Number Facts progression, 2nd step
The purpose of the activity
In this activity, the learners develop strategies that will help them remember and recall the basic addition and subtraction facts. The learners focus on learning those facts they are not able to recall quickly.
The teaching points
Basic facts for addition are the combinations where both addends are less than 10.
Recalling basic facts is often referred to as ‘mastery’ and means that a learner can give a quick response (within about 3 seconds) without having to work out the fact by a method such as counting.
Number relationships are the foundation for strategies that help learners remember basic facts.
All of the addition basic facts are conceptually related, which means you can figure out new or unknown facts from those you already know. For example, if you know that 8 + 8 = 16, you can work out that 8 + 9 = 17 by adding one more.
Subtraction facts correspond to addition facts. For example, 3 + 4 = 7, 4 + 3 = 7, 7 – 3 = 4, 7 – 4 = 3.
Traditionally drill has been the most popular approach used in schools for students to learn to recall their basic facts. However, the very fact that some adult learners do not know their addition and/or multiplication basic facts suggests that drill alone does not work for many learners.
It is important that the learners are not drilled in a basic fact until they at least have an efficient strategy for working it out. For example, if the learner has to count to work out 7 + 8 = 15, they are not ready to practise it for quick recall. Once they can work it out quickly, for example, by working from 7 + 7 = 14, then they could use drill or practice activities to develop mastery of the basic facts.
Discuss with the learners the reasons why they need to be able to work out facts, rather than just rely on memory.
Flash cards for the addition basic facts.
Flash cards for the subtraction basic facts.
Addition facts chart.
The guided teaching and learning sequence
1. First you need to find out the ‘gaps’ for each learner. Do this by ‘testing’ the addition basic facts, one at a time, using flash cards. If the learner responds quickly (within 3 seconds) and without obviously counting to solve the fact, place it in their ‘known’ pile. Continue with all the facts until they are sorted into two piles – those that are known and those that need to be learnt.
2. Give the learners an addition facts grid and show them how to record facts from their ‘known’ pile on the grid.
For example: All the + 0 and + 1 and most of the + 2 facts and doubles.
Recording the known facts on the grid allows the learner to see the facts they know and the ones they need to learn. The focus should be on developing strategies to learn the unknown ones. The remainder of this sequence is presented as a series of ideas or approaches to help the learners fill the specific gaps in their quick recall of the addition basic facts. Rather than working through each idea, choose the ones that best suit the learner’s gaps. As the learner builds on their mastery of addition facts, add these to the chart and to the ‘known’ pile of facts.
Facts with 0
Write out the 0 facts and ask the learner what they notice. They should observe that irrespective of whether the 0 is the first or the second addend, the result is the non-zero addend. For example 3 + 0 = 3.
One and two more than facts
The learners should be able to count on from the highest number to quickly find the answer to the facts.
Make a dice labelled (+1, + 2, –1, –2, +1, –1) and another dice labelled (4, 5, 6, 7, 8, 9). After each roll of the dice, the learner should immediately state the complete fact.
The double facts seem to be relatively easy to learn and then form a good base for learning the near doubles. For example, 6 + 7 as double 6 and 1 more.
Make 5 and 10 facts
These facts are also relatively straightforward as they can be ‘seen’, using the fingers on one hand (5 facts) or two hands (10 facts).
Subtraction facts linked to addition facts
Subtraction facts tend to be more difficult to recall than the addition facts. Begin by sorting the subtraction facts into ‘known’ and ‘unknown’ piles for each learner. Ask the learners to take one of their ‘unknown’ facts and see if they can think which addition fact it is related to. For example, encourage them to see the link between 14 – 6 = 9 and 6 + 9 = 14 and therefore use known addition facts to recall subtraction facts.
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