Learning Tracks

Foolproof method for finding factors

Posted on by Dr. Don

Knowing when you’ve found ALL the factors is the hard part.

Students have to learn how to find the factors of a number because several tasks in working with fractions require students to find the factors of numbers. Thinking of some of the factors of a number is not hard. What is hard is knowing when you have thought of ALL the factors. Here is a foolproof, systematic method I recommend: starting from 1 and working your way up the numbers. This is what student practice in the Worksheet Program Factors Learning Track.  Students also learn the pairs of factors in this sequence in the Online Game.

Dr Don has a white board type video lesson that explains this in 6 minutes.

https://www.educreations.com/lesson/view/how-to-find-all-the-factors-of-a-number/46790401/

Bookmark this link so you can show it to your students.

How to find all the factors of numbers
Always begin with 1 and the number itself-those are the first two factors. You write 1 x the number.  Then go on to 2. Write that under the 1. If the number you are finding factors for is an even number then 2 will be a factor. Think to yourself “2 times what equals the number we are factoring?” The answer will be the other factor.
However, if the number you are finding factors for is an odd number, then 2 will not be a factor and so you cross it out and go on to 3. Think to yourself “3 times what equals the number we are factoring?” There’s no easy rule for 3s like there is for 2s. But if you know the multiplication facts you will know if there is something. Then you go on to four—and so on.

The numbers on the left start at 1 and go up in value.  The numbers on the right go down in value.  You know you are done when you come to a number on the left that you already have on the right.  Let’s try an example.

Factors Answers d

Let’s find the factors of 18.  (To the left you see a part of a page from the Rocket Math factoring program.)
We start with the first two factors, 1 and 18. We know that one times any number equals itself. We write those down.
Next we go to 2. 18 is an even number, so we know that 2 is a factor. We say to ourselves, “2 times what number equals 18?” The answer is 9. Two times 9 is 18, so 2 and 9 are factors of 18.
Next we go to 3. We say to ourselves, “3 times what number equals 18?” The answer is 6. Three times 6 is 18, so 3 and 6 are factors of 18.
Next we go to 4. We say to ourselves, “4 times what number equals 18?” There isn’t a number. We know that 4 times 4 is 16 and 4 times 5 is 20, so we have skipped over 18. We cross out the 4 because it is not a factor of 18.
Next we go to 5. We might say to ourselves, “5 times what number equals 18?” But we know that 5 is not a factor of 18 because 18 does not end in 5 or 0 and only numbers that end in 5 and 0 have 5 as a factor. So we cross out the five.
We would next go to 6, but we don’t have to. If we look up here on the right side we see that 6 is already identified as a factor. So we have identified all the factors there are for 18. Any more factors that are higher we have already found. So we are done.

Now let’s do another number.  Let’s find the factors of 48. 

We start with the first two factors, 1 and 48.  We know that one times any number equals itself.

Next we go to 2.  48 is an even number, so we know that 2 is a factor.  We say to ourselves, “2 times what number equals 48?”  We might have to divide 2 into 48 to find the answer is 24.  But yes 2 and 24 are factors of 48.

Next we go to 3.  We say to ourselves, “3 times what number equals 48?”   The answer is 16.  We might have to divide 3 into 48 to find the answer is 16.  But yes 3 and 16 are factors of 48.

Next we go to 4.  We say to ourselves, “4 times what number equals 48?”  If we know our 12s facts we know that 4 times 12 is 48.  So 4 and 12 are factors of 48.

Next we go to 5.  We might say to ourselves, “5 times what number equals 48?”   But we know that 5 is not a factor of 48 because 48 does not end in 5 or 0 and only numbers that end in 5 and 0 have 5 as a factor. So we cross out the five.

Next we go to 6. We say to ourselves, “6 times what number equals 48?”  If we know our multiplication facts we know that 6 times 8 is 48.  So 6 and 8 are factors of 48.

Next we go to 7.   We say to ourselves, “7 times what number equals 48?”   There isn’t a number.  We know that 7 times 6 is 42 and 7 times 7 is 49, so we have skipped over 48.  We cross out the 7 because it is not a factor of 48.

We would next go to 8, but we don’t have to.  If we look up here on the right side we see that 8 is already identified as a factor.  So we have identified all the factors there are for 48.  Any more factors that are higher we have already found.  So we are done.

How can you improve writing speed?

Posted on by Dr. Don

Tina asks:
Hello Don,
Do you have any recommendations for improving writing speed? My son’s school does not use Rocket Math, but we use it at home. He knows his addition facts rather quickly orally but is stuck at a much lower level at school because he cannot write them fast enough.
Thanks, Tina

Dr. Don answers:
Tina,
That is a very good question. Yes, you can improve writing speed. Increasing writing speed will come with practice, but a special kind of practice. The biggest problem slow writers have is that they “draw” the numerals. That is to say, they decide how to make the numerals look like they should and then draw them, rather than having a set way of doing the numbers. Step 1 is for them to learn how to most efficiently write the numerals using strokes that consistently go down and from left to write. Students need to learn the right way to form the numerals and then practice it exactly the same way over and over until it becomes habit. In Step 2 the students need to practice writing the numerals small enough to fit on the line, while still forming them the right way. In Step 3 and 4 students need to practice writing the numerals until they are fluent (speedy and still form them correctly and legibly).

A student can practice each page of Rocket Writing several times. How many times you ask? See my blog on the topic of How much practice is enough in Rocket Writing, because it is interesting to see that you can arrange it so that you trust your son to know how much practice he needs.

Rocket Writing for Numerals is part of the Universal Level of the Worksheet Program. If you only have a basic level subscription, you can upgrade to that.

How much practice is enough in Rocket Writing for Numerals?

Posted on by Dr. Don

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.