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First we encourage learners to draw out the ratio as boxes and label the boxes - moving from the abstract to the concrete. If we further provide a rational as to why Eva gets less than Francis (such as Eva worked for 3 hours and Francis worked for 5) then we have removed that worry form our learners minds.

Making In making problems more concrete enables learners towe

1. 1. offer methods that require smaller working memory
   2. b
   3. c
   4. d
   5. ensure most problems our learners encounter they can answer independently and accurately

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This is more than just encouragement, the teacher is getting the learner to recall the "feeling of pride in a job well done" and establishing both the learner and the teachers belief in a "growth mindset". 

So by accepting that leaning learning of some topics will interfere with the learning of other topics and embracing this - we are able to help the learners to match the ideas and the names attached to those ideas. To summarise we 

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Our topics add NC, subtract NC, multiply - pdf & mp4, divide - pdf & mp4  are designed so that it is hard, with a casual glance, to decide how hard any particular question is. Due to the nature of retrieval practice or spaced learning any learner might find the odd very easy question in their timely practice assignment -  in both these ways the potential to feel shame is reduced.

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Once shame is less likely to be felt and since each topic is so finely divided into strands (see scaffolding) learners can ordinarily do at least one strand in add NC and multiply - pdf & mp4 - although admittedly not in a "Gove approved" method. In fact "Gove approved" methods have high requirements for short term working memory so are generally best avoided. Our experience is that if teachers use mastery learning to teach numeracy skills and learners can feel "safe enough", they can build up their "forgotten or never learned" numeracy skills.

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high → height

By using these tricks we can offer our learners these advantagescan 

1. 1. offer methods that require smaller working memory
   2. use retrieval practice or spaced learning so the memories we require learners to use are deeply embedded
   3. c
   4. help learners to transfer skills form one situation to another
   5. ensure most problems our learners encounter they can answer independently and accurately
      
      

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