Known factsUsing known facts to solve problems reduces the cognitive demand on our brains. Sometimes 'known facts' are easy to see and sometimes we have to move the numbers around to see them or change the numbers to suit our brains.
When we learn facts, we learn them best through investigating, playing games, exploring and using them. We aren't hoping for memorised facts and procedures but rather such familiarity and understanding that ideas, information and strategies "stick". Some number facts are particularly useful when working with addition and subtraction, such as: Friends of ten (number bonds to 10) Friends of ten are two numbers that combine to make ten. |
Friends of twenty (bonds to 20)
Friends of twenty are pairs of numbers that combine to make twenty. We can apply our understanding of friends of 10 to help us with friends of 20. |
Doubles
Doubles are identical pairs of numbers I want to combine together. Doubles are important as they are a link between addition and multiplication. Once we understand, know and use doubles up to 'double 10', we then learn how to apply those facts to larger, more complex numbers. E.g. If I know 2 sevens is the same as 14, I can use that to help me work out 70 + 70 because 7 tens and 7 tens equals 14 tens which is the same as 140. |
Near doubles
Near doubles are almost a double fact, but, there is a difference of one. For example, 5 and 6 is a near double. I can solve it by knowing double 5 is 10 and then add 1 more to make 11. Or, I can use my knowledge of 6 + 6 = 12 and subtract 1 to make 11. We need to know how to describe near doubles in two ways - one where we add one more and the other where we subtract one. |
A VERY IMPORTANT NOTE
From Professor Jo Boaler (at https://www.youcubed.org/fluency-without-fear/ )
"Mathematics facts are important but the memorisation of math facts through times table repetition, practice and timed testing is unnecessary and damaging... Math facts, themselves, are a small part of mathematics and they are best learned through the use of numbers in different ways and situations. Unfortunately many classrooms focus on math facts in unproductive ways, giving students the impression that math facts are the essence of mathematics, and, even worse that the fast recall of math facts is what it means to be a strong mathematics student. Both of these ideas are wrong and it is critical that we remove them from classrooms, as they play a large role in the production of math anxious and disaffected students. It is useful to hold some math facts in memory. I don’t stop and think about the answer to 8 plus 4, because I know that math fact. But I learned math facts through using them in different mathematical situations, not by practicing them and being tested on them."
Something else to note:
Not all known facts fall under these categories. Sometimes we have information we just 'know'. These are also important known facts we can use to help us solve problems.
From Professor Jo Boaler (at https://www.youcubed.org/fluency-without-fear/ )
"Mathematics facts are important but the memorisation of math facts through times table repetition, practice and timed testing is unnecessary and damaging... Math facts, themselves, are a small part of mathematics and they are best learned through the use of numbers in different ways and situations. Unfortunately many classrooms focus on math facts in unproductive ways, giving students the impression that math facts are the essence of mathematics, and, even worse that the fast recall of math facts is what it means to be a strong mathematics student. Both of these ideas are wrong and it is critical that we remove them from classrooms, as they play a large role in the production of math anxious and disaffected students. It is useful to hold some math facts in memory. I don’t stop and think about the answer to 8 plus 4, because I know that math fact. But I learned math facts through using them in different mathematical situations, not by practicing them and being tested on them."
Something else to note:
Not all known facts fall under these categories. Sometimes we have information we just 'know'. These are also important known facts we can use to help us solve problems.
Summary poster |