Gaps and Misconceptions in Maths

a Learning Diagnostic and Teaching Tool

Fractions (FDPRP) Objectives

Fractions and decimal objectives

Each objective is linked to a probing question. Each probing question has been written to expose a gap in understanding or misconception. There are links to a number of images/models that will illustrate how to address these gaps/misconceptions.

Year
Group
 
Objective
Diagnostic
Question
4

1999 FWK • Understand decimal notation and place value for tenths and hundredths and use in context [p28]

2006 FWK • Y4: Use decimal notation for tenths and hundredths...relate the notation to money and measurement

Fra Q01
4

1999 FWK • Use fraction notation [p22]

2006 FWK • Y3: Read and write proper fractions...

Fra Q02
4

1999 FWK • Recognise equivalence of simple fractions [p22]

2006 FWK • Y4: Use diagrams to identify equivalent fractions

Fra Q03
4

1999 FWK • Order simple fractions [p22]

2006 FWK • Y4: Use diagrams to identify equivalent fractions, e.g. 6/8 and ¾ or 70/100 and 7/10; interpret mixed numbers and position them on a number line e.g. 3½

Fra Q04
4

1999 FWK • Begin to relate fractions to division and find simple fractions of numbers or quantities [p24]

2006 FWK • Y4: Use diagrams to identify equivalent fractions, e.g. 6/8 and ¾ or 70/100 and 7/10; interpret mixed numbers and position them on a number line e.g. 3½

Fra Q05
4
5

1999 FWK • Relate fractions to their decimal representations [p31]

1999 FWK • Recognise the equivalence between the decimal and fraction forms of one half, one quarter, three quarters..., one tenth, one hundredth [p31]

2006 FWK • Y4: Use diagrams to identify equivalent fractions

2006 FWK • Y5: Express a smaller whole number as a fraction of a larger one, e.g. recognise that 5 out of 8 is 5/8; find equivalent fractions, e.g. 7/10 = 14/20, or 19/10 = 1 9/10; relate fractions to their decimal representations

Fra Q08
5

1999 FWK • Multiply and divide any positive integer up to 10 000 by 10 or 100 and understand the effect [p7]

2006 FWK • Y5: Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100, 1000

Fra Q06
5

1999 FWK • Round a number with one or two decimal places to the nearest integer [p31]

2006 FWK • Y5: Explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers

Fra Q07
5

1999 FWK • Use fraction notation including mixed numbers [p23]

2006 FWK • Y4: Use diagrams to identify equivalent fractions, e.g. 6/8 and ¾ or 70/100 and 7/10; interpret mixed numbers and position them on a number line e.g. 3½

Fra Q09
5

1999 FWK • Recognize when 2 simple fractions are equivalent [p23]

2006 FWK • Y5: Express a smaller whole number as a fraction of a larger one, e.g. recognise that 5 out of 8 is 5/8; find equivalent fractions, e.g. 7/10 = 14/20, or 19/10 = 1 9/10; relate fractions to their decimal representations

Fra Q10
5

1999 FWK • Order a set of fractions and position them on a number line [p23]

2006 FWK • Y4: Use diagrams to identify equivalent fractions, e.g. 6/8 and ¾ or 70/100 and 7/10; interpret mixed numbers and position them on a number line e.g. 3½

Fra Q11
5
6

1999 FWK • Relate fractions to division [p25]

2006 FWK • Y5: Find fractions using division, eg. 1/100 of 5kg

Fra Q12
6

1999 FWK • Order a mixed set of numbers with up to 3 decimal places [p29]

2006 FWK • Y6: Use decimal notation for tenths, hundredths and thousandths, partition, round and order decimals with up tp three places, and position them on the number line

Fra Q13
6

1999 FWK • Know what each digit represents in a number with up to three decimal places [p29]

2006 FWK • Y6: Use decimal notation for tenths, hundredths and thousandths, partition, round and order decimals with up tp three places, and position them on the number line

Fra Q14
6

1999 FWK • Multiply and divide decimals mentally by 10 or 100 and integers by 1000 and understand the effect [p7]

1999 FWK • Y5: Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100, 1000

Fra Q15
6

1999 FWK • Round a number with two decimal places to the nearest tenth or nearest whole number [p31]

2006 FWK • Y6: ...round and order decimals with up to three places, and position them on the number line

Fra Q16
6

1999 FWK • Relate fractions to their decimal representations [p31]

1999 FWK • Recognise the equivalence between the decimal and fraction forms of one half, one quarter, three quarters..., one tenth, one hundredth [p31]

2006 FWK • Y6: ...find equivalent percentages, decimals and fractions

Fra Q08
 
Fra Q17
6

1999 FWK • Reduce a fraction to its simplest form by cancelling common factors [p23]

2006 FWK • Y6: ...simplify fractions by cancelling common factors

Fra Q18
6

1999 FWK • Use fractions as an operator to find fractions of numbers or quantities [p25]

2006 FWK • Y5: Find fractions using division, eg. 1/100 of 5kg

Fra Q19
Babcock LDP