Equivalence - quarters and eighths

  • Equivalence - quarters and eighths
  • Course: Mathematics
  • Grade: Year 3
  • Section: Fractions and decimals
  • Outcome: A half, quarter and eighth of shapes and objects.
  • Activity Type: Printable
  • Activity ID: 3776

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United Kingdom – National Curriculum expand/collapse

  • KS1 – Key Stage 1
    • KS1.Ma2 – Number
      • Knowledge, skills and understanding

        • Calculations

          • KS1.Ma2.3 – Pupils should be taught to:

            • Number operations and the relationships between them

              • KS1.Ma2.3.b – Understand multiplication as repeated addition; understand that halving is the inverse of doubling and find one half and one quarter of shapes and small numbers of objects; begin to understand division as grouping (repeated subtraction); use vocabulary associated with multiplication and division

  • 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.d – Understand unit fractions [for example, one-third or one-eighth] then fractions that are several parts of one whole [for example, two-thirds or five-eighths], locate them on a number line and use them to find fractions of shapes and quantities

              • 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 1
    • Number and Algebra
      • Fractions and decimals

        • ACMNA016 – Recognise and describe one-half as one of two equal parts of a whole.

  • Year 2
    • Number and Algebra
      • Fractions and decimals

        • ACMNA033 – Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

  • Year 3
    • Number and Algebra
      • Fractions and decimals

        • ACMNA058 – Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole

  • Year 4
    • Number and Algebra
      • Fractions and decimals

        • ACMNA077 – Investigate equivalent fractions used in contexts

New Zealand – National Standards expand/collapse

  • 3 – Year 3
    • 3.NA – Number and algebra
      • 3.NA.1 – Apply basic addition facts and knowledge of place value and symmetry to:

        • 3.NA.1.b – Find fractions of sets, shapes, and quantities

  • 4 – Year 4
    • 4.NA – Number and algebra
      • 4.NA.1 – Apply basic addition and subtraction facts, simple multiplication facts, and knowledge of place value and symmetry to:

        • 4.NA.1.b – Find fractions of sets, shapes, and quantities

  • 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

  • 1 – Grade 1
    • 1.G – Geometry
      • Mathematics

        • 1.G.3 – Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

  • 2 – Grade 2
    • 2.G – Geometry
      • Mathematics

        • 2.G.3 – Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

  • 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.1 – Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

        • 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.

          • 3.NF.3.d – Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

    • 3.G – Geometry
      • Mathematics

        • 3.G.2 – Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

  • 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.2 – Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.