Children are often confused and mystified by the need to carry numbers in addition and multiplication. It’s up to you to unveil the secrets and make it simple. Hope you’re ready to unleash your inner math teacher!
- Have the child learn (and memorize) the basic addition facts.
- Write out a Solve a Wordy Math Problem with two digits on the top and bottom. Draw a line between the “units” and the “tens” column to help align and use “place values” in columns. It is not important for your child to already know how to do two column addition.
- Ask the child to answer the units column first, placing both numbers in the correct (lower) positions. Do not have them put a “1” over the numbers, yet.
- Ask the child to answer the tens column next. Make certain the child places the Quickly Multiply Single Digits by 9 in the correct position (no digit should be in the units column.) If they are confused, cover up the units column. Have the child write the number(s) underneath the number already written in the “tens” column from the “units” column addition.
- Tell the child that the problem is not finished. Review what you have completed so far.
- If you were using the example above, you might say, “We’re almost done. You did seven plus five equals twelve. Good. Four plus three equals seven. Correct. Notice that the four and the three are in the tens position, so you are really adding forty and thirty.”
- Explain that some addition still remains. Have the child bring the amount in the units column down to the bottom. Point to the numbers in the “tens” column and ask the child to add them up.
- Make certain that the child is comfortable with this before proceeding. By now, the child should already be familiar with the commutative law of addition or (at least) know that the order of Addition and Subtraction is unimportant.
- Tell the child that, instead of writing the “1” under the tens digit, they are to place the “1” over the “tens” column.
- Ask the child to add the “1” to the top number of the “tens” column; then add the bottom number to that sum. Tell the child that this is a shortcut we call “carrying”, and more commonly called “regrouping” in classrooms today.
This is a more complicated version of the method used in addition. A fringe benefit of this method is that it reveals why estimation works. Before you begin,
There are so many different ways to teach adding and subtracting with two or three digit numbers. The idea of regrouping is very important for students to understand in order to feel comfortable either adding and/or subtracting larger numbers.
“Regrouping” is defined as the process of making groups of tens when adding or subtracting two digit numbers (or more) and is another name for carrying and borrowing.
When first introducing regrouping it’s best to use concrete manipulatives* and relate it to place value. The best manipulatives to use are base ten blocks. Base ten blocks help students “see” the value of each digit in the number and help to understand the “carrying or borrowing.”
Once students have moved past the concrete stage, they can use pictorials to help them with regrouping. Many students prefer this “pictorial” phase because it’s easy for them to draw the blocks quickly and really understand if their answer makes sense.
Student’s work: The student can now see how many hundreds or “flats” (5 hundreds – 500), how many tens or “longs” (13 tens – 130, and so regroup those by circling 10 tens to make 100, with 3 tens – 30 left over) and how many ones (11 ones – 11, so regrouping by circling 10 ones to make 10, with 1 one – 1 left over).
So now: 600 + 40 + 1 = 641
The same can be done for subtracting:
Another great way that doesn’t involve manipulatives or drawing models is using “split” addition or subtraction. Again, students can “see” the place value in each number and can understand the regrouping.
647 –> 600 + 40 + 7
+ 285 –> 200 + 80 + 5
800 + 120 + 12 = 932
All of these strategies lead a child into computing the standard algorithm with ease. Of course whichever strategy a child chooses – the most important thing is they understand what they’re doing. We don’t want them memorizing steps without having any idea of what or why they’re doing those steps!
Toddlers are always looking for new ways to explore their world. For many of them, counting is a skill that can be both fun and educational. Teaching toddlers how to count will not only help them learn the basics of math but also give you an opportunity to bond with them! We’ve put together some great tips on how to teach your child the joys of counting.
When you teach toddlers to count, we recommend using fingers as visual aids. If the child can already identify numbers mentally and see your fingers as you count, they will start to associate your hand gestures with specific numbers.
At What Age Should You Teach Toddlers to Count?
Toddlers can start counting as early as two years old, and sometimes even younger! Remember that the primary goal at this age is still language development. So, don’t put too much pressure on them if they’re not ready.
The best thing to do is let your child be curious about numbers and have fun with you! As long as children enjoy learning how to count, you can always teach them. Even if counting doesn’t click until later on, the time and effort are still well-spent.
How Many Numbers Should You Teach Your Toddler?
In the English language, we have the numbers zero through ten. However, you should start teaching your child to count up to five or six. Once they have mastered these numbers, they can begin to learn more on their own.
Can Most Two-Year-Olds Count to Ten??
It’s true! Many two-year-old children can already mentally identify numbers from one to ten, while others can even do more. However, each child has a unique pace when it comes to learning numbers. So, don’t force them to count if you see others do, and it’s not a big deal if they can’t. But here are a few steps you can do to help you teach your child how to count like a pro in no time.
Steps You Can Do to Teach Toddlers to Count
1. Start by showing your toddler all of your fingers, from pinky to thumb.
2. Point to each finger one by one, and say the number that corresponds with each finger, in order. For example, say, “One,” and point to your ring finger. Then say, “Two,” and point to your middle finger, and say, “Three.” and point to your pointer finger. Repeat this a few times until your toddler gets the hang of it.
3. Show your toddler all of your fingers again, and this time say each number as you point to each finger. Do this a few times until your toddler feels comfortable counting with you.
4. Now that your toddler has learned how to count from one to three, you can practice counting fingers. Show just one of your fingers to your toddler, then show the other fingers. Point at both fingers and say “[number] plus [number].” For example, say, “One plus two.” Say this a few times until your toddler feels comfortable. Then say it with more fingers.
5. Now that your toddler knows how to count fingers, and knows the number names in order, you can practice counting objects together. There are two ways of doing this: one is by pointing to the object and saying the number name of that object, then showing another object and saying the number name for that object.
For example, you might say, “One apple. Two kites.” Or you can say a random number of objects first, then show your child all of the corresponding fingers after counting objects, so he or she knows how many objects there are in total. Then, you can count one object at a time and say the number name of that object. For example, “There are five trucks,” and then after pointing to all fingers, “One truck.” Repeat this a few times for each object.
It’s okay if your child says the wrong number during this exercise. As long as your little one is practicing and trying, that’s what matters the most. Your toddler will get it right after repeated exposure. You can also play games with toddlers like BINGO using numbers, and when they get three in a row, they win!
At Mrs. Myers’ Learning Lab, we offer small group programs that teach toddlers to count in fun yet engaging ways. Contact us today for more information!
The first relationship to mathematics children have begins with the understanding and recognition of numbers. Some children begin to recognize numbers on a preschool level and are able to count to and recognize the numbers 1-20. In addition to children learning to recognize numbers, a great benefit would come to those children who also learn to count.
The kindergarten preparedness tests expect children to have the basic recognition knowledge of numbers 1-20, the sequence awareness of counting to 10 and the understanding of the relationship numbers have to math. No matter how much experience your child has with numbers there are great tips to help you give your child a quick and effective understanding of the basic math concepts. We’ll break down easy steps to aid in your effort to teach your children how to recognize numbers 1-20 for their growth and future success.
When children start early with their understanding of math facts they will have a more comprehensible ability to complete the additional concepts the teachers in each grade level present. It is like a stair step of information they must understand and recognize numbers to learn to count, to learn to add, to learn to subtract, to learn to multiply, etc. This basic math concept amazingly starts at recognizing numbers and flows directly into High school algebra, if you miss a concept in any grade level you will struggle to keep up.
Allow young children to be a part of simple daily tasks, such as having them dial the telephone numbers for you when you are using the phone. Point to each number that has to be dialed and read aloud the number, doing this daily with help reinforce numbers 1-9. Another great way to do this is to allow them to change the channels on the TV remote control, using the same concept as the phone, pointing to the numbers and then reading the number aloud. You can also do the same thing with a computer and a calculator; a calculator is a great gift to give your child to help them recognize numbers 1-9.
There are so many number games on the market, the hardest thing will be to choose which one will both teach your child number recognition while giving them a fun experience. Another great tool to use when teaching your children number recognition is to print out number worksheets. This will not only teach your children to recognize numbers, but also how to write those numbers.
Main points to address:
- Have a number of toys or other devices; phones, remote controls, computers, etc. around the house.
- Play games that encourage number recognition.
- Use print outs to have your children trace the numbers.
With the ability to recognize numbers you can introduce larger numbers to your children. The concept of reciting and recognizing numbers beyond twenty can sometimes be confusing for children, but with persistence and patience, your little darling will pick this up in no time. One way to teach this early is to use the work sheet method and print out the corresponding numbers you are introducing.
Explain the concept of the 10’s to your child. “When you see a two and zero together, write it down or show them from something that is printed, “this means twenty, three and zero is thirty, etc. “When you see these numbers it is basically that number with a TY on the end, three is thir-ty, four is for-ty, etc.”
Main points to address:
- Use more evolved and larger numbers.
- Explain the concept of 10’s to your child.
Resources that can help you in your venture include:
If you’re the parent of an elementary schooler, you’ve probably already figured out that your child’s math class is different from math class when you were young. Kids today are engaged in hands-on activities, technology, and small group teaching. They’re not learning to "borrow" numbers and "carry the one." In fact, one of the major changes in how math is being taught now involves the use of language. Your child is probably using new math terms daily and focusing on building number sense, decomposing numbers, and using different models to show her thinking. She’s using 100 charts, ten frames, and building fact fluency every day — terms that may leave you scratching your head and wondering why you can’t figure out a 1st grade worksheet. (Trust us, you’re not alone.)
But understanding what your child is being taught in class will help you to have deeper conversations about his learning, and stay informed of (and be able to help with) his daily lessons. Below are 10 frequently used terms your child may be exposed to in math class that will help you stay tuned in — and that’s a (math) fact.
1. Mental Math: This is the ability to see, solve, and calculate math problems in your mind without the use of a pencil, paper, or calculator. It’s very important to build strategies for your child to increase their mental math skills.
2. Number Sense: Think of number sense as your child’s overall understanding of numbers and flexible thinking about them. (Read more about number sense in our helpful article.) The ability to understand, relate, and connect numbers to each other and see numbers in many different ways. Developing your child’s number sense is imperative to mathematical success.
3. Decompose: This is the ability to break apart numbers into smaller parts. For example, your child will learn in kindergarten and first grade to decompose the number 10 — this number can be broken apart into the numbers 9 and 1; 8 and 2; 7 and 3; etc. See an example below:
Are you confused by unfamiliar-looking math problems in your child’s homework? The approach to teaching math has changed in recent years. The examples below, created with the help of math specialist Heidi Cohen, can help you help your child with “new math.”
A ten-frame is a set of 10 boxes with dots in some or all of the boxes. Kids can see how different combinations of numbers add up to 10. The ten-frame is especially good for showing how subtraction works.
A number bond uses lines to link a group of numbers together, showing how they are related. In the first drawing, the relationship between the numbers 3 and 10 is shown by adding the number 7 to the empty circle (3 + 7 = 10). This helps kids see how a single number can be broken down into smaller parts.
Open number line
An open number line has no numbers already written in. The student can use any number as the starting place. (Here, 37 is the starting place because that is how many yards Brett walked. The 26 yards that Adam walked are then added.) The open number line lets kids add or subtract in a visual way. It is often used to help solve word problems.
Decomposing (also called “expanded form”)
Decomposing is a strategy to solve math problems by breaking a number down into its digit values. For example, 37 becomes 30 and 7. Once you break the number down, you can add or subtract the individual digit values to get the answer.
Base ten is a strategy to solve addition and subtraction problems by using a table divided into hundreds, tens, and ones. You’ll probably see the term “regrouping” used for this method. Each number goes into the chart according to its place value. For example, 43 would mean 4 tens and 3 ones. This helps kids see when to “borrow” and “carry” numbers from one place value to another.
Box multiplication is a method of breaking numbers down into digit values. In a table, the numbers are broken down by value and multiplied separately. After each number has been multiplied, the total values are added together. This method can be helpful for kids who have trouble with traditional multiplication using larger numbers.
An area model uses the length and width of a rectangle or square to break down a multiplication problem. Each shape is calculated and the answers are added together. It’s another way to make math more visual for kids.
Like an area model, an array is an arrangement of objects that represent a number. This model is often used to help kids see the different qualities of addition and multiplication.
Bar modeling (also known as a “tape diagram”)
A bar model uses bars to visually represent numbers and unknowns in a word problem. It can help kids see how quantities compare to each other. Kids can adapt a bar model to solve many kinds of problems.
For more ways to help your child with math, download these free graphic organizers . You can also get tips on how to help your child with tricky math homework .
About the Author
About the Author
Understood Team is made up of passionate writers and editors. Many of them have kids who learn and think differently.
Bob Cunningham, EdM serves as executive director of learning development at Understood.
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How to carry-over on subtraction, or some people refer to it as borrowing, can be confusing to young students. They know how to subtract 15-9 and get the correct answer. But when the problem looks like this 65-29, it becomes more difficult. Many students know you cannot have 5 items and take 9 away without getting a negative number. However, when they are working an entire page of subtraction problems, they may decide to do 9 – 5 instead of using the carry-over or borrow strategy. So, what do you do?
First, start with the basics of how to carry-over on subtraction by teaching students that you always subtract top to bottom. Because we teach them that with addition, it doesn’t matter which way you add the numbers (5+6 or 6+5), they may believe that same rule is true with subtraction. Do several easy problems with students–maybe have students work problems on the chalkboard–to show that with subtraction, you start with the top number and subtract the bottom number.
You can get out manipulatives for each student and ask them to put 5 blocks on their desk. Now, ask them to take 9 away. They will easily see that this is impossible.
Before students learn how to carry-over on subtraction, they need to understand these basic subtraction rules–it doesn’t hurt for any student having difficulty to review these during one class period.
Carry-Over or Borrowing Teaching Ideas
Many times, we teach students the process of working a math problem–but not the “why” behind it. If students don’t understand why and how to carry-over on subtraction, then they may have difficulty with these problems.
One way teachers show students why borrowing works is with base-10 blocks. If students are working this problem: 33-17=?, they can use base-10 blocks to understand why borrowing works. This teaching strategy is especially helpful for tactile and visual learners. Students take 3 tens bars and 3 ones cubes and put these at the top of their desks. The problem states that they need to take 7 ones cubes away–but they only have 3, so what can they do? Borrow from the tens. They learn to exchange one tens block for 10 ones cubes. Now they have 13 ones cubes, and they can take 7 away. Once students work the problems with base-10 blocks and understand what it means to carry-over on subtraction, then teachers can show them how to work the problems on paper.
Other students will respond better to a story about how to carry-over on subtraction. With the same problem as above, teachers tell students that 33 wants to take away 7 ones, but she doesn’t have 7 ones to give–what can she do? She can borrow some ones from her neighbor the tens place–just like your mom might have to borrow sugar from a neighbor to bake a cake. When 33 borrows 10 ones from the tens place, the tens won’t have as many left–they’ll only have 2 now and the ones will have 13. Just like the neighbor won’t have as much sugar if Mom takes some from her. A story like this will work for some students because they understand what “borrow” means and can remember stories well.
The important thing to remember when teaching how to carry-over on subtraction is that different methods and strategies will work for different learners.
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simple addition – learn to add two numbers, both from zero to ten. Keeping the numbers between zero and ten prevents the children from having to "carry the one" at this point in the learning process.
simple subtraction – also from zero to ten.
Grade 1, Level two:
Adding three rows of numbers. The level three stage will sometimes require the children to "carry the one". By adding a few pages from the level two group, the children will become familiar with the process of adding three rows of numbers.
You'll notice in these worksheets that the top number is always "1". We won't need to carry anything other than "1" until we start learning multiplication, so at this point all of the formulas on the worksheets start with "1".
Grade 1, Level Three:
Adding and subtracting one number between 10 and 19 and one number between 0 and 9.
Grade 2, Level one:
Adding and subtracting one number between 10 and 99 and one number between 0 and 9.
Grade 2, Level two:
Add the numbers across. Add the numbers down. Add the answers you came up with across and down as well. Notice that the sum of the answers across = the sum of the answers down. You don't have to spend loads of time analyzing this with the kids. it just helps them start to form the basis of mathematical relationships, seeing math as more than just an exercise in memorization.