比的记法与关系

理解两个数量之间的乘法关系可以用比来表示；会使用比的记法；会化简比。

Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios

学习证据 / Evidence

• 解释为什么“每有2颗红色珠子就有5颗蓝色珠子”可以写成2:5，也可以写成蓝色珠子数量的2/5。
• 在数值表中识别乘法关系（例如，y总是x的3倍）。
• 将比a:b与分数a/b以及线性函数 y=(a/b)x 联系起来。

• Explain why 'for every 2 red beads there are 5 blue beads' can be written as 2:5 or as 2/5 of the blue count
• Identify the multiplicative relationship in a table of values (e.g. y is always 3 times x)
• Connect the ratio a:b to the fraction a/b and to the linear function y = (a/b)x

评估问题 / Assessment

{{name}}能解释为什么像3:4这样的比实际上等同于分数¾，并说明这种关系如何与经过原点的直线图形联系起来吗？

Can {{name}} explain why a ratio like 3:4 is really the same as the fraction ¾ — and show how that relationship connects to a straight-line graph through the origin?