Just as much I tried to develop reading fluency in my child from the age of 3, I thought it was just as important to begin developing number fluency. Math fluency isn't just about mere memorization or following mathematical procedures following each problem step by step until we reach the right answer, and not really knowing or understanding how we came to that answer. Being fluent is a skill that is learnt and developed, in math it is to be accurate, have automaticity, be flexible and efficient, they are all integral parts needed to have math fluency. And having it will benefit your child later on to think about math in smarter ways, by providing a solid foundation upon which later stage of education can be built;
- They become better at mental math
- They visualize math problems
- They solve math problems with reasoning and deep understanding
- They are more flexible in using different math strategies to reach their answer.
- They have better number sense and become more confident in their math abilities
Often we start teaching children math of counting, addition and subtraction is by modelling exactly what the question is asking. For example 3 + 4 the child would count out three blue objects and four red objects then count one by one til they reach the answer, children who do this are most of the time very accurate, although the may get the right answer, they lack flexibility and efficiency, because it takes them a very long time to solve this equation. So instead, when the child gets to this stage of addition, you should encourage counting on. So, rather than counting one by one from number 1, encourage them to count on from the bigger number so that the child solves the problem in less time. For example 3 + 4, hold 4 in your head and count on 3 more. This is one step better. But even better is to memorize this math fact that 3 plus 4 equals 7. They have started from the very beginning and built on additional skills to help them understand how they reached the answer and its process. So now we get the child to memorize this fact. So that they know it off the back of their hand. But the only problem with this is that what happens if the child is not so good at memorizing facts? What is their back up plan? Well, the child will revert back to what they trust will get them the right answer, counting one by one. This is derived facts, these are facts that we tend to gravitate towards more and know better than others. So how do we develop this so it makes sense to us and gives us that automaticity, flexibility and efficiency to apply number facts to other math operations?
The first thing we learn how to do something is what we end up revert back to forever. So do not spend all your time in teaching counting, but teach in steps and always build on to your child's knowledge to gain better strategies so that this is what becomes their foundation and this is what they becomes their comfort zone with and will be their revert strategy. And the more strategies you use to develop your child's skill the more connections they will make with numbers. So the best strategy to learn 3 + 4 is to teach your child double facts 3 + 3 = 6, we then to go from that answer doubling plus one 3 + 3 = 6 now + 1 = 7.
When teaching your child math begin with math facts, by modelling out the math question and demonstrating to the child how we reach the answer, this is will be your child's solid foundation that they will rely on for every math operation they may come across in their lives, simple or complex.
Math fluency is gained by learning math facts at a young age until it becomes ingrained into your child as a matter of fact, their answer is recalled automatically without hesitation. Thus strengthening your child's mental math abilities, and you need a strong foundation of math fluency to have strong mental math abilities, it is a skill that needs to be developed and worked on.
I made my own plan for my daughter as I couldn't find a anything after researching it. And I went by my daughters capabilities and progressed in stages, and only moved forward at her pace. Once she had learnt a new concept, I could tell that she could apply the same strategies to other math operations.
After covering the very basics and your child is confident in the following;
- Counting in 1s to 20 forwards and backwards fluently
- Understanding quantities and able to give a realistic estimate to 20
- Knowing which number is more than and less than to 20
- Able to sequence numbers accurately to 20
- Able to accurately identify the missing number from any part of the number line up to 20
- Able to do addition and subtraction with the aid of manipulative's up to 10
- Able to identify odds and evens upto 10
It's time to move onto the next stage and build on to attaining the following skills
- Knowing how to count from 1 to 100
- Accurately identifying the missing number in a sequence
- Accurately identifying what number comes next from numbers with 1 - 9 in them e.g. 32 > 33
- Accurately identifying which is the next tens number after calling out a number with 9 in it e.g. 39 > 40
- Able to add 1 to any number from 1 - 100 e.g. if you asked them what is 78 + 1 they can easily answer 79. They attain this answer by simply counting on once.
- Able to add 2 to any number from 1 - 100. e.g if you asked them what is 54 + 2 they can easily answer 56. They attain this answer by applying the same method but counting on twice. We used to say jump over one to get to your answer.
- Able to minus 1 to any number
- Able to minus 2 to any number
- Able to add 10 to any number up to 100
- Able to minus 10 from any number to 100
- Able to count in 10's up to 100
- Then in 2's
- Then in 5's
- Able to count backwards in 10's, 2's and 5's from 100
- Accurately identifying how many tens are in each number e.g. 70 has 7 tens.
- Understanding place value e.g. 53 is 50 and 3 not a 5 and a 3.
- Knowing number bonds up to 10
- Able to double numbers
- Able to double plus 1
- Able to add 9 to any number up to 10.
- Able to decompose numbers; 5 and 10.
I have designed a free guide for you to keep and refer back to.
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| Math Fluency Framework |
When introducing each concept I would use manipulative's to aid my child's understanding. This gave them that sensorial simulation they needed to develop the skill, engaging different parts of the brain. Through visualizing the math operation and understanding the process of how we get to an answer by physically modelling out the question, thus, helping the child to think more clearly. Let your child naturally develop on their own you will notice they being ready to independently work through to the answer without to the use of manipulative's when they are ready. Their math fluency will get better through practice and from this mental math is gained too.
We used a variety of material and stuck with ones that they particularly favor for that new concept. Here is a list of the things we used regularly;
We used a variety of material and stuck with ones that they particularly favor for that new concept. Here is a list of the things we used regularly;
- 100 chart that we printed and laminated
- Montessori math beads
- Montessori Number cards
- Counters
- 100 wooden board
- Wooden numbers and math symbols
- A4 white board
- Wall displays
For doubling and number bonds we made wall displays together for them to frequently refer to. For doubling we used everyday examples;
1 + 1 = 2 we drew around each hand and cut it out
2 + 2 = 4 we drew a car with two wheels on both side
3 + 3 = 6 we drew a lady bug with three legs on both side
4 + 4 = 8 we a spider with four legs on both sides
5 + 5 = 10 we drew around the five fingers of both hands
5 + 5 = 10 we drew around the five fingers of both hands
Or you can use my free printable of Ladybug Doubling Facts.
This is how I spent the last year teaching my daughter and it has helped her enjoy math and gain number sense with numbers.
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