Set Z in Multiplication. Students have to play the game to learn.

 

Students must participate to learn: Monitor and Recognize Effort

A screenshot of Rocket Math's mini calendar that shows how students are progressing.Assigning an effective intervention will not help unless students are engaged and participate. Instead of reporting on benchmarks of academic achievement, why not report on benchmarks of effort? Each time students login and complete a session (five, ten, or fifteen minutes in length) on the Online Game, the Review Progress screen will record their session. A mini calendar shows the number of sessions per day. As shown in this screenshot, one student completed 7 sessions on the previous Friday. Another student completed 3 sessions on Sunday. The students below the hard workers, whose mini-calendars showed “F” for Friday and “S” for Sunday, did not complete any sessions because there was no number for those days.

A screenshot of Rocket Math's calendar to show how a student is progressing.Even more discriminative, the Review Progress screen shows the total number of sessions completed in the last two weeks. The picture shows data from our demo accounts. The one for Test3 shows 38 sessions in the last 14 days, while others have only 2 sessions. This total data tells us the level of effort students have been putting forth to learn their math facts. If you monitor this number and recognize students putting forth great effort, you’ll get more students participating. I would say that 10 to 14 sessions in the last two weeks are a good effort. 15 to 24 sessions is a very good effort. Any student with 25 or more sessions in the last two weeks is putting forth great effort and should be recognized as a star!

Screenshot of Rocket Math's reward cards.You might consider giving out Award Certificates once a month for students who are putting forth super-star effort. If you reward effort, we guarantee you’ll get achievement. We have sets of Award certificates available on our supplements store site. Soon after doing that, you’ll probably have to start awarding Learning Track certificates for students who are completing Learning Tracks. Those are available on the Admin page on the light blue tab in the main rainbow navigation bar.

 


Using Rocket Math to Help Students Reach Math Benchmarks

Rocket Math Online Game and Worksheet program will help students reach each grade level math benchmark. By systematically teaching students to be math fact fluency, they will be able to not only succeed but learn to enjoy math.

4th Grade Math Worksheets

By 4th grade, students need to stop counting on their fingers and be able to recall math facts immediately. If not, then they will find it hard to learn multiplication and division. Rocket Math offers 4th grade math worksheets that will push your students towards success and prepare them for 5th grade.

 

A student counts on his fingers while working through a math problem.

 

What should a 4th grader know in math?

By the end of fourth grade, students should have memorized all four basic operations of math facts: addition, subtraction, multiplication, and division. Typically, students in fourth grade learn division. However, if your fourth grade students haven’t mastered multiplication, you must help them develop multiplication math fact automaticity first and then teach them, division, if there is enough time in the school year. Without math fact fluency in multiplication, students will struggle with division and learning all higher-order forms of math including algebra.

The only way for students to successfully memorize math facts is systematical. Practicing random math facts or playing math games will never help students memorize. They will simply count the facts out over and over again–coming to hate math. 

 

How how to measure math fact fluency

Not sure if your students are fluent in multiplication math facts and are ready to learn division? If you see a student counting on their fingers, it’s a sure bet they have NOT memorized these basic single-digit facts. If you don’t know for sure, here’s our free resource with all you need to pre-test students on math facts.

 

Why Rocket Math Worksheets help students develop math fact mastery 

Rocket Math’s Worksheet Program is very different from any other math facts practice worksheets. 

The program only teaches a couple of math facts at a time, helping students succeed every day.

Once students learn the correct answers, the Worksheet Program includes a lot of fast-paced practice. With this “learn first, practice second” method, students easily commit their math facts to memory.

The program is graduated and progressive. It mixes newly memorized math facts with previously memorized math facts, helping students develop over time the ability to answer more than 400 math facts instantly from recall.

When students develop automaticity (facts so well learned that their recall is instantaneous), all math becomes easier.

Two students using 4th grade math worksheets practice in class by asking each other questions from Rocket Math's worksheet program.

A unique component of the Worksheet Program is oral student practice. This allows students to receive corrective feedback from their partner, who has the answer key. You cannot learn without corrective feedback from either a person or a computer. Having teachers give corrective feedback by checking and grading written practice is very time-consuming, as well as being too late for effective learning. Having student partners with answer keys correct immediately, during practice, means teachers only have to grade check-point tests instead of monitoring daily practice–a huge plus for time-strapped teachers!

The Worksheet Program is designed to build strong multiplication fact fluency and recall. Memorizing these facts avoids the problem of students having to look up facts in times tables, over and over again.

 

How to teach MULTIPLICATION with Rocket Math’s 4th Grade Math Worksheets

Since many students begin fourth grade without mastery of multiplication facts, let’s start with Rocket Math’s first multiplication worksheet of Set A. As you can see, the worksheet has only “1 times” problems, such as 3 times 1, and 1 times 2. These are very easy, and students can typically answer them quickly, with no hesitation.

 

Screenshot of Rocket Math worksheet on multiplication math facts, set A.

 

First, students practice orally with a partner around the outside of the worksheet. For example, one student practices saying the problems and the answers while the other student offers corrections. You need to teach students that the checker’s role is to correct any fact that isn’t answered instantly without hesitation. The checker needs to follow this special correction procedure.

After two to three minutes of oral practice, students should switch roles and help their partner practice. 

Finally, all students take a one-minute test of these facts on the inside of the worksheet. They will be able to write the answers to those facts as fast as their fingers can carry them. 

 

Writing Speed Test

Before beginning the Worksheet Program, students need to establish goals with a writing speed test. Students who can answer the problems in the one-minute daily test at their established speed will pass on to learn the next set of facts the following day.

 

Screenshot of Rocket Math worksheet on addition fact family, set B.

Once your students master Set A, move on to Set B, then Set C, and so on. Get all of the Multiplication 1s to 9s worksheets from rocketmath.com. Each worksheet follows the same procedure:

  1. Students practice saying the answers to the “outer ring” problems out loud with a partner. 
  2. Partners follow the special correction procedure for any fact that isn’t answered instantly without hesitation. 
  3. After 2-3 minutes of partner practice, all students take a one-minute test of the recently learned facts located on the inside part of the worksheet.
  4. Students that answer the correct amount of math fact problems in 1 minute (based on their writing speed) progress to the next worksheet set. Students that fail the test, repeat steps 1-4 using the same worksheet set the following day.

It usually only takes students a few days to memorize a set.

 

Screenshot of Rocket Math worksheet on Division math facts set F.

How to teach DIVISION with Rocket Math’s 4th Grade Math Worksheets

Once your fourth graders master multiplication math facts, it’s time to teach them division.

To teach your fourth graders division with Rocket Math’s worksheets, use the Division 1s through 9s worksheet and follow the same procedure described in the previous section on multiplication.

The Common Core suggested that students learn math facts up through the 12s. Rocket Math has two Worksheet Programs that do just that. One is Multiplication 10s, 11s, 12s. and the other is Division 10s, 11s, 12s. Each builds upon and reviews facts from the 1s-9s program while keeping learning fun for students who learn faster and need additional challenges.

Graphic of family figures with the math fact family for 12, 3, and 4.

Fact Family Worksheets are another way to study facts

Fact families worksheets provide an alternative way for fourth graders to learn multiplication and division facts. A fact family in multiplication and division is 4 x 3, 3 x 4, 12 ÷ 3, and 12 ÷ 4. By learning these four facts simultaneously, students can internalize the reciprocal nature of multiplication and division. This is also a viable way for students to learn facts initially if that is the teacher’s preference. This can also be a great review for students who begin the year having mastered multiplication and division.

 

Screenshot of Rocket Math worksheet on addition and subtraction fact families up to 20.

Rocket Math Worksheet Program’s specially designed Fact Families

Much like Rocket Math’s single operation worksheets, each Fact Family worksheet in the Rocket Math program asks students to memorize only one fact family at a time. You can see the first fact family students learn in Set A is 1 x 2, 2 x 1, 2 ÷ 1, and 2 ÷ 2. Each set in this program introduces only one fact family to help students easily memorize fact families and work quickly through Sets A to Z.. 

Rocket Math’s Worksheet Program starts with the first level of Multiplication and Division Fact Families to 20, followed by Multiplication and Division Fact Families from 21. Practicing with fact families reinforces the reciprocal nature of multiplication and division and gives extra practice to increase fluency. 

Two students are using 4th grade math worksheets in class by asking each other a math question and testing each other.

4th grade worksheets for learning fractions and factor pairs

Rocket Math Worksheet Program works through a daily routine of oral practice with peers and one-minute tests to determine how fast a student should progress through the A to Z steps. By establishing a daily routine, students can use it to study fractions, factors, and decimals in the more advanced pre-algebra programs available in Rocket Math. These will seriously give students a “leg-up” when they come to pre-algebra concepts that students find slow or cumbersome.

 

Screenshot of Rocket Math worksheet on Identifying Fractions.

Identifying Fractions Worksheets

One such Rocket Math program is the Identifying Fractions Worksheet program. In it, students learn to identify pictures of proper fractions, improper fractions, and mixed numbers. Each A to Z set teaches a new set of three closely related fractions so that students learn to identify the fractions quickly and easily. Students learn this rule: Fractions have a top and a bottom number. The bottom number tells how many parts in each whole. The top number tells how many parts are shaded. When the whole figure is not divided into parts, it is a whole number. The program also presents whole numbers to identify mixed in with fractions. If you have ever seen students struggle with identifying fractions when they are looking at them, you’ll appreciate the power of these worksheets.

 

Screenshot of Rocket Math worksheet practicing the factors of 12 and 36.

Factors (how to find all the factor pairs) Worksheets

Rocket Math Worksheet Program Factors have worksheets to quickly teach students how to name all the factor pairs of common numbers. What are the factors of 36? Answer: 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6. This is what students learn by memory. Here’s a blog about the foolproof method that students learn. Students practice with a partner, take a daily one-minute timing, fill in a Rocket Chart, just like regular Rocket Math. Simplifying fractions will be a breeze after students learn this easy method and practice finding all the factors of these common numbers.

Students learn all the factors for these numbers in this sequence: 12, 36, 24, 48, 18, 32, 16, 64, 10, 40, 20, 72, 8, 25, 50, 6, 21, 30, 60, 15, 45, and 100. Click here to learn “How to Factor” from Dr. Don’s Educreations lesson on the web.

A screenshot of the 4th grade math worksheet for equivalent fractions from Rocket Math's worksheet program.

 

Equivalent Fractions

Students need to know that six-eighths is equivalent to three-fourths and that four-twelfths is equivalent to one-third. While they can calculate these, it is very helpful to know the most common equivalent fractions by memory. One of the most common problems students have with fractions is not “reducing their answers to simplest form.”

Here’s a 5-minute Educreations lesson on How the Equivalent Fractions program works.

The Equivalent Fractions Worksheet Program is part of the Universal Level subscription to the Worksheet Program. Equivalent fractions will help students commit 100 common equivalent fractions to memory. Each set (A through Z) has four fractions, which are displayed on a fraction number line. Students frequently learn fractions equivalent to one, such as ten-tenths, and fractions that can’t be reduced. For example, three-fourths is equivalent to three-fourths. Using the fraction number line will help with students’ understanding of why those fractions are equivalent.

Click here for the full sequence of 100 Equivalent fractions that students will learn in this program.

Start Rocket Math’s Worksheet Program today

Rocket Math’s unique worksheet program is not only great at teaching fourth graders multiplication and division, but the program also offers beginning numerals, addition, subtraction, and pre-algebra concepts for ages K-12. Each worksheet follows the same effective methodology described in this article and is guaranteed to help your students memorize math facts. Get a Rocket Math Worksheet Subscription for your school or home today.

Quick links to all 4th grade math worksheets:

2nd Grade Math Games to Teach Math Facts

What Math Facts Should Students Know By 2nd Grade?

Students entering 2nd grade should have memorized basic addition facts to a high level of fluency. There should be no hesitations and no finger counting. But not every first-grade teacher has the skill or tools to help students effectively memorize addition facts.  Attempting to teach subtraction facts and the process of subtraction to students who did not successfully memorize addition is VERY difficult. Like, so hard as to cause tears, and not just from the students! Rocket Math offers 2nd grade math worksheets and 2nd grade math games.

 

What is Covered in 2nd Grade Math?

In 2nd grade, teachers need to help students master at least four math skills in three steps. It’s important that 2nd graders learn these skills in the correct order because each step is dependent on the completion of the prior step. 

 

Step 1. Fully memorize addition facts.

Second-grade teachers must ensure that students have fully memorized the basic addition facts. Most 2nd grade math games will not accomplish this goal. Memorizing addition facts early in the year is crucial because the class needs time to do the next two steps during the year. For this reason, the 2nd-grade teacher needs a systematic, effective, and efficient math facts learning curriculum, such as Rocket Math. If the 2nd-grade teacher is lucky, that was accomplished during first grade. If it was not, it still must be done. 

 

Step 2. Master addition computation while memorizing subtraction facts.

Second-grade teachers must ensure that students master addition computation up to three digits. If students are automatic with the addition facts, this process becomes easy and fun for students. Rocket Math’s Learning Addition Computation worksheet program is a systematic way of teaching computation skills. 

The 2nd grade teacher also needs to help their students memorize basic subtraction facts. Learning subtraction facts should not be attempted until students have memorized addition facts fully. Because time is of the essence, a teaching tool with a systematic method of teaching facts efficiently and effectively is needed. Rote memorization is the best method. However, the teacher can have students work on memorizing subtraction facts while working on addition computation. 

Step 3. Master subtraction computation.

Second-grade teachers must ensure that students master subtraction computation up to three digits, with and without regrouping. If students are automatic with the subtraction facts, this process becomes easy and fun. Rocket Math’s Learning Subtraction Computation worksheet program is a systematic way of teaching computation skills. 

What Should 2nd Graders Know Before Entering 3rd Grade Math?

Before going into 3rd-grade, students should be able to read and write numbers up to 1,000 and have developed a comfortable number sense of numbers up to 100. 2nd graders need to memorize addition and subtraction facts and be comfortable completing addition and subtraction computations. Before 3rd grade, 2nd graders need to start learning how to skip count as a precursor to learning multiplication and have learned the concept of multiplication (be able to figure out a multiplication fact). Rocket Math has a worksheet-based version of Skip Counting that students enjoy. They also sell Skip Counting Flashcards, which I’ve never seen anywhere else. 

Rocket Math 2nd Grade Math Worksheets & 2nd Grade Math Game

Both Rocket Math Worksheet Program and Rocket Math Online Game are great tools that will help students learn their math facts. Each program has a different way of teaching, but the idea and ultimate goal for both are the same; students learn math fact fluency and can recall answers instantly. Teachers can choose one or both of these programs to help their 2nd grade students be successful in math.

H3: 2nd Grade Math Worksheets

Students practice math facts using the Rocket Math Worksheet program.

The Rocket Math Worksheet Program is uniquely effective by using paired practice and having students saying the facts aloud. Students partner up and practice quickly recalling facts together. One student reads the problems and answers from memory. The checker watches for when their partner hesitates to answer. He or she then gives his or her partner more opportunities to practice the “hesitant” facts.

 

The students switch roles, and after both have answered questions, they take a one minute test on the facts that they have learned so far. If students answer as fast as their fingers will carry them, they pass the level and move on to the next worksheet in the sequence.

 

Learn Addition and Subtraction facts with  these Worksheet Programs for 2nd Graders

For 2nd Grade math students, it’s essential that they master addition math facts and begin learning subtraction math facts. Here are the addition and subtraction fact Worksheet Programs 2nd graders will need to work through. They are listed in the order of priority.  Few students will finish all six in one year, but the more they accomplish the better they will know these facts.

 

(1) Addition (1s to 9s) (3) Fact Families (+, -) to 10 (5) Add to 20 

(e.g., 13+6, 4+11, 15+5)

(2) Subtraction (1s to 9s) (4) Fact Families (+, -) from 11 (6) Subtract from 20 (e.g., 18-15, 15-5, 19-8)

 

Rocket Math Online Game

Students and teacher playing multiplication games with dice sitting in a circle in a classroom

In addition to worksheets, schools of education tell teachers to use games to “teach” math facts. Unfortunately, most games and fun activities do not help individual students learning math facts to the level of fluency. These games, such as bingo or dice, have several problems:

  •  Students spend most of their time waiting for their turn rather than practicing facts.
  • They do not focus on teaching a small group of facts in a manner that helps students commit them to memory.
  •  The games do not adjust to an individual student’s level of fluency.
  • Students can pace the game slowly enough to have time to figure out facts rather than requiring recall.
  •  It is difficult to keep every student engaged, as those behind are less likely to participate.

Rocket Math Online Game is an Effective Way to Teach Math Fact Fluency

Student holding tablet with a math fact fluency app by Rocket Math

Unlike card or dice games, some online math games are very effective at building math fact fluency. Games such as the Rocket Math Online Game have several important features that make a big difference.

  1. Every student is engaged —not waiting for a turn.
  2. Students learn only a few facts at a time, enabling memorization and recall.
  3. The game provides lots of focused practice on each set of facts. 
  4. Students only get enough time to use recall to come up with the answers.
  5. The game gives an immediate correction and extra practice on any facts that students cannot answer quickly.
  6. The game only introduces new facts once students demonstrate mastery of prior facts.
  7. The game gives students explicit feedback so they have a sense of accomplishment.

 

Learn Addition and Subtraction facts with  these Online Game Learning Tracks for 2nd Graders

Compared to the Worksheet Program, the Online Game moves students through the Learning Tracks much faster–in a few weeks, rather than months. Therefore you can send every one of the same age through in the same order. For 2nd graders, this is the online game learning track recommended by Rocket Math:

  • Addition (1s – 9s)
  • Subtraction (1s – 9s)
  • Fact Families (+, -) to 10.
  • Fact Families (+, -) from 11.
  • Add to 20.
  • Subtract from 20.

2nd grade math games are a great way to teach students their addition and subtraction facts. Just be sure to find ones like Rocket Math that understand the importance of fact fluency and instant recall. 

Rocket Math’s Foolproof Method to Finding Factors (A.K.A. Factor Pairs)

In order for a student to expand or reduce fractions or to add and subtract unlike fractions, they need to know how to find factors for each number in the fraction. Students may know multiplication facts, but still, find it difficult to come up with all the possible factor pairs for a given number. The key to helping students with this task is to teach students a systematic method of identifying all factor pairs and then committing both the process and some common numbers to memory.  

Both the Rocket Math Online Game and Worksheet Program uses a foolproof, systematic method for teaching students how to find all the factors of a number. By reading this article, you’ll learn what factors are, how to help students find all the factors systematically, and how both the game and worksheets incorporate the method into each program.

 

What are Factors of a Number

Factors of a number, such as 12, are pairs of whole numbers whose product is that number. For example, 2 x 6 = 12, 12 is the product, and the factor pair is 2 x 6. Other factor pairs for 12 include 1 x 12 and 3 x 4 because multiplied together, each of those factor pairs equals 12. 

 

Finding Factors: How do You Know When You Have Found all of them?

Identifying some of the factors of a target number isn’t hard, but knowing when you have accounted for ALL the factors can be hard for students. Rocket Math’s Worksheet Program helps students find and memorize all the factors for 22 common numbers. Watch this video to see how Dr. Don uses the worksheet program to teach students how to find all of a number’s factors in a systematic way.

Worksheet finding the factors of the number 15.

  1. The best method for teaching students how to find factor pairs is to have them start at 1 and work their way up. Give your students a target number and ask them to put “1 x” below it. Let them fill in the right side with the number itself. We know that any number has one “factor pair” of 1 times itself. 
  2. Then ask them to move on to 2, and ask themselves, “What number times 2 equals the target number?” If the target number is even, there will be a number on the right-hand side of that pair. If the target number is odd (like 15), there won’t be, and the student should cross out the 2, as it is not a factor of the target number.
  3. Next, the student moves on to 3. They ask themselves, “What number times 3 equals 15?” Because 3 x 5 equals 15, students write 5 down because that is the next factor pairing 15. 
  4. Next, students move on to 4. They ask themselves, “What number times 4 equals 15?” When students run across a number that is not a factor of the target number, they should cross it out. So they cross out the 4.
  5. The next number is 5, but it is already showing on the right side of the factor pairs. When that happens, students can be sure they have found all the factor pairs of the target number.

In the end, students will be left with a list of factor pairs that multiply to create the target and a list of crossed-out numbers that are not factors.

 

Rocket Math Online Game – Finding Factors & Primes Track

Building on what the Worksheet Program has to offer students, Learning Track #15 (Factors & Primes) of the Rocket Math Online Game helps students systematically identify, practice, and memorize factor pairs of every number from 2 through 40 and 42, 45, 48, 49, 50, 64, 72, 75, and 100.

 

Students answer with the NEXT factor pair in order

Example of Rocket Math's Finding Factors worksheet.The Learning Track Factors and Primes has a unique way of teaching students the factors. Students learn the factor pairs, in order, starting with 1 and itself. For example the factor pairs of 36, in order, are 1 x 36, 2 x 18, 3 x 12, 4 x 9 and 6 x 6.   Students are shown some factor pairs in the display (see problems displayed in N.1 through O.1). They must either enter the next factor pair in order or hit the checkmark if there are no more pairs. You can see the five problems that deal with the factors of 36 that students encounter in the Factors and Primes Learning Track.  

When students see problem N.1 displaying “Factors of 36, 1 x 36” they learn that the next factor pair is 2 x 18, so they enter a 2, a 1, and an 8, and the game displays them as shown.  If the student does not enter the next correct factor pair, the game’s audio voice recording (called Mission Control) says, “The factors of 36, in order, are 1 times 36 then, 2 times 18. Go again.” The game then provides an opportunity to answer that problem again, twice, and then interspersed with other problems, twice more before the game considers that pair of factors learned.    

When students see problem O.1 they see all the factor pairs of 36 displayed. They know that they have all the factor pairs because the same number is in the left-hand column and the right-hand column. Students are to hit the checkmark √, to indicate there are no more factor pairs. The game’s audio voice recording correction is, “There are no more factors of 36. Just hit the checkmark. Go again.”

 

Prime numbers

An example of the Rocket Math's Finding Prime numbers worksheet.Any of the numbers that students learn are prime numbers will begin with the first factor pair of 1 times the number itself. For example, in problem, O.2 students see “Factors of 37. 1 x 37.”  Students are to hit the checkmark to indicate that a number is a prime number.  The game’s audio voice correction is, “37 is a prime number because its only factors are 1 times itself. Just hit the checkmark. Go again.”  In this manner, students learn all the prime numbers from 2 to 40 in this Learning Track.  

Students should learn their multiplication and division facts first before working on Factors and Primes. Once those are mastered in the Online Game, students who are already trying to find the greatest common denominators in working with fractions the Factors & Primes Learning Track will help them greatly.  They will exit knowing the factor pairs of these most common numbers and they will find this work much easier.

 

Make finding factors easier (and more fun!) for your students with Rocket Math

With Rocket Math’s Factor Worksheet and the Online Game, your students can say goodbye to slow progress and hit-and-miss strategies. The Worksheet and Online Game can be used separately or in tandem for extra practice.

Get Rocket Math’s Factor Worksheet!   

Try Learning Track #15 (Factors & Primes) of the Rocket Math Online Game for Free!

 

Teach Multiplication Facts to Struggling Pre-Algebra Students

You want your middle-grade students to complete the pre-algebra math topics so they are ready to begin to study algebra in 8th or 9th grade. A disheartening number of middle-grade students have not memorized basic multiplication facts (times tables). Students must know multiplication facts to follow, absorb, and implement pre-algebra topics.  How to teach multiplication facts to struggling students? How can a teacher help their struggling students learn multiplication facts when a lot of their students do not need to do that work? 

Rocket Math Online Game includes learning tracks for pre-algebra skills as well as basic multiplication and division facts. Within the Rocket Math Online Game, teachers assign students the learning tracks that they most need.

 

Math Strategies for Struggling Students

a student who does not know her math facts is counting on her fingers.

Students who do not know their multiplication facts are constantly distracted from learning math strategies by having to stop and “figure out” basic facts. Every time they are asked to provide the answer to a multiplication fact, they have to turn their attention to working it out or looking it up. By the time they have gone through their process, they have lost the thread of the strategy they are supposed to be learning. The most important thing a math teacher can do for struggling math students is to help them bring math facts to automaticity. Then answering math fact questions no longer interferes with learning multi-step strategies for solving math problems. 

 

Why Multiplication facts are Important to Learn Before Middle School Math

A student sits frustrated in class because he doesn't understand his basic math facts.

Many pre-algebra math topics assume students have a ready knowledge of multiplication facts to even understand. When I was a middle-grade teacher, my remedial students were unable to follow or understand topics such as Finding factor pairs, reducing fractions, equivalent fractions, converting fractions, unlike fractions, and so on. I realized that it was because they did not know basic multiplication facts. When I reduced 8/24 to ⅓ it was like magic because they did not quickly recognize the multiplication facts involved. They didn’t understand the concepts we were trying to learn because they did not see the relationships they were supposed to know. When I asked them to think of the factor pairs of 36 they were unable to find them all, no matter how much time I gave them. While students can do multi-digit multiplication problems using a times table chart, it does them no good in pre-algebra topics because it takes too long, even if they know what to look up. Now let’s look at how to teach multiplication to struggling students using Rocket Math Worksheets or Rocket Math Online Game. 

 

How to Teach Multiplication to Struggling Students Using Rocket Math

Two students use Rocket Math Worksheets to practice their math facts.

Students who have not yet mastered multiplication facts are going to require a very effective teaching methodology to learn them. The haphazard, leave-it-up-to-the-student methods have already failed them. By now, these students lack confidence in their ability to learn the facts, so you need a sure-fire system. 

Rocket Math is just such a system. Both the Worksheet Program and the Online Game systematically introduce students to the facts in a careful sequence that they can do. The Worksheet Program and Online Game ask students to memorize only two facts and their reverses at a time.  

Students demonstrate mastery of those facts by answering them without hesitation. Then Rocket Math will add two more facts and their reverses. Small steps at a time, systematically the students can memorize the facts and answer them instantly from memory. If students practice every day, within a few weeks you’ll see a dramatic improvement in their recall of multiplication facts. 

But what about the students who already know their multiplication facts? Rocket Math has something for them as well. 

 

Rocket Math Programs for Advanced Students 

Teachers can assign Rocket Math as a 10-minute warm-up or cool down for all their students whether they are behind or advanced. Rocket Math has several pre-algebra topics for those students who already know their multiplication facts. Each of these topics will help them do pre-algebra processes more fluently and to quickly recognize relationships that they have memorized.

 

Learning Track 13: Identifying Fractions

Screenshot of Rocket Math Online Game for identifying fractions.When students initially learn about fractions they are often only shown proper fractions. As a result, they have a limited understanding of fractions and can be confused by improper fractions or mixed numbers. The Rocket Math programs (both Worksheet and Online) prevent this problem.  From the start, we teach students using examples of both proper and improper fractions as well as whole numbers and mixed numbers. Students learn to identify over 90 different fractions quickly and easily by getting lots of practice. Their understanding of fractions will deepen and become more flexible as they learn to recognize many examples of fractions.

 

Learning Track 14: Equivalent Fractions

Screenshot of Rocket Math Online Game of Equivalent Fractions practice.Students will memorize the most common equivalent fractions with this Rocket Math Learning Track. They will also learn to identify a number of fractions, such as 2/9,  that do not “reduce” or for which there are no equivalent fractions in lower terms. Students also learn to recognize a fraction equal to 1 whole in its various forms. When students don’t instantly know the answer they are told the equivalent fraction and given practice on it. The computer gives help in the Online Game.  Their partner gives that help in the Worksheet Program. By the end of the program, students will learn over 90 equivalent fractions. This gives students an excellent start on being able to manipulate fractions quickly and easily.

 

Learning Track 15: Factors & Primes

factors and primes game screensStudents are required to “find the factors” when dealing with unlike fractions and reducing fractions. Rocket Math Worksheet and Online Game teach students how to find factor pairs. Students learn how to find all the factor pairs and what they all are for many common numbers. They also learn to identify prime numbers and their characteristic of having only one and themselves as factors. Students learn the factor pairs in order and know the “last” factor pair when they see it. When the game asks “What’s next?” students can provide the next pair of factors or click the checkmark to indicate there are no more factors. When students go through this Learning Track they will no longer hesitate when asked for the factors of common numbers.

 

Learning Track 16: Fraction & Decimal Equivalents

Screenshot of Rocket Math Online Game of Fraction & Decimal Equivalents practice.

Common fraction and decimal equivalents should not require a laborious process to “figure out.” Students should just know these, so this Learning Track in the Online Game allows them to memorize a bunch of common decimal and fraction equivalents. Having a facility with a lot of fraction and decimal equivalents means faster computation as well as a way to check their process when manipulating fractions and decimals. Students also learn another essential pre-algebra skill that often confuses them.  They learn to correctly and fluently translate a fraction into a division problem and vice-versa.

“Test Drive” any of the 16 Learning Tracks in our Online Game demo accounts. 

Register for a 14-day free trial of Online Game for all your students

Explore the options for subscribing to the Worksheet Program.

Teaching Math Fact Fluency | Why Rote Learning Works best

Developing math fact fluency requires memorization and enables success in math

In case you have any doubt, every set of official recommendations about elementary math recognizes that children need to “know facts from memory,” which is to say recall. Memorization is required to develop math fact fluency or easy, automatic recall. Teaching math fact fluency is necessary, of course, for fluent computation. Math fact fluency is also required for understanding and manipulating fractions. Instant recall of math facts is required to be able to recognize when the calculator is not showing the right answer. How students should learn facts, and when they should begin the process is not as well understood.

What Students must know before beginning to memorize math facts

Students need to understand the operation, whether it is addition, subtraction, multiplication, or division, before they begin to memorize the math facts in that operation. What does it mean to say a student “understands” an operation? It means that given some time, they can figure out the answer to a math fact problem in that operation. A student who can add 8 and 7 and get the answer of 15 by drawing lines or counting on their fingers understands the operation. A student who can add 6 five times to get 30 understands multiplication well enough to begin learning answers. Really if you think about math facts, there are only two things to know: how to figure it out and what the answer is. Once students can “figure it out,” then all that’s left is memorizing the answer, so they don’t have to keep figuring it out over and over!

What students do NOT need to know before beginning memorization

There is a very widespread belief that students must play around with math facts before they begin memorization. That they need to experience a variety of ways of figuring out facts. Or that they need to first learn relationships among facts, like the doubles or doubles plus one. It is believed they need to do these before they begin memorization. Yes, done poorly, timed tests of ALL the facts without a program of instruction, is bad for students. Timed tests without learning results in students reconfirming their worst fears, that they are “bad at math.” That is counter-productive. We want students to develop confidence in their ability to learn and do the math. But do they need to play a lot of games or spend a lot of time figuring out math facts?  Maybe not.

Experimental Research has NEVER Shown the Necessity of Games.

Some advocates suggest that students must learn how to figure out facts “efficiently” before beginning memorization. But there is no cognitive difference between being able to figure out a fact efficiently or inefficiently. John A. Van de Walle, an author of “developmental” and “student-centered” math textbooks, is quite emphatic. He says,”Do not subject any student to fact drills unless the student has developed an efficient strategy for the facts included in the drill. … Drill prior to development of efficient methods is simply a waste of precious instructional time,” (Van de Walle, John A. Elementary and Middle School Math).

It is a bold claim, but not one that is backed up by any experimental evidence. Proponents like Van de Walle often cite “research” to “prove” that students must explore and play with numbers before memorization can begin. The “research”  citations are not experimental studies with control groups. They are simply recommendations or observations of what students do when they try to memorize on their own. 

It is true that if there is no systematic instruction, students will start finding ways to remember facts on their own. These little techniques are not bad in themselves but are abandoned when students finally learn the facts. When you can instantly recall the answer to a fact, you know it without going through any intervening thought. In fact, there’s no time for that. If you know that 8 plus 9 is 17 in a straight recall, instantly, you don’t need anything else. You no longer benefit from thinking through that “8 plus 8 is 16 and since 8 plus 9 is one more, the answer is one more than 16 or 17.”

 

Real research into teaching math fact fluency is desperately needed.  

An interesting experiment, that has never been done, would be to put randomly selected students into two groups after they had learned how to figure out an operation. One group could do these various non-rote, playing with numbers activities. That play-time would be followed with a program of memorization of math facts. The second group would go ahead with the program of memorization without bothering with all exploratory activities. Rocket Math would gladly fund such a research study and provide the math facts practice materials to do it. Seriously, which group do you think would have learned the facts soonest?

Common Non-Rote Activities that Just Waste Time

Students and teacher playing multiplication games with dice sitting in a circle in a classroom, to learn math facts.

Dice. 

The various types of activities that have students roll dice and add numbers together are usually a waste of time. Generally, most of the students are not doing math at all; they are just watching. The ones who are doing math, are just practicing figuring out the facts–but that’s something they already knew.

Cards.

Some recommendations include having children play cards–hoping they will learn more about numbers by doing that.  If you don’t know math facts, you will find playing most card games that involve combinations to be difficult.  You might start trying to remember some common combinations on your own.  That does not help you memorize facts any faster, however.

Combinations.  

One popular idea is having students make up combinations of numbers that add up to ten. Here’s an example of one version. Use a large dice and a whiteboard with a blank number bond drawn on it. Put the number 10 in the middle circle, and tell the students that you are going to make a number bond that equals 10. Roll the dice, and whatever number comes up, it goes into the top circle. The students then have to decide what number goes in the bottom circle to complete the bond.

Here is another variation of the same thing.  Set up three hula hoops in the yard. Take ten students at a time and roll the dice. Four of them moved into one hula hoop and the other six crowded into the other. Then have them get back together as a group of ten. Roll the dice again, and then have them split into two pairs again. It may take several rounds of this moving in variations of 10 before the students “get it.”

No time left to teach math fact fluency.

These activities take up a lot of valuable instructional time, to no clear end. The real result of these recommended activities is that teachers NEVER get enough time to work on memorization of facts. In the United States, a huge percentage of our children are not fluent in math facts or computation or the prerequisite skills for algebra. These games and activities waste the time needed to actually develop math fact fluency.

How to Improve Math Fact Fluency with Rote Learning

Students can only memorize a few facts at a time.  Almost no one can memorize ten similar facts at the same time.  Instruction must introduce a careful sequence of a few facts at a time, followed by plenty of practice.  Well-designed instruction makes memorization easy.  Students can instantly recall the answers to facts they have committed to long-term memory.  Facts introduced too quickly can overwhelm a student’s memory capacity.  The task requires a steady process of accumulating these facts over several weeks.  Students learn at a pace based on their ability.  Everyone can memorize the facts, but just not all at the same speed.  Everyone can do rote learning, but it takes time and patient practice.

How to Get Kids to Memorize Math Facts (And Love Doing It!)

A student holds up their Rocket Math score sheet, which teaches math fact fluency to students.

There isn’t anything less intrinsically interesting than learning math facts. However, students and teachers commonly tell me that “doing Rocket Math” is their favorite time of the day. Why is that?  Both the Rocket Math worksheets and the new Online Game are designed to carefully introduce facts at a rate based on student learning. Students are continuously successful and are not overwhelmed.

A second reason students love Rocket Math are its built-in milestones.  As they achieve them, students can recognize the progress they are making. Students love feeling themselves achieving mastery–it is fun. They know they are in school to learn, and they love it when they can tell that they are learning. Far from being harmful, learning math facts can help build the self-esteem of all students. Not to mention making math easier in the long run. Don’t let anyone tell you that you have to postpone this important aspect of your students’ education.

**Nor do the proponents of these various math activities and games say which grades should do these and which ones should stop playing games and get to memorizing. Consequently, many teachers keep doing these games all the way through elementary school and never do get around to the memorization part.

 

20 years of Rocket Math shows that going straight to memorization works fine

Teachers have been using, and students have been learning from Rocket Math for over 20 years, without first doing these games, and not having any problems. You can too. Try it for yourself and see. We have a 60-day free trial of Rocket Math Online Game. Call us if you need an extension.  

Writing Numbers Backward: Why Kids Do It & How To Help

The group “The Who” was correct when it comes to kids writing their numbers backward: The kids are alright.  Children writing their numbers backward is not something to worry about. It is natural and expected. With instruction and encouragement, children can learn to write their numbers correctly with ease. 

Why Do Kids Write Numbers Backward?

A chair mirrored is still a chair, while a seven mirrored is not the same to help children who are writing numbers backwards.

For the first several years of our lives, we learn that “orientation-in-space” does not change an object’s identity. Turn a chair any which way, and it is still a chair. We learn this lesson well enough that we stop paying attention to an object’s orientation in space.

So, it is not surprising that kids sometimes write their numbers backward. It would be more surprising if they never did. Students need to learn to write certain symbols to face a specific direction.

 

What Does it Mean When Kids Write Numbers Backward?

When children write their numbers backward, they are mirror writing their letters or numbers backward or upside down. They need to learn that while a chair may be mirrored and is still a chair, a 7 mirrored is no longer a 7.

Is it Normal for a Child to Write Numbers Backward?

Students work with together to learn how to write their numbers.It’s perfectly normal for kids to write numbers backward. Some kids will even write from right to left, reversing all their numbers. It’s important for children to learn how numbers face, but don’t feel you must prevent your kid from writing this way or make them instantly correct it. Instead, you want to tell them that it is “better” or “more grown-up” to make the number face this direction. It will take time and gentle reminders.

Writing Numbers Backward in Kindergarten at Age 5 & 6

At age 5 and 6, it’s normal for kids to write numbers backward. But it is still important to begin working with them to understand which way numbers face. It may still seem random at age 5, but focusing on encouraging them that it’s better to write numbers “the smart way” will be effective.

 

Writing Numbers Backward at age 7 & 8

At age 7, students who are still writing their letters backward may have started a bad habit that’ll take a good bit of practice to break. If beyond age 7, a student is still writing their numbers backward or upside down, this could be a sign that they are having difficulty with reading or language. This is NOT a sign of dyslexia.

 

Is Writing Numbers Backward a Sign of Dyslexia?

A chair mirrored is still a chair, but a d reversed turns into a b.

Writing numbers backward isn’t a sign of dyslexia. Dyslexia is a reading disorder that involves problems identifying speech sounds and how they relate to letters and words. Writing backward is a sign of not learning which way symbols face.

It’s common, however, for students with difficulties learning to read to continue reversing their letters such as b and d. Reversing “b” and “d” has the same cause as writing numbers backward: learning that orientation in space does matter. However, when it comes to “b” and “d,” the reversal is actually “that other letter” and isn’t just “backward.” The distinction between which is b and which is d is somewhat harder for children to learn. Students who have problems with hearing the sounds in words (called phonemic awareness) will find it harder to remember which letter is in which word. But, even children with dyslexia can learn to read; it just takes more focused instruction.

 

Do Kids Grow Out of Writing Numbers Backward?

It’s important for children to learn to write symbols in a certain way and why by a teacher and or parents. It helps to have someone tell them when they have written a number backward and to reinforce them when they get it right. Some children notice this without much prompting, so we say they “grew” out of it. But really, they just learned it on their own. If you want them to be successful, don’t hesitate to help them learn to write their letters and numbers correctly. Be nice and supportive, but do give clear information.A mom congratulates her son at a baseball game.

How Can I Help my Child if they are Writing Numbers Backward?

An example worksheet from Rocket Math with an example of a 7 at the top to help kids who are writing numbers backwards..

The best way to help is to make an example of “the way it is supposed to face” on any paper before your child starts working. Say something like, “See if you can make all your sevens face this way. It is hard, but you might be able to do it.” Your child can then check each time he or she writes the number to make sure they are making it face the same way as your example.

By the way, writing “7” a hundred times won’t help because after the first one it is just doing the same thing over and over. The issue is remembering which way it has to face when you write it. So having it available as a reference means your child has to remember, “Oops. Which way does a seven face? Oh, that’s how it faces. Hey! I got it right!”

Another powerful way to help is to notice and be impressed when they write their numbers the right way and congratulate them. “Wow! All your sevens on this page are facing the right way. Way to go! You are really learning this.” If you are impressed by their learning, they will be motivated to keep remembering and it will boost their self-esteem.

When Is it Time to Talk to Their Teacher?

If you notice your child is frustrated after school when they were trying to write their numbers, you can bring it up with the teacher at the conference time. Ask them if they are giving your child an example of how to write the number to look at when writing their numbers. But other than consistently helping your child learn the arbitrary rule about which way certain numbers face, there is nothing else the teacher can or should do. Please don’t ask them to “test” your child for dyslexia on account of these backward numbers.

Image of worksheet to help kids who are writing numbers backwords learn to write them correctly.How Can Rocket Math Help?

Rocket Math offers worksheets that may help your child learn how to write their numerals correctly. Each worksheet focuses on a group of numbers to show children how to write their numbers in the right direction and with the right form. Learning to write numbers correctly takes time, patience, and encouragement from teachers and parents.

Online Math Drills to Help Develop Math Fact Fluency

What are Math Drills? 

Math drills are exercises given to students that can help improve their speed and ease of recall. The goal of math drills is to help students develop automaticity, allowing them to instantly recall from memory the answer to any math fact. If carefully designed timed math drills can help check which facts the student has learned and which ones the student needs to work on. If not carefully designed, they can be a terror to children. Carefully designed math drills in the elementary grades can smooth the way for easy success later on in math.

Why Is Math Fact Fluency Important? 

Math fact fluency is important because it is the first step to developing automaticity. Automaticity frees up the students’ short term memory for more important questions. It means students can answer basic math facts like 7 x 9 or 4 + 8 instantly, by recall without effort. Students who aren’t fluent in math facts, have to stop and figure out facts, and then won’t be able to focus on higher-order math lessons. This could lead to them missing parts of the instruction.

How Do Online Math Drills Help Children Develop Math Fact Fluency?

Correctly recalling the answer to a math fact strengthens the neural connection between the problem such as 9 plus 7, and its answer, 16. [Note that repeating a fact over and over does not achieve the same result. Finding the answer in memory and producing it is what strengthens that connection.] Math drills that ask students to recall answers to a couple of targeted facts, mixed in with other facts the student already knows, makes those neural connections stronger until they can answer those targeted facts correctly, and eventually without any conscious thought. The curriculum should not go on to target any more new facts to learn until the student is fluent with the ones learned so far. A computer program is able to patiently provide this practice for as long as each student needs, which is wonderful.

Why are Math Tests Timed?

Math tests are timed to tell if students are solving math facts by recall rather than deriving the answer. By timing the tests, teachers can tell which students are able to recall answers instantly and which ones need more help to develop automaticity.

Before I understood this, I made students do pages of mixed math facts, which they did by figuring them out.  However, that practice was not helping them become fluent. Timing those pages of mixed facts would not have helped either. In graduate school, I was taught the learning principles that would help students develop fluency. Students need to focus on a small number of facts so they can recall them. So math drills should be composed of a carefully selected set of facts.  This is the key to the design of Rocket Math and is why it works so well.

What Kind Of Drills Should Your Child Do?

At the very least, your child should learn the basic 1s through 9s math facts of addition, subtraction, multiplication, and division. These will make a huge difference in your child’s success in math. However, if you want to help your child become really proficient and confident in math, there are more things you can drill at each grade level.

Kindergarten Math Drills

Kindergarteners need to be able to count objects as well as rote count. They should practice counting up to 20, at least, and counting by tens to 100. They should learn how to write the numerals and be given drills to practice numeral formation. Obviously this is not something that can be practiced online, but a good writing practice program such as Rocket Writing for Numerals will set your child up for success.

1st Grader Math Drills

In first-grade, learning how to count and write numerals is assumed. The key skill to drill on in first-grade is addition facts 1 through 9. Once those are learned, children can drill on addition facts to 20, such as 13+6, or 4+15. You can also drill first-grade students on fact families, which combine addition and subtraction facts. A fact family example is 3+2, 2+3, 5-2, 5-3. In first-grade fact families (+, -) up to 10 is a reasonable amount to learn.

2nd Grader Math Drills

If addition skills from first-grade are mastered, then drilling on subtraction facts 1s through 9s are the top priority. Once those are learned, students will benefit from drilling up to the 20s in subtraction, such as 17-5 or 19-8. You can also drill second-grade students on fact families, which combine addition and subtraction facts. In second-grade, once fact families up to 10 are mastered, you can drill them on fact families from 11, such as 8+5, 5+8, 13-5, 13-8. Skip counting, or counting by a number (such as by fours- 4, 8, 12, 16, 20, 24, 28, 32, 36, 40), is useful to learn in second-grade. Also, second-grade is not too soon to begin drilling students on identifying fractions.

3rd Grader Math Drills

Starting in third-grade multiplication facts is essential from this point onward and can’t be counted on fingers. The basic multiplication facts 1 through 9 must be memorized and drills are the only way to do that. Even if addition and subtraction are not yet mastered it is essential to get multiplication facts learned. Then you can go back and pick up addition and subtraction.

Alternatively, or additionally, students can begin drilling on fact families in multiplication and division. An example of this kind of fact family is 4 x5 , 5 x 4, 20 ÷ 4, 20 ÷ 5. Fact families up to 20 are enough in third-grade.

After multiplication facts 1 through 9, you can move on to drilling the 10s-11s-12s. Also, Identifying Fractions is something that third-grade students can become fluent in. Factors (finding all the factors of a number) can be drilled at this grade level or any time in the next three years.

4th Grader Math Drills

In fourth-grade, it is essential that multiplication facts 1s through 9s are in place first before drilling on division facts. Students will quickly realize division facts are just the opposite of multiplication facts. Once division facts 1s through 9s are learned, you should go back and make sure that addition and subtraction are mastered. After addition and subtraction facts are automatic, then start students on multiplication 10s-11s-12s and division 10s-11s-12s. Once all of these are mastered, students can work on either identifying fractions or factors. Another skill that can greatly help students in later grades is memorizing equivalent fractions.

5th Grader Math Drills

Students in fifth-grade or higher should be fluent in all these basic math areas: multiplication (1s through 9s), addition (1s through 9s), subtraction (1s through 9s), and division (1s through 9s). These can be strengthened by doing fact families with each of these operations: fact families (+, -) to 10, fact families (+, -) from 11, fact families (x, ÷) to 20, and fact families (x, ÷) from 21. Once these are done, students can start drilling on factors, identifying fractions, equivalent fractions, then learning to add and subtract integers. Then the students can start multiplication 10s-11s-12s and division 10s-11s-12s. The same sequence applies in any grade after fifth. The more facts learned in math to the level of automaticity, the easier the rest of math will be.

 

How Can Rocket Math Online Game Help Your Child Learn?

The Rocket Math Online Game provides the right amount of drill to help your child learn these basic skills. Providing plenty of practice, it is timed and requires students to recall facts (answering within 3 seconds) before moving on to learn more facts. They work their way up through 26 sets, from Set A to Set Z, learning more facts as they go along. The game provides many milestones of progress, lots of little breaks and congratulations as students progress through the twelve Learning Tracks. You can place your child in these tracks in the order you choose. The Rocket Math Online Game includes the following twelve Learning Tracks.

  1. Addition 1s through 9s
  2. Subtraction 1s through 9s
  3. Multiplication 1s through 9s
  4. Division 1s through 9s
  5. Fact Families (+, -) to 10, ex.4+6, 6+4, 10-4, 10-6
  6. Fact Families (+, -) from 11, ex. 5+6, 6+5, 11-6, 11-5.
  7. Add to 20, example 13+4, 4+13,
  8. Subtract from 20, example 15-3, 15-12,
  9. Multiplication 10s-11s-12s,
  10. Division 10s-11s-12s.
  11. Fact Families (x, ÷) to 20, example 4×5, 5×4, 20÷4, 20÷5
  12. Fact Families (x, ÷) from 21, example 3×7, 7×3, 21÷3, 21÷7

See a video of how it teaches here.

The Rocket Math Worksheet Program also provides math drills

Math drills are important for setting your students up for success later in life. Help them build their automaticity and become fluent in the basic math facts through Rocket Math Worksheet Program. The Rocket Math Worksheet Program includes more Learning tracks than the Online Games and you can use this program to help your students with basic math skills.

Here is a list of the worksheets in the Rocket Math Worksheet Program.