enVision Grade 5 Topic 17 Lesson 8: Problem Solving | enVision 五年级第17章第8课：问题解决

📚 enVision Grade 5 Topic 17 Lesson 8: Problem Solving | enVision 五年级第17章第8课：问题解决

In Topic 17, students have learned how to find perimeter, area, and volume of different shapes. In Lesson 8, the focus shifts to problem solving: applying those skills to unfamiliar, real-world situations. The goal is not just to get an answer, but to understand the problem, choose a good strategy, and check the result.

在第17章中，同学们学习了如何计算不同图形的周长、面积和体积。第8课的重点转向问题解决：将这些技能应用到陌生而真实的情境中。目标不仅是得到一个答案，而是理解题意、选择合适策略并检验结果。

---

1. Understand the Problem | 理解题意

Before doing any calculation, read the problem twice. Identify what is given and what is asked. Underline key numbers and units. If possible, draw a sketch of the shape described.

在做任何计算之前，先读两遍题目。找出已知条件和所求问题。在关键数字和单位下划线。如果可能，画出题目描述图形的草图。

Ask yourself: Is this a perimeter, area, or volume question? For example, “how much fencing is needed” suggests perimeter, “how much carpet is needed” suggests area, and “how much water fits” suggests volume.

问自己：这是求周长、面积还是体积的问题？例如，“需要多少篱笆”提示周长，“需要多少地毯”提示面积，“能装多少水”提示体积。

A clear understanding of the problem prevents rushed calculations and wrong formulas.

清晰理解题意可以避免匆忙计算和用错公式。

---

2. Choose a Strategy | 选择策略

Use a formula when the shape is regular and all needed dimensions are known.

当图形规则且所需尺寸都已知时，直接使用公式。

Draw a diagram when the problem involves a composite shape or a missing dimension.

当题目涉及组合图形或未知尺寸时，先画图。

Make a table when data is given in a sequence or when several cases must be compared.

当数据按序列给出或需要比较多种情况时，列表整理。

Work backwards when the total is known but one measurement is missing.

当总量已知但某个测量值未知时，用逆推的方法。

There is no single perfect strategy. Good problem solvers are flexible and willing to try another approach if the first one does not work.

没有一种万能的策略。优秀的问题解决者会灵活变通，并在第一种方法行不通时愿意尝试另一种思路。

---

3. Use Measurement Formulas | 使用测量公式

For a rectangle, the perimeter is the sum of all sides, or twice the sum of length and width.

对于长方形，周长等于所有边的和，也就是长与宽之和的二倍。

P = 2 × (l + w)

The area of a rectangle is the product of its length and width.

长方形的面积等于长乘宽。

A = l × w

For a triangle, the area is half the base times the height.

三角形的面积等于底乘高的一半。

A = ½ × b × h

For a parallelogram, the area is base times the perpendicular height.

平行四边形的面积等于底边乘对应的高。

A = b × h

For a rectangular prism, the volume is length times width times height.

长方体的体积等于长乘宽乘高。

V = l × w × h

Always match the formula to the shape in the question. A common mistake is using a perimeter formula to find an area, or using an area formula to find a volume.

一定要让公式与题目中的图形匹配。常见错误是用周长公式求面积，或用面积公式求体积。

---

4. Work with Composite Figures | 组合图形

A composite figure is made of two or more simpler shapes. To find the total area or volume, split the figure into parts, calculate each part separately, and then add or subtract.

组合图形由两个或多个简单图形组成。要求总面积或总体积，先把图形拆分成几部分，分别计算，再相加或相减。

For example, an L-shaped floor can be split into two rectangles. The total area is the sum of both rectangles.

例如，一个L形地面可以分成两个长方形。总面积就是两个长方形面积之和。

Sometimes the composite part is a larger shape with a smaller shape removed. In that case, subtract the smaller area or volume from the larger one.

有时组合图形是一个较大图形中挖去一个较小图形。在这种情况下，用大面积或大体积减去小面积或小体积。

Draw the split lines clearly and label each part. This makes the calculation easier to follow and easier to check.

清楚地画出分割线并标号每一部分。这样既便于计算，也便于检查。

---

5. Pay Attention to Units | 注意单位

Always include units in the final answer. Area uses square units, such as cm² or m². Volume uses cubic units, such as cm³ or m³. Perimeter uses ordinary units, such as cm or m.

最终答案中必须写上单位。面积用平方单位，如 cm² 或 m²；体积用立方单位，如 cm³ 或 m³；周长用普通长度单位

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）