YEAR 7 MATHS FOCUS
NUMBER AND ALGEBRA
Ratios & Rates
Learning Experiences
Concept Teaching
Ratios & Rates
RATIOS & RATES
OUTCOME
A student:
MA4-7NA:
operates with ratios and rates, and explores their graphical representation
TEACHING POINTS | In Stage 3 Fractions and Decimals, students study fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100. A unit fraction is any proper fraction in which the numerator is 1, eg 12, 13, 14, 15, … |
| The process of writing a fraction in its ‘simplest form’ involves reducing the fraction to its lowest equivalent form. In Stage 4, this is referred to as ‘simplifying’ a fraction. | |
| When subtracting mixed numerals, working with the whole-number parts separately from the fractional parts can lead to difficulties, particularly where the subtraction of the fractional parts results in a negative value, e.g. in the calculation of 2 1/3−1 5/6, 1/3−5/6 results in a negative value. |
LANGUAGE | Students should be able to communicate using the following language: whole, equal parts, half, quarter, eighth, third, sixth, twelfth, fifth, tenth, hundredth, thousandth, fraction, numerator, denominator, mixed numeral, whole number, number line, proper fraction, improper fraction, is equal to, equivalent, ascending order, descending order, simplest form, decimal, decimal point, digit, round to, decimal places, dollars, cents, best buy, percent, percentage, discount, sale price. |
| The decimal 1.12 is read as ‘one point one two’ and not ‘one point twelve’. | |
| The word ‘cent’ is derived from the Latin word centum, meaning ‘one hundred’. ‘Percent’ means ‘out of one hundred’ or ‘hundredths’. | |
| A ‘terminating’ decimal has a finite number of decimal places, eg 3.25 (2 decimal places), 18.421 (3 decimal places). |
Expectations of Attainment
Recognise and solve problems involving simple ratios (ACMNA173) | use ratios to compare quantities measured in the same units |
| write ratios using the : symbol, e.g. 4:7 {Literacy} | |
| – express one part of a ratio as a fraction of the whole, e.g. in the ratio 4:7, the first part is 4/11 of the whole {Communicating} | |
| simplify ratios, e.g. 4:6=2:3, 12:2=1:4, 0.3:1=3:10 | |
| apply the unitary method to ratio problems | |
| divide a quantity in a given ratio |
Solve a range of problems involving ratios and rates, with and without the use of digital technologies (ACMNA188) | interpret and calculate ratios that involve more than two numbers |
| solve a variety of real-life problems involving ratios, e.g. scales on maps, mixes for fuels or concrete | |
| use rates to compare quantities measured in different units | |
| – distinguish between ratios, where the comparison is of quantities measured in the same units, and rates, where the comparison is of quantities measured in different units | |
| convert given information into a simplified rate, e.g. 150 kilometres travelled in 2 hours = 75 km/h | |
| – solve a variety of real-life problems involving rates, including problems involving rate of travel {speed, Critical and creative thinking} |
Investigate, interpret and analyse graphs from authentic data (ACMNA180) | interpret distance/time graphs (travel graphs) made up of straight-line segments |
| – write or tell a story that matches a given distance/time graph {Communicating, Literacy} | |
| – match a distance/time graph to a description of a particular journey and explain the reasons for the choice {Communicating, Reasoning, Literacy} | |
| – compare distance/time graphs of the same situation, decide which one is the most appropriate, and explain why {Communicating, Reasoning, Literacy, Critical and creative thinking} | |
| recognise concepts such as change of speed and direction in distance/time graphs | |
| – describe the meaning of straight-line segments with different gradients in the graph of a particular journey {Communicating} | |
| – calculate speeds for straight-line segments of given distance/time graphs {Problem Solving} | |
| recognise the significance of horizontal line segments in distance/time graphs | |
| determine which variable should be placed on the horizontal axis in distance/time graphs | |
| draw distance/time graphs made up of straight-line segments | |
| sketch informal graphs to model familiar events, e.g. noise level during a lesson | |
| – record the distance of a moving object from a fixed point at equal time intervals and draw a graph to represent the situation, e.g. move along a measuring tape for 30 seconds using a variety of activities that involve a constant rate, such as walking forwards or backwards slowly, and walking or stopping for 10-second increments {Problem Solving} | |
| use the relative positions of two points on a line graph, rather than a detailed scale, to interpret information |
Learning Experiences
To be added
Concept Teaching
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