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.  

Kids Who Write Their Numbers Backwards

The group “The Who” was correct when it comes to kids writing their numbers backwards: The kids are alright.  Children writing their numbers backwards 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 Backwards?

A chair mirrored is still a chair, while a seven mirrored is not the same.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 backwards. It would be more surprising if they never did.. Students need to learn to write certain symbols to face a certain direction. 

What Does it Mean When Kids Write Numbers Backwards?

When children write their numbers backwards, they are mirror writing – writing letters or numbers backwards 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 Backwards?

Students work with together to learn how to write their numbers.It’s perfectly normal for kids to write numbers backwards. 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 stop your kid from writing this way or make them correct it. It will take time and gentle reminders.

Is Writing Numbers Backwards a Sign of Dyslexia?

A chair mirrored is still a chair, but a d reversed turns into a b.Writing numbers backwards 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 backwards 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 backwards: learning that orientation in space does matter. However, when it comes to “b” and “d,” the reversal isn’t just “backwards.” So the distinction between b and d is somewhat harder for children to learn. Students who have problems with phonemic awareness will find it harder to remember which is which. But, even children with dyslexia can learn to read, it just takes more focused instruction.

Do Kids Grow Out of Writing Numbers Backwards?

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 backwards 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 Backwards?

An example worksheet from Rocket Math with an example of a 7 at the top.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, “Be sure to make all your sevens face this way.” 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 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.

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.

Math Fact Benchmarks: Why Writing Speed Matters

Math drills are used to help students learn their basic single-digit math facts. The goal is to help students answer basic math facts from recall and develop automaticity. The only way to tell if a student is recalling the answer rather than figuring it out is by using timed math drills as benchmarks. But students cannot learn how to recall a full page of math facts by drilling on them. The drills will likely cause anxiety and frustration for students. Here are some common pitfalls that are wise to avoid when teaching students basic single-digit facts.  

Common Problems With Math Benchmarks 

Schools typically set “benchmarks” to evaluate whether students have achieved their educational goals.  When it comes to math fact memorization, schools will set benchmarks to distinguish between knowing the answers by a quick recall from the slow process of figuring out the facts. There are two main problems with these benchmarks.

Learned one at a time. 

The first problem is that math facts are learned individually and students meet the benchmark one problem at a time. The benchmark should be to answer a problem in less than a second. If they can, then it would be clear which math facts a student has memorized and which ones they don’t. It is more common for schools to give tests on all the facts in an operation and these tests can’t tell the schools which facts are memorized. A more meaningful report would be which facts in an operation can a student answer instantly.

 

Time to write the answer. 

The second main problem is that no matter how well students know facts, they cannot write answers to facts any faster than they can write. Elementary students vary in speed and can write answers anywhere from 10 answers in a minute to 50 in a minute. If a student can answer 40 problems in a minute, they have achieved mastery of math facts. But if they can’t write answers that quickly, they can not meet their school’s benchmark. In order to set a reasonable standard, teachers need to know how fast students can write and a writing speed test will help determine this.

Common Core Math Fact Fluency Need Not Cause Anguish

The Common Core Idea says that students must have a quick recall of math facts to progress successfully in math. For some reason, almost all children have memorized 2+2=4 and can answer this problem from recall. It is not stressful or hard and will not cause math phobia. So, we know that learning how to answer a math problem instantly from recall is doable and can be done without being stressful. The challenge is that there are a lot of facts to learn, but taken a few at a time, they can all be learned equally easily. 

To do this though, it takes a systematic effort, daily practice, and careful monitoring. Teachers need a facts program of some kind to help their students commit a large number of facts to memory. Before developing the design principles behind Rocket Math, I had thought this was a nearly impossible task. But in the last 20 years, I have seen how Rocket Math has been used successfully to teach math facts to students. With plenty of time, patience, and encouragement, students can learn to recall math facts from memory and with Rocket Math they can do this while having fun.

Rocket Math Writing Speed Test

 The writing speed test for Rocket Math

Here is a simple easy-to-use Writing Speed Test to help figure out how fast a student is able to answer when they have all the facts in an operation memorized. The test is a mix of one and two-digit numbers so it works with addition and multiplication. 

Simply give the test to your students and have them write the numbers they see in each box for one minute. You will be able to find out how many boxes they can complete in one minute. That number is the upper limit of math fact problems you can expect them to be able to answer–if they are answering from recall rather than by figuring them out.

Writing speed is number of boxes completed. 

When the student has finished the test, you will have the number of boxes they can complete in a minute. You can expect the student to be able to finish at least 80% of that number if they can recall the facts instantly.  If the student can answer 90%, they don’t need any fact work. If they are between 80 and 90% of that number, they are good, but more facts work would help them. Anything below 80% and they are having to stop to figure out some of the facts and need more work.

If you’re not interested in doing the math over and over, here is a goal sheet for pre-tests, where the numbers are worked out for you. You can print it from this link.

Benchmarks must be based on writing speed. 

Benchmarks that don’t take into account the speed at which children can write, leave a lot of children with an impossible expectation. Asking children to do something they are physically incapable of doing will cause a lot of unnecessary anguish.   

 

 

Kindergarten Math Benchmarks

Students should be taught how to write numerals correctly and efficiently in kindergarten. The methods of drawing numerals that children invent on their own can be slow, cumbersome, and inefficient – causing them to have a slow writing speed later. Rocket Math Writing for Numerals is a systematic method that will help students learn how to form their numerals. Benchmarks for kindergarteners should focus on the speed of writing numerals, which takes a good amount of practice and instruction.

Kindergarten Numeral Writing Fluency Benchmarks (digits)

    • Mid-year       
      • 20 digits per minute        
    • End of year     
      • 40 digits /minute       

First-grade Math Benchmarks

First-grade students need to be fluent in writing numerals. Not every kindergarten does this, so teachers should test and give some kind of numeral writing program to students who do not meet these writing standards.

First Grade Numeral Writing Fluency Benchmarks (digits)

    • Start of year  
      • 40 digits per minute               
    •  Mid-year   
      • 60 digits per minute                         
    •  End of year     
      • 60 digits per minute

We also want first-graders to learn addition facts to the level of instant recall. The student’s writing speed is the number of boxes they can complete in one minute.   

First Grade Math Fact Fluency Benchmarks (problems)

    • Start of year   
      • Addition 20% of writing speed   
    •  Mid-year  
      • Addition 40% of writing speed    
    • End of year  
      • Addition 80% of writing speed  
      • Subtraction 20% of writing speed 

Second-grade Math Benchmarks

In second-grade we want students to master subtraction facts as well as addition.  

    • Start of year  
      • Addition 80% of writing speed  
    • Mid-year   
      • Addition 80% of writing speed 
      • Subtraction 40% of writing speed
    • End of Year
      • Addition 80% of writing speed
      • Subtraction 80% of writing speed

Third-grade Math Benchmarks

In third-grade it is important that students master subtraction and begin working on multiplication. 

    • Start of year 
      • Addition 80% of writing speed  
      • Subtraction 80% of writing speed 
    • Mid-year 
      • Addition 80% of writing speed 
      • Subtraction 80% of writing speed 
      • Multiplication 40% of writing speed
    • End of year 
      • Addition 80% of writing speed  
      • Subtraction 80% of writing speed 
      • Multiplication 80% of writing speed

Fourth-grade Math Benchmarks

In fourth-grade it is important for the students to have multiplication mastered and begin division.

    • Start of the Year
      • Addition 80% of writing speed
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
    • Mid-year   
      • Addition 80% of writing speed 
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 40% of writing speed  
    • End of year 
      • Addition 80% of writing speed  
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 80% of writing speed

Fifth-grade (and up) math fact benchmarks

In fifth-grade it is important for the students to have mastered their basic math facts in addition, subtraction, multiplication, and division.

    • Start of year  
      • Addition 80% of writing speed  
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 80% of writing speed
    •  
    •  
    • Mid-year  
      •  Addition 80% of writing speed 
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 80% of writing speed  
    • End of year 
      • Addition 80% of writing speed
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 80% of writing speed                      

All the 1-minute pre-tests and the writing speed tests and the goal sheet can be found on this page https://rocketmath.com/pre-tests/.

 

 

 

 

 

 

 

 

 

 

 

 

 

Rocket Math Is A Fun Way For Students To Learn

Rocket Math has a systematic approach to teaching students how to become fluent in basic math facts and still have fun learning math. Math can seem daunting to learn and if not taught properly, using a good math program, students can build a math phobia. Teachers have been using Rocket Math for over 20 years now and believe it to be an invaluable tool to help their students learn math. 

 

Math Facts Practice Online: Add, Subtract, Multiply, Divide

Searching for a program to practice math facts online that will help your learner power through their math facts and have fun?

Rocket Math Online Game offers effective addition, subtraction, multiplication, and division practice, and students have a blast doing it! Why do they love the game? The game helps students quickly and methodically memorize math facts, which means less frustration and more fun! The game also shows students their progress with exciting, rocket ship-themed graphics and audio to keep them motivated to learn more. It turns out that students learn better and are more motivated to continue when they can clearly see their progress. Who knew?

How Rocket Math’s online math game works

Too many children still count on their fingers to figure out basic addition facts. If a child continues to spend hours counting on their fingers, it is a sure way to make them hate math. Professors of education frequently teach that “all rote learning is bad for children.” This is not true when it comes to math facts. Memorizing basic facts is a necessary step (to free up working memory) on the path to higher-order thinking in math, and by skipping math fact memorization, teachers are handicapping their students. As a result of the dogma against memorization, few new teachers have any idea how to effectively help their students memorize.

For example, giving students a worksheet full of problems that they haven’t been able to memorize isn’t going to help. Nor will a computer practice game that randomly gives problems for students to solve. A good math program will provide students with a few math facts at a time to work through before adding more. 

Student with Rocket Chart filled out

Rocket Math Online Game does just this. Starting with two math facts and their reverse, the game won’t let the student move on until they can answer these math problems instantly. Rocket Math Online Game will then gradually, carefully, and systematically add new facts to those already learned. Students have to answer in 3 seconds or less, or they have to do that part over until they can answer the math fact immediately. They will work through set A to set Z with 26 levels in three phases; Take-Off, Orbit, and Universe. Each time they complete a set, the tile for that set explodes and falls away. As students progress through the levels, they can fill out the Rocket Chart to see their progress and stay motivated. 

Addition Math Facts Practice in Rocket Math Online Game

First-grade students should begin working on the first Learning Track: Addition 1s through 9s math facts and have all those facts memorized first. With Rocket Math Online Game, there are three Learning Tracks to choose from for your first-grade class.

  • The Basic Learning Track
    • 1. Addition 1s through 9s
  • The Alternative Learning Track: learning addition and subtraction facts in families
    • 5. Fact Families (+, -) to 10
  • Optional Learning Track
    • 7. Add to 20

If you notice a student is taking more than a week to pass a level in sets A-Z of Addition 1s through 9s, that’s a sign for you to intervene. Often this means that the child is struggling and needs to practice more. They need to logon and practice at home in addition to their practice in school. The first graders who can finish the Learning Track for Addition 1s though 9s, can move on to the Optional Learning Track, Add to 20. Advanced first graders who are very quickly mastering facts can certainly move into the Learning Tracks recommended below for 2nd grade.  

There is an alternative sequence of learning addition and subtraction facts, through Fact Families.  Fact Families introduces addition and subtraction facts at the same time in “families” such as 1+3, 3+1, 4-3, 4-1. Because the facts are introduced in families students are able to switch back and forth between addition and subtraction as they are learning. Rocket Math breaks up the fact families into a Learning Track with addition and subtraction facts up to 10 to begin in first grade and then a second Learning Track of facts from 11 that follows after, either in first grade or second.   

Subtraction Math Facts Practice in Rocket Math Online Game

Many teachers think subtraction facts are harder for children to learn.The reason they seem harder to learn is that most children don’t fully master addition before they start memorizing subtraction facts. When that happens, the two operations interfere with one another (officially, it’s known as proactive and retroactive inhibition), and subtraction facts become harder to learn.

Students who work through the addition sets in Rocket Math Online Game, will not find this to be a problem. Once the student has mastered the addition facts, they will quickly recognize that subtraction facts are “the opposite” of addition. The interference does not happen, and the students will feel good about their progress and learn to do computation with ease. 

Rocket Math Online Game offers these Learning Tracks for second graders to master subtraction:

  • The Basic Learning Tracks
    • 1. Addition 1s through 9s
    • 2. Subtraction 1s through 9s
  • The Alternative Learning Tracks: learning addition and subtraction facts in families
    • 5. Fact Families (+, -) to 10
    • 6. Fact Families (+, -) from 11
  • Optional Learning Tracks
    • 7. Add to 20
    • 8. Subtract from 20

Second graders who did not learn addition Math Facts in first grade must focus on addition facts first. After they have gotten through Set Z of addition, they can move on to 2. Subtraction 1s through 9s.

Second-grade students who complete addition and subtraction 1s-9s can start Add to 20 and then go on to Subtracting from 20. 

As noted above,  learning by fact families is an alternative route to learning basic addition and subtraction facts.  The first Learning Track would be #5 Fact Families (+, -) to 10 followed by #6 Fact Families (+, -) from 11. 

 

Multiplication Math Facts Practice in Rocket Math Online Game

Being able to multiply is harder than addition or subtraction because you can’t count on your fingers. While it is necessary for students to memorize the “times facts,” they are seldom systematically taught. Preservice teachers are frequently taught that “rote learning is bad for children.” This is not true, but as a result, most new teachers have no idea how to effectively help their students memorize. Memorizing basic facts is a necessary step (to free up working memory) on the path to higher-order thinking in math, and by skipping math fact memorization, teachers are handicapping their students.

Rocket Math Online Game offers these Learning Tracks for third graders to master multiplication: 

 

 

  • The Basic Learning Tracks
    • 3. Multiplication 1s through 9s (priority)
    • 1. Addition 1s through 9s (if still not mastered)
    • 2. Subtraction 1s through 9s (if still not mastered)
  • The Alternative Learning Track: learning multiplication and division facts in families
    • 11. Fact Families (x,÷) to 20 
  • Optional Learning Track
    • 9. Multiplication 10s-11s-12s 

In third grade, multiplication has priority, and students must master it first even if they have not mastered addition and subtraction. Higher-level math students who may not have mastered addition and subtraction will only be crippled more without learning multiplication. Once the student has mastered multiplication, then go back and work on mastering addition and subtraction. When students have mastered all three of these basic operations, they can move on to 9. Multiplication 10s-11s-12s. And of course, advanced third graders who have learned the concept of division can move into the Learning Tracks recommended below for fourth grade students.  

There is an alternative sequence of learning multiplication and division facts, through Fact Families.  Fact Families introduces multiplication and division facts at the same time in “families” such as 4×5, 5×4, 20÷4, 20÷5. Because the facts are introduced in families students are able to switch back and forth between multiplication and division as they are learning.  Rocket Math breaks up the multiplication and division fact families into facts up to 20 to begin in third grade and then a second Learning Track of facts from 20 follows after, either in third grade or fourth.

Division Math Facts Practice in Rocket Math Online Game

The key to learning division facts is to learn them gradually. Students should work a few minutes at a time and then take a break. Rocket Math Online Game has students work for five minutes at a time (although the teacher can increase it to 10 or 15 minutes if the student wants it), and then the game pauses for a 20-minute break. Breaks will help keep students from becoming tired of the game and ensure they want to keep playing. Learning Math Facts is a marathon, not a sprint, so we want them to do Rocket Math once or twice a day for a few months. That’s how they will come to master the math facts.

Typically, students learn division in fourth or fifth grade, but they can learn it earlier if they understand the concept. Division isn’t harder than multiplication, but it will be if students have not mastered multiplication first. That’s why having students work through Set Z of multiplication before starting division is essential.

Here are the Learning Tracks offered by Rocket Math Online Game:

 

 

  • The Basic Learning Tracks
    • 3. Multiplication 1s through 9s (priority)
    • 4. Division 1s through 9s (secondary priority)
  • The Alternative Learning Tracks: learning multiplication and division facts in families
    • 11. Fact Families (x,÷) to 20 
    • 12. Fact Families (x,÷) from 21
  • Optional Learning Tracks
    • 9. Multiplication 10s-11s-12s
    • 10. Division 10s-11s-12s

When they have mastered multiplication and the 1s-9s of division, students can go on to Multiplication 10s-11s-12s and Division 10s-11s-12s.

As noted above, learning by fact families is an alternative route to learning basic multiplication and division facts.  The first Learning Track would be #11 Fact Families (x,÷) to 20 followed by #12 Fact Families (x,÷) from 21. 

Rocket Math Online Game – The Best Tool to Learn Math Facts

Mastering the basic facts in addition, subtraction, multiplication, and division will not only help students succeed in school, but are essential skills to have outside of the classroom. If you want your students to be successful at math and enjoy learning, memorizing these math facts is vital. With Rocket Math Online Game, your students will be engaged and excited to play. Students will be able to see their progress, celebrate their wins, and take pride in what they learn. It doesn’t take much to motivate your students, just a sincere recognition of their achievement. They will know when they have accomplished something, and if you recognize it as well, then they will feel proud of themselves.

There’s a free two-week trial of the Rocket Math Online Game so you can see for yourself how well it works and how students love it.