Fractions, decimals, percentages | Stage 4 | Mathematics | Year 7 What percentage of your household's grocery bill is spent on you? Summary of Substrands Duration: 4 weeks 2 days S3 Fractions and Decimals (Review) S4 Fractions, Decimals and Percentages (part) Start Date: Completion Date: Teacher and Class: Outcomes Mathematics K-10 MA4-1WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols MA4-2WM applies appropriate mathematical techniques to solve problems MA4-3WM recognises and explains mathematical relationships using reasoning MA4-5NA operates with fractions, decimals and percentages
fractions, mixed numerals and decimals on a number line to compare their relative values interpret a given scale to determine fractional values represented on a number line (Problem Solving) choose an appropriate scale to display given fractional values on a number line, eg when plotting thirds or sixths, a scale of 3 cm for every whole is easier to use than a scale of 1 cm for every whole (Communicating, Reasoning) placing fractions and decimals on the number line. Start with a scale with missing fractions such as: Construct a number line using string or wire in the classroom and divide it into simple multiples. Extend it into other multiples. For example, start with a number line with a scale of and then extend to quarters. Adjustment Ask students to plot a number on the number line that is not a multiple of the denominator given. For example on the number line above ‘Where would you plot ‘? String or wire Fractions cards
Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153) add and subtract fractions, including mixed numerals and fractions with unrelated denominators, using written and calculator methods Revise the addition and subtraction of fractions with the same denominator. Use diagrams to assist if necessary. For fractions with different denominators, use equivalent fractions to change into the same denominator or use the method below: Point out that this method may not be the shortest method but it will always give the correct solution. With mixed numerals, show two methods: Changing both fractions to improper fraction. For example: Fraction Quiz Program NLVM: Adding fractions interactive. Magnetic Fractions
2.3' (Communicating, Problem Solving) order fractions, decimals and percentages Use number lines to order fractions, decimals and percentages Adjustment Use the calculator to look for patterns when changing fractions to recurring decimals. Start with fractions with a denominator of 3 and 9. More confident students can explore algebraic methods of changing recurring decimals to fractions. Start with more simple decimals such as Investigate the concept of irrational numbers, including (ACMNA186) investigate 'irrational' numbers, such as and describe, informally, the properties of irrational numbers (Communicating) Students can investigate the concept of by measuring the diameter and circumference of various circles. Introduce the button on the calculator. Variety of circles (eg tin cans, glue stick, protractor) String The pi song (utube) (different versions available)