Reasoning with Equivalences
Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms
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“When your child sees a sequence of equivalent fractions — like 1/2, 2/4, 3/6… — can they describe the rule and use it to find the next few terms, or to quickly convert between fractions and percentages?”
Full guide and materials
- Activity. Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms
What to notice. Notice that multiplying any number by 25 can be done by multiplying by 100 then dividing by 4, and explain why • Describe the general rule for a sequence and predict the 20th term • Generalise: to find 10% divide by 10, to find 5% halve 10%, and use this to find 35% of any number
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When your child sees a sequence of equivalent fractions — like 1/2, 2/4, 3/6… — can they describe the rule and use it to find the next few terms, or to quickly convert between fractions and percentages?
Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms
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Check understanding
- Notice that multiplying any number by 25 can be done by multiplying by 100 then dividing by 4, and explain why
- Describe the general rule for a sequence and predict the 20th term
- Generalise: to find 10% divide by 10, to find 5% halve 10%, and use this to find 35% of any number
“When your child sees a sequence of equivalent fractions — like 1/2, 2/4, 3/6… — can they describe the rule and use it to find the next few terms, or to quickly convert between fractions and percentages?”
Curriculum record
- Type
- Meta
- Subject
- Mathematics
- Domain
- Mathematical Thinking
- Age range
- Ages 9–10