Math Fact Benchmarks: Guarantee To Meet Them With Student Effort & Rocket Math Online Game

Not meeting benchmarks: what should it mean?

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 working in schools across the country, I know this to be the case.  Without systematic practice and effort, 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.  So “not meeting benchmark” should mean that here is an area where the school needs to provide some intervention to build fluency.

Are you certain your fluency intervention is effective?

The teacher and the school have an obligation to provide an intervention that is effective.  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.

If you measure the same way for the same amount of time, you can see if fluency is increasing. You can see that the student’s fluency is increasing if the student can complete more items during the timed test each time you measure. If the vast majority of all of the students improve in fluency, then you can be certain that the intervention is effective. The graph above shows that for Multiplication, 23,540 students have increased in fluency as they worked through the Rocket Math Online Game.  See evidence from all 16 Learning Tracks here.

Rocket Math Online Game is effective

As students work through the levels in each Learning Track in the Rocket Math Online Game, they are tested after completing the first level (A), then after completing 33% at level I, and then after completing 66% at level R, and then after they finish at 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. When the number goes up at each point in the curriculum, you can be sure that students are increasing in fluency.  The chart to the right shows site-wide data. You can see students improve on average as they work through the Learning Tracks in the Online Game.  You would not expect students to meet benchmarks until they have completed Set Z in the Learning Track.

Math fact fluency benchmarks in the Online Game: 16/minute in addition and subtraction.

The 1-minute RACEs in the Rocket Math Online Game are a good way to measure math fact fluency.  On average students exceed 16 per minute correct at Set Z and the average at the beginning is much less.  So a reasonable benchmark is 16 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 as well as be exported from the button that gives “Results from Assigned races.”  However, the best measure of whether a student can meet the benchmark is after Set Z, when they have completed the Learning Track.  You can see the score by clicking on the pink button for exporting “Results from Scheduled Races.”

You can see the screenshot of an example of the results from scheduled races for all 16 Learning Tracks across our website.  You can see the Account Average shows improvement at each level.   Those scores after Set Z 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. At the Level Z test data there are no scores for students who had not completed Set Z in Multiplication.  Students have to actually play the game in order to learn.

Students must participate to learn: monitor and recognize effort

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 their session is recorded towards their effort score for the last 14 days.  Students should complete a session every day in school and some at home for homework.  In the effort rating system every four sessions completed earns a star, so 15  completed sessions over the last 14 days earned the student to the left 3 and 1/2 stars.

If you monitor the effort scores and recognize students who are putting forth great effort, you’ll get more students participating.  Completing 12 sessions in the last two weeks is good effort and earns 3 stars.  16 sessions over the last two weeks would earn 4 stars!

You might consider giving out Star Effort Awards (available in the teacher section of the site) once a month for students who are putting forth super-star effort.  If you reward effort, we guarantee you’ll get achievement.   Soon after doing that, you’ll probably have to start awarding Learning Track certificates for students who are completing Learning Tracks. All awards are available on the admin page on Tab (K) in the main rainbow navigation bar.

 

 

 

 

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

 

 

 

 

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!

 

The Online Game never teaches anything wrong.

Are your students complaining that the Online Game said they were wrong, when they were right?  This is similar to a problem we found with students and their checkers in the Worksheet Program. Bear with me a second while I explain.

In the Worksheet Program students often complain to their teacher that their checker made them do the problem over, even though they weren’t wrong.  Trying to adjudicate such a dispute is nearly impossible, as veteran teachers have learned the hard way.  The extra practice didn’t hurt the students and you’re going to be inundated with complaints if you try to adjudicate them. In workshops we always counseled teachers to respond to such complaints with, “The checker is always right.  Just do the problem over again.”

The extra practice that the Online Game) makes a student do is never harmful.  The problem and the answer that Mission Control gives is never wrong.  When students complain to you about the game telling them a right answer was wrong, just tell the student, “The game is always right. Just do the problem over again.

The Online Game only says right answers, so it’s not wrong.

The correction procedure says both the problem and the correct answer.   Students may say, “But, that’s what I put!” They are not confused. They are just complaining that they were “unjustly” corrected.  An unjust correction is relatively unimportant compared to an actual error.

The program never says a student’s answer is “wrong.”  The game does a correction whenever it does not process the correct answer within the time limit.  The student may hit the correct answer just a fraction of a second too late to be processed by the game. Even though correct, the game will say “Time’s Up” and do a correction.

Sometimes a student misses the button they mean to hit, they make a “typo,” and the game buzzes and the screen shakes “no.” Sometimes, a glitch occurs and it skips ahead to the next problem and processes the last answer as incorrect. However, the game can only say a problem and its correct answer as those are the only words that are recorded.  There are no recorded errors.  For example the game will say, “Six plus two equals eight. Go again.”  After that the game waits for the student to enter the correct answer AND waits for the student to hit the checkmark. No amount of arguing, “But that is what I put!” or “But that wasn’t the problem I was answering” will change it.

The extra practice caused by an “unjust correction” is not harmful.

Students should listen to Mission Control while it is displaying and saying a problem and the correct answer.  Then the game will show the problem just stated without the answer.  Students will know what they should do. They should just enter the answer and hit the checkmark.  Students should just do the problem over again regardless of whether or not they think they entered the right answer.  The game never says anything incorrect and the extra practice won’t hurt them. While an unjust red “X” for an error seems terrible to students, it will not do anything other than give them more practice, which is good for them.

We  offer a $50 gift certificate to the store of your choice if you can capture an error by the game on video, as we have never seen the game make an error and can’t replicate the problem.

Strategies for teaching automaticity of math facts

Above are students playing our Race for the Stars game.  This game prompts everyone to race against each other and the clock to answer 24 fact problems as fast as they can.  This activity can help develop automaticity of math facts. Not all activities in which students “practice” answering math facts will help develop automaticity.  In fact, a lot of math fact practice activities require students to “figure out” math facts over and over. Automaticity only comes about through recall.  Recall is instantaneous, whereas “figuring out” takes time. All the activities that give students “time” to derive the fact will not help develop automaticity.

What is automaticity?

high school marching band with brass instruments and drumsAutomaticity is the level of learning you have achieved when you can do something accurately and quickly while you are doing something else.  It is “automatic” because you don’t have to stop and think about it; you can do it while concentrating on something else. As the picture illustrates, you need to develop automaticity to function in a marching band, which is why it takes a lot of practice.  You have to march while simultaneously playing music and keep up with everyone else. That takes automaticity.

 

What is automaticity good for?

tools to build math fact fluencyIn academics, students use certain “tool skills” while they are multitasking.  These tool skills must become automatic so students can use them without thinking.  One tool skill is decoding in reading–getting the words off the page. That has to be automatic so the reader can focus on the message of the material they are reading.  Spelling is another tool skill that has to be automatic. A student who is writing something should not be distracted by trying to remember how to spell the words they are writing.

 

Why is automaticity of math facts important?

A student figuring out math facts slowlyIn math, the tool skill that must be automatic is remembering math facts.  Students must be able to recall the answer to single digit facts like 9 + 7 while simultaneously doing more complex problems.  They need to be able to recall those facts without losing their place in what they are computing, just like a member of a marching band.

No matter how clever the strategy for remembering a math fact, if it is not recalled instantly and automatically, it disrupts the thinking process of the learner.  The steps in the overall math procedure will become confusing, or the point of the computation may be lost. Strategies for developing automaticity must guard against allowing students to repeatedly “figure out” facts and must direct them to “just remember” the fact.  This can be a surprise for some teachers and some students!

Practice strategies that develop automaticity of math facts

Two students participating in one of Rocket Math's math fluency programsStudents can recall some facts instantly but have not yet learned others enough to be recalled instantly.  New math facts are learned one at a time. Although most students can work on memorizing three or four new facts at a time, if the facts are too similar, even three will be too many.

The best method of practice is to read problems aloud and say the answer from memory.  If there is any hesitation after the problem is read aloud (which gives the learner enough time to remember) then extra practice is needed on that fact.  The procedure should happen immediately, as there is no time to waste. The learner needs to understand that the goal is to instantly recall facts, rather than puzzle them out. 

Figuring out math facts will not develop automaticity

Rocket Math mobile math fact game interfaceAllowing students extended time to work out the answer to a math fact teaches the wrong lesson.  If there is any hesitation in answering, extra practice should involve being told the fact and the answer immediately (no more puzzling it out, is the message!).  After hearing the correct answer, the learner should say the problem and the answer aloud two or three times. They should then go on and practice two or three different problems before returning to the problem that the learner was slow to answer.  And finally, the learner should try to answer the first math fact again, this time without any hesitation. This process of being told the answer, trying to commit it to memory and trying to recall it a few seconds later will develop automaticity of math facts. Consistently allowing students extended time to figure out facts will not lead to automaticity.

Similarly, the Rocket Math Online Game only allows students 3 seconds to input an answer.  If they can’t answer instantly, automatically, then the game shows, “Time’s Up!”  and Mission Control says, “You gotta be faster!” Next, the game gives the student extra practice on that fact and starts them over in the part.  The game expects automaticity of math facts and teaches students that they can in fact do that.

Students will be able to remember and recall the answer, as long as only a couple of new facts are introduced at a time.  They will come to realize that instant recall is possible, and that is their goal. Once they can recall facts without having to figure them out, math will become a breeze.

Use Rocket Math’s automatic response worksheets for testing not teaching

The Rocket Math Worksheet Program has students practice in pairs as described above.  Then each day the pair will do timed or “automatic response” worksheets—but as a test.  The worksheets proceed from A to Z as students learn more facts in the operation. Each worksheet only tests the facts introduced thus far.  Students practice the same set of facts, using the oral procedure outlined above until all of the facts introduced thus far are automatic.

Rocket Math Addition Set D Worksheet that develops automaticity of math factsWhat facts are on each math worksheet matter.  A worksheet cannot contain a mix of all of the facts in an operation; you cannot expect facts to become automatic by doing the sheet repetitively. No one can learn 80 facts at once.  The curriculum must break down the facts in an operation into bite-size pieces so that students can practice and learn them. You see here set D, which has added 7+1 and 8+1 and their reverses as new facts.  The One-Minute Test only presents the facts learned up through set D. For the first couple of days, the student will not be able to answer all the facts instantly; but after a few days of practice, the students will be automatic with all the facts.  Then the student will pass the set. The curriculum should add more facts to be learned in the next set.

Slow and steady wins the race. It takes months to learn all of the facts in an operation to the level of automaticity, but everyone can do it.

 

How much practice is enough in Rocket Writing for Numerals?

Students balance a desire for comfortable mastery against a desire for novelty.

A home-schooling mom asks:
After having read the Rocket Writing for Numerals teacher’s directions, I have a question about implementation: Should I have her do the same page twice in one day (at separate times) to help her get more practice? After re-reading the teacher directions again today, I also think I need to go back and do more demonstration and air writing.

Dr. Don answers:
Regarding Rocket Writing for Numerals, the focus of the air writing and demonstrations is to achieve accuracy and consistency in the way to form the numeral. Once she consistently knows how to form the letter (starting in the right place, making the strokes in the right direction, etc) then the rest is developing the motor skills. More air writing is not needed once formation is consistently correct.

Yes, you can have her do a page twice in a day. How many days in a row is needed before you can move on to a new page is not established by research. It would be different for each student anyway. If you watch her, then you can decide, or you can encourage her to decide.

You want a page to become easy or routine for her. She doesn’t have to do it perfectly, but don’t move on if she still seems to be struggling or having to go very slowly. You should move on if she seems to be unchallenged by the page. You can also engage her in deciding if she feels she is ready to go on to the next sheet or wants to practice on the same page some more. Generally, once children get the idea of what it feels like to master a performance, they want to do so and students balance that desire for comfortable mastery against a desire for novelty. My favorite image is of skateboarders in the park who practice and practice until they have a particular move down–but then move on to try something new when they think they have it.