How to set math fact fluency goals and objectives for IEPs

Setting IEP goals and short term objectives is a snap when you measure growth in fluency.  Not only are fluency growth goals easy to write and set, they are easy to measure and monitor.  You can adjust the intensity of the intervention ensuring the student can achieve the goals and objectives.   Finally, you’ll be able to demonstrate growth and improve student achievement.

Fluency with math facts ensures success in math

A student thinks through an equation by recalling their math facts.Math facts are a “tool skill” of mathematics.  Students need to be able to call math facts to mind instantly.  Students should not have to hesitate or stop to “figure out” single digit math facts.  This is a tool they need in order to do math assignments quickly and easily. Knowing math facts instantly enables students to concentrate better and learn math more easily than students who are distracted by figuring out facts.  Once students are fluent in math facts they can keep up successfully in regular math classes.

 

Test the student’s present level of performance (PLOP) on facts

It only takes a minute to have students take a timed test in an operation to see how well they know their facts. You want to know how many facts in that operation the student can answer in one minute.  Test first-grade students in addition and second-graders on subtraction. Starting in 3rd grade and up, multiplication has priority, so test and focus on multiplication facts for your IEP.  You can move on to other operations once multiplication facts are fluent.  Here is a link to a page with Rocket Math’s one-minute pre-tests in all four basic operations.  However, you can’t evaluate whether a given student is fluent until you know how fast they can write. Students who are fluent with facts can answer them about as fast as they can write.  But they cannot answer them any faster than they can write.

You must also test the student’s writing speed

You cannot set achievable goals of how many facts a student should answer in a minute without first knowing how fast they can write.  That sets the upper limit.  So test their writing speed by having them write a mix of one and two digit numbers for one minute.  See to the left, Rocket Math’s one-minute Writing Speed Test From the link you can print it out for free.  Once you know how fast your student can write you can evaluate their performance on the one-minute fluency tests.

Is math fact fluency an area of need?

Now that you know the student’s writing speed you can evaluate their present level of performance.  Rocket Math has a handy evaluation sheet you can use to determine if there’s a need.  Or you can do the math yourself.  If students answer math facts at a rate less than 75% of their writing speed, they are weak and math facts is an area of need. Putting math fact fluency on the IEP and working on it as a goal would be very helpful.  If the student can answer math facts at a rate that is 90% of their writing speed, they are strong and this is not an area of need.  Between 75 and 90% of their writing speed they are good, but could benefit from some more work.

Get a starting point on the progress monitoring measure

If you’re going to test every week with 1-minute timings and you have a bunch of those available, you already have a 1-minute timing starting point.  If you’re using the Rocket Math Worksheet Program as your intervention, it uses 2-minute timings to measure progress weekly, so you’ll want to use one of those for your starting point.  (You can’t just double the 1-minute score because students don’t usually keep up at the same rate for two minutes.)  So give one of the 2-minute timings, in the operation you’re going to focus on, to set a starting point.

Set the math fact fluency goal based on writing speed

Students who have successfully developed math fact fluency in an operation can write answers to math facts almost as fast as they can write. As fast as their fingers can carry them is the most you could expect.  You could set a goal at 80% of their writing speed. It would still be rigorous enough.  If they met that goal the student would be fluent in math facts.

You can do the math yourself from their writing speed test. The Rocket Math Worksheet Program has weekly progress monitoring 2-minute timings.  In that case, your student’s goal for the 2-minute timing is on the handy goal sheet ** that you put into each student’s folder.  You can see the student shown here filled in 24 boxes on the Writing Speed Test, so his or her goal for 2-minute timings would be 38 for the annual goal for the IEP.

 

Create a graph and draw an aimline from starting point to goal

Now the coolest thing about progress-monitoring a fluency goal is that it is easy to graphically see on a weekly basis if the student is on track to meet the goal.  You simply create a graph, with enough spots at the bottom for all the weeks in the year.  Next you put in the starting point performance in the first week of the graph (or whenever you tested).  Then put in your goal performance at the end of the year.  Then draw a line between those two points.  That line is called the aimline and is shown in the example at the top of this article.

The pictured student began at 29 problems in 2-minutes.  Their PLOP was 29 problems correct in 2 minutes.  The student had a writing speed of 40 problems in a minute.  Therefore 80% of that is 32 problems in a minute or 64 problems in two minutes by the end of the year.  The aimline is simply a straight line between those two.  You can see that the first couple of two-minute tests did not meet the aimline, but by the third test the student was right on track for meeting the goal by the end of the year.

Short term objectives (STOs) are set by the aimline

Once the aimline is drawn, the STOs are found by reading up from the date of the quarterly STO reporting date.  Wherever the aimline is on that date, that’s the STO.  In the example above the quarter 1 objective looks to be about 38 problems in two minutes.  The second quarter looks to be 45 problems in two minutes with the 3rd quarter at 53.  Very simple and easy to set and to read and report.  Since every student in Rocket Math should have a graph like this reporting to parents on a quarterly basis would be more more than showing them this graph.

What if they aren’t meeting the aimline?

In all the struggle with writing and evaluating IEPs many times we forget the purpose.  IEPs are designed to evaluate whether our intervention is adequate to meet the student’s needs.  So if the student is falling below the aimline or doesn’t make the STOs what are we supposed to do?  Wringing our hands or shaking our heads sadly at the IEP meeting at the end of the year is not what is supposed to happen.  Instead we are supposed to be using these goals as a way to determine if we need to intensify our intervention.

How do you intensify your intervention?

So if a student is not meeting the aimline when we monitor their progress we should re-double our efforts.  With Rocket Math that’s quite doable.  If the student is falling below the aimline for three weeks in a row, add another practice session each day.  The standard ten minutes a day for Rocket Math may not be enough for this student. So you need to arrange for them to get in another practice session each day.  Often a short trip to the Special Education room for a second quick session with the teacher or an aide will do the trick.  If two a day at school aren’t enough, maybe you can add one each evening at home.  Some students do need more practice to meet these goals.  The good news is that you can find out quickly with your graph and get going soon.

**The Goal Sheet was updated in 2021 to reflect the 80% expectation for IEP goals.  The update shows that students who can fill in 15 boxes in a minute can go ahead and do Rocket Math, while those who can only fill in 14 boxes are candidates for help with writing numerals in the Rocket Writing for Numerals Learning Track.

 

Motivating Students & Recognizing Effort Keeps Kids Engaged

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

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

Motivating Students by Praises and Recognizing Effort Instead of Achievement

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

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

What is a Good Effort and Participation?

You should expect, at a minimum. for students to complete a session every day at school. Ten to 14 sessions in the last two weeks indicates a good “C” effort. A very good “B” effort would be completing 15 to 24 sessions in two weeks. That many sessions translate into a session every day and more than one session a day sometimes. Any student with 25 or more sessions in the last two weeks is putting forth a great “A” effort. Be sure to praise and recognize them and hold them up as an example, no matter what they have accomplished.

Motivating Students with the Award Certificates to Recognize & Reward Effort

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

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

To have a successful ceremony, we recommend these steps:

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

 

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

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

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

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

After Effort Improves Accomplishment, Begin Rewarding Accomplishment also

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

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

Rocket Math Knows How to Motivate Students to Excel in Math 

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

Counting Objects Worksheets for Kindergarten | Do They Work?

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

How to use counting objects worksheets in the classroom

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

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

 

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

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

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

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

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

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

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

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

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

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

We Do: Narration to Count Objects in an Image

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

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

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

 

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

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

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

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

Benefits of using counting objects worksheets for kindergarten

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

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

Counting objects worksheets can transition students to fingers and lines

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

Worksheets can properly space out the objects to be counted

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

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

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

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

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

Worksheets can limit displays to numbers the students have learned.

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

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

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

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

 

 

 

 

Instant assessment for basic math fact fluency: Ask ’em!

Teachers and parents often ask, “How do I know if my children need to study math facts?” Here’s an instant math assessment you can do to test them for math fact fluency. Ask a student a “hard one” such as, “What’s 9 times 7?” or if they are in first or second grade, “What’s 8 plus 9?” If they start counting on their fingers or hesitate while puzzling it out, they do not have “math fact fluency.” They need a program of systematic math facts practice until they know them all “by memory,” as the Common Core State Standards (CCSS) say.

Math fact fluency means instant recall

A student thinks through an equation by recalling their math facts.Some teachers and schools teach “tricks” for remembering facts that are supposed to help children. However, they should at most be a temporary crutch. Such techniques need to be replaced with instant recall. The student shown here is using the commonly-taught “doubles plus one” trick for figuring out the answer to, “What’s 8 plus 9?” This is not fluency. He needs practice in math facts so they become “automatic” in recall. If he is still having to do this in fourth or fifth grade, he’ll find math work slow-going and drudgery. He’ll also find it hard to follow a math lesson when he has to stop and puzzle out simple facts like this.

Math fact fluency makes math easy

Students who know the math facts instantly can fly through their math assignments. They enjoy the exercise and feel good about their math abilities. On the other hand, students who have to count on their fingers, or use a number line or a times tables chart to do their math assignments come to hate math. It is so-o-o-o-o slow. I’m sad to say that when I taught elementary and middle school remedial students I knew they hated math because they had to puzzle out most of the facts. What else could I do but assign lots of math fact practice that they hated?

In graduate school, I learned how to design a math facts practice program in a way that every student can succeed in memorizing the facts. I put a paper-and-pencil program together back in the ‘90s and have been sharing it with people ever since. I called it Mastering Math facts, but everyone else just called it Rocket Math. That became its official name in 2007.

Teachers have been successfully using my nearly secret curriculum with wild success for decades. Oddly enough, students actually enjoy the Rocket Math Worksheet program. They enjoy the paired practice with a partner, and can actually see themselves learning and getting better.

Two students participating in one of Rocket Math's math fluency programs

How to assess students in math

Before you start Rocket Math’s Online Game or Worksheet Program, it’s a good idea to find out which operations your student needs to practice most. Rocket Math offers a few tests to identify where your student should start their Rocket Math journey.

 

Writing Speed Test

Many students aren’t able to write the answers to 40 problems in one minute, which is normal and doesn’t affect their math fact knowledge. Before administering the Operation Pretests, evaluate your student’s writing speed to make sure the results reflect your student’s true proficiency, and that they are not held back by their writing speed. 

Get the One-Minute Rocket Math Writing Speed Test.

 

Operation Pretests

Once your student has completed the Writing Speed Test, give them a pretest in one or more of the four basic operations. 

 

Evaluate Results 

For students in 3rd grade and above, test multiplication first and then division. If students struggle with either of those two operations, they should start learning those operations. For 3rd graders and above who don’t struggle with multiplication and division, test addition and subtraction to assess any weakness. For students in 1st and 2nd grade, test addition first and then subtraction. 

Evaluate your student’s results based on their individual writing speed with the Evaluation Chart for Pretests. Use their writing speed to determine if their performance on the Pretest is weak and shows a real need for work on math facts, or is good but could use some help, or strong and no practice is needed. 

Free Online Game subscription as long as you need to decide

There is no reason for students to be bogged down and discouraged by math, especially by lack of math fact fluency. This doesn’t need to happen to children. Every student is capable of memorizing basic math facts with a little effort and a carefully sequenced curriculum, like the Rocket Math Worksheet Program.

Or if a paper-and-pencil curriculum like the Rocket Math Worksheet Program involves standing at the copy machine, is not what you are looking for, Rocket Math is now online. The Online Game app starts with a complimentary initial subscription of 14 days. You can learn more about it at that link. Or you can just go ahead and register an account and start it on this link

 

Send an email to me at don at rocketmath.com and I’ll extend the complimentary subscription as long as you need to decide.** If you need one to ten seats it is a whopping $4.50 a seat for a year. Twenty or more seats are $2.50 each for the year and per-seat prices go down from there. Really there’s no reason to leave kids counting on their fingers.

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. 

A student must re-do part of Rocket Math? Motivate with the Toughness Certificate.

To encourage perseverance recognize and promote it when it is needed.

There are a variety of circumstances in which a student must re-do part of Rocket Math.  Sometimes you may accidentally re-set them back to Set A in the Online Game.  On occasion, a student’s folder may be lost in the Worksheet Program.  Sometimes they move in from elsewhere claiming they already completed up to some level for which they have no evidence.  You may see they are not at mastery at the level they are on and wisely decide to have them repeat the sequence over  at Set A.  These all call for perseverance and call for the Toughness Certificate.

Introduce the student to the Toughness Certificate

To make use of the Toughness Certificate, post it somewhere in your room.  When a student has to re-do part of Rocket Math or when they complain about too many Start-Overs in the Online Game, or starts to complain about having to re-do part of a Learning Track, take them over to the certificate, point to it and introduce them to the Toughness Certificate.

Toughness Certificate pep talk

“This certificate is for people who have to do hard things.  I know it is hard having to re-do Rocket Math.  It takes a lot of perseverance to keep going all the way to Z.  If you can do it without whining about it, then you will earn this Toughness Certificate.  Not everyone can earn this, but if you can prove you’re NOT A WHINER, I will award this to you.  Dr Don knows how hard this is and he and I will have signed this for you and you will have earned it!  Do you think you can do this even though it is hard?  Are you tough enough?”

Remind them of the certificate when they complain

Each time a student complains about having to re-do Rocket Math, remind them of the Toughness Certificate and that they can earn it, if they can hang in without complaining.  If they don’t complain, also remind them of the Toughness Certificate and how they are clearly earning it by not complaining. “You are really tough.  I can see you are earning a Toughness Certificate.”

When the student passes Level Z award the Toughness Certificate publicly

When students complete a Learning Track or pass Set Z in the Worksheet Program, you should make a ceremony of awarding the Toughness Certificate.   Call them to the front of the room.  Read the copy at the bottom aloud in front of the class.  Say, “Dr. Don and I are awarding this Toughness Certificate to (insert name) for extraordinary perseverance for starting over in parts of Rocket Math without whining about it.  We know it was tough, but we admire how you did it anyway.”  Encourage a round of applause for the student and shake their hand as you hand it to them.  You might also award a Learning Track certificates for finishing a Learning Track.  You’ll make the student proud and you’ll be on your way to teaching a valuable life lesson: perseverance.

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.