你用手指能数到多大？（剧透：远超10）- 詹姆斯·坦顿 (James Tanton)：英语精读讲义

用“How high can you count on your fingers?”开场，主要起到什么作用？

1. 它询问某人数数有多快。
2. 它询问手指离地面有多高。
3. 它在引出主题之前就给出最终答案。
4. 它询问数值上限，并把一个熟悉的动作变成值得探究的主题。

哪句话自然地表达了一个之后可能会被修正的初步印象？

1. It seems an easy problem like, but there may be a hidden difficulty.
2. It proves like an easy problem, but there may be a hidden difficulty.
3. It seems like an easy problem, but there may be a hidden difficulty.
4. The problem is definitely easy, and no other answer is possible.

要让第二句成为支持前一句的理由，哪个连接语最适合放在第二句开头？We can take our time. The museum is open until eight.

1. In contrast
2. At first
3. After all

哪个短语最适合把 at 10:15 引出为 in the morning 的更准确说法？

1. after all
2. to be more precise
3. on the other hand

用目标结构表示两盒合起来有24支铅笔：The two boxes contain ____.

哪一个句子正确使用了逗号 + which 从句，补充说明前面已提到物品的用途？

1. I packed a compass which can we use to find north?
2. I packed a compass, which we can use to find north.
3. I packed a compass, that we can use to find north.

用本课表示“这种联系并非偶然”的四词框架补全句子：____ both devices failed after the same update.

在这个句子中，our modern numbering system 指什么？

1. 一份当前电话号码的清单
2. 给一本书添加页码的动作
3. 一套使用 0 到 9 和位值规则表示数的方法
4. 给现代发明分配编号的日程安排

这句话中的 as well 帮助说明了什么？

1. 这些符号使用的名称与身体部位的名称不同。
2. 这些符号和手指都可以用 digit 这个词来描述。
3. 这十个符号全都是手指的图画。
4. Digit 只表示完整的记数系统。

哪句话先承认一种方法，然后为其他选择留下了空间？

1. Taking the bus is convenient, but it's not the only way to get downtown.
2. Taking the bus is too slow; it's no way to get downtown on time.
3. Taking the bus is the only way to get downtown today.

例句中的“it's customary to go up to 12”是什么意思？

1. 在一些地方，按惯例会一直数到12。
2. 法律要求每个人必须正好数12个数。
3. 人们通常会走到一个叫作“12”的地方。

用 divide 的现在时被动形式和所需介词完成句子：The course ____ four short units.

在这句话中，a natural pointer 指什么？

1. 计数时，拇指可以指向每个部分。
2. 拇指被分成了十二个部分。
3. 拇指会在屏幕上显示数字。
4. 拇指会自动算出总数。

请用 give us an easy way to 的正确形式完成句子：The color code ____ organize the files.

哪句话用 if we want to count higher 设定目标，然后给出一种方法？

1. If we want to count higher, we can use a place-value chart.
2. We can use a place-value chart, but we do not want to count higher.
3. Although we can count higher, a place-value chart is impossible.

用表示“持续跟踪”的高亮表达补全句子：I use a calendar to ____ assignment deadlines as they change.

请用一个以 each 开头、表示“每次都”的两个单词短语补全英文句子：Move one marker ____ you reach ten.

哪句话表示30人是容量上限，但人数也可以更少？

1. The room can hold up to 30 people.
2. The room can hold exactly 30 people.
3. The room can hold at least 30 people.

哪一句使用 Better yet 引出说话人认为更好的方案？

1. We can send you a printed map. In other words, the map is made of paper.
2. We can send you a printed map. Better yet, we can send live directions to your phone.
3. We can send you a printed map. Also, the envelope is white.

用本课的两个单词完成分组表达：Twenty-four beads are arranged into three ____ eight.

在一段讲解中，“That's a pretty big improvement”在这里最自然的作用是什么？

1. 它表示这项改进在外观上很漂亮。
2. 它把前一种方法完全否定为失败。
3. 它先肯定地总结取得的进展，然后说话人再进入下一步。

把 reuse 改成放在 by 后面的正确形式：We reduced waste by ____ glass bottles.

在这个句子中，more countable parts 是什么意思？

1. 更多已经数过的部位
2. 更多可以辨认并分别计数的部位
3. 更多属于可数名词的单词

哪句话表示这个群体目前有 50 人？

1. The group can have up to 50 members.
2. The group needs 50 more members.
3. The group is now up to 50 members.

哪句话中的 mark 与例句一样，表示“通过标记来追踪记录”？

1. The teacher will mark the quiz after class.
2. The holiday marks the start of summer.
3. Move one bead to mark each group of ten.

用本课短语补全下面的英文句子，该短语表示“把我们带到一个相当远的终点”：This bus ____ the national park.

在讲解中，刚刚给出一个结果后，Can we go any higher? 的主要作用是什么？

1. 它把当前结果与下一个可能的步骤连接起来。
2. 它在与当前结果毫无关联的情况下转换话题。
3. 它给出最终答案并结束讲解。

It looks like we've reached the limit 最准确的意思是什么？

1. 在某个未知的时间，一定会到达某个极限。
2. 目前的证据表明，可能已经到达边界。
3. 说话人已经证明未来不可能有任何改进。

用表示“达到有实际意义的精确程度”的目标短语完成句子：In the fog, we couldn't estimate the distance ____.

在讲解中，'So let's think of something different.' 表示什么？

1. 从当前方法转向一个新想法
2. 要求更详细地说明同一个想法
3. 声称先前的每个想法都是正确的

请用 be 的一般现在时形式完成句子：One of our best players ____ absent right now.

下列哪项正确描述了 positional notation？

1. 在 positional notation 中，每个数字无论出现在哪里，数值都相同。
2. 在 positional notation 中，数字的位置改变时，它的数值也可能改变。
3. Positional notation 指某一个数字在某一个具体数位上的值。

用 allow for 的正确形式完成句子：A flexible schedule ____ unexpected delays.

哪一句正确使用 even though，把一个真实事实与出人意料的结果形成对比？

1. Because the boxes look identical, they contain different tools.
2. Even if the boxes look identical, they may contain different tools.
3. Even though the boxes look identical, they contain different tools.

哪句话表示这些位置代表不同的十倍尺度？

1. Each position represents the same order of magnitude.
2. Each position represents a different order of magnitude.
3. Each position represents a different value, but the scale is unchanged.

哪句话正确解释了 positional value？

1. We can use positional value, so a symbol's value can depend on where it appears.
2. We can use positional value, so position has no effect on value.
3. We can use positional value, so every symbol must always have the same value.

哪个句子自然地表示这个群体希望超过自己先前的最佳成绩？

1. With more practice, we hope to match our previous record.
2. With more practice, we hope to remember our previous record.
3. With more practice, we hope to beat our previous record.

使用 Let's forget about ... for a moment 这一框架完成句子：____ the spelling rules ____ and listen to the sound first.

哪句话能自然地引入只有一个变量的简化情况？

1. Let's look at the simplest case of having only one variable.
2. Let's look for the simplest case of having only one variable.
3. Let's look at the simplest case of have only one variable.

用 per 补全这个速率表达：The machine can pack thirty boxes ____ minute.

在这个语境中，up and down 是什么意思？

1. 告诉某人从高处移动到低处。
2. 表示两种可能的状态：抬起或放下。
3. 描述反复向上和向下移动。

哪句话正确使用了 allow + 宾语 + to 不定式？

1. This model allows us to represent the data visually.
2. This model allows to us represent the data visually.
3. This model allows us representing the data visually.

下面哪个数是 2 的幂？

1. 12
2. 18
3. 32

用本课中的三个词命名表达补全句子：Sodium chloride, ____ table salt, is used in cooking.

用 double 和 value 补全句子：The $20 voucher has ____ of the $10 voucher.

用 assign + 对象 + a value of 结构补全句子：In our scoring system, we ____ each star ____ ten.

哪个数是 positive integer？

1. -3
2. 2.5
3. 7
4. 0

用 can be expressed as a sum of 完成句子：Ten ____ six and four.

哪一句正确使用 by having + 宾语 + 状态 来说明方法？

1. We can mark the correct box by having highlight it in green.
2. We can mark the correct box by have it highlighted in green.
3. We can mark the correct box by having it highlighted in green.

Meanwhile 在本句中的主要作用是什么？

1. 它表示计算已经结束。
2. 它引入另一个相关的例子。
3. 它证明两个计算恰好同时进行。

哪句话使用 would be 表示根据规则推导出的结果？

1. When the display updates, the next number will be 64.
2. According to the pattern, the next number would be 64.
3. The printed answer says the next number is 64.

把直接问句“How confident do you feel?”改成嵌入式问句，完成句子：It depends on ____.

哪句话对 dexterous 的使用是自然的？

1. A dexterous watchmaker can handle very small parts.
2. A dexterous thunderstorm crossed the coast.
3. A dexterous encyclopedia contains many facts.

哪句话正确使用 if 从句，先设定一个身体动作条件，再说明结果？

1. If you can turned the dial just halfway, the light will become dimmer.
2. If can you turn the dial just halfway, the light will become dimmer.
3. If you can turn the dial just halfway, the light will become dimmer.

哪句话自然地使用 three different 来引出三个不同的选项？

1. The lamp has different three settings: off, dim, and bright.
2. The lamp has three different settings: off, dim, and bright.
3. The lamp has three difference settings: off, dim, and bright.

哪一项正确描述了三进制位置记数系统？

1. 每一位都有一个以 3 的幂为基础的位值。
2. 每个数都必须包含数字 3。
3. 每一位的值始终都是 3。

用本课由两个单词组成的短语完成句子，使 four 表示包含四在内的最低数量：The club needs four members ____.

哪句话表示对方可以选择开会时间？

1. The meeting time depends on when the train arrives.
2. You need to arrive before the meeting starts.
3. We can meet at ten or eleven; the time is up to you.

哪句话准确地用 flexibility 和 ingenuity 表达了这两种能力？

1. Her ingenuity made her joints bend farther, and her flexibility invented a new tool.
2. Her flexibility and ingenuity both mean that she memorized the instructions.
3. Her flexibility helped her reach through the narrow opening, and her ingenuity helped her design a tool to pull the key closer.

哪句话正确地在 Even with 后使用了名词短语？

1. Even with Maya had limited time, she finished the poster.
2. Even with limited time, Maya finished the poster.
3. Even if limited time, Maya finished the poster.

在 "The new heating system works efficiently," 中，works efficiently 是什么意思？

1. 这个系统运行良好，而且不会浪费太多能源。
2. 这个系统外观很漂亮。
3. 有一个人受雇于这个系统。

阅读："The library is popular. In fact, every seat is taken by noon." In fact 在这里起什么作用？

1. 它表示第一句只是想象出来的。
2. 它转向一个无关的话题。
3. 它补充一个具体事实，加强第一句的说法。

用 be based on 的正确形式完成这个现在时句子：The museum's new safety plan ____ expert advice.

用 consist of 的正确形式完成这个现在时句子：The starter kit ____ a map, a flashlight, and a whistle.

请用成对结构 either ... or 完成句子：The workshop can be ____ online ____ in person.

哪个句子使用 meaning that 从一个事实推进到其所说明的结果？

1. The toy will not turn on because the battery is empty.
2. Although the battery is full, the toy will not turn on.
3. The battery is empty, meaning that the toy will not turn on.

本句中的 the default way 是什么意思？

1. 只有违反规则后才使用的方法。
2. 已经停止运行的方法。
3. 除非另选一种，否则自动采用的方法。

输入开头的两个单词，完成 Just as X, Y 类比结构："____ a map helps travelers find a route, an outline helps readers follow an argument."

哪一句表示 Leo 数到 100 后，又继续往更大的数数？

1. Leo counted to one hundred.
2. Leo counted past one hundred.
3. Leo started counting at one hundred.

哪一句自然地描述设备执行计算任务？

1. A small chip can perform millions of operations per second.
2. A small chip can perform millions of songs per second.
3. A small chip can play millions of operations per second.

在这个句子中，“just by counting off ones and zeros”表达了什么意思？

1. 通过倒数直到零
2. 在运行前删除所有的1和0
3. 仅仅通过依次处理一串1和0