Here are some key aspects of the math curriculum for ratio, proportion and rate for students aged 13 to 14:

Advanced Proportional Relationships: Students deepen their understanding of proportional relationships. They explore concepts such as constant of proportionality, direct and inverse variation, and joint variation. They analyze these relationships using tables, graphs, and equations, and apply them to solve complex problems.

Scale Drawings and Maps: Students learn to create and interpret scale drawings and maps. They understand the concept of scale and how it relates to ratios. They use scale factors to enlarge or reduce figures and solve problems involving scale drawings and maps.

Similar Figures: Students explore the properties of similar figures. They learn to identify and analyze corresponding angles and proportional side lengths in similar figures. They use ratios to determine missing side lengths and solve problems involving similar figures.

Rates and Proportional Reasoning: Students deepen their understanding of rates and proportional reasoning. They explore rates of change, constant rates, and average rates. They apply these concepts to analyze real-world situations, interpret graphs, and solve problems involving rates.

Percentages and Applications: Students extend their knowledge of percentages. They explore topics such as percent increase and decrease, compound interest, and percent error. They solve problems involving these concepts and apply percentages to various real-life scenarios.

Proportional Relationships in Geometry: Students apply proportional reasoning to geometric concepts. They explore properties of triangles, quadrilaterals, and other polygons using ratios and proportions. They investigate relationships between side lengths, angles, and areas of similar figures.

Solving Complex Ratio Problems: Students tackle more complex ratio problems that require multiple steps and a combination of different concepts. They solve problems involving compound ratios, continuous proportions, and proportional reasoning in a variety of contexts.

Data Analysis and Statistics: Students analyze and interpret data using ratios, proportions, and rates. They learn to create and analyze various types of graphs, such as bar graphs, line graphs, and circle graphs. They use these tools to draw conclusions, make predictions, and solve problems related to ratios and rates.

Throughout the curriculum, students engage in hands-on activities, mathematical modeling, and real-world applications to reinforce their understanding of ratios, proportions, and rates. They develop their skills in logical reasoning, critical thinking, and applying mathematical concepts to solve complex problems. Communication of mathematical ideas, justifications, and mathematical language usage is also emphasized.

- Place value: measures
- Imperial to metric
- Metric to imperial
- Ratio
- Percentages
- Proportions
- Compound units
- Scale

Convert cm³ to mm³

Convert cubic centimetres (cm³) to cubic millimetres (mm³) by multiplying by 1000

Convert m³ to cm³

Convert cubic metres (m³) to cubic centimetres (cm³) by multiplying by 1,000,000

Convert miles to kilometres

Use the approximation 1 mile ≈ 1.6 km to convert imperial miles to kilometres

Convert inches to cm

Use the approximation 1 inch ≈ 2.54 cm to convert imperial inches to centimetres to 2 d.p.

Convert km to miles

Use the approximation 1.6 kilometres ≈ 1 mile to convert kilometres to imperial miles to 1 d.p.

Convert cm to feet

Use the approximation 1 foot ≈ 30 cm to convert centimetres to imperial feet to 1 d.p.

Convert cm to inches

Use the approximation 1 inch ≈ 2.5 cm to convert centimetres to imperial inches

Express fractions as ratios

Express each of the given fractions as a part to whole ratio

Express percentages as ratios

Express each of the given percentages as a part to whole ratio

Express decimals as ratios

Express each of the given decimals as a part to whole ratio

Equivalent ratios

Identify the ratios that are equivalent e.g. 1:2 and 3:6

Express ratios as fractions

Express part to part ratios as fraction proportions of the whole

Express ratios as percentages

Express each part to whole ratio as a part to whole percentage

Specific parts and quantity

Pair up specific quantities with specific parts

Increase by a percentage

Derive the actual increase from the percentage increase and add it to the original quantity or amount

Decrease by a percentage

Derive the actual decrease from the percentage decrease and subtract it from the original quantity

Express as a percentage

Express quantities as percentages by creating a fraction and multiplying by 100

Calculate percentage increase

Get the percentage increase by expressing the increase as a fraction of the original and multiplying by 100

Calculate percentage decrease

Get the percentage decrease by expressing the decrease as a fraction of the original and multiplying that amount by 100

Express quantities as % with calculator

Express quantities of wholes as percentages by converting to a fraction and multiplying by 100 to (1 d.p.)

Increase by % with calculator

Derive the actual increase from the percentage increase and add it to the original quantity or amount (to 1 d.p.)

Decrease by % with calculator

Calculate the new quantity or amount by using a decimal multiplier; answers to 2 d.p.

Inverse proportion problems

Solve problems involving inverse proportion where one quantity increases as the other decreases (to 2 d.p.)

Directly or inversely proportional

Identify which of the graphs and equations are directly proportional, inversely proportional or neither

Direct proportion problems

Solve problems involving direct proportion where two quantities increase at the same rate

Calculate speed

Use the speed formula speed s = distance d / time t to calculate speeds to 1 d.p.

Calculate distance, time

Re-arrange the speed formula to calculate distance or time to 1 d.p.

Speed from a graph

Using speed time graphs find the speed at the given time

Fastest speed, slowest speed

Using speed time graphs identify the highest speed or the lowest speed attained

Calculate density

In each instance calculate the density using the density formula d = mass / volume to 1 d.p.

Unit price: best value

Identify the better value for money option by doing unit price calculations

Actual distance

Work out the real distance between two points represented on maps and scale diagrams (to 2 d.p.)

Distance on a map or diagram

Use a scale and an actual distance to work out the distance between 2 points on a map or scale diagram to 2 d.p.

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