Here are the key components of the math curriculum for Ratio and proportion for ages 10 to 11:
Understanding Ratios: Students develop an understanding of ratios as a comparison of two quantities. They learn to express ratios using the "a to b" or "a:b" notation and understand that ratios can be written in different equivalent forms.
Ratio Relationships: Students explore ratio relationships in various contexts. They learn to identify and describe proportional relationships between quantities and understand that ratios can represent part-to-part or part-to-whole relationships.
Simplifying Ratios: Students practice simplifying ratios by dividing both terms by their greatest common factor. They learn to identify and work with equivalent ratios, allowing them to compare and relate different ratios to one another.
Proportional Reasoning: Students develop proportional reasoning skills by analyzing and solving problems involving ratios and proportions. They learn to identify proportional relationships in tables, graphs, and real-life situations. They also solve problems using the concept of cross-multiplication.
Solving Proportion Problems: Students learn strategies for solving proportion problems. They apply the idea that two ratios are equal to set up and solve proportions. They also solve problems involving unit rates and scale factors.
Scaling: Students explore scaling in the context of ratios and proportions. They learn to scale measurements, shapes, and objects up or down by multiplying or dividing by the same factor.
Problem Solving: Ratio and proportion concepts are applied to solve a variety of real-life and mathematical problems. Students analyze word problems, identify the relevant information, and determine the appropriate ratio or proportion strategy to find solutions. They also practice explaining their reasoning and justifying their answers.
The curriculum aims to foster a deep understanding of ratio and proportion concepts, including comparisons, simplification, proportional reasoning, and problem-solving. By the age of 10 to 11, students are expected to have a solid foundation in ratio and proportion and be ready to apply their knowledge in more complex mathematical contexts.
Double the size
Use multiplication and division to get double the size of the objects or values
Triple the size
Use multiplication and division to find triple the given values and measures
Five times the size
Use multiplication and division to find five times the given sizes
Half the size
Use multiplication and division to find half of the given quantities and measures
A third of the size
Use multiplication and division to find a third of the size of the given values and measures
A fifth of the size
Use multiplication and division to find a fifth of the given values and measures
Total size from decimal portion
Use multiplication and division to calculate the whole value or measure from the given decimal portion
Relative size: find scale factor
Use multiplication and division to find the scale factor given original and final sizes
Find 10%
From 100% find out what 10% is using division (without using your calculator)
Find 30%
Find 30% by breaking up each given value into 3 lots of 10% (no calculator)
Find 15%
Find 15% by breaking up each given value into a 10% and a 5% and adding them together
Find 15% with calculator
Find 15% with your calculator using the multiplier 0.15
Find 8% with calculator
Find 8% with your calculator using the multiplier 0.08
Find 80% with calculator
Find 80% with your calculator using the multiplier 0.8
Express 2 values as a percentage
Express 2 values as a percentage by creating a fraction from the 2 numbers and multiplying by 100
Compare fractions, decimals, percent
Compare proportions using fractions, decimals and percent and say which is the biggest part of the whole
Percentages of different measures
Identify which percentage of a length is the longest
Scale factors: calculate dimensions
Use the scale factor and model or drawing dimensions to calculate the real dimensions
Similar shapes: find scale factor
Use the properties of similar shapes to find the scale factor
Counting * Comparing numbers * Pattern * Place value * Addition * Subtraction * Add + Subtract * Multiplication * Division * Multiply + Divide * Fractions * Decimals * Ratio + proportion * Measurements * Shapes * Position + Direction * Statistics * Algebra *
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