Equivalence - thirds and sixths

  • Equivalence - thirds and sixths
  • Course: Mathematics
  • Grade: Year 5
  • Section: Fractions and decimals
  • Outcome: Modelling equivalent fractions.
  • Activity Type: Printable
  • Activity ID: 4003


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United Kingdom – National Curriculum expand/collapse

  • KS2 – Key Stage 2
    • KS2.Ma2 – Number and algebra
      • Knowledge, skills and understanding

        • Numbers and the number system

          • KS2.Ma2.2 – Pupils should be taught to:

            • Fractions, percentages and ratio

              • KS2.Ma2.2.e – Understand simple equivalent fractions and simplify fractions by cancelling common factors; compare and order simple fractions by converting them to fractions with a common denominator, explaining their methods and reasoning

Australia – Australian Curriculum expand/collapse

  • Year 4
    • Number and Algebra
      • Fractions and decimals

        • ACMNA077 – Investigate equivalent fractions used in contexts

        • ACMNA078 – Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line

New Zealand – National Standards expand/collapse

  • 5 – Year 5
    • 5.NA – Number and algebra
      • 5.NA.1 – Apply additive and simple multiplicative strategies and knowledge of symmetry to:

        • 5.NA.1.b – find fractions of sets, shapes, and quantities

United States – Common Core State Standards expand/collapse

  • 4 – Grade 4
    • 4.NF – Number & Operations—Fractions (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.)
      • Mathematics

        • 4.NF.1 – Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

  • 3 – Grade 3
    • 3.NF – Number & Operations—Fractions¹ (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.)
      • Mathematics

        • 3.NF.2 – Understand a fraction as a number on the number line; represent fractions on a number line diagram.

          • 3.NF.2.a – Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

          • 3.NF.2.b – Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

        • 3.NF.3 – Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

          • 3.NF.3.a – Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

          • 3.NF.3.b – Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.