Basic Math

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Math

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Learning math is extremely important but fortunately teaching the basics is extremely easy compared to teaching your child to read (probably because it follow a logical and undeniable methodology, but I digress).  Basic mathematical methods follow the same course: counting.

To add: count forward.  To subtract: count backwards. To multiply: skip count.

Needless to say learning to count is vital in learning the latter methods. I used this idea very effectively to teach my son how to add subtract and multiply shortly before his 5th birthday. Division? Well, teaching this took a bit longer for me to figure out but I worked through it as well.

The first two methods, counting and number recognition, most parents tend to do instinctively, but since the idea of this lesson is to ultimately teach your child addition, subtraction, multiplication, and division, the initial method of when and how to teach counting and number recognition cannot be ignored.

Teaching Your Child Basic Math
  • STEP 1: Learning to count
  • STEP 2: Number recognition
  • STEP 3: Colors and Shapes
  • STEP 4: Adding
  • STEP 5: Subtracting
  • STEP  6: Skip Counting
  • STEP 7: Multiplication
  • STEP 8: Division

There is no science to Counting. Learning to count is generally a matter of exposure and repetition. Use everyday scenarios as opportunities to teach.   Count to 10 and your child will attempt to repeat you.

Once your child has mastered counting by memory, begin counting items: fruit, toys, books and fingers, anything within your line of sight. Ask your child how many plates you need on the table or how many cups you need to serve a group of friends. Have her count out her M&Ms and give her only up to the number she can count. There are so many methods for teaching. And while Mobile Apps will help, in general the best lessons are verbal.

Continue working to have your child learn to count by memory. Once your child can count to twenty begin number recognition.

NOTE: You may consider allowing your child to watch  Preschool Prep “Meet the numbers’  at this age.

Like letter recognition, number recognition is a matter of presenting numbers in visual form. Again, since numbers are logical and repetitive, it will be easy for your child to recognize them with constant and consistent exposure. At this stage you just want to ensure that your child can connect the word ‘one’ to the visual element ‘1’.

  • Begin to use flash cards and posters so that you can point to numbers and allow your child to identify them
  • Point to numbers on outings and ask your child to count cars or other objects.
  • Use this as a time to incorporate two subjects at once by allowing your child to count certain aspects of nature: flowers, trees, deer, butterflies.
  • As always incorporate games that connect the sound of the number with its visual.
  • NOTE: While teaching number recognition I also began teaching letter, shape and color recognition and used many of the same procedures.

Colors and shapes are two of the most frequently observed factors that children will notice about objects. These concepts are easy to comprehend and more importantly, they lay the foundation for grasping more complicated concepts in the future. Your child’s ability to discern shapes and colors will allow them to organize items accordingly and discern between them.

The most basic shapes are two dimensional items such as these below.  I personally opted not to introduce 3D figures at this time.

Shapes

There are so many ways to incorporate learning about shapes and toys in your child’s age range are also extremely helpful in teaching these concepts. Beyond using these items, I enjoyed the following methods.

We would often play ‘I Spy’ both around the house and while on the road. I would identify items that I ‘spied’ which were a certain shape or a certain color and he would have to find it and either bring it to me or tell me what it is. When out, we also would each try to be first to identify shapes like stop signs (as hexagons) or street signs (as rectangles).

Beyond this, I introduced games that continued to reinforce these concepts.

I obtained all of these great games from the Dollar store.

  • Matching Games
  • Flash Cards
  • Shape and Color Bingo

Although I did not find the Meet the Shapes video until much later, I purchased it for a family member and her son knew all of his shapes by age 2 1/2.

Now that your child recognizes numbers in visual form, you can help her begin identifying how these numbers work together.  Your child must first begin to recognize the concept of ‘how many’. Ask your child how many apples there are and they may begin to count the apples. If they do, this means they understand the progressive nature of numbers. Starting at the most basic level (i.e. 1+1) allow your child to identify what happens when you ‘add’ one more item, that is, allow them to identify ‘how many’. Use common items, toys, fruit, table settings etc to illustrate this at first and your child will see that adding is just an extension of counting and subtraction is just counting backwards. Once your child is comfortable adding items, begin incorporating numbers.

Below are a few ideas and items I used.

  • As previously stated, I used common items at first to illustrate  the idea of adding two items but by far the most wonderful purchased resource was the abacus. Because it is visual and has 10 small spheres on each column it gave us infinite opportunities.
  • Use pictures of coins or other items that must be counted and ask what happens if you add ‘X’ items and what happens if you take ‘Y’ items away.
  • With workbooks this is usually standard but if you desire to create your own, use content that shows both pictures and numbers to add until your child is comfortable enough adding numbers alone. FINGERS: your child’s most valuable resource is right on his or her hand. Give them two numbers to add and they can use their fingers to add them together.  When using workbooks (or face to face questions) with numbers alone, allow them to use their fingers or the abacus to find the answer.  Use pictures of coins or other items that must be counted and ask what happens if you add ‘X’ items and what happens if you take ‘Y’ items away.
  • Take turns. I always encourage parents to allow children to also play teacher. If you are using a workbook, flash cards or even if you are just quizzing each other take turns asking one another to add basic numbers.

For some reason teaching my son how to add and multiply was far easier than teaching him how to subtract. (Go figure) But from what I have read elsewhere, this is normal. In general I applied the same methodology above and but I taught the concept of subtraction after he was proficient in addition.   I did not find worksheets useful for learning this subject because most worksheets that used visual methods did not make sense because children could not SEE things being taken away. Until my son became proficient I relied heavily on visual methods: the abacus, fruit, fingers, small toys and other common items which were available to visually illustrate the idea of taking away. Once he grasped this concept, I incorporated workbooks (again do not use worksheets that attempt to use visual methods, its very confusing to see something like this.

Since Addition and Subtraction materials typically come as a set, I used the same ideas and resources as identified in the addition section above with the concept of removing items instead of adding them.

After traditional counting, skip counting is one of the easiest concepts to teach. Skip counting refers to a mathematical method that teaches children to count by 2s, 5s, and 10s  to identify number patterns and multiplication facts. (NOTE: some schools of thought incorporate skip counting by 3 and 4, I do not. I find that it does not have such a simple or easy to learn pattern).   Skip Counting helps children to easily transition from the simple concept of counting and addition to multiplication.  Teaching skip counting is a matter of repetition and allowing your child to visually see the pattern. The Worksheet below from Right Start Math does a great job of visually illustrating each of the skip counting variations.

Skip Counting Patterns

  • Begin by counting by 10: This concept should come easy since counting by 10s simply requires that you understand how to count naturally by ‘1’ and attach a 0 (ie. 10, 20, 30, 40, 50…) Ensure your child notices how this is simple this is and the slight difference between counting by 10s and counting by 1s. Once this is identified, begin to ask how many ‘times’ did they add 10 to get to a number like say 50.  Allow your child to see that in each instance you are simply adding 10 to each number to get to the next.
  • Next allow your child to count by 5: Like counting by tens, this concept will also come easily since the answer can only end in either 0 or 5 (i.e. 5, 10, 15, 20, 25…) If you apply the counting method visually consider also doing addition of 5 to illustrate more than one way of getting to a certain number. For instance, Skip counting to 25 is done by  counting:  5, 10, 15, 20, 25, so is 5+5+5+5+5 or adding 5 five ‘times’. (Be sure to use the word ‘times’ to get your child use to the language).
  • Finally Lets count by 2: Though it involves more thought and pattern memory than counting by 10s and 5s rest assured that teaching your child to count by 2s is still very easy, especially now that he or she has had experience with the other numbers.  Like other methods counting by 2s involves repetition, but when visually illustrating counting by 2s do so in a way that shows the repeating numbers of 2, 4, 6, 8 and 0 in each column, such as
2 4 6 8 10
12 14 16 18 20
22 24 26 28 30

In this written form your child will be able to easily identify the connections and similarities between numbers.  It is important to verbalize that skip counting is also another form of adding and making the logical progression of counting faster. And, to reiterate, is also important that you encourage your child to count how many ‘times’ he adds the number. Specifically, if you ask your child to skip count by twos to the number 20, help them understand that they had to skip count by twos 10 times. See there goes that word again ;).

The information above gives insight on what you should be focused on but here are ways you can also make it fun.

  • Make a skip counting song. This makes the variations easier to remember and fun.  If you cannot come up with a song of your own check out youtube there are a number of videos available for parents who want to teach skip counting (or other things for that matter).
  • Workbooks (or printable worksheets) and mobile apps are also great for this activity. Find resources that skip a number and allow your child to fill in the right one or create your own.
  • Play hop scotch and allow your child to only jump on the numbers they are skip counting. If you want to do higher numbers like 5’s and 10’s consider modifying the hop scotch board so that it shows variations of these numbers.
  • As your child masters 2s you can incorporate 3s, 4s, and 6s. Remind your child that its merely the idea of adding.
  • Use the number line method to show your child how to skip forward.
  • Take turns on counting by 2s, 3s and 4s without using paper. This will be a constant recommendation since teaching and acting out activities encourages retention. Additionally your child will begin to apply these concepts mentally and more quickly.

You have reached what I believe is the ultimate goal of teaching basic math: Multiplication. Please do not allow yourself to be intimidated by the concept of multiplying your child can do it and you can teach them. In fact you already have. The skip counting techniques above have given you all you need in order to teach your child the next step.

By now you have begun skip counting by numbers and your child understands that this is simply just adding the number several times. What you now must communicate is that multiplication is another way of writing the same skip counting or adding concept. To elaborate, by now your child understands that 2+2+2+2+2 is the number ‘2’ added 5 ‘times’ so you can now communicate that he can write or say the exact same concept in a simpler form.

Specifically:

  • [2+2+2+2+2]
  •   is the same as     [ the number ‘2’ added 5 ‘times’ ]
  • which is the same as      [2 x 5].

Do this with each of the easy skip counting concepts that your child has already learned.  Once your child has seen this visual depiction several times, he or she will be able to do actual simple multiplication problems involving single digits. His mental process will first rely on his knowledge of addition and sometimes he may even write it out in its native form [2+2+2+2+2] but as with anything, with practice, he or she will begin memorize certain multiplication tables.

The vast majority of work will involve using worksheets but encourage fun by using some of the below resources.

Although with division you use the same concepts as with multiplication, for me teaching division was a bit more difficult.

To start the introduction, identify division as the idea of separating a group of things into equal parts. One way to do this that I found very effective is using the concept of fairness.  For instance,  remind your child to ask  “how do you need to divide (split up/separate) candy, toys or some other item in order to ensure that everyone gets an equal amount.” Using actual products (pizza, candy, pictures of items) was extremely helpful in illustrating this idea.

Another way to illustrate this is to use multiplication to divide. Using multiplication tables and a small visual your child can see immediately how the concepts coincide.

A final way is backwards skip counting. Using a number line, show your child how to skip count backwards. The picture below shows how you would use skip counting to divide 16 by 4. (This method might also come in handy when teaching remainders.)

  • As with multiplication, games and worksheets have been the most effective way of illustrating division with the exception of the bullet below.
  • Make your child the “fairness expert” giving him responsibility for dividing up food items equally amongst family members.  (This also works with toys, games and other products.)
Resources for division are generally the same as with multiplication.

 

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