Equivalence - halves and quarters

  • Equivalence - halves and quarters
  • Course: Mathematics
  • Grade: Year 7
  • Section: Fractions
  • Outcome: Calculating equivalent fractions
  • Activity Type: Printable
  • Activity ID: 3556

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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

              • KS2.Ma2.2.f – Recognise the equivalence between the decimal and fraction forms of one half, quarters, tenths and hundredths; understand that 'percentage' means the 'number of parts per 100' and that it can be used for comparisons; find percentages of whole number quantities, using a calculator where appropriate

Australia – Australian Curriculum expand/collapse

  • Year 4
    • Number and Algebra
      • Fractions and decimals

        • ACMNA077 – Investigate equivalent fractions used in contexts

  • Year 5
    • Number and Algebra
      • Fractions and decimals

        • ACMNA103 – Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator

        • ACMNA105 – Compare, order and represent decimals

  • Year 6
    • Number and Algebra
      • Fractions and decimals

        • ACMNA125 – Compare fractions with related denominators and locate and represent them on a number line

        • ACMNA127 – Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies

        • ACMNA131 – Make connections between equivalent fractions, decimals and percentages

  • Year 7
    • Number and Algebra
      • Real numbers

        • ACMNA152 – Compare fractions using equivalence. Locate and represent fractions and mixed numerals on a number line

        • ACMNA157 – Connect fractions, decimals and percentages and carry out simple conversions

New Zealand – National Standards expand/collapse

  • 7 – Year 7
    • 7.NA – Number and algebra
      • 7.NA.1 – Apply additive and multiplicative strategies flexibly to whole numbers, ratios, and equivalent fractions (including percentages)

  • 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.

        • 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.

      • Mathematics

        • 4.NF.5 – Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

        • 4.NF.6 – Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

  • 5 – Grade 5
    • 5.NF – Number & Operations—Fractions
      • Mathematics

        • 5.NF.1 – Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)