Teaching Strategies for Mathematics.
Chunking
Depending on your age the teaching strategies used in math when you went to school would have varied from learning the written algorithm or doing mental math calculations.
It is a crying shame that the two seem to be mutually exclusive in education theories. Such is the nature of the education pendulum that it swings between one phase and another.
I have seen the pendulum swing many times moving from one extreme to another.
When in comes to mathematics, there should be no extremes. It is important for success in mathematics, that students be presented with a wide range of teaching strategies. Written mathematics strategies must co-exist with mental math strategies.
And when I am relief teaching I make a point of demonstrating many math strategies.
This type of mathematics really suits relief teaching because the teaching focus is active engagement.
When relief teaching, I try to use a variety of teaching strategies particularly for mathematics.
As a teaching strategy, CHUNKING is a fabulous balance of written math skills and mental math skills.
CHUNKING is one of those math strategies best attacked in the written format first.
What is CHUNKING?
CHUNKING is where numbers are broken down into smaller CHUNKS, to make mental maths easier to calculate.
The teaching strategies needed to develop the skills start with understanding place value.
Students need to be able to break numbers down.
Let's start with the teaching strategies used in addition. Obviously this is one of the most important math strategies that children should develop early.
Step 1
This is pretty straight forward. There is nothing difficult about this teaching strategy. This is one of the first math skills children need to develop.
I would introduce this as written math strategy. Younger grades would be fine. When I have been relief teaching in older grades they are insulted when asked to write this down but they have to bear with it.
The second teaching strategy and math procedure is to move the CHUNKS together.
From here the teaching strategy becomes showing the kids the maths behind adding tens and one to arrive at the answer.
This math is pretty straight forward.
I have used this PowerPoint in a lot of my relief teaching gigs and CHUNKING as a teaching strategy to develop the math skills the kids need.
Initially the children should write down the process but this should become part of their mental math skills.
Teaching Strategies of Mental Maths
There is considerable debate about vertical and horizontal algorithm. Like all education debate it tends to assume the maths skills are exclusive.They are not - Teach them both.
Mental math is still a vitally important to confidence in maths.
Adding horizontally direction has several desirable advantages
- the left to right method promotes a better understanding of place value,
- it can be done as mental math with much greater ease, and
- it does not require that numbers be lined up in a column.
As you move from left to right, you keep a cumulative total, so it is simply a number of smaller addition problems.
Consider the example, 677 + 938.
Begin by adding the left most place values. In the example this is 600 + 900 = 1500.
Add the values in the next place, one at a time, to the previous sum, and keep track of the new sum each time.
- 1500 + 70 = 1570,
- 1570 + 30 is 1600.
For students who are more proficient at mental math, they don't necessarily think "plus 70" or "add 30."
Their thought process, if said out loud might sound like, "600, 1500, 1570, 1600, . . ."
Continue adding the values in each subsequent place until finished.
The final steps in the example are
As you can imagine, students need to be proficient at single digit addition and have an understanding of place value before attempting left to right addition.
When they are first learning it, they might try repeating sums as they go along (e.g. 1500, 1570, 1570, 1570, 1600, . . .) to help them retain the newest sums.
They might also cross out digits as they are adding. There is no rule about having to add in this way mentally. Students could write down the sums as they proceed.
Left to right addition promotes a better understanding of place value than right to left addition.
In the example, right to left addition such as1246 + 586, students add 6 + 6 to get 12; they write down the 2 and carry the 1 when they should be carrying the ten. In the next step, they add 8 + 4 + 1 to get 13; they write down the 3 and carry the 1 when they should be adding 80 + 40 + 10, writing the 3 in the tens place (i.e. 30) and carrying the hundred. Essentially, right to left addition excludes vocabulary related to place value.
Left to right addition is well-suited to mental math since the sum is cumulative with no steps in between.
To illustrate this, consider the simple example, 64 + 88. In left to right addition, the sum is simple to find: 60, 140, 144, 152. Only one number had to be remembered at any point.
In left to right addition, the emphasis is on finding a certain place value in each number.
Students, of course, need to be able to recognize the math strategies of place value before they can be successful at this method.
Making Math Fun
Mental Mathematics and Relief Teaching
Their thought process, if said out loud might sound like, "600, 1500, 1570, 1600, . . ."
Continue adding the values in each subsequent place until finished.
The final steps in the example are
- 1600 + 7 is 1607,
- 1607 plus 8 is 1615.
- The answer is 1615.
As you can imagine, students need to be proficient at single digit addition and have an understanding of place value before attempting left to right addition.
When they are first learning it, they might try repeating sums as they go along (e.g. 1500, 1570, 1570, 1570, 1600, . . .) to help them retain the newest sums.
They might also cross out digits as they are adding. There is no rule about having to add in this way mentally. Students could write down the sums as they proceed.
Left to right addition promotes a better understanding of place value than right to left addition.
In the example, right to left addition such as1246 + 586, students add 6 + 6 to get 12; they write down the 2 and carry the 1 when they should be carrying the ten. In the next step, they add 8 + 4 + 1 to get 13; they write down the 3 and carry the 1 when they should be adding 80 + 40 + 10, writing the 3 in the tens place (i.e. 30) and carrying the hundred. Essentially, right to left addition excludes vocabulary related to place value.
Left to right addition is well-suited to mental math since the sum is cumulative with no steps in between.
To illustrate this, consider the simple example, 64 + 88. In left to right addition, the sum is simple to find: 60, 140, 144, 152. Only one number had to be remembered at any point.
In left to right addition, the emphasis is on finding a certain place value in each number.
Students, of course, need to be able to recognize the math strategies of place value before they can be successful at this method.
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Chunking PowerPoint for Younger Students (contains movement)
Mental Mathematics and Relief Teaching
